tag:blogger.com,1999:blog-121333352017-10-19T04:20:40.527-04:00Walk Like a SabermetricianOccasional commentary on baseball and sabermetricsphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.comBlogger556125tag:blogger.com,1999:blog-12133335.post-84496559428856971392017-10-03T17:39:00.001-04:002017-10-03T17:40:37.431-04:00End of Season Statistics, 2017The spreadsheets are published as Google Spreadsheets, which you can download in Excel format by changing the extension in the address from "=html" to "=xls". That way you can download them and manipulate things however you see fit. <br /><br />The data comes from a number of different sources. Most of the data comes from Baseball-Reference. KJOK's park database is extremely helpful in determining when park factors should reset. Data on bequeathed runners for relievers comes from Baseball Prospectus. <br /><br />The basic philosophy behind these stats is to use the simplest methods that have acceptable accuracy. Of course, "acceptable" is in the eye of the beholder, namely me. I use Pythagenpat not because other run/win converters, like a constant RPW or a fixed exponent are not accurate enough for this purpose, but because it's mine and it would be kind of odd if I didn't use it. <br /><br />If I seem to be a stickler for purity in my critiques of others' methods, I'd contend it is usually in a theoretical sense, not an input sense. So when I exclude hit batters, I'm not saying that hit batters are worthless or that they *should* be ignored; it's just easier not to mess with them and not that much less accurate. <br /><br />I also don't really have a problem with people using sub-standard methods (say, Basic RC) as long as they acknowledge that they are sub-standard. If someone pretends that Basic RC doesn't undervalue walks or cause problems when applied to extreme individuals, I'll call them on it; if they explain its shortcomings but use it regardless, I accept that. Take these last three paragraphs as my acknowledgment that some of the statistics displayed here have shortcomings as well, and I've at least attempted to describe some of them in the discussion below.<br /><br />The League spreadsheet is pretty straightforward--it includes league totals and averages for a number of categories, most or all of which are explained at appropriate junctures throughout this piece. The advent of interleague play has created two different sets of league totals--one for the offense of league teams and one for the defense of league teams. Before interleague play, these two were identical. I do not present both sets of totals (you can figure the defensive ones yourself from the team spreadsheet, if you desire), just those for the offenses. The exception is for the defense-specific statistics, like innings pitched and quality starts. The figures for those categories in the league report are for the defenses of the league's teams. However, I do include each league's breakdown of basic pitching stats between starters and relievers (denoted by "s" or "r" prefixes), and so summing those will yield the totals from the pitching side. The one abbreviation you might not recognize is "N"--this is the league average of runs/game for one team, and it will pop up again.<br /><br />The Team spreadsheet focuses on overall team performance--wins, losses, runs scored, runs allowed. The columns included are: Park Factor (PF), Home Run Park Factor (PFhr), Winning Percentage (W%), Expected W% (EW%), Predicted W% (PW%), wins, losses, runs, runs allowed, Runs Created (RC), Runs Created Allowed (RCA), Home Winning Percentage (HW%), Road Winning Percentage (RW%) [exactly what they sound like--W% at home and on the road], Runs/Game (R/G), Runs Allowed/Game (RA/G), Runs Created/Game (RCG), Runs Created Allowed/Game (RCAG), and Runs Per Game (the average number of runs scored an allowed per game). Ideally, I would use outs as the denominator, but for teams, outs and games are so closely related that I don’t think it’s worth the extra effort.<br /><br />The runs and Runs Created figures are unadjusted, but the per-game averages are park-adjusted, except for RPG which is also raw. Runs Created and Runs Created Allowed are both based on a simple Base Runs formula. The formula is:<br /><br />A = H + W - HR - CS<br />B = (2TB - H - 4HR + .05W + 1.5SB)*.76<br />C = AB - H<br />D = HR<br />Naturally, A*B/(B + C) + D.<br /><br />I have explained the methodology used to figure the PFs before, but the cliff’s notes version is that they are based on five years of data when applicable, include both runs scored and allowed, and they are regressed towards average (PF = 1), with the amount of regression varying based on the number of years of data used. There are factors for both runs and home runs. The initial PF (not shown) is:<br /><br />iPF = (H*T/(R*(T - 1) + H) + 1)/2<br />where H = RPG in home games, R = RPG in road games, T = # teams in league (14 for AL and 16 for NL). Then the iPF is converted to the PF by taking x*iPF + (1-x), where x = .6 if one year of data is used, .7 for 2, .8 for 3, and .9 for 4+. <br /><br />It is important to note, since there always seems to be confusion about this, that these park factors already incorporate the fact that the average player plays 50% on the road and 50% at home. That is what the adding one and dividing by 2 in the iPF is all about. So if I list Fenway Park with a 1.02 PF, that means that it actually increases RPG by 4%. <br /><br />In the calculation of the PFs, I did not take out “home” games that were actually at neutral sites (of which there were a rash this year).<br /><br />There are also Team Offense and Defense spreadsheets. These include the following categories:<br /><br />Team offense: Plate Appearances, Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Walks and Hit Batters per At Bat (WAB), Isolated Power (SLG - BA), R/G at home (hR/G), and R/G on the road (rR/G) BA, OBA, SLG, WAB, and ISO are park-adjusted by dividing by the square root of park factor (or the equivalent; WAB = (OBA - BA)/(1 - OBA), ISO = SLG - BA, and SEC = WAB + ISO).<br /><br />Team defense: Innings Pitched, BA, OBA, SLG, Innings per Start (IP/S), Starter's eRA (seRA), Reliever's eRA (reRA), Quality Start Percentage (QS%), RA/G at home (hRA/G), RA/G on the road (rRA/G), Battery Mishap Rate (BMR), Modified Fielding Average (mFA), and Defensive Efficiency Record (DER). BA, OBA, and SLG are park-adjusted by dividing by the square root of PF; seRA and reRA are divided by PF.<br /><br />The three fielding metrics I've included are limited it only to metrics that a) I can calculate myself and b) are based on the basic available data, not specialized PBP data. The three metrics are explained in this post, but here are quick descriptions of each:<br /><br />1) BMR--wild pitches and passed balls per 100 baserunners = (WP + PB)/(H + W - HR)*100<br /><br />2) mFA--fielding average removing strikeouts and assists = (PO - K)/(PO - K + E)<br /><br />3) DER--the Bill James classic, using only the PA-based estimate of plays made. Based on a suggestion by Terpsfan101, I've tweaked the error coefficient. Plays Made = PA - K - H - W - HR - HB - .64E and DER = PM/(PM + H - HR + .64E)<br /><br />Next are the individual player reports. I defined a starting pitcher as one with 15 or more starts. All other pitchers are eligible to be included as a reliever. If a pitcher has 40 appearances, then they are included. Additionally, if a pitcher has 50 innings and less than 50% of his appearances are starts, he is also included as a reliever (this allows some swingmen type pitchers who wouldn’t meet either the minimum start or appearance standards to get in).<br /><br />For all of the player reports, ages are based on simply subtracting their year of birth from 2017. I realize that this is not compatible with how ages are usually listed and so “Age 27” doesn’t necessarily correspond to age 27 as I list it, but it makes everything a heckuva lot easier, and I am more interested in comparing the ages of the players to their contemporaries than fitting them into historical studies, and for the former application it makes very little difference. The "R" category records rookie status with a "R" for rookies and a blank for everyone else; I've trusted Baseball Prospectus on this. Also, all players are counted as being on the team with whom they played/pitched (IP or PA as appropriate) the most. <br /><br />For relievers, the categories listed are: Games, Innings Pitched, estimated Plate Appearances (PA), Run Average (RA), Relief Run Average (RRA), Earned Run Average (ERA), Estimated Run Average (eRA), DIPS Run Average (dRA), Strikeouts per Game (KG), Walks per Game (WG), Guess-Future (G-F), Inherited Runners per Game (IR/G), Batting Average on Balls in Play (%H), Runs Above Average (RAA), and Runs Above Replacement (RAR).<br /><br />IR/G is per relief appearance (G - GS); it is an interesting thing to look at, I think, in lieu of actual leverage data. You can see which closers come in with runners on base, and which are used nearly exclusively to start innings. Of course, you can’t infer too much; there are bad relievers who come in with a lot of people on base, not because they are being used in high leverage situations, but because they are long men being used in low-leverage situations already out of hand.<br /><br />For starting pitchers, the columns are: Wins, Losses, Innings Pitched, Estimated Plate Appearances (PA), RA, RRA, ERA, eRA, dRA, KG, WG, G-F, %H, Pitches/Start (P/S), Quality Start Percentage (QS%), RAA, and RAR. RA and ERA you know--R*9/IP or ER*9/IP, park-adjusted by dividing by PF. The formulas for eRA and dRA are based on the same Base Runs equation and they estimate RA, not ERA.<br /><br />* eRA is based on the actual results allowed by the pitcher (hits, doubles, home runs, walks, strikeouts, etc.). It is park-adjusted by dividing by PF.<br /><br />* dRA is the classic DIPS-style RA, assuming that the pitcher allows a league average %H, and that his hits in play have a league-average S/D/T split. It is park-adjusted by dividing by PF.<br /><br />The formula for eRA is:<br /><br />A = H + W - HR<br />B = (2*TB - H - 4*HR + .05*W)*.78<br />C = AB - H = K + (3*IP - K)*x (where x is figured as described below for PA estimation and is typically around .93) = PA (from below) - H - W<br />eRA = (A*B/(B + C) + HR)*9/IP<br /><br />To figure dRA, you first need the estimate of PA described below. Then you calculate W, K, and HR per PA (call these %W, %K, and %HR). Percentage of balls in play (BIP%) = 1 - %W - %K - %HR. This is used to calculate the DIPS-friendly estimate of %H (H per PA) as e%H = Lg%H*BIP%.<br /><br />Now everything has a common denominator of PA, so we can plug into Base Runs:<br /><br />A = e%H + %W<br />B = (2*(z*e%H + 4*%HR) - e%H - 5*%HR + .05*%W)*.78<br />C = 1 - e%H - %W - %HR<br />cRA = (A*B/(B + C) + %HR)/C*a<br /><br />z is the league average of total bases per non-HR hit (TB - 4*HR)/(H - HR), and a is the league average of (AB - H) per game.<br /><br />In the past I presented a couple of batted ball RA estimates. I’ve removed these, not just because batted ball data exhibits questionable reliability but because these metrics were complicated to figure, required me to collate the batted ball data, and were not personally useful to me. I figure these stats for my own enjoyment and have in some form or another going back to 1997. I share them here only because I would do it anyway, so if I’m not interested in certain categories, there’s no reason to keep presenting them.<br /><br />Instead, I’m showing strikeout and walk rate, both expressed as per game. By game I mean not nine innings but rather the league average of PA/G. I have always been a proponent of using PA and not IP as the denominator for non-run pitching rates, and now the use of per PA rates is widespread. Usually these are expressed as K/PA and W/PA, or equivalently, percentage of PA with a strikeout or walk. I don’t believe that any site publishes these as K and W per equivalent game as I am here. This is not better than K%--it’s simply applying a scalar multiplier. I like it because it generally follows the same scale as the familiar K/9.<br /><br />To facilitate this, I’ve finally corrected a flaw in the formula I use to estimate plate appearances for pitchers. Previously, I’ve done it the lazy way by not splitting strikeouts out from other outs. I am now using this formula to estimate PA (where PA = AB + W):<br /><br />PA = K + (3*IP - K)*x + H + W<br />Where x = league average of (AB - H - K)/(3*IP - K)<br /><br />Then KG = K*Lg(PA/G) and WG = W*Lg(PA/G).<br /><br />G-F is a junk stat, included here out of habit because I've been including it for years. It was intended to give a quick read of a pitcher's expected performance in the next season, based on eRA and strikeout rate. Although the numbers vaguely resemble RAs, it's actually unitless. As a rule of thumb, anything under four is pretty good for a starter. G-F = 4.46 + .095(eRA) - .113(K*9/IP). It is a junk stat. JUNK STAT JUNK STAT JUNK STAT. Got it?<br /><br />%H is BABIP, more or less--%H = (H - HR)/(PA - HR - K - W), where PA was estimated above. Pitches/Start includes all appearances, so I've counted relief appearances as one-half of a start (P/S = Pitches/(.5*G + .5*GS). QS% is just QS/(G - GS); I don't think it's particularly useful, but Doug's Stats include QS so I include it.<br /><br />I've used a stat called Relief Run Average (RRA) in the past, based on Sky Andrecheck's article in the August 1999 By the Numbers; that one only used inherited runners, but I've revised it to include bequeathed runners as well, making it equally applicable to starters and relievers. I use RRA as the building block for baselined value estimates for all pitchers. I explained RRA in this article, but the bottom line formulas are:<br /><br />BRSV = BRS - BR*i*sqrt(PF)<br />IRSV = IR*i*sqrt(PF) - IRS<br />RRA = ((R - (BRSV + IRSV))*9/IP)/PF<br /><br />The two baselined stats are Runs Above Average (RAA) and Runs Above Replacement (RAR). Starting in 2015 I revised RAA to use a slightly different baseline for starters and relievers as described here. The adjustment is based on patterns from the last several seasons of league average starter and reliever eRA. Thus it does not adjust for any advantages relief pitchers enjoy that are not reflected in their component statistics. This could include runs allowed scoring rules that benefit relievers (although the use of RRA should help even the scales in this regard, at least compared to raw RA) and the talent advantage of starting pitchers. The RAR baselines do attempt to take the latter into account, and so the difference in starter and reliever RAR will be more stark than the difference in RAA.<br /><br />RAA (relievers) = (.951*LgRA - RRA)*IP/9<br />RAA (starters) = (1.025*LgRA - RRA)*IP/9<br />RAR (relievers) = (1.11*LgRA - RRA)*IP/9<br />RAR (starters) = (1.28*LgRA - RRA)*IP/9<br /><br />All players with 250 or more plate appearances (official, total plate appearances) are included in the Hitters spreadsheets (along with some players close to the cutoff point who I was interested in). Each is assigned one position, the one at which they appeared in the most games. The statistics presented are: Games played (G), Plate Appearances (PA), Outs (O), Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Runs Created (RC), Runs Created per Game (RG), Speed Score (SS), Hitting Runs Above Average (HRAA), Runs Above Average (RAA), Hitting Runs Above Replacement (HRAR), and Runs Above Replacement (RAR).<br /><br />Starting in 2015, I'm including hit batters in all related categories for hitters, so PA is now equal to AB + W+ HB. Outs are AB - H + CS. BA and SLG you know, but remember that without SF, OBA is just (H + W + HB)/(AB + W + HB). Secondary Average = (TB - H + W + HB)/AB = SLG - BA + (OBA - BA)/(1 - OBA). I have not included net steals as many people (and Bill James himself) do, but I have included HB which some do not.<br /><br />BA, OBA, and SLG are park-adjusted by dividing by the square root of PF. This is an approximation, of course, but I'm satisfied that it works well (I plan to post a couple articles on this some time during the offseason). The goal here is to adjust for the win value of offensive events, not to quantify the exact park effect on the given rate. I use the BA/OBA/SLG-based formula to figure SEC, so it is park-adjusted as well.<br /><br />Runs Created is actually Paul Johnson's ERP, more or less. Ideally, I would use a custom linear weights formula for the given league, but ERP is just so darn simple and close to the mark that it’s hard to pass up. I still use the term “RC” partially as a homage to Bill James (seriously, I really like and respect him even if I’ve said negative things about RC and Win Shares), and also because it is just a good term. I like the thought put in your head when you hear “creating” a run better than “producing”, “manufacturing”, “generating”, etc. to say nothing of names like “equivalent” or “extrapolated” runs. None of that is said to put down the creators of those methods--there just aren’t a lot of good, unique names available. <br /><br />For 2015, I refined the formula a little bit to:<br /><br />1. include hit batters at a value equal to that of a walk<br />2. value intentional walks at just half the value of a regular walk<br />3. recalibrate the multiplier based on the last ten major league seasons (2005-2014)<br /><br />This revised RC = (TB + .8H + W + HB - .5IW + .7SB - CS - .3AB)*.310<br /><br />RC is park adjusted by dividing by PF, making all of the value stats that follow park adjusted as well. RG, the Runs Created per Game rate, is RC/O*25.5. I do not believe that outs are the proper denominator for an individual rate stat, but I also do not believe that the distortions caused are that bad. (I still intend to finish my rate stat series and discuss all of the options in excruciating detail, but alas you’ll have to take my word for it now).<br /><br />Several years ago I switched from using my own "Speed Unit" to a version of Bill James' Speed Score; of course, Speed Unit was inspired by Speed Score. I only use four of James' categories in figuring Speed Score. I actually like the construct of Speed Unit better as it was based on z-scores in the various categories (and amazingly a couple other sabermetricians did as well), but trying to keep the estimates of standard deviation for each of the categories appropriate was more trouble than it was worth.<br /><br />Speed Score is the average of four components, which I'll call a, b, c, and d:<br /><br />a = ((SB + 3)/(SB + CS + 7) - .4)*20<br />b = sqrt((SB + CS)/(S + W))*14.3<br />c = ((R - HR)/(H + W - HR) - .1)*25<br />d = T/(AB - HR - K)*450<br /><br />James actually uses a sliding scale for the triples component, but it strikes me as needlessly complex and so I've streamlined it. He looks at two years of data, which makes sense for a gauge that is attempting to capture talent and not performance, but using multiple years of data would be contradictory to the guiding principles behind this set of reports (namely, simplicity. Or laziness. You're pick.) I also changed some of his division to mathematically equivalent multiplications.<br /><br />There are a whopping four categories that compare to a baseline; two for average, two for replacement. Hitting RAA compares to a league average hitter; it is in the vein of Pete Palmer’s Batting Runs. RAA compares to an average hitter at the player’s primary position. Hitting RAR compares to a “replacement level” hitter; RAR compares to a replacement level hitter at the player’s primary position. The formulas are:<br /><br />HRAA = (RG - N)*O/25.5<br />RAA = (RG - N*PADJ)*O/25.5<br />HRAR = (RG - .73*N)*O/25.5<br />RAR = (RG - .73*N*PADJ)*O/25.5<br /><br />PADJ is the position adjustment, and it is based on 2002-2011 offensive data. For catchers it is .89; for 1B/DH, 1.17; for 2B, .97; for 3B, 1.03; for SS, .93; for LF/RF, 1.13; and for CF, 1.02. I had been using the 1992-2001 data as a basis for some time, but finally updated for 2012. I’m a little hesitant about this update, as the middle infield positions are the biggest movers (higher positional adjustments, meaning less positional credit). I have no qualms for second base, but the shortstop PADJ is out of line with the other position adjustments widely in use and feels a bit high to me. But there are some decent points to be made in favor of offensive adjustments, and I’ll have a bit more on this topic in general below.<br /><br />That was the mechanics of the calculations; now I'll twist myself into knots trying to justify them. If you only care about the how and not the why, stop reading now. <br /><br />The first thing that should be covered is the philosophical position behind the statistics posted here. They fall on the continuum of ability and value in what I have called "performance". Performance is a technical-sounding way of saying "Whatever arbitrary combination of ability and value I prefer".<br /><br />With respect to park adjustments, I am not interested in how any particular player is affected, so there is no separate adjustment for lefties and righties for instance. The park factor is an attempt to determine how the park affects run scoring rates, and thus the win value of runs.<br /><br />I apply the park factor directly to the player's statistics, but it could also be applied to the league context. The advantage to doing it my way is that it allows you to compare the component statistics (like Runs Created or OBA) on a park-adjusted basis. The drawback is that it creates a new theoretical universe, one in which all parks are equal, rather than leaving the player grounded in the actual context in which he played and evaluating how that context (and not the player's statistics) was altered by the park.<br /><br />The good news is that the two approaches are essentially equivalent; in fact, they are precisely equivalent if you assume that the Runs Per Win factor is equal to the RPG. Suppose that we have a player in an extreme park (PF = 1.15, approximately like Coors Field pre-humidor) who has an 8 RG before adjusting for park, while making 350 outs in a 4.5 N league. The first method of park adjustment, the one I use, converts his value into a neutral park, so his RG is now 8/1.15 = 6.957. We can now compare him directly to the league average:<br /><br />RAA = (6.957 - 4.5)*350/25.5 = +33.72<br /><br />The second method would be to adjust the league context. If N = 4.5, then the average player in this park will create 4.5*1.15 = 5.175 runs. Now, to figure RAA, we can use the unadjusted RG of 8:<br /><br />RAA = (8 - 5.175)*350/25.5 = +38.77<br /><br />These are not the same, as you can obviously see. The reason for this is that they take place in two different contexts. The first figure is in a 9 RPG (2*4.5) context; the second figure is in a 10.35 RPG (2*4.5*1.15) context. Runs have different values in different contexts; that is why we have RPW converters in the first place. If we convert to WAA (using RPW = RPG, which is only an approximation, so it's usually not as tidy as it appears below), then we have:<br /><br />WAA = 33.72/9 = +3.75<br />WAA = 38.77/10.35 = +3.75<br /><br />Once you convert to wins, the two approaches are equivalent. The other nice thing about the first approach is that once you park-adjust, everyone in the league is in the same context, and you can dispense with the need for converting to wins at all. You still might want to convert to wins, and you'll need to do so if you are comparing the 2015 players to players from other league-seasons (including between the AL and NL in the same year), but if you are only looking to compare Jose Bautista to Miguel Cabrera, it's not necessary. WAR is somewhat ubiquitous now, but personally I prefer runs when possible--why mess with decimal points if you don't have to? <br /><br />The park factors used to adjust player stats here are run-based. Thus, they make no effort to project what a player "would have done" in a neutral park, or account for the difference effects parks have on specific events (walks, home runs, BA) or types of players. They simply account for the difference in run environment that is caused by the park (as best I can measure it). As such, they don't evaluate a player within the actual run context of his team's games; they attempt to restate the player's performance as an equivalent performance in a neutral park.<br /><br />I suppose I should also justify the use of sqrt(PF) for adjusting component statistics. The classic defense given for this approach relies on basic Runs Created--runs are proportional to OBA*SLG, and OBA*SLG/PF = OBA/sqrt(PF)*SLG/sqrt(PF). While RC may be an antiquated tool, you will find that the square root adjustment is fairly compatible with linear weights or Base Runs as well. I am not going to take the space to demonstrate this claim here, but I will some time in the future. <br /><br />Many value figures published around the sabersphere adjust for the difference in quality level between the AL and NL. I don't, but this is a thorny area where there is no right or wrong answer as far as I'm concerned. I also do not make an adjustment in the league averages for the fact that the overall NL averages include pitcher batting and the AL does not (not quite true in the era of interleague play, but you get my drift). <br /><br />The difference between the leagues may not be precisely calculable, and it certainly is not constant, but it is real. If the average player in the AL is better than the average player in the NL, it is perfectly reasonable to expect the average AL player to have more RAR than the average NL player, and that will not happen without some type of adjustment. On the other hand, if you are only interested in evaluating a player relative to his own league, such an adjustment is not necessarily welcome.<br /><br />The league argument only applies cleanly to metrics baselined to average. Since replacement level compares the given player to a theoretical player that can be acquired on the cheap, the same pool of potential replacement players should by definition be available to the teams of each league. One could argue that if the two leagues don't have equal talent at the major league level, they might not have equal access to replacement level talent--except such an argument is at odds with the notion that replacement level represents talent that is truly "freely available".<br /><br />So it's hard to justify the approach I take, which is to set replacement level relative to the average runs scored in each league, with no adjustment for the difference in the leagues. The best justification is that it's simple and it treats each league as its own universe, even if in reality they are connected.<br /><br />The replacement levels I have used here are very much in line with the values used by other sabermetricians. This is based both on my own "research", my interpretation of other's people research, and a desire to not stray from consensus and make the values unhelpful to the majority of people who may encounter them.<br /><br />Replacement level is certainly not settled science. There is always going to be room to disagree on what the baseline should be. Even if you agree it should be "replacement level", any estimate of where it should be set is just that--an estimate. Average is clean and fairly straightforward, even if its utility is questionable; replacement level is inherently messy. So I offer the average baseline as well.<br /><br />For position players, replacement level is set at 73% of the positional average RG (since there's a history of discussing replacement level in terms of winning percentages, this is roughly equivalent to .350). For starting pitchers, it is set at 128% of the league average RA (.380), and for relievers it is set at 111% (.450). <br /><br />I am still using an analytical structure that makes the comparison to replacement level for a position player by applying it to his hitting statistics. This is the approach taken by Keith Woolner in VORP (and some other earlier replacement level implementations), but the newer metrics (among them Rally and Fangraphs' WAR) handle replacement level by subtracting a set number of runs from the player's total runs above average in a number of different areas (batting, fielding, baserunning, positional value, etc.), which for lack of a better term I will call the subtraction approach.<br /><br />The offensive positional adjustment makes the inherent assumption that the average player at each position is equally valuable. I think that this is close to being true, but it is not quite true. The ideal approach would be to use a defensive positional adjustment, since the real difference between a first baseman and a shortstop is their defensive value. When you bat, all runs count the same, whether you create them as a first baseman or as a shortstop. <br /><br />That being said, using "replacement hitter at position" does not cause too many distortions. It is not theoretically correct, but it is practically powerful. For one thing, most players, even those at key defensive positions, are chosen first and foremost for their offense. Empirical research by Keith Woolner has shown that the replacement level hitting performance is about the same for every position, relative to the positional average.<br /><br />Figuring what the defensive positional adjustment should be, though, is easier said than done. Therefore, I use the offensive positional adjustment. So if you want to criticize that choice, or criticize the numbers that result, be my guest. But do not claim that I am holding this up as the correct analytical structure. I am holding it up as the most simple and straightforward structure that conforms to reality reasonably well, and because while the numbers may be flawed, they are at least based on an objective formula that I can figure myself. If you feel comfortable with some other assumptions, please feel free to ignore mine.<br /><br />That still does not justify the use of HRAR--hitting runs above replacement--which compares each hitter, regardless of position, to 73% of the league average. Basically, this is just a way to give an overall measure of offensive production without regard for position with a low baseline. It doesn't have any real baseball meaning. <br /><br />A player who creates runs at 90% of the league average could be above-average (if he's a shortstop or catcher, or a great fielder at a less important fielding position), or sub-replacement level (DHs that create 3.5 runs per game are not valuable properties). Every player is chosen because his total value, both hitting and fielding, is sufficient to justify his inclusion on the team. HRAR fails even if you try to justify it with a thought experiment about a world in which defense doesn't matter, because in that case the absolute replacement level (in terms of RG, without accounting for the league average) would be much higher than it is currently. <br /><br />The specific positional adjustments I use are based on 2002-2011 data. I stick with them because I have not seen compelling evidence of a change in the degree of difficulty or scarcity between the positions between now and then, and because I think they are fairly reasonable. The positions for which they diverge the most from the defensive position adjustments in common use are 2B, 3B, and CF. Second base is considered a premium position by the offensive PADJ (.97), while third base and center field have similar adjustments in the opposite direction (1.03 and 1.02).<br /><br />Another flaw is that the PADJ is applied to the overall league average RG, which is artificially low for the NL because of pitcher's batting. When using the actual league average runs/game, it's tough to just remove pitchers--any adjustment would be an estimate. If you use the league total of runs created instead, it is a much easier fix.<br /><br />One other note on this topic is that since the offensive PADJ is a stand-in for average defensive value by position, ideally it would be applied by tying it to defensive playing time. I have done it by outs, though.<br /><br />The reason I have taken this flawed path is because 1) it ties the position adjustment directly into the RAR formula rather than leaving it as something to subtract on the outside and more importantly 2) there’s no straightforward way to do it. The best would be to use defensive innings--set the full-time player to X defensive innings, figure how Derek Jeter’s innings compared to X, and adjust his PADJ accordingly. Games in the field or games played are dicey because they can cause distortion for defensive replacements. Plate Appearances avoid the problem that outs have of being highly related to player quality, but they still carry the illogic of basing it on offensive playing time. And of course the differences here are going to be fairly small (a few runs). That is not to say that this way is preferable, but it’s not horrible either, at least as far as I can tell.<br /><br />To compare this approach to the subtraction approach, start by assuming that a replacement level shortstop would create .86*.73*4.5 = 2.825 RG (or would perform at an overall level of equivalent value to being an average fielder at shortstop while creating 2.825 runs per game). Suppose that we are comparing two shortstops, each of whom compiled 600 PA and played an equal number of defensive games and innings (and thus would have the same positional adjustment using the subtraction approach). Alpha made 380 outs and Bravo made 410 outs, and each ranked as dead-on average in the field.<br /><br />The difference in overall RAR between the two using the subtraction approach would be equal to the difference between their offensive RAA compared to the league average. Assuming the league average is 4.5 runs, and that both Alpha and Bravo created 75 runs, their offensive RAAs are:<br /><br />Alpha = (75*25.5/380 - 4.5)*380/25.5 = +7.94<br /><br />Similarly, Bravo is at +2.65, and so the difference between them will be 5.29 RAR.<br /><br />Using the flawed approach, Alpha's RAR will be:<br /><br />(75*25.5/380 - 4.5*.73*.86)*380/25.5 = +32.90<br /><br />Bravo's RAR will be +29.58, a difference of 3.32 RAR, which is two runs off of the difference using the subtraction approach.<br /><br />The downside to using PA is that you really need to consider park effects if you do, whereas outs allow you to sidestep park effects. Outs are constant; plate appearances are linked to OBA. Thus, they not only depend on the offensive context (including park factor), but also on the quality of one's team. Of course, attempting to adjust for team PA differences opens a huge can of worms which is not really relevant; for now, the point is that using outs for individual players causes distortions, sometimes trivial and sometimes bothersome, but almost always makes one's life easier.<br /><br />I do not include fielding (or baserunning outside of steals, although that is a trivial consideration in comparison) in the RAR figures--they cover offense and positional value only). This in no way means that I do not believe that fielding is an important consideration in player evaluation. However, two of the key principles of these stat reports are 1) not incorporating any data that is not readily available and 2) not simply including other people's results (of course I borrow heavily from other people's methods, but only adapting methodology that I can apply myself).<br /><br />Any fielding metric worth its salt will fail to meet either criterion--they use zone data or play-by-play data which I do not have easy access to. I do not have a fielding metric that I have stapled together myself, and so I would have to simply lift other analysts' figures. <br /><br />Setting the practical reason for not including fielding aside, I do have some reservations about lumping fielding and hitting value together in one number because of the obvious differences in reliability between offensive and fielding metrics. In theory, they absolutely should be put together. But in practice, I believe it would be better to regress the fielding metric to a point at which it would be roughly equivalent in reliability to the offensive metric.<br /><br />Offensive metrics have error bars associated with them, too, of course, and in evaluating a single season's value, I don't care about the vagaries that we often lump together as "luck". Still, there are errors in our assessment of linear weight values and players that collect an unusual proportion of infield hits or hits to the left side, errors in estimation of park factor, and any number of other factors that make their events more or less valuable than an average event of that type. <br /><br />Fielding metrics offer up all of that and more, as we cannot be nearly as certain of true successes and failures as we are when analyzing offense. Recent investigations, particularly by Colin Wyers, have raised even more questions about the level of uncertainty. So, even if I was including a fielding value, my approach would be to assume that the offensive value was 100% reliable (which it isn't), and regress the fielding metric relative to that (so if the offensive metric was actually 70% reliable, and the fielding metric 40% reliable, I'd treat the fielding metric as .4/.7 = 57% reliable when tacking it on, to illustrate with a simplified and completely made up example presuming that one could have a precise estimate of nebulous "reliability").<br /><br />Given the inherent assumption of the offensive PADJ that all positions are equally valuable, once RAR has been figured for a player, fielding value can be accounted for by adding on his runs above average relative to a player at his own position. If there is a shortstop that is -2 runs defensively versus an average shortstop, he is without a doubt a plus defensive player, and a more valuable defensive player than a first baseman who was +1 run better than an average first baseman. Regardless, since it was implicitly assumed that they are both average defensively for their position when RAR was calculated, the shortstop will see his value docked two runs. This DOES NOT MEAN that the shortstop has been penalized for his defense. The whole process of accounting for positional differences, going from hitting RAR to positional RAR, has benefited him.<br /><br />I've found that there is often confusion about the treatment of first baseman and designated hitters in my PADJ methodology, since I consider DHs as in the same pool as first baseman. The fact of the matter is that first baseman outhit DH. There are any number of potential explanations for this; DHs are often old or injured, players hit worse when DHing than they do when playing the field, etc. This actually helps first baseman, since the DHs drag the average production of the pool down, thus resulting in a lower replacement level than I would get if I considered first baseman alone.<br /><br />However, this method does assume that a 1B and a DH have equal defensive value. Obviously, a DH has no defensive value. What I advocate to correct this is to treat a DH as a bad defensive first baseman, and thus knock another five or so runs off of his RAR for a full-time player. I do not incorporate this into the published numbers, but you should keep it in mind. However, there is no need to adjust the figures for first baseman upwards --the only necessary adjustment is to take the DHs down a notch. <br /><br />Finally, I consider each player at his primary defensive position (defined as where he appears in the most games), and do not weight the PADJ by playing time. This does shortchange a player like Ben Zobrist (who saw significant time at a tougher position than his primary position), and unduly boost a player like Buster Posey (who logged a lot of games at a much easier position than his primary position). For most players, though, it doesn't matter much. I find it preferable to make manual adjustments for the unusual cases rather than add another layer of complexity to the whole endeavor.<br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRcb2zLEtaXv5GEGMLQuUUnb4KAOFcGWh6wfOn-MnY3gR9LbvvJJtGcqXmKSXqUBNQDeL9pQop6zFji/pub?output=html"><br />2017 League</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTqqWsLzxQ9uSkyzgLcHmoEKSAGrx6zoadd6sZNK8EgG_sMwlr1uJvsW6qbtaGH7Bpo32hsCpvXMNhh/pub?output=html">2017 Park Factors</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTbe9Bvv3L4pwYb5qJC1AAiIZwV2invYT5HKIqYKWhGHweE9zEyzewU-80OrLbT6uPc6Kfkigs-J5BF/pub?output=html">2017 Teams</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQxpPvgc4bmrHqBYXxOlfFGhcDhefJqwp0wa4-O6RM6VnzTlTNxjRhAsxlxGEdgLqgH3EhVBIyfwqNQ/pub?output=html">2017 Team Offense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vR6-vk6pPcXPiF7OjlxKSOAx6dpKrpM72Lv9aHRTTmt2vE5VrBCP2ZuMlC-IQ6N0_cjZo3_aBkl6rZN/pub?output=html">2017 Team Defense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vSqgjP8LES2aBeI4vY7Z1GiWZQ_o5xifZepKEBqYstzMCGMcwB1XTehljVBUjsEc__-8B0J95wgKBUV/pub?output=html">2017 AL Relievers</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQAxZzDcveBMh_b78cQbtf_5vPPcJ-47L17uSNNuzoPE5XjrrDWNfOmjO1TBGw_uiiCrHhNGc_czbeq/pub?output=html">2017 NL Relievers<br /></a><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQrMIiv_ufFUHoH3P5r6F_-S7bBGKQ00HKJGCeq57UjA6j24QFLYUV238Dgca5yih1GJNxpDUhTSlf1/pub?output=html">2017 AL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRXa-m_byBIx9TQ5Jqqto4Am-xiP4X22tUlMrm3xWXGdwz9A5TauYM23asTQ_2btMMeCzNU9V0380p4/pub?output=html">2017 NL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQpRFDFgsnkk8de6PBS6a-nqDZfQrVVqyo3TJCP9y2sJjRBGjJRrnLZZOWYU26GarOheT_RWEzcPyf1/pub?output=html">2017 AL Hitters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQfxVtrW43CPz227jxGKq_Gc0gGus6OVKvLUID0D578iymbKBNmdB9xTHKa9FofYpIoTGgBHUQT_u2u/pub?output=html">2017 NL Hitters</a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-23113546112861404382017-10-02T17:58:00.000-04:002017-10-03T19:54:55.134-04:00Crude Playoff Odds--2017These are very simple playoff odds, based on my crude rating system for teams using an equal mix of W%, EW% (based on R/RA), PW% (based on RC/RCA), and 69 games of .500. They account for home field advantage by assuming a .500 team wins 54.2% of home games (major league average 2006-2015). They assume that a team's inherent strength is constant from game-to-game. They do not generally account for any number of factors that you would actually want to account for if you were serious about this, including but not limited to injuries, the current construction of the team rather than the aggregate seasonal performance, pitching rotations, estimated true talent of the players, etc.<br /><br />The CTRs that are fed in are:<br /><br /><a href="https://4.bp.blogspot.com/-QNp2ZSN6m9I/WdK1v7wd4_I/AAAAAAAACZA/gyJrCH3OwZMaZloWqdWH7ptfau7kHmElwCLcBGAs/s1600/playodd17a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-QNp2ZSN6m9I/WdK1v7wd4_I/AAAAAAAACZA/gyJrCH3OwZMaZloWqdWH7ptfau7kHmElwCLcBGAs/s400/playodd17a.jpg" width="400" height="387" data-original-width="217" data-original-height="210" /></a><br /><br />Notable here is that three AL teams rank ahead of the Dodgers, which includes New York rather than Boston. NYA’s raw EW% and PW% are very close to LA, and LA played the second-weakest schedule in MLB while the Red Sox and Yankees played the toughest schedules of any playoff teams.<br /><br />Wilcard game odds (the least useful since the pitching matchups aren’t taken into account, and that matters most when there is just one game):<br /><br /><a href="https://2.bp.blogspot.com/-brFOMr65c2Q/WdK114T01uI/AAAAAAAACZE/Sk99AOCRB_cdjwK7xDCoMAaBV9IMPRuMACLcBGAs/s1600/playodd17b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-brFOMr65c2Q/WdK114T01uI/AAAAAAAACZE/Sk99AOCRB_cdjwK7xDCoMAaBV9IMPRuMACLcBGAs/s400/playodd17b.jpg" width="400" height="81" data-original-width="288" data-original-height="58" /></a><br /><br />LDS:<br /><br /><a href="https://4.bp.blogspot.com/-ZE-Biq7wL18/WdK1_Pxm9SI/AAAAAAAACZI/6Ur1aAuRthITXbD4_Vz_z7BzDAyEVT4rQCLcBGAs/s1600/playodd17c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ZE-Biq7wL18/WdK1_Pxm9SI/AAAAAAAACZI/6Ur1aAuRthITXbD4_Vz_z7BzDAyEVT4rQCLcBGAs/s400/playodd17c.jpg" width="400" height="106" data-original-width="505" data-original-height="134" /></a><br /><br />I think most people would pick WAS/CHN as the most compelling on paper, which is backed up by the odds. Unfortunately for me, CLE/NYA would be a sneaky-good series.<br /><br />LCS:<br /><br /><a href="https://3.bp.blogspot.com/-LEokV4AhuDc/WdK2GF0c7AI/AAAAAAAACZM/XtYznK2rgN0w0nBJ_hG4yfdwWdYi1HwmQCLcBGAs/s1600/playodd17d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-LEokV4AhuDc/WdK2GF0c7AI/AAAAAAAACZM/XtYznK2rgN0w0nBJ_hG4yfdwWdYi1HwmQCLcBGAs/s400/playodd17d.jpg" width="400" height="197" data-original-width="505" data-original-height="249" /></a><br /><br />World Series:<br /><br /><a href="https://4.bp.blogspot.com/-JM5tFMYAvFA/WdK2LnluBpI/AAAAAAAACZQ/3keRDCdRoREd93iJ1zO4WvouAbVKl021ACLcBGAs/s1600/playodd17e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-JM5tFMYAvFA/WdK2LnluBpI/AAAAAAAACZQ/3keRDCdRoREd93iJ1zO4WvouAbVKl021ACLcBGAs/s400/playodd17e.jpg" width="400" height="394" data-original-width="503" data-original-height="495" /></a><br /><br />Because I set this spreadsheet up when home field advantage went to a particular league (as it has been for the entire history of the World Series prior to this year), all of the NL teams are listed as the home team. But the probabilities all consider which team would actually have the home field advantage in each matchup.<br /><br />Put it all together:<br /><br /><a href="https://4.bp.blogspot.com/-ogVSkEB2mJo/WdK2RfTpZCI/AAAAAAAACZU/YXyXMcHqC6MJ9EPc3hRNQty9ETCDVMu5QCLcBGAs/s1600/playodd17f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ogVSkEB2mJo/WdK2RfTpZCI/AAAAAAAACZU/YXyXMcHqC6MJ9EPc3hRNQty9ETCDVMu5QCLcBGAs/s400/playodd17f.jpg" width="400" height="234" data-original-width="361" data-original-height="211" /></a><br /><br />This one should make it clear why I don’t have much to say this year.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-24173031964119195442017-08-22T10:23:00.000-04:002017-08-22T10:23:06.181-04:00Enby Distribution, pt. 4: Revisiting W%In my first series about runs per game distributions, I wrote about how to use estimates of the probability of scoring k runs (however these probabilities were estimated, Enby distribution or an alternative approach) to estimate a team’s winning percentage. I’m going to circle back to that here, and most of the content is a repeat of the earlier post. <br /><br />However, I think this is an important enough topic to rehash. In fact, a winning percentage estimator strikes me as the most logical application for a runs per game distribution, albeit one that is not particularly helpful to everyday sabermetric practice. After all, multiple formulas to estimate W% as a function of runs scored and runs allowed have been developed, and most of them work quite well when working with normal major league teams--well enough to make it difficult to imagine that there is any appreciable gain in accuracy to be had. Better yet, these W% estimators are fairly simple--even the most complex versions in common use, Pythagenport/pat, can be quickly tapped out on a calculator in about thirty seconds.<br /><br />Given that there are powerful, relatively simple W% models already in use, why even bother to examine a model based on the estimated scoring distribution? There are three obvious reasons that come to my mind. The first is that such a model serves as a check on the others. Depending on how much confidence one has in the underlying run distribution model, it is possible that the resulting W% estimator will produce a batter estimate, at least at the extremes. We know of course that some of the easier models don’t hold up well in extreme situations--linear estimators will return negative or greater than one figures at some point, and fixed Pythagorean exponents will fray at some point. While we know that Pythagenpat works at the known point of 1 RPG and appears to work well at other extreme values, it doesn’t hurt to have another way of estimating W% in those extremes to see if Pythagenpat is corroborated, or whether the models disagree. This can also serve as a check on Enby--if the results vary too much from what we expect, it may imply that Enby does not hold up well at extremes itself.<br /><br />A second reason is that it’s plain fun if you like esoteric sabermetrics (and if you’re reading this blog, it’s a good bet that you do). I’ve never needed an excuse to mess around with alternative methods, particularly when it comes to W% estimators, which along with run estimators are my own personal favorite sabermetric tools.<br /><br />But the third reason is the one that I want to focus on here, which is that a W% estimator based on an underlying estimate of the run distribution is from one perspective the simplest possible estimator. This may seem to be an absurd statement given all of the steps that are necessary to compute Enby estimates, let alone plugging these into a W% formula. But from a first principles standpoint, the distribution-based W% estimator is the simplest to explain, because it is defined by the laws of the game itself.<br /><br />If you score no runs, you don’t win. If you score one run, you win if you allow zero runs. If you score two runs, you win if you allow either zero or one run, and on it goes ad infinitum. If at the end of nine innings you have scored and allowed an equal number of runs, you play on until there is an inning in which an unequal, greater than zero number of runs are scored. This fundamental identity is what all of the other W% estimators attempt to approximate, the mechanics which they attempt to sweep under the rug by taking shortcuts to approximate. The distribution-based approach is computationally dense but conceptually easy (and correct). Of course, to bring points one and three together, the definition may be correct, but the resulting estimates are useless if the underlying model (Enby in this case) does not work.<br /><br />In order to produce our W% estimate, we first need to use Enby to estimate the scoring distribution for the two teams. This is not as simple as using the Enby parameters we have already developed based on the Tango Distribution with c = .767. Tango has found that his method produces more accurate results for two teams when c is set equal to .852 instead.<br /><br />In the previous post, I walked through the computations for the Enby distribution with any c value, so this is an easy substitution to make. But why is it necessary? I don’t have a truly satisfactory answer to that question--it's trite to just assert that it works better for head-to-head matchups because of the covariance between runs scored and runs allowed, even if that is in fact the right answer.<br /><br />How will modifying the control value alter the Enby distribution? All of the parameters will be effected, because all depend on the control value in one way or another. First, B and r (the latter as it is initially figured before zero modification):<br /><br />VAR = RG^2/9 + (2/c - 1)*RG<br />r = RG^2/(VAR - RG)<br />B = VAR/RG - 1<br /><br />When c is larger, the variance of runs scored will be smaller. We can see this by examining the equations for variance with c = .767 and .852:<br /><br />VAR (.767) = RG^2/9 + 1.608*RG<br />VAR (.852) = RG^2/9 + 1.347*RG<br /><br />This results in a larger value for r and a smaller value for B, but these parameters don’t have an intuitive baseball explanation, unlike variance. It’s difficult to explain (for me at least) why variance of a single team’s runs scored should be lower when considering a head-to-head matchup, but that’s the way it works out.<br /><br />It should be noted that if the sole purpose of this exercise is to estimate W%, we don’t have to care whether the actual probability of each team scoring k runs is correct. All we need to do is have an accurate estimate of how often Team A’s runs scored are greater than Team B’s. <br /> <br />By increasing c, we also reduce the probability of a shutout, as can be seen from the formula for z:<br /><br />z =(RI/(RI + c*RI^2))^9<br /><br />Originally, I had intended to display some graphs showing the behavior of the three parameters by RG with each choice of c, but these turned out to be not of any particular interest. I ran <a href="http://walksaber.blogspot.com/2012/07/on-run-distributions-pt-6.html">similar graphs</a> earlier in the series with parameters based on the earlier variance model, and the shape of the resulting functions are quite similar. The only real visual difference when c varies is what appears to be linear shifts for r and B (the B shift is linear, the r not quite).<br /><br />What might be more interesting is looking at how c shapes the estimated run distribution for a team with a given RG. I’ll look at three teams--one average (4.5 RG), one extremely low-scoring (2.25 RG), and one extremely high-scoring (9 RG). First, the 4.5 RG team:<br /><br /><a href="https://3.bp.blogspot.com/-Y_-NRFvlIeQ/WZpFjKn9TQI/AAAAAAAACYk/LJWiJj0acHYpr90_3ntBtw31E4lJQZiHwCLcBGAs/s1600/45rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-Y_-NRFvlIeQ/WZpFjKn9TQI/AAAAAAAACYk/LJWiJj0acHYpr90_3ntBtw31E4lJQZiHwCLcBGAs/s400/45rg.jpg" width="400" height="203" data-original-width="1566" data-original-height="796" /></a><br /><br />As you may recall from earlier, Enby consistently overestimates the frequency with which a normal major league team will score 2-4 runs. Using the .852 c value exacerbates this issue; in fact, the main thing to take away from this set of graphs is that the higher c value clusters more probability around the mean, while the lower c value leaves more probability for the tails.<br /><br />The 2.25 RG team:<br /><br /><a href="https://1.bp.blogspot.com/-yp_tHHSKr6o/WZpFnug1eFI/AAAAAAAACYo/BFBoMYBTB3USxlMx1eUPjQNN93RbK9UFwCLcBGAs/s1600/225rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-yp_tHHSKr6o/WZpFnug1eFI/AAAAAAAACYo/BFBoMYBTB3USxlMx1eUPjQNN93RbK9UFwCLcBGAs/s400/225rg.jpg" width="400" height="204" data-original-width="1563" data-original-height="799" /></a><br /><br />And the 9 RG team:<br /><br /><a href="https://1.bp.blogspot.com/-hE2EmLUqMX4/WZpFukgTScI/AAAAAAAACYs/_OrCcur9k3UknSQbfssFwg5LGitMl9sPgCLcBGAs/s1600/9rg.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-hE2EmLUqMX4/WZpFukgTScI/AAAAAAAACYs/_OrCcur9k3UknSQbfssFwg5LGitMl9sPgCLcBGAs/s400/9rg.jpg" width="400" height="202" data-original-width="1554" data-original-height="783" /></a><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-45693263701828212692017-08-10T16:38:00.000-04:002017-08-10T16:38:24.296-04:00Bottoming OutOn June 5, OSU Athletic Director Gene Smith unceremoniously fired Thad Matta, the winningest men’s basketball coach in the history of the school. He did so months after the normal time to fire coaches had passed, and he did so in a way that ensured that the end of Matta’s tenure would be the dominant story in college basketball over the next week. Matta won four regular season Big Ten championships, went to two Final Fours, and was as close to universally respected and beloved by his former players as you will ever find in college basketball. He did all of this while dealing with a debilitating condition that made routine tasks like walking and taking off his shoes a major challenge; it was a side effect of a surgery performed at the university’s own hospital. OSU was coming off a pair of seasons without making the NCAA Tournament, but basketball is a sport in which a roster can get turned around in a hurry, and this author feels that Matta had more than earned another year or two in which to have the opportunity to do just that. Gene Smith felt otherwise.<br /><br />On May 20, the OSU baseball team lost to Indiana 4-3 at home. This brought an end to a season in which they went 22-34, the school’s worst record since going 6-12 in 1974. They went 8-16 in the Big Ten, the worst showing since going 4-12 in 1987. The season brought Greg Beals’ seven-year record at OSU to 225-167 (.574) and his Big Ten record to 85-83 (.506). Setting aside 2008-2014, a seven-year stretch in which OSU had a .564 W% (since four of the seasons were coached by Beals), the seven-year record is OSU’s worst since 1986-1992. The seven-year stretch in the Big Ten is the worst since 1984-1990 (.486). The Buckeyes finished eleventh in the Big Ten, which in fairness wasn’t possible until the addition of Nebraska, but since the Big Ten eliminated divisions in 1988, the lowest previous conference standing had been seventh (out of 10 in 2010, out of 11 in 2014, out of 13 in 2015).<br /><br />The OSU season is hardly worth recapping in detail, except to point out that baseball is such that Oregon State could go 56-6 on the year let have one of those losses come to the Buckeyes (February 24, 6-1; the Beavers won a rematch 5-1 two days later). The other noteworthy statistical oddity is that in eight Big Ten series, Ohio won just one (2-1 at Penn State). They were swept once (home against Minnesota) and the other six were all 1-2 for the opposition. The top eight teams in the conference qualify for the tournament; OSU finished four games out of the running, eliminated even before the final weekend.<br /><br />The Buckeyes’ .393 overall W% and .412 EW% were both eleventh of thirteen Big Ten teams (the forces of darkness led at .724 and .748 respectively), and their .463 PW% was eighth (again, the forces of darkness led with .699). OSU was twelfth with 5.07 R/G and tenth with 6.05 RA/G, although Bill Davis Staidum is a pitcher’s park and those are unadjusted figures. OSU’s .659 DER was last in the conference.<br /><br />None of this was surprising; OSU lost a tremendous amount of production from 2016, which was Beals’ most successful team, notching his only championship (Big Ten Tournament) and NCAA appearance. With individual exceptions, outside of the 2016 draft class, Beals has failed to recruit and develop talent, often patching his roster with copious amounts of JUCO transfers rather than underclassmen developed in the program. Never was this more acute than in 2017. None of this is meant to be an indictment of the players, who did the best they could to represent their school. It is not their fault that the coach put them in situations that they couldn’t handle or weren’t ready for.<br /><br />Sophomore catcher Jacob Barnwell had a solid season, hitting .254/.367/.343 for only -1 RAA; his classmate and backup Andrew Fishel only got 50 PA but posted a .400 OBA. First base/DH was a real problem position, as senior Zach Ratcliff was -8 RAA and JUCO transfer junior Bo Coolen chipped in -6; both had secondary averages well below the team average. Noah McGowan, another JUCO transfer started at second (and got time in left as well), with -3 RAA in 162 PA before getting injured. True freshman Noah West followed him into the lineup, but a lack of offense (.213/.278/.303 in 105 PA) gave classmate Connor Pohl a shot. Pohl is 6’5” and his future likely lies at third, but his bat gave a boost to the struggling offense (.325/.386/.450 in 89 PA).<br /><br />Senior Jalen Washington manned shortstop and acquitted himself fine defensively and at the plate (.266/.309/.468), and was selected by San Diego in the 28th round. Sophomore third baseman Brady Cherry did not build on the power potential his freshman year seemed to show, hitting four homers in 82 more PA than he had when he hit four in 2016. His overall performance (.260/.333/.410) was about average (-2 RAA). <br /><br />Outfield was definitely the bright spot for the offense, despite getting little production out of JUCO transfer Tyler Cowles (.190/.309/.314 in 129 PA). Senior Shea Murray emerged from a pitching career marred by injuries to provide adequate production and earn the left field job (.252/.331/.449, 0 RAA) and was drafted in the 18th round by Pittsburgh, albeit as a pitcher. Junior center fielder Tre’ Gantt was the team MVP, hitting .314/.426/.426, leading the team with 18 RAA, and was drafted in the 29th round by Cleveland. True freshman right fielder Dominic Canzone was also a key contributor, challenging for the Big Ten batting average lead (.343/.398/.458 for 8 RAA).<br /><br />On the mound, OSU never even came close to establishing a starting rotation due to injuries and ineffectiveness. Nine pitchers started a game, and only one of them had greater than 50% of his appearances as a starter. That was senior Jake Post, who went 1-7 over 13 starts with a 6.41 eRA. Sophomore lefty Connor Curlis was most effective, starting eight times for +3 RAA with 8.3/2.7 K/W. He tied for team innings lead with classmate Ryan Feltner, who was -13 RAA with a 6.71 eRA. Junior Yianni Pavloupous, the closer a year ago, was -10 RAA over 40 innings between both roles. Junior Adam Niemeyer missed time with injuries, appearing in just ten games (five starts) for -3 RAA over 34 innings. Freshman Jake Vance was rushed into action and allowed 20 runs and walks in 26 innings (-4 RAA). And JUCO transfer Reece Calvert gave up a shocking 39 runs in 39 innings.<br /><br />I thought the bullpen would be the strength of the team before the season. In the case of Seth Kinker, I was right. The junior slinger was terrific, pitching 58 innings (21 relief appearances, 3 starts) and leading the team by a huge margin with 13 RAA (8.4/2.0 K/W). But the rest of the bullpen was less effective. Junior Kyle Michalik missed much of the season with injuries and wasn’t that effective when on the mound (6.85 RA and just 4.8 K/9 over 22 innings). Senior Joe Stoll did fine in the LOOGY role, something Beals has brought to OSU, with 3 RAA in 23 innings over 25 appearances. Junior Austin Woodby had a 6.00 RA over 33 innings but deserved better with a 4.79 eRA and 5.5/1.8 K/W. The only other reliever to work more than ten innings was freshman sidearmer Thomas Waning (3 runs, 11 K, 4 W over 12 innings). Again, it’s hard to describe the roles because almost everyone was forced to both start and relieve.<br /><br />It’s too early to hazard a prognosis for 2018, but given the lack of promising performances from young players, it’s hard to be optimistic. What remains to be seen is whether Smith’s ruthlessness can be transferred from coaches who do not deserve it to those who have earned it in spades. No, baseball is not a revenue sport, and no, baseball is not bringing the athletic department broad media exposure. But when properly curated, the OSU baseball program is a top-tier Big Ten program, with the potential to make runs in the NCAA Tournament, and bring in more revenue than most of the “other” 34 programs that are not football or men’s basketball. Neglected in the hands of a failed coach, it is capable of putting up a .333 W% in conference play. Smith, not Beals, is the man who will most directly impact the future success of the program.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-26196007280938452472017-07-12T07:21:00.000-04:002017-07-12T07:21:02.283-04:00Enby Distribution, pt. 3: Enby Distribution CalculatorAt this point, I want to re-explain how to use the Enby distribution, step-by-step. While I already did this in part 6 of the original series, I now have the new variance estimator as found by Alan Jordan to plug in, and so to avoid any confusion and to make this is easy if anyone ever wants to implement it themselves, I will recount it all in one location. I will also re-introduce a spreadsheet that you can use to estimate the probability of scoring X runs based on the Enby distribution.<br /><br />Step 1: Estimate the variance of runs scored per game (VAR) as a function of mean runs/game (RG):<br /><br />VAR = RG^2/9 + (2/c - 1)*RG<br />where c is the control value from the <a href="http://tangotiger.net/wiki_archive/Tango_Distribution.html">Tango Distribution</a>. For normal applications, we’ll assume that c = .767.<br /><br />Step 2: Use the mean and variance to estimate the parameters (r and B) of the negative binomial distribution:<br /><br />r = RG^2/(VAR - RG)<br />B = VAR/RG - 1<br /><br />B will be retained as a parameter for the Enby distribution.<br /><br />Step 3: Find the probability of zero runs scored as estimated by the negative binomial distribution (we’ll call this value a):<br /><br />a = (1 + B)^(-r)<br /><br />Step 4: Use the Tango Distribution to estimate the probability of being shutout. This will become the Enby distribution parameter z:<br /><br />z =(RI/(RI + c*RI^2))^9<br />where RI is runs/inning, which we’ll estimate as RG/9. <br /><br />Step 5: Use trial and error to estimate a new value of r given the modified value at zero. B and z will stay constant, but r must be chosen so as to ensure that the correct mean RG is returned by the Enby distribution. Use the following formula to estimate the probability of k runs scored per game using the non-modified negative binomial distribution:<br /><br />q(0) = a<br />q(k) = (r)(r + 1)(r + 2)(r + 3)…(r + k - 1)*B^k/(k!*(1 + B)^(r + k)) for k >=1<br /><br />Then modify by taking:<br /><br />p(0) = z<br />p(k) = (1 - z)*q(k)/(1 - a)for k >=1<br /><br />The mean is calculated as:<br /><br />mean = sum (from k = 1 to infinity) of (k*p(k)) = p(1) + 2*p(2) + 3*p(3) + ...<br /><br />Now you have the parameters r, B, and z and the probability of scoring k runs in a game. <br /><br />I previously published a spreadsheet that provided the approximate Enby distribution parameters at each .05 increment of RG between 3 and 7. The link below will take you to an updated version of this calculator. It is updated in two ways: first, the Tango Distribution estimate of variance developed by Alan Jordan is used as in the example above. Secondly, I have added lines for RG levels between 0-3 and 7-15 RG (at intervals of .25). Previously, you could enter in any value between 3-7 RG and the calculator would round it to nearest .05; now I’m going to make you enter a legitimate value yourself or accept whatever vlookup() gives you.<br /><br />P(x) is the probability of scoring x runs in a game, P(<= x) is the probability of scoring that many or fewer, and P(> x) is the probability of scoring more than x runs.<br /><br /><a href="https://docs.google.com/spreadsheets/d/1ibSqb1qjuBPVEaT7QHpEDpj75xkEIfcZqqOf7YpDALM/pub?output=xlsx">Enby Calculator</a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-80293292655783244672017-06-20T07:19:00.000-04:002017-06-20T07:19:05.726-04:00Enby Distribution, pt. 2: Revamping the Variance EstimateAll models are approximations of reality, but some are more useful than others. The notion of being able to estimate the runs per game distribution cleanly in one algorithm (rather than patching together runs per inning distributions or using simulators) is one that can be quite useful in estimating winning percentage or trying to distinguish between the effectiveness of team offense beyond similar noting their runs scored total. I’d argue that a runs per game distribution is a fundamentally useful tool in classical sabermetrics.<br /><br />However, while such a model would be useful, Enby as currently constructed falls well short of being an ideal tool. There are a few major issues:<br /><br />1) It is not mathematically feasible to solve directly for the parameters of a zero-modified negative binomial distribution, which forces me to use trial and error to estimate Enby coefficients. In doing so, the distribution is no longer able to exactly match the expected mean and variance--instead, I have chosen to match the mean precisely, and hope that the variance is not too badly distorted.<br /><br />2) The variance that we should expect for runs per game at any given level of average R/G is itself unknown. I developed a simple formula to estimate variance based on some actual team data, but that formula is far from perfect and there’s no particular reason to expect it to perform well outside of the R/G range represented by the data from which it was developed.<br /><br />3) An issue with run distribution models found by Tom Tango in the course of his research on runs per inning distribution is that the optimal fit for a single team’s distribution may not return optimal results in situations in which two teams are examined simultaneously (such as using the distribution to model winning percentage). One explanation for this phenomenon is the covariance between runs scored and runs allowed in a given game, due to either environmental or strategic causes.<br /><br />I have recently attempted to improve the Enby distribution by focusing on these obvious flaws. Unfortunately, my findings were not as useful as I had hoped they would be, but I would argue (hope?) that they represent at least small progress in this endeavor.<br /><br />During the course of writing the original series on this topic, I was made aware of work being done by Alan Jordan, who was developing a spreadsheet that used the Tango Distribution to estimate scoring distributions and winning percentage. One of the underpinnings was that he found (or found <a href="http://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1050&context=mathfac">work by Darren Glass and Phillip Lowry that demonstrated</a>) that the variance of runs scored per inning as predicted by the Tango Distribution could be calculated as follows (where RI = runs per inning and c is the Tango Distribution constant):<br /><br />Variance (inning) = RI*(2/c + RI - 1) = RI^2 + (2/c - 1)*RI<br /><br />Assuming independence of runs per inning (this is a necessary assumption to use the Tango Distribution to estimate runs per game), the variance of runs per game will simply be nine times the variance of runs per inning (assuming of course that there are precisely nine innings per game, as I did in estimating the z parameter of Enby from the Tango Distribution). If we attempt to simply this further by assuming that RI = RG/9, where RG = runs per game:<br /><br />Variance (game) = 9*(RI^2 + (2/c - 1)*RI) = 9*((RG/9)^2 + (2/c - 1)*RG/9) = RG^2/9 + (2/c - 1)*RG<br /><br />The traditional value of c used to estimate runs per inning for one team is .767, so if we substitute that for c, we wind up with:<br /><br />Variance (game) =1.608*RG + .111*RG^2<br /><br />When I worked on this problem previously, I did not have any theoretical basis for an estimator of variance as a function of RG, so I experimented with a few possibilities and found what appeared to be a workable correlation between mean RG and the ratio of variance to mean. I used linear regression on a set of actual team data (1981-1996) and wound up with an equation that could be written as:<br /><br />Variance (game) = 1.43*RG + .1345*RG^2<br /><br />Note the similarities between this equation and the equation based on the Tango Distribution - they both take the form of a quadratic equation less the constant (I purposefully avoided constants in developing my variance estimator so as to avoid unreasonable results at zero and near-zero RG). The coefficients are somewhat different, but the form of the equation is identical.<br /><br />On one hand, this is wonderful for me, because it vindicates my intuition that this was a reasonable way to estimate variance. On the other hand, this is very disappointing, because I had hoped that Jordan’s insight would allow me to significantly improve the variance estimate. Instead, any gains to be had here are limited to improving the equation by using a more theoretical basis to estimate its coefficients, but there is no change in the form of this equation.<br /><br />In fact, any revision to the estimator will reduce accuracy over the 1981-96 sample that I am using, since the linear regression already found optimal coefficients for this particular dataset. This by no means should be taken as a claim on my part that the regression-based equation should be used rather than the more theoretically-grounded Tango Distribution estimate, simply an observation that any improvement will not show up given the confines of the data I have at hand.<br /><br />What about data from out of that set? I have easy access to the four seasons from 2009-2012. In these seasons, major league teams have averaged 4.401 runs per game and the variance of runs scored per game is 9.373. My equation estimates the variance should be 8.90, while the Tango-based formula estimates 9.23. In this case, we could get a near-precise match by using c = .757.<br /><br />While we know how accurate each estimator is with respect to variance for this case, what happens when we put Enby to use to estimate the run distribution? The Enby parameters for 4.40 RG using my original equation are (B = 1.0218, r = 4.353, z = .0569). If we instead use the Tango estimated variance of 9.23, the parameters become (B = 1.0970, r = 4.041, z = .0569). With that, we can calculate the estimated frequencies of X runs scored using each estimator and compare to the empirical frequencies from 2009-2012:<br /><br /><a href="https://3.bp.blogspot.com/-WR4AxLkuSGA/WUhCRq6UyXI/AAAAAAAACYQ/LcwoxkOzBIwcYhOq905aR9IFU4ZQfPM0ACLcBGAs/s1600/freqest.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-WR4AxLkuSGA/WUhCRq6UyXI/AAAAAAAACYQ/LcwoxkOzBIwcYhOq905aR9IFU4ZQfPM0ACLcBGAs/s400/freqest.jpg" width="300" height="400" data-original-width="307" data-original-height="409" /></a><br /><br />Eyeballing this, the Tango-based formula is closer for one run, but exacerbates the recurring issue of over-estimating the likelihood of two or three runs. It makes up for this by providing a better estimate at four and five runs, but a worse estimate at six. After that the two are similar, although the Tango estimate provides for more probability in the tail of the distribution, which in this case is consistent with empirical results.<br /><br />For now, I will move on to another topic, but I will eventually be coming back to this form of the Tango-based variance estimate, re-estimating the parameters for 3-7 RG, and providing an updated Enby calculator, as I do feel that there are distinct advantages to using the theoretical coefficients of the variance estimator rather than my empirical coefficients.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-77582682249648788522017-05-09T10:42:00.000-04:002017-05-09T10:42:00.964-04:00Enby Distribution, pt. 1: PioneersA few years ago, I attempted to <a href="http://walksaber.blogspot.com/2012/07/on-run-distributions-pt-6.html">demonstrate</a> that one could do a decent job of estimating the distribution of runs scored per game by using the negative binomial distribution, particularly a zero-modified version given the propensity of an unadulterated negative binomial distribution to underestimate the probability of a shutout. I dubbed this modified distribution Enby.<br /><br />I’m going to be re-introducing this distribution and adopting a modification to the key formula in this series, but I wanted to start by acknowledging that I am not the first sabermetrician to adopt the negative binomial distribution to the matter of the runs per game distribution. To my knowledge, a zero-modified negative binomial distribution had not been implemented prior to Enby, and while the zero-modification is a significant improvement to the model, it would be disingenuous not to acknowledge and provide an overview of the two previous efforts using the negative binomial distribution of which I am aware.<br /><br />I acknowledged one of these in the original iteration of this <a href="http://walksaber.blogspot.com/2012/06/on-run-distributions-pt1.html">series</a>, but inadvertently overlooked the first. In the early issues of Bill James’ <U>Baseball Analyst</u> newsletter, Dallas Adams published a series of articles on run distributions, ultimately developing an unwieldy formula I discussed in the linked post. What I overlooked was an article in the August 1983 edition in which the author noted that the Poisson distribution worked for hockey, it would not work for baseball because the variance of runs per game is not equal to the mean, but rather is twice the mean. But a "modified Poisson" distribution provided a solution.<br /><br />The author of the piece? Pete Palmer. Palmer is often overlooked to an undue extent when sabermetric history is recounted. While one could never omit Palmer from such a discussion, his importance is often downplayed. But the sheer volume of methods that he developed or refined is such that I have no qualms about naming him the most important technical sabermetrician by a wide margin. Park factors, run to win converters, linear weights, relative statistics, OPS for better or worse, the construct of an overall metric by adding together runs above average in various discrete components of the game...these were all either pioneered or greatly improved by Palmer. And while it is not nearly as widespread in use as his other innovations, you can add using the negative binomial distribution for the runs per game distribution the list.<br /><br />Palmer says that he learned about this “modified Poisson” in a book called <U>Facts From Figures</u> by Maroney. The relevant formulas were:<br /><br />Mean (u) = p/c<br />Variance (v) = u + u/c<br />p(0) = (c/(1 + c))^p<br />p(1) = p(0)*p/(1 + c)<br />p(2) = p(1)*(p + 1)/(2*(1 + c))<br />p(3) = p(2)*(p + 2)/(3*(1 + c))<br />p(n) = p(0)*(p*(p + 1)*(p + 2)*...*(p + n - 1)/(n!*(1 + c)^n)<br /><br />The text that I used renders the negative binomial distribution as:<br /><br />p(k) = (1 + B)^(-r) for k = 0<br />p(k) = (r)(r + 1)(r + 2)(r + 3)…(r + k - 1)*B^k/(k!*(1 + B)^(r + k)) for k >=1<br />mean (u) = r*B<br />variance(v) = r*B*(1 + B)<br /><br />You may be forgiven for not immediately recognizing these two as equivalent; I did not at first glance. But if you recognize that r = p and B = 1/c, then you will find that the mean and variance equations are equivalent and that the formulas for each n or k depending on the nomenclature used are equivalent as well.<br /><br />So Palmer was positing the negative binomial distribution to model runs scored. He noted that the variance of runs per game is about two times the mean, which is true. In my original Enby implementation, I estimated variance as 1.430*mean + .1345*mean^2, which for the typical mean value of around 4.5 R/G works out to an estimated variance of 9.159, which is 2.04 times the mean. Of course, the model can be made more accurate by allowing the ratio <br />if variance/mean to vary from two.<br /><br />The second use of the negative binomial distribution to model runs per game of which I am aware was implemented by Phil Melita. Mr. Melita used it to estimate winning percentage and sent me a copy of his paper (over a decade ago, which is profoundly disturbing in the existential sense). Unfortunately, I am not aware of the paper ever being published so I hesitate to share too much from the copy in my possession. <br /><br />Melita’s focus was on estimating W%, but he did use negative binomial to look at the run distribution in isolation as well. Unfortunately, I had forgotten his article when I started messing around with various distributions that could be used to model runs per game; when I tried negative binomial and got promising results, I realized that I had seen it before. <br /><br />So as I begin this update of what I call Enby, I want to be very clear that I am not claiming to have “discovered” the application of the negative binomial distribution in this context. To my knowledge using zero-modification is a new (to sabermetrics) application of the negative binomial, but obviously is a relatively minor twist on the more important task of finding a suitable distribution to use. So if you find that my work in this series has any value at all, remember that Pete Palmer and Phil Melita deserve much of the credit for first applying the negative binomial distribution to runs scored per game.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-19612886446556010922017-04-13T22:19:00.000-04:002017-04-13T22:19:20.964-04:00Great Moments in CBS Sports Box Scores<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-JmDINVy9ces/WPAxnTEHCjI/AAAAAAAACYA/kHHq3a03rlg4_w3z_nxUJkhW9cclhxtIQCLcB/s1600/nicasio.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-JmDINVy9ces/WPAxnTEHCjI/AAAAAAAACYA/kHHq3a03rlg4_w3z_nxUJkhW9cclhxtIQCLcB/s400/nicasio.jpg" width="400" height="102" /></a></div>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-65544633692861292372017-04-01T15:04:00.000-04:002017-04-01T15:04:40.780-04:002017 PredictionsAll the <a href="http://sportsdataresearch.com/difficulties-associated-with-preseason-projections/">usual disclaimers</a>. This is not serious business.<br /><br />AL EAST<br /><br />1. Boston<br />2. Toronto (wildcard)<br />3. New York<br />4. Baltimore<br />5. Tampa Bay<br /><br />I have noted the last couple years that I always pick the Red Sox--last year was one of the years where that was the right call. Boston has question marks, and they have less talent on hand to fill holes than in past years, but no one else in the division is making a concerted push with the Blue Jays retrenching and the Yankees in transition. While much has been made of the NL featuring more of a clear dichotomy between contenders and rebuilders, the AL features three strong division favorites and a void for wildcard contention that Toronto may well once again fill. New York looks like a .500 team to me, and one with as strong a recent history of overperforming projections/Pythagorean as darlings like Baltimore and Kansas City, but get far less press for it. (I guess the mighty Yankees aren’t a good sell as a team being unfairly dismissed by the statheads). The Orioles offense has to take step back at some point with only Machado and Schoop being young, and if that happens the rotation can’t carry them. It’s not that I think the Rays are bad; this whole division is filled with potential wildcard contenders.<br /><br />AL CENTRAL<br /><br />1. Cleveland<br />2. Detroit<br />3. Kansas City<br />4. Minnesota<br />5. Chicago<br /><br />I have a general policy of trying to pick against the Indians when reasonable, out of irrational superstition and an attempt to counteract any unconscious fan-infused optimism. Last year I felt they were definitely the best team in this division on paper but picked against them regardless. But the gap is just too big to ignore this season, so I warily pick them in front. There are reasons to be pessimistic--while they didn’t get “every break in the world last season” as Chris Russo says in a commercial that hopefully will be off the air soon, it’s easy to overstate the impact of their pitching injuries since the division was basically wrapped up before the wheels came off the rotation. Consider the volatility of bullpens, the extra workload for the pitchers who were available in October, the fact that the two that weren’t aren’t the best health bets in the world, and you can paint a bleaker picture than the triumphalism that appears to be the consensus. On the other hand, Michael Brantley, the catchers, the fact that the offense didn’t score more runs than RC called for last year. I see them as the fourth-strongest team out of the six consensus division favorites. Detroit is the team best-positioned to challenge them; I used the phrase “dead cat bounce” last year and it remains appropriate. The less said about Kansas City the better, but as much fun as it was to watch the magic dissipate last season, the death throes of this infuriating team could be even better. The Twins have famously gone from worst to first in their franchise history; given the weakness of the division and some young players who may be much better than they’ve shown so far, it’s not that far-fetched, but it’s also more likely that they lose 95 again. The White Sox rebuilding might succeed in helping them compete down the road and finally ridding the world of the disease that is Hawk Harrelson.<br /><br />AL WEST<br /><br />1. Houston<br />2. Seattle (wildcard)<br />3. Los Angeles<br />4. Texas<br />5. Oakland<br /><br />Houston looks really good to me; if their rotation holds together (or if they patch any holes with the long awaited Jose Quintana acquisition), I see them as an elite team. Maybe the third time is the charm picking Seattle to win the wildcard. Truth be told, I find it hard to distinguish between most AL teams including the middle three in this division. Picking the Angels ahead of the Rangers is more a way to go on record disbelieving that the latter can do it again than an endorsement of the former, but even with a shaky rotation the Angels should be respectable. My Texas pick will probably look terrible when Nomar Mazara breaks out, Yu Darvish returns healthy, and Josh Hamilton rises from the dead or something. Oakland’s outlook for this year looks bleak, but am I crazy to have read their chapter in <U>Baseball Prospectus</U> and thought there were a number of really interesting prospects who could have a sneaky contender season in 2018? Probably.<br /><br />NL EAST<br /><br />1. Washington<br />2. New York (wildcard)<br />3. Miami <br />4. Atlanta<br />5. Philadelphia<br /><br />It’s very tempting to pick New York over Washington, based on the superficial like the Nationals sad-Giants even year pattern and cashing in most of their trade chits for Adam Eaton, but there remains a significant on-paper gap between the two. Especially since the Mets stood pat from a major league roster perspective. This might be the best division race out there in a season in which there are six fairly obvious favorites. Sadly, Miami is about one 5 WAR player away from being right in the mix…I wonder where on might have found such a player? Atlanta seems like a better bet than Philadelphia in both the present and future tense, but having a great deal of confidence in the ordering of the two seems foolhardy.<br /><br />NL CENTRAL<br /><br />1. Chicago<br />2. Pittsburgh<br />3. St. Louis<br />4. Milwaukee<br />5. Cincinnati<br /><br />The Cubs’ starting pitching depth is a little shaky? Kyle Schwarber doesn’t have a position and people might be a little too enthusiastic about him? Hector Rondon struggled late in the season and Wade Davis’ health is not a sure thing? These are the straws that one must grasp at to figure out how Chicago might be defeated. You also have to figure out whether Pittsburgh can get enough production from its non-outfielders while also having some good fortune with their pitching. Or whether St. Louis’ offense is good enough. Or whether Milwaukee or Cincinnati might have a time machine that could jump their rebuild forward a few years. You know, the normal questions you ask about a division.<br /><br />NL WEST<br /><br />1. Los Angeles<br />2. San Francisco<br />3. Arizona<br />4. Colorado<br />5. San Diego<br /><br />Last year I picked the Giants over the Dodgers despite the numbers suggesting otherwise because of injury concerns. I won’t make that mistake again, as it looks as if LA could once again juggle their rotation and use their resources to patch over any holes. The Giants are strong themselves, but while the two appear close in run prevention, the Dodgers have the edge offensively. The Diamondbacks should have a bounce back season, but one that would still probably break Tony LaRussa’s heart if he still cared. The Rockies seem like they should project better than they do, with more promise on the mound than they usually do. The Padres are the consensus worst team in baseball from all of the projection systems, which can be summed up with two words: Jered Weaver.<br /><br />WORLD SERIES<br /><br />Los Angeles over Houston<br /><br />Just about every projection system out there has the Dodgers ever so slightly ahead of the Cubs. That of course does not mean they are all right--perhaps there is some blind spot about these teams that player projection systems and/or collation of said projections into team win estimates share in common. On the other hand, none of these systems <i>dislike</i> the Cubs—everyone projects them to win a lot of games. I was leaning towards picking LA even before I saw that it was bordering on a consensus, because the two teams look fairly even to me but the Dodgers have more depth on hand, particularly in the starting pitching department (the natural rebuttal is that the Dodgers are likely to need that depth, while the Cubs have a four pretty reliable starters). The Dodgers bullpen looks better, and their offense is nothing to sneeze at. <br /><br />AL Rookie of the Year: LF Andrew Benintendi, BOS<br />AL Cy Young: Chris Sale, BOS<br />AL MVP: CF George Springer, HOU<br />NL Rookie of the Year: SS Dansby Swanson, ATL<br />NL Cy Young: Stephen Strasburg, WAS<br />NL MVP: 1B Anthony Rizzo, CHN<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-45318868325340846342017-03-14T07:50:00.000-04:002017-03-14T07:50:06.276-04:00Win Value of Pitcher Adjusted Run AveragesThe most common class of metrics used in sabermetrics for cross-era comparisons use relative measures of actual or estimated runs per out or sother similar denominator. These include ERA+ for pitchers and OPS+ or wRC+ for batters (OPS+ being an estimate of relative runs per out, wRC+ using plate appearances in the denominator but accounting for the impact of avoiding outs). While these metrics provide an estimate of runs relative to the league average, they implicitly assume that the resulting relative scoring level is equally valuable across all run environments.<br /><br />This is in fact not the case, as it is well-established that the relationship between run ratio and winning percentage depends on the overall level of run scoring. A team with a run ratio of 1.25 will have a different expected winning percentage if they play in a 9 RPG environment than if they play in a 10 RPG environment. Metrics like ERA+ and OPS+ do not translate relative runs into relative wins, but presumably the users of such metrics are ultimately interested in what they tell us about player contribution to wins.<br /><br />There are two key points that should be acknowledged upfront. One is that the difference in win value based on scoring level is usually quite small. If it wasn’t, winning percentage estimators that don’t take scoring level into account would not be able to accurately estimate W% across the spectrum of major league teams. While methods that do consider scoring level are more accurate estimators of W% than similar methods that don’t, a method like fixed exponent Pythagorean can still produce useful estimates despite maintaining a fixed relationship between runs and wins.<br /><br />The second is that players are not teams. The natural temptation (and one I will knowingly succumb to in what follows) is to simply plug the player’s run ratio into the formula and convert to a W%. This approach ignores the fact that an individual player’s run rate does not lead directly to wins, as the performance of his teammates must be included as well. Pitchers are close, because while they are in the game they are the team (more accurately, their runs allowed figures reflect the totality of the defense, which includes contributions from the fielders), but even ignoring fielding, non-complete games include innings pitched by teammates as well.<br /><br />For the moment I will set that aside and instead pretend (in the tradition of Bill James’ Offensive Winning %) that a player or pitcher’s run ratio can or should be converted directly to wins, without weighting the rest of the team. This makes the figures that follow something of a freak show stat, but the approach could be applied directly to team run ratios as well. Individuals are generally more interesting and obviously more extreme, which means that the impact of considering run environment will be overstated.<br /><br />I will focus on pitchers for this example and will use Bob Gibson’s 1968 season as an example. Gibson allowed 49 runs in 304.2 innings, which works out to a run average of 1.45 (there will be some rounding discrepancies in the figures). In 1968 the NL average RA was 3.42, so Gibson’s adjusted RA (aRA for the sake of this post) is RA/LgRA = .423 (ideally you would park-adjust as well, but I am ignoring park factors for this post). As an aside, please resist the temptation to instead cite his RA+ of 236 instead. <a href="http://www.hardballtimes.com/of-pluses-and-minuses/">Please</a>.<br /><br />.423 is a run ratio; Gibson allowed runs at 42.3% of the league average. Since wins are the ultimate unit of measurement, it is tempting to convert this run ratio to a win ratio. We could simply square it, which reflects a Pythagorean relationship. Ideally, though, we should consider the run environment. The 1968 NL was an extremely low scoring league. Pythagenpat suggests that the ideal exponent is around 1.746. Let’s define the Pythagenpat exponent to use as:<br /><br />x = (2*LgRA)^.29<br /><br />Note that this simply uses the league scoring level to convert to wins; it does not take into account Gibson’s own performance. That would be an additional enhancement, but it would also strongly increase the distortion that comes from viewing a player as his own team, albeit less so for pitchers and especially those who basically were pitching nine innings/start as in the case of Gibson.<br /><br />So we could calculate a loss ratio as aRA^x, or .223 for Gibson. This means that a team with Gibson’s aRA in this environment would be expected to have .223 losses for every win (basic ratio transformations apply; the reciprocal would be the win ratio, the loss ratio divided by (1 + itself) would be a losing %, the complement of that W%, etc.)<br /><br />At this point, many people would like to convert it to a W% and stop there, but I’d like to preserve the scale of a run average while reflecting the win impact. In order to do so, I need to select a Pythagorean exponent corresponding to a reference run environment to convert Gibson’s loss ratio back to an equivalent aRA for that run environment. For 1901-2015, the major league average RA was 4.427, which I’ll use as the reference environment, which corresponds to a 1.882 Pythagenpat exponent (there are actually 8.94 IP/G over this span, so the actual RPG is 8.937 which would be a 1.887 exponent--I'll stick with RA rather than RPG for this example since we are already using it to calculate aRA).<br /><br />If we call that 1.882 exponent r, then the loss ratio can be converted back to an equivalent aRA by raising it to the (1/r) power. Of course, the loss ratio is just an interim step, and this is equivalent to:<br /><br />aRA^(x*(1/r)) = aRA^(x/r) = waRA<br /><br />waRA (excuse the acronyms, which I don’t intend to survive beyond this post) is win-Adjusted Run Average. For Gibson, it works out to .450, which illustrates how small the impact is. Pitching in one of the most extreme run environments in history, Gibsons aRA is only 6.4% higher after adjusting for win impact. <br /><br />In 1994, Greg Maddux allowed 44 runs in 202 innings for a run average of 1.96. Pitching in a league with a RA of 4.65, his aRA was .421, basically equal to Gibson. But his waRA was better, at .416, since the same run ratio leads to more wins in a higher scoring environment.<br /><br />It is my guess that consumers of sabermetrics will generally find this result unsatisfactory. There seems to be a commonly-held belief that it is easier to achieve a high ERA+ in a higher run scoring environment, but the result of this approach is the opposite--as RPG increases, the win impact of the same aRA increases as well. Of course, this approach says nothing about how “easy” it is to achieve a given aRA--it converts aRA to an win-value equivalent aRA in a reference run environment. It is possible that it could be simultaneously “easier” to achieve a low aRA in a higher scoring environment and that the value of a low aRA be enhanced in a higher scoring environment. I am making no claim regarding the impressiveness or aesthetic value, etc. of any pitcher’s performance, only attempting to frame it in terms of win value.<br /><br />Of course, the comparison between Gibson and Maddux need not stop there. I do believe that waRA shows us that Maddux’ rate of allowing runs was more valuable in context than Gibson’s, but there is more to value than the rate of allowing runs. Of course we could calculate a baselined metric like WAR to value the two seasons, but even if we limit ourselves to looking at rates, there is an additional consideration that can be added.<br /><br />So far, I’ve simply used the league average to represent the run environment, but a pitcher has a large impact on the run environment through his own performance. If we want to take this into account, it would be inappropriate to simply use LgRA + pitcher’s RA as the new RPG to plug into Pythagenpat; we definitely need to consider the extent to which the pitcher’s teammates influence the run environment, since ultimately Gibson’s performance was converted into wins in the context of games played by the Cardinals, not a hypothetical all-Gibson team. So I will calculate a new RPG instead by assuming that the 18 innings in a game (to be more precise for a given context, two times the league average IP/G) is filled in by the pitcher’s RA for his IP/G, and the league’s RA for the remainder.<br /><br />In the 1968 NL, the average IP/G was 9.03 and Gibson’s 304.2 IP were over 34 appearances (8.96 IP/G), so the new RPG is 8.96*1.45/9 + (2*9.03 - 8.96)* 3.42/9 = 4.90 (rather than 6.84 previously). This converts to a Pythagenpat exponent of 1.59, and an pwaRA (personal win-Adjusted Run Average?) of .485. To spell that all out in a formula:<br /><br />px = ((IP/G)*RA/9 + (2*Lg(IP/G) - IP/G)*LgRA/9) ^ .29<br />pwaRA = aRA^(px/r)<br /><br />Note that adjusting for the pitcher’s impact on the scoring context reduces the win impact of effective pitchers, because as discussed earlier, lowering the RPG lowers the Pythagenpat exponent and makes the same run ratio convert to fewer wins. In fact, considering the pitcher’s effect on the run environment in which he operates actually brings most starting pitchers’ pwaRA closer to league average than their aRA is. <br /><br />pwaRA is divorced from any real sort of baseball meaning, though, because pitchers aren’t by themselves a team. Suppose we calculated pwaRA for two teammates in a 4.5 RA league. The starter pitches 6 innings and allows 2 runs; the reliever pitches 3 innings and allows 1. Both pitchers have a RA of 3.00, and thus identical aRA (.667) or waRA (.665). Furthermore, their team also has a RA of 3.00 for this game, and whether figured as a whole or as the weighted average of the two individuals, the team also has the same aRA and waRA.<br /><br />However, if we calculate the starter’s pwaRA, we get .675, while the reliever is at .667. Meanwhile, the team has a pwaRA of .679, which makes this all seem quite counterintuitive. But since all three entities have the same RA, the lower the run environment, the less win value it has on a per inning basis. <br /><br />I hope this post serves as a demonstration of the difficulty of divorcing a pitcher’s value from the number of innings he pitched. Of course, the effects discussed here are very small, much smaller than the impact of other related differences, like the inherent statistical advantage of pitchers over shorter stints, attempts to model differences in replacement level between starters and relievers, and attempts to detect/value any beneficial side effects of starters working deep into games.<br /><br />One of my long-standing interests has been the proper rate stat to use to express a batter’s run contribution (I have been promising myself for almost as long as this blog has been existence that I will write a series of posts explaining the various options for such a metric and the rationale for each, yet have failed to do so). I’ve never had the same pull to the question for pitchers, in part because the building block seems obvious: runs/out (which depending on how one defines terms can manifest itself as RA, ERA, component ERA, FIP-type metrics, etc.)<br /><br />But while there are a few adjustments that can theoretically made between a hitter’s overall performance expressed as a rate and a final value metric (like WAR), the adjustments (such as the hitter’s impact on his team’s run scoring beyond what the metric captures itself, and the secondary effect that follows on the run/win conversion) are quite minor in scale compared to similar adjustments for pitchers. While the pitcher (along with his fielders) can be thought as embodying the entire team while he is the game, that also means that said unit’s impact on the run/win conversion is significant. And while there are certainly cases of batters whose rates may be deceiving because of how they are deployed by their managers (particularly platooning), the additional playing time over which a rate is spread increases value in a WAR-like metric without any special adjustment. Pitchers’ roles and secondary effects thereof (like any potential value generated by “eating” innings) have a more significant (and more difficult to model) impact on value than the comparable effects for position players.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-26287845358202567992017-02-13T17:58:00.000-05:002017-02-13T17:58:52.196-05:00Rebuilding a Strip Mall"Rebuilding", as commonly thrown around in sports discussions, is an interesting term. It inherently implies that something had been built on the same spot previously. It does not, however, give an indication whether what was built there was a blanket fort or the Taj Mahal, a strip mall or the Sears Tower. If one rebuilds on the site of a strip mall, does "re-" imply they are building another strip mall, or might they be building something else? <br /><br />The baseball program that Greg Beals has presided over for six seasons at The Ohio State University has been much more of a strip mall than a Sears Tower. After his most successful season, which saw OSU tie for third in the Big Ten regular season, win the Big Ten Tournament, and qualify for their first NCAA regional since 2009, Beals is now faced with a rebuilding project in the classic sports sense. Of the nine players with the most PA in 2016, OSU must replace seven, so it would be fair to say that there will be seven new regulars. OSU must also replace two of its three weekend starters; the bullpen is the only area of the roster not decimated by graduation and the draft.<br /><br />Note: The discussion of potential player roles that follows is my own opinion, informed by my own knowledge of the players and close watching of the program and information released by the SID, particularly the season preview posted <a href="http://www.ohiostatebuckeyes.com/sports/m-basebl/spec-rel/020817aaf.html">here</a>.<br /><br />Sophomore Jacob Barnwell will almost certainly be the primary catcher; he played sparingly last season (just 29 PA). This is one of the few open positions not due to loss, but rather to a position switch which will be discussed in a moment. Classmate Andrew Fishel (8 PA) will serve as his backup.<br /><br />First base/DH will be shared by senior Zach Ratcliff, who has flashed power at times during his career but has never earned consistent playing time, and Boo Coolen, a junior Hawaii native who played at Cypress CC in California. Junior Noah McGowan, a transfer from McLennan CC in Texas, would appear to have the inside track at the keystone; his JUCO numbers are impressive but come with obvious caveats. Sophomore Brady Cherry, who got off to a torrid start in 2016 but then cooled precipitously (final line .218/.307/.411 in 143 PA) is likely to play third and bat in the middle of the order. At shortstop, senior captain Jalen Washington moves out from behind the plate to captain the infield; he spent his first two years as a Buckeye as a utility infielder, so it was the move to catcher, not to shortstop that really stands out. Unfortunately, Washington didn’t offer much with the bat as a junior (.249/.331/.343 in 261 PA). Other infield contenders include true freshman shortstop Noah West, redshirt freshman middle infielder Casey Demko, true freshman Conor Pohl at the corners, and redshirt sophomore Nate Romans and redshirt freshman Matt Carpenter in utility roles.<br /><br />The one thing that appears clear in the outfielder is that junior Tre’ Gantt will take over as center fielder; he struggled offensively last season (.255/.311/.314 in 158 PA). True freshman Dominic Canzone may step in right away in right field, while left field/DH might be split between a pair of transfers. Tyler Cowles, a junior Columbus native who hit well at Sinclair CC in Georgia will attempt to join Coolen and satisfy the Beals’ desperate need for bats with experience and power. Other outfielders include senior former pitcher Shea Murray and little-used redshirt sophomore Ridge Winand.<br /><br />The pitching staff is slightly more intact, but not much so. Redshirt junior captain Adam Niemeyer will likely be the #1 starter as the only returning weekend starter; his 2016 campaign can be fairly described as average. Sophomore Ryan Feltner was the #4 starter last year and so is a safe bet to pitch on the weekend; his 5.67 eRA was not encouraging but 8 K/3.9 W suggest some raw, harness-able ability. The third spot will apparently go to an erstwhile reliever. Junior Yianni Pavlopoulos was a surprising choice as closer last year, but pitched very well (10.3 K/3.3 W, 3.72 eRA), while senior Jake Post returns from a season wiped out by injury. Neither pitcher has been the picture of health throughout their careers, but Pavlopoulos seems the more likely choice to start. Junior Austin Woodby (7.75 eRA in 39 innings) and sophomore lefty Connor Curlis (six relief innings) will jockey for weekday assignments along with junior JUCO transfer Reece Calvert (a teammate of McGowan) and three true freshmen: lefty Michael McDonough and righties Collin Lollar and Gavin Lyon.<br /><br />The bullpen will be well-stocked, even assuming Pavlopoulos takes a spot in the rotation. Junior sidearmer Seth Kinker was a workhorse (team-high 38 appearances) and behind departed ace Tanner Tully was arguably Ohio’s most valuable pitcher in 2016. Senior Jake Post will return from a season lost to injury looking to return to a setup role, and junior sidearmer Kyle Michalik pitched well in middle relief last season. These four form a formidable bullpen that will almost certainly be augmented by a lefty specialist, a favorite of Beals. He’ll choose from senior Joe Stoll (twelve unsuccessful appearances), true freshman Andrew Magno, and the favorite in my book is Curlis should be not best Woodby for a starting spot. It appears that sophomore JUCO transfer Thomas Waning (also a sidearmer; one of the few positives about Beals as a coach is his affinity for sidearmers). Other right-handed options for the pen will include junior Dustin Jourdan (a third JUCO transfer from McLennan), sophomore Kent Axcell (making the jump from the club team), and true freshman Jake Vance.<br /><br />The non-conference schedule is again rather unambitious. The season opens the weekend of February 17 in central Florida with neutral site games against Kansas State (two), Delaware, and Pitt. Two games each against Utah and Oregon State in Arizona will follow as part of the Big Ten/Pac 12 challenge. The Bucks will then play true road series in successive weekends against Campbell and Florida Gulf Coast, then play midweek neutral site games in Port Charlotte, FL against Lehigh and Bucknell. The home schedule opens March 17 with a weekend series against Xavier (the Sunday finale being played in at XU), and the next two weekends see the Buckeyes open Big Ten play by hosting Minnesota and Purdue.<br /><br />Subsequent weekend series are at Penn State, at Michigan State, home against UNC-Greensboro, home against Nebraska, at the forces of evil, at Iowa, and home against Indiana. Midweek opponents are Youngstown State, OU, Kent State, Cincinnati, Eastern Michigan, Northern Kentucky, Texas Tech (two), Bowling Green, Ball State, and Toledo, all at home, giving OSU 28 scheduled home dates.<br /><br />Should OSU finish in the top eight in the Big Ten, the Big Ten Tournament is shifting from the recent minor league/MLB/CWS venues (including Huntington Park in Columbus, Target Field, and TD Ameritrade Park in Omaha) to campus sites, although scheduled in advance instead of at the home park of the regular season champ as was the case for many years in the past. This year’s tournament will be in Bloomington, and it speaks to both the volume of players lost and Beals’ uninspiring record that participation in this event should not be taken for granted.<br /><br /><br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-25658568319880827582017-02-09T18:49:00.000-05:002017-02-09T22:42:40.712-05:00Simple Extra Inning Game Length ProbabilitiesWith the recent news that MLB will be testing starting an extra inning with a runner on second in the low minors, it might be worthwhile to crunch some numbers and estimate the impact on the average length of extra innings game under various base/out situations to start innings. I used empirical data on the probability of scoring X runs in an inning given the base/out situation based on a nifty calculator <a href="https://gregstoll.dyndns.org/~gregstoll/baseball/runsperinning.html#about">created by Greg Stoll</a>. Stoll’s description says it is based on MLB games from 1957-2015, including postseason. <br /><br />Obviously using empirical data doesn’t allow you to vary the run environment…the expected runs for the rest of the inning with no outs, bases empty is .466 so the average R/G here is around 4.2. It also doesn’t account for any behavioral changes due to game situation, as strategy can obviously differ when it is an extra innings situation as opposed to a more mundane point in the game. Plus any quirks in the data are not smoothed over. Still, I think it is a fun exercise to quickly estimate the outcome of various extra inning setups.<br /><br />These results will be presented in terms of average number of extra innings and probability of Y extra innings assuming that the rule takes effect in the tenth inning (i.e. each extra inning is played under the same rules).<br /><br />If you know the probability of scoring X runs, assume the two teams are of equal quality, and assume independence between their runs scored (all significant assumptions), then it is very simple to calculate the probabilities of various outcomes in extra innings. If Pa(x) is the probability that team A scores x runs in an inning, and Pb(x) is the probability that team B scores x runs in an inning, then the probability that team A outscores team B in the inning (i.e. wins the game this inning) is:<br /><br />P(A > B) = Pa(1)*Pb(0) + Pa(2)*[Pb(0) + Pb(1)] + Pa(3)*[Pb(0) + Pb(1) + Pb(2)] + ….<br /><br />Since we’ve assumed the teams are of equal quality, the probability for team B is the same, just switching the Pas and Pbs. We can calculate the probability of them scoring the same number of runs (i.e. the probability the game extends an additional inning) by taking 1 – P(A > B) – P(B > A) = 1 – 2*P(A >B) since the teams are even, or directly as:<br /><br />P(A = B) = Pa(0)*Pb(0) + Pa(1)*Pb(1) + Pa(2)*Pb(2) + … = Pa(0)^2 + Pa(1)^2 + Pa(2)^2 + … since the teams are even<br /><br />I called this P. The probability that game continues past the tenth is equal to P. The probability that the game terminates after the tenth is 1-P. The probability that the game continues past the eleventh is P^2; the probability that the game terminates after the eleventh is P*(1 – P). Continue recursively from here. The average length of the game is 10*P(terminates after 10) + 11*P(terminates after 11) + …<br /><br />I used Stoll’s data to estimate a few probabilities of game length for a rule that would start each extra innings with the teams in each of the 24 base/out situations. For a given inning-initial base/out situation, P(10) is the probability that the game is over after 10 innings, P(11) the probability it is over after 11 or fewer extra innings, etc. “average” is the average number of innings in an extra inning game played under that rule, and R/I is the average scored in the remainder of the inning from Stoll’s data for teams in that base/out situation.<br /><br />It will come as no surprise that generally the higher the R/I, the lower the probability of the game continuing is. In a low scoring environment, the teams are more likely to each score zero or one run; as the scoring environment increases, so does the variance (I should have calculated the variance of runs per inning from Stoll’s data to really drive this point home, but I didn’t think of it until after I’d made the tables), and differences in inning run totals between the two teams are what ends extra inning games.<br /><br />The highlighted roles are bases empty, nobody out (i.e. the status quo); runner at second, nobody out (the proposed MLB rule); runners at first and second, nobody out (the international rule, starting from the eleventh inning; this chart assumes all innings starting with the tenth are played under the same rules, so it doesn’t let you compare these two rules directly); and bases loaded, nobody out, which maximizes the run environment and minimizes the duration of extra innings (making games beyond 12 innings as theoretically rare as games beyond 15 innings are under traditional rules). Of course, these higher scoring innings would take longer to play, so simply looking at the duration of game doesn’t fully address the alleged problems that tinkering with the rules would be intended to solve. <br /><br />I did separately calculate these probabilities for the international rule--play the tenth inning under standard rules, then start subsequent innings with runners on first and second. It produces longer games than starting with a runner at second in the tenth, which is not surprising.<br /><br /><a href="https://3.bp.blogspot.com/-nlFkDuHBuFI/WJz_YJuLuFI/AAAAAAAACXg/tNN4znGcg-Urrt2htmqRgOYKbM1DUixFQCLcB/s1600/extrainnprob.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-nlFkDuHBuFI/WJz_YJuLuFI/AAAAAAAACXg/tNN4znGcg-Urrt2htmqRgOYKbM1DUixFQCLcB/s400/extrainnprob.jpg" width="400" height="261" /></a><br /><br /><a href="https://2.bp.blogspot.com/-ykslq2yWoQ4/WJz_cs9vWLI/AAAAAAAACXk/sBfxx4ZKvywE-wsn38-NQHwwQrbD5WubwCLcB/s1600/extrainnwbcprob.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-ykslq2yWoQ4/WJz_cs9vWLI/AAAAAAAACXk/sBfxx4ZKvywE-wsn38-NQHwwQrbD5WubwCLcB/s400/extrainnwbcprob.jpg" width="400" height="22" /></a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-67475038795339924882017-01-30T09:49:00.000-05:002017-01-30T09:49:08.424-05:00Run Distribution and W%, 2016Every year I state that by the time this post rolls around next year, I hope to have a fully functional Enby distribution to allow the metrics herein to be more flexible (e.g. not based solely on empirical data, able to handle park effects, etc.) And every year during the year I fail to do so. “Wait ‘til next year”...the Indians taking over the longest World Series title drought in spectacular fashion has now given me an excuse to apply this to any baseball-related shortcoming on my part. This time, it really should be next year; what kept me from finishing up over the last twelve months was only partly distraction but largely perfectionism on a minor portion of the Enby methodology that I think I now have convinced myself is folly.<br /><br />Anyway, there are some elements of Enby in this post, as I’ve written enough about the model to feel comfortable using bits and pieces. But I’d like to overhaul the calculation of gOW% and gDW% that are used at the end based on Enby, and I’m not ready to do that just yet given the deficiency of the material I’ve published on Enby.<br /><br />Self-indulgence, aggrandizement, and deprecation aside, I need to caveat that this post in no way accounts for park effects. But that won’t come in to play as I first look at team record in blowouts and non-blowouts, with a blowout defined as 5+ runs. Obviously some five run games are not truly blowouts, and some are; one could probably use WPA to make a better definition of blowout based on some sort of average win probability, or the win probability at a given moment or moments in the game. I should also note that Baseball-Reference uses this same definition of blowout. I am not sure when they started publishing it; they may well have pre-dated by usage of five runs as the delineator. However, I did not adopt that as my standard because of Baseball-Reference, I adopted it because it made the most sense to me being unaware of any B-R standard.<br /><br />73.0% of major league games in 2015 were non-blowouts (of course 27.0% were). The leading records in non-blowouts:<br /><br /><a href="https://4.bp.blogspot.com/-ZSgAUfnwS00/WIzdl5JsVhI/AAAAAAAACWw/N1vmeYtq5lMYU5vUzubloUuhNiJHSanvQCLcB/s1600/rd16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-ZSgAUfnwS00/WIzdl5JsVhI/AAAAAAAACWw/N1vmeYtq5lMYU5vUzubloUuhNiJHSanvQCLcB/s400/rd16a.jpg" width="134" height="400" /></a><br /><br />Texas was much the best in close-ish games; their extraordinary record in one-run games which of course are a subset of non-blowouts was well documented. The Blue Jays have made it to consecutive ALCS, but their non-blowout regular season record in 2015-16 is just 116-115. Also, if you audit this you may note that the total comes to 1771-1773, which is obviously wrong. I used <a href="http://www.baseballprospectus.com/sortable/index.php?cid=1819116">Baseball Prospectus' data</a>.<br /><br />Records in blowouts:<br /><br /><a href="https://4.bp.blogspot.com/-cFItaQ5n6AQ/WIzdqjtD_MI/AAAAAAAACW0/RdZGZu1opGYZJ44so-uXuornCNExJb6nACLcB/s1600/rd16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-cFItaQ5n6AQ/WIzdqjtD_MI/AAAAAAAACW0/RdZGZu1opGYZJ44so-uXuornCNExJb6nACLcB/s400/rd16b.jpg" width="134" height="400" /></a><br /><br />It should be no surprise that the Cubs were the best in blowouts. Toronto was nearly as good last year, 37-12, for a two-year blowout record of 66-27 (.710). <br /><br />The largest differences (blowout - non-blowout W%) and percentage of blowouts and non-blowouts for each team:<br /><br /><a href="https://1.bp.blogspot.com/-roAGb5GmGF4/WIzdumZCaLI/AAAAAAAACW4/Sbj4-j49POEfOB9CBWy7ln_7sUFqHQIOgCLcB/s1600/rd16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-roAGb5GmGF4/WIzdumZCaLI/AAAAAAAACW4/Sbj4-j49POEfOB9CBWy7ln_7sUFqHQIOgCLcB/s400/rd16c.jpg" width="133" height="400" /></a><br /><br />It is rare to see a playoff team with such a large negative differential as Texas had. Colorado played the highest percentage of blowouts and San Diego the lowest, which shouldn’t come as a surprise given that scoring environment has a large influence. Outside of Colorado, though, the Cubs and the Indians played the highest percentage of blowout games, with the latter not sporting as a high of a W% but having the second most blowout wins.<br /><br />A more interesting way to consider game-level results is to look at how teams perform when scoring or allowing a given number of runs. For the majors as a whole, here are the counts of games in which teams scored X runs:<br /><br /><a href="https://4.bp.blogspot.com/-UJgIvw3VBeo/WIzd6YJ_WjI/AAAAAAAACW8/6qWa_DqaL3EIOn_3B-l6orl_2_vBYIVJgCLcB/s1600/rd16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-UJgIvw3VBeo/WIzd6YJ_WjI/AAAAAAAACW8/6qWa_DqaL3EIOn_3B-l6orl_2_vBYIVJgCLcB/s400/rd16d.jpg" width="400" height="272" /></a><br /><br />The “marg” column shows the marginal W% for each additional run scored. In 2015, the third run was both the run with the greatest marginal impact on the chance of winning, while it took a fifth run to make a team more likely to win than lose. 2016 was the first time since 2008 that teams scoring four runs had a losing record, a product of the resurgence in run scoring levels.<br /><br />I use these figures to calculate a measure I call game Offensive W% (or Defensive W% as the case may be), which was suggested by Bill James in an old Abstract. It is a crude way to use each team’s actual runs per game distribution to estimate what their W% should have been by using the overall empirical W% by runs scored for the majors in the particular season. <br /><br />The theoretical distribution from Enby discussed earlier would be much preferable to the empirical distribution for this exercise, but I’ve defaulted to the 2016 empirical data. Some of the drawbacks of this approach are:<br /><br />1. The empirical distribution is subject to sample size fluctuations. In 2016, all 58 times that a team scored twelve runs in a game, they won; meanwhile, teams that scored thirteen runs were 46-1. Does that mean that scoring 12 runs is preferable to scoring 13 runs? Of course not--it's a quirk in the data. Additionally, the marginal values don’t necessary make sense even when W% increases from one runs scored level to another (In figuring the gEW% family of measures below, I lumped games with 12+ runs together, which smoothes any illogical jumps in the win function, but leaves the inconsistent marginal values unaddressed and fails to make any differentiation between scoring in that range. The values actually used are displayed in the “use” column, and the invuse” column is the complements of these figures--i.e. those used to credit wins to the defense.)<br /><br />2. Using the empirical distribution forces one to use integer values for runs scored per game. Obviously the number of runs a team scores in a game is restricted to integer values, but not allowing theoretical fractional runs makes it very difficult to apply any sort of park adjustment to the team frequency of runs scored.<br /><br />3. Related to #2 (really its root cause, although the park issue is important enough from the standpoint of using the results to evaluate teams that I wanted to single it out), when using the empirical data there is always a tradeoff that must be made between increasing the sample size and losing context. One could use multiple years of data to generate a smoother curve of marginal win probabilities, but in doing so one would lose centering at the season’s actual run scoring rate. On the other hand, one could split the data into AL and NL and more closely match context, but you would lose sample size and introduce more quirks into the data.<br /><br />I keep promising that I will use Enby to replace the empirical approach, but for now I will use Enby for a couple graphs but nothing more.<br /><br />First, a comparison of the actual distribution of runs per game in the majors to that predicted by the Enby distribution for the 2016 major league average of 4.479 runs per game (Enby distribution parameters are B = 1.1052, r = 4.082, z = .0545):<br /><br /><a href="https://1.bp.blogspot.com/-rfOvKAk1X8U/WIzeAcucDoI/AAAAAAAACXA/hBeNKXqFlpUdmJqQssDC8270gl0mgw-RQCLcB/s1600/rd16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-rfOvKAk1X8U/WIzeAcucDoI/AAAAAAAACXA/hBeNKXqFlpUdmJqQssDC8270gl0mgw-RQCLcB/s400/rd16e.jpg" width="400" height="263" /></a><br /><br />This is pretty typical of the kind of fit you will see from Enby for a given season: a few important points where there’s a noticeable difference (in this case even tallies two, four, six on the high side and 1 and 7 on the low side), but generally acquitting itself as a decent model of the run distribution.<br /><br />I will not go into the full details of how gOW%, gDW%, and gEW% (which combines both into one measure of team quality) are calculated in this post, but full details were provided <a href="http://walksaber.blogspot.com/2009/01/perfunctory-look-at-run-distribution.html">here</a> and the paragraph below gives a quick explanation. The “use” column here is the coefficient applied to each game to calculate gOW% while the “invuse” is the coefficient used for gDW%. For comparison, I have looked at OW%, DW%, and EW% (Pythagenpat record) for each team; none of these have been adjusted for park to maintain consistency with the g-family of measures which are not park-adjusted.<br /><br />A team’s gOW% is the sumproduct of their frequency of scoring x runs, where x runs from 0 to 22, and the empirical W% of teams in 2015 when they scored x runs. For example, Philadelphia was shutout 11 times; they would not be expected to win any of those games (nor would they, we can be certain). They scored one run 23 times; an average team in 2016 had a .089 W% when scoring one run, so they could have been expected to win 2.04of the 23 games given average defense. They scored two runs 22 times; an average team had a .228 W% when scoring two, so they could have been expected to win 5.02 of those games given average defense. Sum up the estimated wins for each value of x and divide by the team’s total number of games and you have gOW%.<br /><br />It is thus an estimate of what W% a team with the given team’s empirical distribution of runs scored and a league average defense would have. It is analogous to James’ original construct of OW% except looking at the empirical distribution of runs scored rather than the average runs scored per game. (To avoid any confusion, James in 1986 also proposed constructing an OW% in the manner in which I calculate gOW%).<br /><br />For most teams, gOW% and OW% are very similar. Teams whose gOW% is higher than OW% distributed their runs more efficiently (at least to the extent that the methodology captures reality); the reverse is true for teams with gOW% lower than OW%. The teams that had differences of +/- 2 wins between the two metrics were (all of these are the g-type less the regular estimate):<br /><br />Positive: MIA, PHI, ATL, KC<br />Negative: LA, SEA<br /><br />The Marlins offense had the largest difference (3.55) between their corresponding g-type W% and their OW%/DW%, so I like to include a run distribution chart to hopefully ease in understanding what this means. Miami scored 4.167 R/G, so their Enby parameters (r = 3.923, B = 1.0706, z = .0649) produce these estimated frequencies:<br /><br /><a href="https://1.bp.blogspot.com/-cvIBFY6ofC0/WIzeF8_zQCI/AAAAAAAACXE/lNOA9-HdeV0CHaTFH4Hj-9pDOLm5EuXLgCLcB/s1600/rd16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-cvIBFY6ofC0/WIzeF8_zQCI/AAAAAAAACXE/lNOA9-HdeV0CHaTFH4Hj-9pDOLm5EuXLgCLcB/s400/rd16f.jpg" width="400" height="263" /></a><br /><br />Miami scored 0-3 runs in 47.8% of their games compared to an expected 47.9%. But by scoring 0-2 runs 3% less often then expected and scoring three 3% more often, they had 1.3 more expected wins from such games than Enby expected. They added an additional 1.2 wins from 4-6 runs, and lost 1.1 from 7+ runs. (Note that the total doesn’t add up to the difference between their gOW% and OW%, nor should it--the comparisons I was making were between what the empirical 2016 major league W%s for each x runs scored predicted using their actual run distribution and their Enby run distribution. If I had my act together and was using Enby to estimate the expected W% at each x runs scored, then we would expect a comparison like the preceding to be fairly consistent with a comparison of gOW% to OW%).<br /><br />Teams with differences of +/- 2 wins between gDW% and standard DW%:<br /><br />Positive: CIN, COL, ARI<br />Negative: NYN, MIL, MIA, TB, NYA<br /><br />The Marlins were the only team to appear on both the offense and defense list, their defense giving back 2.75 wins when looking at their run distribution rather than run average. <br /><br />Teams with differences of +/- 2 wins between gEW% and standard EW%:<br /><br />Positive: PHI, TEX, CIN, KC<br />Negative: LA, SEA, NYN, MIL, NYA, BOS<br /><br />The Royals finally showed up on these lists, but turning a .475 EW% into a .488 gEW% is not enough pixie dust to make the playoffs. <br /><br />Below is a full chart with the various actual and estimated W%s:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-OlPaAw--tlE/WIzeKU72fqI/AAAAAAAACXM/_Nwm13g6FvAw-xjs6DaXhn_eFcUEyI21ACLcB/s1600/rd16g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-OlPaAw--tlE/WIzeKU72fqI/AAAAAAAACXM/_Nwm13g6FvAw-xjs6DaXhn_eFcUEyI21ACLcB/s400/rd16g.jpg" width="328" height="400" /></a></div>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-22039652526840129942017-01-23T07:57:00.000-05:002017-01-23T07:57:03.013-05:00Crude Team Ratings, 2016For the last several years I have published a set of team ratings that I call "Crude Team Ratings". The name was chosen to reflect the nature of the ratings--they have a number of limitations, of which I documented several when I introduced the <a href="http://walksaber.blogspot.com/2011/01/crude-team-ratings.html">methodology</a>. <br /><br />I explain how CTR is figured in the linked post, but in short:<br /><br />1) Start with a win ratio figure for each team. It could be actual win ratio, or an estimated win ratio.<br /><br />2) Figure the average win ratio of the team’s opponents.<br /><br />3) Adjust for strength of schedule, resulting in a new set of ratings.<br /><br />4) Begin the process again. Repeat until the ratings stabilize.<br /><br />The resulting rating, CTR, is an adjusted win/loss ratio rescaled so that the majors’ arithmetic average is 100. The ratings can be used to directly estimate W% against a given opponent (without home field advantage for either side); a team with a CTR of 120 should win 60% of games against a team with a CTR of 80 (120/(120 + 80)).<br /><br />First, CTR based on actual wins and losses. In the table, “aW%” is the winning percentage equivalent implied by the CTR and “SOS” is the measure of strength of schedule--the average CTR of a team’s opponents. The rank columns provide each team’s rank in CTR and SOS:<br /><br /><a href="https://3.bp.blogspot.com/-PDfdvqttnL4/WH__NXaMyiI/AAAAAAAACV0/GPy-skxeXcMlSC72O_jV6mjNQZdWyZk2QCLcB/s1600/ctr16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-PDfdvqttnL4/WH__NXaMyiI/AAAAAAAACV0/GPy-skxeXcMlSC72O_jV6mjNQZdWyZk2QCLcB/s400/ctr16a.jpg" width="286" height="400" /></a><br /><br />Last year, the top ten teams in CTR were the playoff participants. That was not remotely the case this year thanks to a resurgent gap in league strength. While the top five teams in the AL made the playoffs and the NL was very close, St. Louis slipping just ahead of New York and San Francisco (by a margin of .7 wins if you compare aW%), the Giants ranked only fifteenth in the majors in CTR. Any of the Mariners, Tigers, Yankees, or Astros were considered stronger than the actual NL #3 seed and CTR finisher the Dodgers. <br /><br />The Dodgers had the second-softest schedule in MLB, ahead of only the Cubs. (The natural tendency is for strong teams in weak divisions to have the lowest SOS, since they don’t play themselves. The flip is also true--I was quite sure without checking to verify that Tampa Bay had the toughest schedule). The Dodgers average opponent was about as good as the Pirates or the Marlins; the Mariners average opponent was rated stronger than the Cardinals.<br /><br />At this point you probably want to see just how big of a gap there was between the AL and NL in average rating. Originally I gave the arithmetic average CTR for each divison, but that’s mathematically wrong--you can’t average ratios like that. Then I switched to geometric averages, but really what I should have done all along is just give the arithemetic average aW% for each division/league. aW% converts CTR back to an “equivalent” W-L record, such that the average across the major leagues will be .50000. I do this by taking CTR/(100 + CTR) for each team, then applying a small fudge factor to force the average to .500. In order to maintain some basis for comparison to prior years, I’ve provided the geometric average CTR alongside the arithmetric average aW%, and the equivalent CTR by solving for CTR in the equation:<br /><br />aW% = CTR/(100 + CTR)*F, where F is the fudge factor (it was 1.0012 for 2016 lest you be concerned there is a massive behind-the-scenes adjustment taking place).<br /><br /><a href="https://2.bp.blogspot.com/-rW60f7nqYnU/WIAAflPYsHI/AAAAAAAACWM/xP54B6vAUC0QXiFxDTiNP2XDCq45ePUiQCLcB/s1600/ctr16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-rW60f7nqYnU/WIAAflPYsHI/AAAAAAAACWM/xP54B6vAUC0QXiFxDTiNP2XDCq45ePUiQCLcB/s400/ctr16b.jpg" width="400" height="212" /></a><br /><br />Every AL division was better than every AL division, a contrast from 2015 in which the two worst divisions were the NL East and West, but the NL Central was the best division. Whether you use the geometric or backdoor-arithmetric average CTRs to calculate it, the average AL team’s expected W% versus an average NL team is .545. The easiest SOS in the AL was the Indians, as to be expected as the strongest team in the weakest division; it was still one point higher than that of the toughest NL schedule (the Reds, the weakest team in the strongest division).<br /><br />I also figure CTRs based on various alternate W% estimates. The first is based on game-Expected W%, which you can read about <a href="http://walksaber.blogspot.com/2016/02/run-distribution-and-w-2015.html">here</a>. It uses each team’s game-by-game distribution of runs scored and allowed, but treats the two as independent:<br /><br /><a href="https://1.bp.blogspot.com/-ixtxZHZffWk/WH__htVXuDI/AAAAAAAACV4/b1Ha93tMlIAM44s0NxIfGGFxG62w-RPVwCLcB/s1600/ctr16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-ixtxZHZffWk/WH__htVXuDI/AAAAAAAACV4/b1Ha93tMlIAM44s0NxIfGGFxG62w-RPVwCLcB/s400/ctr16c.jpg" width="286" height="400" /></a><br /><br />Next is Expected W%, that is to say Pythagenpat based on actual runs scored and allowed:<br /><br /><a href="https://2.bp.blogspot.com/-SyUr6m90gtA/WH__qoolH4I/AAAAAAAACV8/XD51IF74mgcCxM4cDBul58N_7kK7ZcbSQCLcB/s1600/ctr16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-SyUr6m90gtA/WH__qoolH4I/AAAAAAAACV8/XD51IF74mgcCxM4cDBul58N_7kK7ZcbSQCLcB/s400/ctr16d.jpg" width="286" height="400" /></a><br /><br />Finally, CTR based on Predicted W% (Pythagenpat based on runs created and allowed, actually Base Runs):<br /><br /><a href="https://4.bp.blogspot.com/--aoyi9oHXeM/WH__1fmscrI/AAAAAAAACWA/Khs8Dsp_sk8WnrRXigE10RPuF0FlQ3PCACLcB/s1600/ctr16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/--aoyi9oHXeM/WH__1fmscrI/AAAAAAAACWA/Khs8Dsp_sk8WnrRXigE10RPuF0FlQ3PCACLcB/s400/ctr16e.jpg" width="286" height="400" /></a><br /><br />A few seasons ago I started including a CTR version based on actual wins and losses, but including the postseason. I am not crazy about this set of ratings, but I can’t quite articulate why.<br /><br />On the one hand, adding in the playoffs is a no-brainer. The extra games are additional datapoints regarding team quality. If we have confidence in the rating system (and I won’t hold it against you if you don’t), then the unbalanced nature of the schedule for these additional games shouldn’t be too much of a concern. Yes, you’re playing stronger opponents, but the system understands that and will reward you (or at least not penalize you) for it. <br /><br />On the other hand, there is a natural tendency among people who analyze baseball statistics to throw out the postseason, due to concerns about unequal opportunity (since most of the league doesn’t participant) and due to historical precedent. Unequal opportunity is a legitimate concern when evaluating individuals--particularly for counting or pseudo-counting metrics like those that use a replacement level baseline--but much less of a concern with teams. Even though the playoff participants may not be the ten most deserving teams by a strict, metric-based definition of “deserving”, there’s no question that teams are largely responsible for their own postseason fate to a much, much greater extent than any individual player is. And the argument from tradition is fine if the issue at hand is the record for team wins or individual home runs or the like, but not particularly applicable when we are simply using the games that have been played as datapoints by which to gauge team quality.<br /><br />Additionally, the fact that playoff series are not played to their conclusion could be seen as introducing bias. If the Red Sox get swept by the Indians, they not only get three losses added to their ledger, they lose the opportunity to offset that damage. The number of games that are added to a team’s record, even within a playoff round, is directly related to their performance in the very small sample of games. <br /><br />Suppose that after every month of the regular season, the bottom four teams in the league-wide standings were dropped from the schedule. So after April, the 7-17 Twins record is frozen in place. Do you think this would improve our estimates of team strength? And I don’t just mean from the smaller sample, obviously their record as used in the ratings could be more heavily regressed than teams that played more games. But it would freeze our on-field observations of the Twins, and the overall effect would be to make the dropped teams look worse than their “true” strength.<br /><br />I doubt that poorly reasoned argument swayed even one person, so the ratings including playoff performance are:<br /><br /><a href="https://4.bp.blogspot.com/-DxGtEQ2UfnE/WIAA1A8qnRI/AAAAAAAACWU/CMCcjsZnxQgD_gXTAjCdaInONNWGT9aFQCLcB/s1600/ctr16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-DxGtEQ2UfnE/WIAA1A8qnRI/AAAAAAAACWU/CMCcjsZnxQgD_gXTAjCdaInONNWGT9aFQCLcB/s400/ctr16f.jpg" width="286" height="400" /></a><br /><br />The teams sorted by difference between playoff CTR (pCTR) and regular season CTR (rsCTR):<br /><br /><a href="https://4.bp.blogspot.com/-GUKhiBcyxcg/WIAA5LzPRAI/AAAAAAAACWY/BkmvMISrvRwkaNmr2ZR2z-VlT1c0n9vRwCLcB/s1600/ctr16g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-GUKhiBcyxcg/WIAA5LzPRAI/AAAAAAAACWY/BkmvMISrvRwkaNmr2ZR2z-VlT1c0n9vRwCLcB/s400/ctr16g.jpg" width="144" height="400" /></a><br /><br />It’s not uncommon for the pennant winners to be the big gainers, but the Cubs and Indians made a lot of hay this year, as the Cubs managed to pull every other team in the NL Central up one point in the ratings. The Rangers did the reverse with the AL West by getting swept out of the proceedings. They still had a better ranking than the team that knocked them out, as did Washington.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-45598727713051888812017-01-10T07:47:00.000-05:002017-01-10T17:17:15.450-05:00Hitting by Position, 2016Of all the annual repeat posts I write, this is the one which most interests me--I have always been fascinated by patterns of offensive production by fielding position, particularly trends over baseball history and cases in which teams have unusual distributions of offense by position. I also contend that offensive positional adjustments, when carefully crafted and appropriately applied, remain a viable and somewhat more objective competitor to the defensive positional adjustments often in use, although this post does not really address those broad philosophical questions.<br /><br />The first obvious thing to look at is the positional totals for 2016, with the data coming from Baseball-Reference.com. "MLB” is the overall total for MLB, which is not the same as the sum of all the positions here, as pinch-hitters and runners are not included in those. “POS” is the MLB totals minus the pitcher totals, yielding the composite performance by non-pitchers. “PADJ” is the position adjustment, which is the position RG divided by the overall major league average (this is a departure from past posts; I’ll discuss this a little at the end). “LPADJ” is the long-term positional adjustment that I use, based on 2002-2011 data. The rows “79” and “3D” are the combined corner outfield and 1B/DH totals, respectively:<br /><br /><a href="https://2.bp.blogspot.com/-U9lu9_Por0Q/WHQe8-FCbHI/AAAAAAAACU0/d5p-OhtBvDYNwK9MEA0OGdind_nFRupYwCLcB/s1600/hitpos16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-U9lu9_Por0Q/WHQe8-FCbHI/AAAAAAAACU0/d5p-OhtBvDYNwK9MEA0OGdind_nFRupYwCLcB/s400/hitpos16a.jpg" width="400" height="80" /></a><br /><br />Obviously when looking at a single season of data it’s imperative not to draw any sweeping conclusions. That doesn’t make it any less jarring to see that second basemen outhit every position save the corner infield spots, or that left fielders created runs at the league average rate. The utter collapse of corner outfield offense left them, even pooled, ahead only of catcher and shortstop. Pitchers also added another point of relative RG, marking two years in a row of improvement (such as it is) over their first negative run output in 2014.<br /><br />It takes historical background to fully appreciate how much the second base and corner outfield performances stack up. 109 for second base is the position’s best showing since 1924, which was 110 thanks largely to Rogers Hornsby, Eddie Collins and Frankie Frisch. Second base had not hit for the league average since 1949. (I should note that the historical figures I’m citing are not directly comparable - they based on each player’s primary position and include all of their PA, regardless of whether they were actually playing the position at the time or not, unlike the Baseball-Reference positional figures used for 2016). Corner outfield was even more extreme at 103, the nadir for the 116 seasons starting with 1901 (the previous low was 107 in 1992).<br /><br />If the historical perspective is of interest, you may want to check out Corrine Landrey’s article in <u>The Hardball Time Baseball Annual</u>. She includes some charts showing OPS+ by position in the DH-era and theorizes that an influx of star young players, still playing on the right-side of the defensive spectrum, has led to the positional shakeup. While I cautioned above about over-generalizing from one year of data, it has been apparent over the last several years that the spread between positions has declined. Landrey’s explanation is as viable as any I’ve seen to explain these season’s results.<br /><br />Moving on to looking at more granular levels of performance, I always start by looking at the NL pitching staffs and their RAA. I need to stress that the runs created method I’m using here does not take into account sacrifices, which usually is not a big deal but can be significant for pitchers. Note that all team figures from this point forward in the post are park-adjusted. The RAA figures for each position are baselined against the overall major league average RG for the position, except for left field and right field which are pooled.<br /><br /><a href="https://2.bp.blogspot.com/-QcEpH0brXT0/WHQfFOypD4I/AAAAAAAACU4/YUtFkK2hEtAKRgbIhVFj3xqZn5RA-kOLwCLcB/s1600/hitpos16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-QcEpH0brXT0/WHQfFOypD4I/AAAAAAAACU4/YUtFkK2hEtAKRgbIhVFj3xqZn5RA-kOLwCLcB/s400/hitpos16b.jpg" width="400" height="282" /></a><br /><br />This is the second consecutive year that the Giants led the league in RAA, and of course they employ the active pitcher most known for his batting. But as usual the spread from top to bottom is in the neighborhood of twenty runs.<br /><br />I don’t run a full chart of the leading positions since you will very easily be able to go down the list and identify the individual primarily responsible for the team’s performance and you won’t be shocked by any of them, but the teams with the highest RAA at each spot were:<br /><br />C--WAS, 1B--CIN, 2B--WAS, 3B--TOR, SS--LA, LF--PIT, CF--LAA, RF--BOS, DH--BOS<br /><br />More interesting are the worst performing positions; the player listed is the one who started the most games at that position for the team:<br /><br /><a href="https://1.bp.blogspot.com/-LwPE4mV3hjc/WHQfKJQcwTI/AAAAAAAACU8/uoInDhAxlbMfqdQSfa_WyOKeN8Wz-dFiQCLcB/s1600/hitpos16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-LwPE4mV3hjc/WHQfKJQcwTI/AAAAAAAACU8/uoInDhAxlbMfqdQSfa_WyOKeN8Wz-dFiQCLcB/s400/hitpos16c.jpg" width="400" height="143" /></a><br /><br />I am have as little use for batting average as anyone, but I still find the Angels .209 left field average to be the single most entertaining number on that chart (remember, that’s park-adjusted; it was .204 raw). The least entertaining thing for me at least was the Indians’ production at catcher, which was tolerable when Roberto Perez was drawing walks but intolerable when Terry Francona was pinch-running for him in Game 7.<br /><br />I like to attempt to measure each team’s offensive profile by position relative to a typical profile. I’ve found it frustrating as a fan when my team’s offensive production has come disproportionately from “defensive” positions rather than offensive positions (“Why can’t we just find a corner outfielder who can hit?”) The best way I’ve yet been able to come up with to measure this is to look at the correlation between RG at each position and the long-term positional adjustment. A positive correlation indicates a “traditional” distribution of offense by position--more production from the positions on the right side of the defensive spectrum. (To calculate this, I use the long-term positional adjustments that pool 1B/DH as well as LF/RF, and because of the DH I split it out by league):<br /><br /><a href="https://1.bp.blogspot.com/-x9TOjZ6QGC0/WHQfO185aqI/AAAAAAAACVA/OCaUMdMN-dAEr1tvbo3mrm-4RhOZwmiSQCLcB/s1600/hitpos16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-x9TOjZ6QGC0/WHQfO185aqI/AAAAAAAACVA/OCaUMdMN-dAEr1tvbo3mrm-4RhOZwmiSQCLcB/s400/hitpos16d.jpg" width="342" height="400" /></a><br /><br />As you can see, there are good offenses with high correlations, good offenses with low correlations, and every other combination. I have often used this space to bemoan the Indians continual struggle to get adequate production from first base, contributing to their usual finish in the bottom third or so of correlation. This year, they rank in the middle of the pack, and while it is likely a coincidence that they had a good season, it’s worth noting that Mike Napoli only was average for a first baseman. Even that is much better than some of their previous showings.<br /><br />Houston’s two best hitting positions (not relative to positional averages, but in terms of RG) were second base and shortstop. In fact the Astros positions in descending order of RG was 4, 6, 9, 2, 5, 3, D, 7, 8. That’s how you get a fairly strong negative correlation between RG and PADJ.<br /><br />The following charts, broken out by division, display RAA for each position, with teams sorted by the sum of positional RAA. Positions with negative RAA are in red, and positions that are +/-20 RAA are bolded:<br /><br /><a href="https://3.bp.blogspot.com/-2-mZSrqUNtg/WHQfdNeindI/AAAAAAAACVE/4edVF-_uAdAc9YZz7i6Dr4x4PpBMM-4uwCLcB/s1600/hitpos16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-2-mZSrqUNtg/WHQfdNeindI/AAAAAAAACVE/4edVF-_uAdAc9YZz7i6Dr4x4PpBMM-4uwCLcB/s400/hitpos16e.jpg" width="400" height="81" /></a><br /><br />Boston had the AL’s most productive outfield, while Toronto was just an average offense after bashing their way to a league leading 118 total RAA in 2015. It remains jarring to see New York at the bottom of an offense list, even just for a division, and their corner infielders were the worst in the majors.<br /><br /><a href="https://2.bp.blogspot.com/-6gIm_vSYOtI/WHQflcYcPuI/AAAAAAAACVI/6gdrGtzknSs1WlHx8rlAqD43AmeOemSDACLcB/s1600/hitpos16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-6gIm_vSYOtI/WHQflcYcPuI/AAAAAAAACVI/6gdrGtzknSs1WlHx8rlAqD43AmeOemSDACLcB/s400/hitpos16f.jpg" width="400" height="80" /></a><br /><br />Other than catcher, Cleveland was solid everywhere, with no bold positions--and in this division, that’s enough to lead in RAA and power a cruise to the division title. Detroit had the AL’s top corner infield RAA (no thanks to third base). Kansas City, where to begin with the sweet, sweet schadenfreude? Eksy Magic? No, already covered at length in the leadoff hitters post. Maybe the fact that they had the worst middle infield production in MLB? Or that the bros at the corners chipped in another -19 RAA to also give them the worst infield? The fact that they were dead last in the majors in total RAA? It’s just too much.<br /><br /><a href="https://3.bp.blogspot.com/-ADrznf0mZtk/WHQfsrtxvKI/AAAAAAAACVM/ZwCRr8MoTOEyDmWAv1oBEQpW6LGvGQfxgCLcB/s1600/hitpos16g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-ADrznf0mZtk/WHQfsrtxvKI/AAAAAAAACVM/ZwCRr8MoTOEyDmWAv1oBEQpW6LGvGQfxgCLcB/s400/hitpos16g.jpg" width="400" height="81" /></a><br /><br />The pathetic production of the Los Angeles left fielders was discussed above. The Mike Trout-led center fielders were brilliant, the best single position in the majors. And so, even with a whopping -31 runs from left field, the Angels had the third-most productive outfield in MLB. Houston’s middle infielders, also mentioned above, were the best in the majors. Oakland’s outfield RAA was last in the AL.<br /><br /><a href="https://4.bp.blogspot.com/-EcmsVB5tUbw/WHQfw7pct1I/AAAAAAAACVQ/RKMU3G9fxMw5qKXxh163C-G7N37PI-P-wCLcB/s1600/hitpos16h.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-EcmsVB5tUbw/WHQfw7pct1I/AAAAAAAACVQ/RKMU3G9fxMw5qKXxh163C-G7N37PI-P-wCLcB/s400/hitpos16h.jpg" width="400" height="89" /></a><br /><br />Washington overcame the NL’s least productive corner infielders, largely because they had the NL’s most productive middle infielders. Miami had a similar but even more extreme juxtaposition, the NL’s worst infield and the majors’ best outfield, and that with a subpar season from Giancarlo Stanton as right field was the least productive of the three spots. Atlanta had the NL’s worst-hitting middle infield, and Philadelphia the majors’ worst outfield despite Odubel Herrera making a fool of me.<br /><br /><a href="https://4.bp.blogspot.com/-uwkwbZtaO_Y/WHQgmxqmb_I/AAAAAAAACVc/du3QefrY8bkT9gljZ3jotdlua32Tpcr9gCLcB/s1600/hitpos16i.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-uwkwbZtaO_Y/WHQgmxqmb_I/AAAAAAAACVc/du3QefrY8bkT9gljZ3jotdlua32Tpcr9gCLcB/s400/hitpos16i.jpg" width="400" height="88" /></a><br /><br />Chicago was tops in the majors in corner infield RAA and total infield RAA. No other teams in this division achieved any superlatives but thanks to Joey Votto and a half-season of Jonathon Lucroy, every team was in the black for total RAA, even if we were to add in Cincinnati’s NL-trailing -9 RAA from pitchers.<br /><br /><a href="https://4.bp.blogspot.com/-3FDg07nAWrQ/WHQg86eLUtI/AAAAAAAACVk/rE4-LYVIxzU_QJhBGbWQzYQshvCei3QhQCLcB/s1600/hitpos16j.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-3FDg07nAWrQ/WHQg86eLUtI/AAAAAAAACVk/rE4-LYVIxzU_QJhBGbWQzYQshvCei3QhQCLcB/s400/hitpos16j.jpg" width="400" height="89" /></a><br /><br />No position grouping superlatives in this division, but it feels like more should be said about Corey Seager. It seems like a rookie shortstop hitting as he did, fielding adequately enough to be a serious MVP candidate for a playoff team in a huge market for one of the five or so most venerated franchises should have gotten a lot more attention than it did. Is it the notion that a move to third base is inevitable? Is he, like the superstar down the road, just considered too boring of a personality?<br /><br />The full spreadsheet is available <a href="https://docs.google.com/spreadsheets/d/1j2IejvjKdVhpeXftxnkbuXyWBt75i9_2JeUiNVA0dwA/pub?output=html">here</a>.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-80926172618068071342016-12-12T10:34:00.000-05:002016-12-12T10:34:00.139-05:00Hitting by Lineup Position, 2016I devoted a whole post to leadoff hitters, whether justified or not, so it's only fair to have a post about hitting by batting order position in general. I certainly consider this piece to be more trivia than sabermetrics, since there’s no analytic content.<br /><br />The data in this post was taken from Baseball-Reference. The figures are park-adjusted. RC is ERP, including SB and CS, as used in my end of season stat posts. The weights used are constant across lineup positions; there was no attempt to apply specific weights to each position, although they are out there and would certainly make this a little bit more interesting:<br /><br /><a href="https://1.bp.blogspot.com/-UarX04aJF64/WExYlKdHuUI/AAAAAAAACUE/2C7P-tdvyHQMSMgoQTW_oMh2AgDHwpW2QCLcB/s1600/lineup16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-UarX04aJF64/WExYlKdHuUI/AAAAAAAACUE/2C7P-tdvyHQMSMgoQTW_oMh2AgDHwpW2QCLcB/s400/lineup16a.jpg" width="384" height="400" /></a><br /><br />The seven year run of NL #3 hitters as the best position in baseball was snapped, albeit by an insignificant .01 RG by AL #3 hitters. Since Mike Trout’s previous career high in PA out of the #3 spot was 336 in 2015 and he racked up 533 this year, I’m going to give full credit to Trout; as we will see in a moment, the Angels’ #3 hitters were the best single lineup spot in baseball. #2 hitters did not outperform #5 in both circuits as they did last year, just the AL. However, the NL made up for hit by having their leadoff hitters create runs at almost the exact same rate as their #5s.<br /><br />Next are the team leaders and trailers in RG at each lineup position. The player listed is the one who appeared in the most games in that spot (which can be misleading, especially for spots low in the batting order where many players cycle through):<br /><br /><a href="https://1.bp.blogspot.com/-tJydjhGZ1yY/WExYw1QyKLI/AAAAAAAACUI/s8C_TiHmFwI8scWNIJ9n5e75TB9DsDauQCLcB/s1600/lineup16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-tJydjhGZ1yY/WExYw1QyKLI/AAAAAAAACUI/s8C_TiHmFwI8scWNIJ9n5e75TB9DsDauQCLcB/s400/lineup16b.jpg" width="400" height="328" /></a><br /><br /><a href="https://1.bp.blogspot.com/-lGHJoWoUL40/WExY1T4-XUI/AAAAAAAACUM/WO1DqwMl5FgJfCOjPla2GkvPozTvanF2QCLcB/s1600/lineup16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-lGHJoWoUL40/WExY1T4-XUI/AAAAAAAACUM/WO1DqwMl5FgJfCOjPla2GkvPozTvanF2QCLcB/s400/lineup16c.jpg" width="400" height="325" /></a><br /><br />A couple things that stood out to me was St. Louis’ dominance at the bottom of the order and the way in which catchers named Perez managed to sabotage lineup spots for two teams. Apologies to Carlos Beltran (the real culprits for the poor showing of Texas #3 hitters were Adrian Beltre, Prince Fielder, and Nomar Mazara) and Luis Valbuena (Carlos Gomez and Marwin Gonzalez). <br /><br />The case of San Diego’s cleanup hitters deserves special attention. Yangervis Solarte was actually pretty good when batting cleanup, as his .289/.346/.485 line in 289 PA compares favorably to the NL average for cleanup hitters. The rest of the Padres who appeared in that spot combined for 399 PA with a dreadful .187/.282/.336 line. Just to give you a quick idea of how bad this is, the 618 OPS would have been the eleventh-worst among any non-NL #9 lineup spot in the majors, leading only 6 AL #9s, 2 #2s, a #7, and the horrible Oakland #2s. It was also worse than the Cardinals’ #9 hitters.<br /><br />The next list is the ten best positions in terms of runs above average relative to average for their particular league spot (so AL leadoff spots are compared to the AL average leadoff performance, etc.):<br /><br /><a href="https://4.bp.blogspot.com/-6AgVZeweLzM/WExY6GgJhGI/AAAAAAAACUQ/tqreTL6Q5KgbnMTmCpFdYnwtyJJXFpxrACLcB/s1600/lineup16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-6AgVZeweLzM/WExY6GgJhGI/AAAAAAAACUQ/tqreTL6Q5KgbnMTmCpFdYnwtyJJXFpxrACLcB/s400/lineup16d.jpg" width="400" height="190" /></a><br /><br />And the ten worst:<br /><br /><a href="https://3.bp.blogspot.com/-e3aeHkkuUmw/WExZAOdU5aI/AAAAAAAACUU/FV5qPH8ZIF4KCF225W2iI1n4h0zheTXzgCLcB/s1600/lineup16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-e3aeHkkuUmw/WExZAOdU5aI/AAAAAAAACUU/FV5qPH8ZIF4KCF225W2iI1n4h0zheTXzgCLcB/s400/lineup16e.jpg" width="400" height="189" /></a><br /><br />Joe Mauer himself wasn’t that bad, with a 799 OPS when hitting third. That’s still well-below the AL average, but not bottom ten in RAA bad without help from his friends.<br /><br />The last set of charts show each team’s RG rank within their league at each lineup spot. The top three are bolded and the bottom three displayed in red to provide quick visual identification of excellent and poor production:<br /><br /><a href="https://1.bp.blogspot.com/-0uYYxFw3Siw/WExZEBQQ2BI/AAAAAAAACUY/VfBmFf7M_3s0--loPsw7xeN4kB-V7C_NgCLcB/s1600/lineup16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-0uYYxFw3Siw/WExZEBQQ2BI/AAAAAAAACUY/VfBmFf7M_3s0--loPsw7xeN4kB-V7C_NgCLcB/s400/lineup16f.jpg" width="400" height="273" /></a><br /><br /><a href="https://1.bp.blogspot.com/-uooMM2-_HT4/WExZKCBTF3I/AAAAAAAACUc/nF0NzBq0j3AnEcX0pista00yYHL27j8MQCLcB/s1600/lineup16g.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-uooMM2-_HT4/WExZKCBTF3I/AAAAAAAACUc/nF0NzBq0j3AnEcX0pista00yYHL27j8MQCLcB/s400/lineup16g.jpg" width="400" height="273" /></a><br /><br />The full spreadsheet is available <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRdf4utYUXyXFB1imn-dHEAgB0VGAvZr_7hHC2HoxS3yvsTQy_FMVfDQ3uZbqXX7zn_X-jAGqGWTFFO/pub?output=html">here</a>.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-69475448580784262142016-12-05T09:24:00.000-05:002016-12-05T09:24:04.751-05:00Leadoff Hitters, 2016I will try to make this as clear as possible: the statistics are based on the players that hit in the #1 slot in the batting order, whether they were actually leading off an inning or not. It includes the performance of all players who batted in that spot, including substitutes like pinch-hitters. <br /><br />Listed in parentheses after a team are all players that started in twenty or more games in the leadoff slot--while you may see a listing like "COL (Blackmon)" this does not mean that the statistic is only based solely on Blackmon's performance; it is the total of all Colorado batters in the #1 spot, of which Blackmon was the only one to start in that spot in twenty or more games. I will list the top and bottom three teams in each category (plus the top/bottom team from each league if they don't make the ML top/bottom three); complete data is available in a spreadsheet linked at the end of the article. There are also no park factors applied anywhere in this article.<br /><br />That's as clear as I can make it, and I hope it will suffice. I always feel obligated to point out that as a sabermetrician, I think that the importance of the batting order is often overstated, and that the best leadoff hitters would generally be the best cleanup hitters, the best #9 hitters, etc. However, since the leadoff spot gets a lot of attention, and teams pay particular attention to the spot, it is instructive to look at how each team fared there.<br /><br />The conventional wisdom is that the primary job of the leadoff hitter is to get on base, and most simply, score runs. It should go without saying on this blog that runs scored are heavily dependent on the performance of one’s teammates, but when writing on the internet it’s usually best to assume nothing. So let's start by looking at runs scored per 25.5 outs (AB - H + CS):<br /><br />1. HOU (Springer/Altuve), 6.9<br />2. COL (Blackmon), 6.7<br />3. DET (Kinsler), 6.6<br />Leadoff average, 5.2<br />ML average, 4.5<br />28. SF (Span), 4.4<br />29. KC (Escobar/Dyson/Merrifield), 4.1<br />30. OAK (Crisp/Burns), 3.4<br /><br />Again, no park adjustments were applied, so the Rockies performance was good but it wasn’t really “best in the NL good”. I’m also going to have a hard time resisting just writing “Esky Magic” every time the Royals appear on a trailers list. <br /><br />The most basic team independent category that we could look at is OBA (figured as (H + W + HB)/(AB + W + HB)):<br /><br />1. CHN (Fowler/Zobrist), .383<br />2. HOU (Springer/Altuve), .375<br />3. STL (Carpenter), .370<br />Leadoff average, .341<br />ML average, .324<br />28. WAS (Turner/Revere/Taylor), .305<br />29. KC (Escobar/Dyson/Merrifield), .298<br />30. OAK (Crisp/Burns), .290<br /><br />Esky Magic. And once again Billy Burns chipping in to Oakland’s anemic showing and of course Kansas City just had to have Billy Burns.<br /><br />The next statistic is what I call Runners On Base Average. The genesis for ROBA is the A factor of Base Runs. It measures the number of times a batter reaches base per PA--excluding homers, since a batter that hits a home run never actually runs the bases. It also subtracts caught stealing here because the BsR version I often use does as well, but BsR versions based on initial baserunners rather than final baserunners do not. Here ROBA = (H + W + HB - HR - CS)/(AB + W + HB).<br /><br />This metric has caused some confusion, so I’ll expound. ROBA, like several other methods that follow, is not really a quality metric, it is a descriptive metric. A high ROBA is a good thing, but it's not necessarily better than a slightly lower ROBA plus a higher home run rate (which would produce a higher OBA and more runs). Listing ROBA is not in any way, shape or form a statement that hitting home runs is bad for a leadoff hitter. It is simply a recognition of the fact that a batter that hits a home run is not a baserunner. Base Runs is an excellent model of offense and ROBA is one of its components, and thus it holds some interest in describing how a team scored its runs, rather than how many it scored:<br /><br />1. CHN (Fowler/Zobrist), .351<br />2. MIA (Gordon/Suzuki/Dietrich/Realmuto), .335<br />3. ATL (Inciarte/Peterson/Markakis), .331<br />4. HOU (Springer/Altuve), .331<br />Leadoff average, .305<br />ML average, .287<br />28. TEX (Choo/Odor/DeShields/Profar), .264<br />29. WAS (Turner/Revere/Taylor), .260<br />30. MIN (Dozier/Nunez), .256<br /><br />Kansas City leadoff hitters finished tied for last in the majors with five home runs (with Miami), so Esky Magic was only good for 23rd place. Twins leadoff hitters, thanks primarily to Dozier, led the majors with 39 homers. So only after around 25.6% of leadoff hitter plate appearances did they actually wind up with a runner on base. Their .320 OBA was well-below average too, but again ROBA describes how an offense plays out--other considerations are necessary to determine how good it was.<br /><br />I also include what I've called Literal OBA--this is just ROBA with HR subtracted from the denominator so that a homer does not lower LOBA, it simply has no effect. It “literally” (not really, thanks to errors, out stretching, caught stealing after subsequent plate appearances, etc.) is the proportion of plate appearances in which the batter becomes a baserunner able to be advanced by his teammates. You don't really need ROBA and LOBA (or either, for that matter), but this might save some poor message board out there twenty posts, by not implying that I think home runs are bad, so here goes. LOBA = (H + W + HB - HR - CS)/(AB + W + HB - HR):<br /><br />1. CHN (Fowler/Zobrist), .360<br />2. HOU (Springer/Altuve), .344<br />3. STL (Carpenter), .342<br />Leadoff average, .313<br />ML average, .297<br />28. OAK (Crisp/Burns), .273<br />29. MIN (Dozier/Nunez), .270<br />30. WAS (Turner/Revere/Taylor), .268<br /><br />The next two categories are most definitely categories of shape, not value. The first is the ratio of runs scored to RBI. Leadoff hitters as a group score many more runs than they drive in, partly due to their skills and partly due to lineup dynamics. Those with low ratios don’t fit the traditional leadoff profile as closely as those with high ratios (at least in the way their seasons played out):<br /><br />1. MIA (Gordon/Suzuki/Dietrich/Realmuto), 2.6<br />2. SD (Jankowski/Jay), 2.3<br />3. ATL (Inciarte/Peterson/Markakis), 2.0<br />6. LAA (Escobar/Calhoun), 1.9<br />Leadoff average, 1.5<br />ML average, 1.0<br />26. STL (Carpenter), 1.3<br />28. BOS (Betts/Pedroia), 1.2<br />29. OAK (Crisp/Burns), 1.2<br />30. MIN (Dozier/Nunez), 1.1<br /><br />This speaks more to me than the measure, but the most interesting thing I learned from that list was that Travis Jankowski was San Diego’s primary leadoff hitter (71 games). Looking at the rest of the list, I think I could have guessed most team’s in two or three, I never would have gotten the Padres.<br /><br />A similar gauge, but one that doesn't rely on the teammate-dependent R and RBI totals, is Bill James' Run Element Ratio. RER was described by James as the ratio between those things that were especially helpful at the beginning of an inning (walks and stolen bases) to those that were especially helpful at the end of an inning (extra bases). It is a ratio of "setup" events to "cleanup" events. Singles aren't included because they often function in both roles. <br /><br />Of course, there are RBI walks and doubles are a great way to start an inning, but RER classifies events based on when they have the highest relative value, at least from a simple analysis:<br /><br />1. MIA (Gordon/Suzuki/Dietrich/Realmuto), 1.8<br />2. ATL (Inciarte/Peterson/Markakis), 1.4<br />3. PHI (Herrera/Hernandez), 1.4<br />6. NYA (Ellsbury/Gardner), 1.2<br />Leadoff average, .8<br />ML average, .7<br />26. COL (Blackmon), .5<br />28. TB (Forsythe/Guyer), .5<br />29. DET (Kinsler), .5<br />30. BAL (Jones/Rickard), .4<br /><br />The Orioles certainly had a non-traditional leadoff profile thanks mostly to Jones; their five stolen base attempts was the fewest of any team, they were tied for third with 30 homers, and they drew 20 less walks than an average team out of the leadoff spot.<br /><br />Since stealing bases is part of the traditional skill set for a leadoff hitter, I've included the ranking for what some analysts call net steals, SB - 2*CS. I'm not going to worry about the precise breakeven rate, which is probably closer to 75% than 67%, but is also variable based on situation. The ML and leadoff averages in this case are per team lineup slot:<br /><br />1. WAS (Turner/Revere/Taylor), 30<br />2. MIL (Villar/Santana), 27<br />3. MIA (Gordon/Suzuki/Dietrich/Realmuto), 22<br />4. CLE (Santana/Davis), 20<br />Leadoff average, 6<br />ML average, 2<br />28. TB (Forsythe/Guyer), -11<br />29. SEA (Aoki/Martin), -13<br />30. PHI (Herrera/Hernandez), -16<br /><br />The Indians are a good example of why I list all players who had at least twenty starts in the leadoff spot; AL steal leader Rajai Davis’ 69 games leading off led to them leading the AL in net steals.<br /><br />Shifting back to quality measures, first up is one that David Smyth proposed when I first wrote this annual leadoff review. Since the optimal weight for OBA in a x*OBA + SLG metric is generally something like 1.7, David suggested figuring 2*OBA + SLG for leadoff hitters, as a way to give a little extra boost to OBA while not distorting things too much, or even suffering an accuracy decline from standard OPS. Since this is a unitless measure anyway, I multiply it by .7 to approximate the standard OPS scale and call it 2OPS:<br /><br />1. COL (Blackmon), 880<br />2. BOS (Betts/Pedroia), 872<br />3. HOU (Springer/Altuve), 865<br />Leadoff average, 775<br />ML average, 745<br />28. SF (Span), 722<br />29. OAK (Crisp/Burns), 654<br />30. KC (Escobar/Dyson/Merrifield), 650<br /><br />Esky Magic.<br /><br />Along the same lines, one can also evaluate leadoff hitters in the same way I'd go about evaluating any hitter, and just use Runs Created per Game with standard weights (this will include SB and CS, which are ignored by 2OPS):<br /><br />1. COL (Blackmon), 6.4<br />2. BOS (Betts/Pedroia), 6.3<br />3. HOU (Springer/Altuve), 6.2<br />Leadoff average, 4.9<br />ML average, 4.5<br />28. SF (Span), 4.1<br />29. KC (Escobar/Dyson/Merrifield), 3.4<br />30. OAK (Crisp/Burns), 3.3<br /><br />Esky Magic. <br /><br />The same six teams make up the leaders and trailers, which shouldn’t be a big surprise. <br /><br />Allow me to close with a crude theoretical measure of linear weights supposing that the player always led off an inning (that is, batted in the bases empty, no outs state). There are weights out there (see The Book) for the leadoff slot in its average situation, but this variation is much easier to calculate (although also based on a silly and impossible premise). <br /><br />The weights I used were based on the 2010 run expectancy table from Baseball Prospectus. Ideally I would have used multiple seasons but this is a seat-of-the-pants metric. The <a href="http://walksaber.blogspot.com/2010/12/leadoff-hitters-2010.html">2010 post</a> goes into the detail of how this measure is figured; this year, I’ll just tell you that the out coefficient was -.224, the CS coefficient was -.591, and for other details refer you to that post. I then restate it per the number of PA for an average leadoff spot (746 in 2014):<br /><br />1. HOU (Springer/Altuve), 30<br />2. COL (Blackmon), 28<br />3. CHN (Fowler/Zobrist), 27<br />Leadoff average, 7<br />ML average, 0<br />28. SF (Span), -8<br />29. KC (Escobar/Dyson/Merrifield), -19<br />30. OAK (Crisp/Burns), -21<br /><br />Esky Magic. Lest anyone think I am being unduly critical of Escobar's performance (he did after all start only half (actually 82) of KC's games as the leadoff hitter), note that Escobar when in the #1 spot hit .242/.272/.289. The rest of the Royals combined for .274/.317/.378, which would only rank second worst in the majors in 2OPS. So the Royals team performance was terrible, but Escobar was dreadful. Just the worst.<br /><br />The spreadsheet with full data is available <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vSkm6NvhEH19p28AHmJjFPIflMAYi68CPBbfI2tsn_FPkaav1dUMzsulBSMdWxcemwQBKEFzo6rXpBe/pub?output=html">here</a>.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-29463351809190628052016-11-28T17:45:00.000-05:002016-11-28T17:45:07.431-05:00Statistical Meanderings, 2016What follows is an abbreviated version of my annual collection of oddities that jump out at me from the year-end statistical reports I publish on this blog. These tidbits are intended as curiosities rather than as sober sabermetric analysis:<br /><br />* The top ten teams in MLB in W% were the playoff participants. The top six were the division winners. A rare case in which obvious inequities aren't created by micro-divisions, in stark constant to 2015's NL Central debacle.<br /><br />* In the NL, only Washington (.586) had a better overall W% than Chicago's road W% (.575). Of course, the Cubs were a truly great team, and with 103 wins and a world title on the heels of 97 wins a year ago, they belong in any discussion of the greatest teams of all-time. In <u>Baseball Dynasties</u>, Eddie Epstein and Rob Neyer used three years as their base time period for ranking the greatest dynasties. Another comparable regular season in 2017, regardless of playoff result, would in my opinion place the Cubs forwardly on a similarly-premised list.<br /><br />Most impressive about the Cubs is that despite winning 103, their EW% (.667) and PW% (.660) outpaced their actual W% of .640.<br /><br />* It is an annual tradition to run a chart in this space that compares the offensive and defensive runs above average for each of the playoff teams. RAA is figured very simply here by comparing park adjusted runs or runs allowed per game to the league average. Often I enjoy showing that the playoff teams were stronger offensively than defensively, but that was not the case in 2016:<br /><br /><a href="https://1.bp.blogspot.com/-Ml7vePbDvIg/WDywdzWV-UI/AAAAAAAACTc/XkLtzv3qffcvIwiIm_ZLN3JhJ2GuIL-zQCLcB/s1600/sm16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-Ml7vePbDvIg/WDywdzWV-UI/AAAAAAAACTc/XkLtzv3qffcvIwiIm_ZLN3JhJ2GuIL-zQCLcB/s400/sm16a.jpg" width="400" height="319" /></a><br /><br />This is another way to show just how great the Cubs were--only two other playoff teams were as many as 80 RAA on either side of the scorecard and the Cubs were +101 offensively and +153 defensively. <br /><br />* The Twins have a multi-year run of horrible starting pitching, and 2016 only added to the misery. Only the Angels managed a worse eRA from their starters (5.61 to 5.58); only A's starters logged fewer innings per start among AL teams (5.39 to 5.40); and the Twins were dead last in the majors in QS% (36%). In their surprising contention blip of 2015, the Twins were only in the bottom third of the AL in starting pitching performance, but in 2014 they were last in the majors in eRA, second-last in IP/S (ahead of only Colorado and QS%; in 2013 they were last in all three categories; and in 2012 they were last in the majors in eRA and second-last in IP/S and QS%. <br /><br />* There were a lot of great things from my perspective about the 2016 season from a team performance perspective, chiefly the Indians winning the pennant and playoffs in which the lesser participants did not advance their way through. Both were helped along by the comeuppance finally delivered to the Royals. It wasn't quite as glorious as it might have been, as they still managed to scrap out a .500 record, but the fundamental problems with their vaunted contact offense were laid bare. KC was easily the lowest scoring team in the AL at 4.05 R/G, with the Yankees of all teams second-worst with 4.19. They were last in the majors with .075 walks/at bat (COL, .084 was second worst). They were last in the AL in isolated power by 12 points (.137) and beat out only Atlanta and Miami, edging out the 30th-ranked Braves by just .007 points. Combining those two, their .212 secondary average was sixteen points lower than the Marlins for last in the majors. But they were at the AL average in batting average at .257, so that's something.<br /><br />* Andrew Miller averaged 17.1 strikeouts and 1.3 walks per 37.2 plate appearances (I use the league average of PA/G for to rest K and W rate per PA on the familiar scale of per nine innings while still using the proper denominator of PA). If you halve his K rate and double his walk rate, that's 8.6 and 2.6, which is still a pretty solid reliever. A comparable but slightly inferior performer this year was Tony Watson (8.2 and 2.8).<br /><br />* Boston's bullpen was built (or at least considered by some preseason) to be a lockdown unit with Tazawa, Uehara, and Kimbrel. Tazawa had a poor season with 0 RAR; Uehara and Kimbrel missed some time with injuries and were just okay when they pitched for 10 RAR each. Combined they had 20 RAR. Dan Otero, a non-roster invitee to spring training with Cleveland, had 26 RAR.<br /><br />* Matt Albers (-18) had the lowest RAR of anyone who qualified for any of my individual stat reports. I don't think that save is very likely at this point.<br /><br />* Just using your impression of Toronto's starters, their talent/stuff/age/etc., just try to associate each to their strikeout and walk rates (the five pitchers are RA Dickey, Marco Estrada, JA Happ, Aaron Sanchez, and Marcus Stroman):<br /><br /><a href="https://1.bp.blogspot.com/-3xabI7b6hhs/WDywsXGLAHI/AAAAAAAACTg/IHghPR_P6ZM1lcyWETLsYrqr2k_4RBekwCLcB/s1600/sm16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-3xabI7b6hhs/WDywsXGLAHI/AAAAAAAACTg/IHghPR_P6ZM1lcyWETLsYrqr2k_4RBekwCLcB/s400/sm16b.jpg" width="400" height="211" /></a><br /><br />The correct answer from A to E is Dickey, Sanchez, Stroman, Estrada, Happ. I never got a chance to play this game without being spoiled, but I'm certain that I would have at least said that Aaron Sanchez was pitcher D.<br /><br />* Jameson Taillon made it to the majors at age 25, and the thing that jumped out at me from his stat line was his very low walk rate (1.5, lower than any NL starter with 15 starts save Clayton Kershaw and Bartolo Colon. note that Taillon just cleared the bar for inclusion).<br /><br />John Lackey, at age 38, chipped in 49 RAR to Chicago (granted, fielding support contributed to his performance). Taillon and Lackey are always linked in my head thanks to a Fangraphs <a href="http://www.fangraphs.com/blogs/pittsburgh-pirates-pitching-prospect-jameson-taillon-scouting-report-video/">prospect post</a> from several years ago that I will endeavor to find. I believe the Fangraphs writer offered Lackey as a comp for Taillon. A commenter, perhaps a Pittsburgh partisan, responded by saying it was a ridiculous comparison, essentially an insult to Taillon. <br /><br />My thought at the time was that if I had any pitching prospect in the minors, and you told me that if I signed on the dotted line he would wind up having John Lackey's career, I would take it every time. That's not to say that there aren't pitchers in the minors who won't exceed Lackey's career, but to think that it's less than the median likely outcome for any pitching prospect is pretty aggressive. And this was before Lackey's late career performance which has further bolstered his standing. What odds would you place now on Jameson Taillon having a better career than John Lackey?<br /><br />* Jeff Francoeur had exactly 0 RAR. Ryan Howard had 1, before fielding/baserunning which would push him negative. <br /><br />* I mentioned in my MVP post how unique it was that Kyle and Corey Seager were both worthy of being on the MVP ballot. They performed fairly comparably across the board:<br /><br /><a href="https://1.bp.blogspot.com/-9kOxshDI6_Q/WDyzQjZ-OyI/AAAAAAAACTw/0dYOyx_MCmAggoMdRdruHF1mCnud1qc7QCLcB/s1600/sm16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-9kOxshDI6_Q/WDyzQjZ-OyI/AAAAAAAACTw/0dYOyx_MCmAggoMdRdruHF1mCnud1qc7QCLcB/s400/sm16c.jpg" width="400" height="22" /></a><br /><br />Chase and Travis d'Arnaud also had pretty similar numbers. Not good numbers, but similar nonetheless (which in Chase's case was probably a triumph whilst a disappointment for Travis):<br /><br /><a href="https://4.bp.blogspot.com/-bhgSEoPnqEg/WDyzUV0ln1I/AAAAAAAACT0/eoThgZb-WIAEbLWBpBXuNkuJTHv8vejQgCLcB/s1600/sm16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-bhgSEoPnqEg/WDyzUV0ln1I/AAAAAAAACT0/eoThgZb-WIAEbLWBpBXuNkuJTHv8vejQgCLcB/s400/sm16d.jpg" width="400" height="22" /></a><br /><br />* It wouldn't be a meanderings post without some Indians-specific comments. It has actually been harder than usual to move on to writing the year-end posts because of the disappointment of seeing the Indians lose their second, third, and fourth-consecutive games with a chance to close out the World Series. Three of those losses have come by one run and two in Game 7 in extra innings. The Indians have now gone 68 seasons without winning the World Series, losing four consecutive World Series after winning the first two in franchise history. That now matches the record of the Red Sox from 1918 - 1986, which if Ken Burns' "Baseball" and plagiarist/self-proclaimed patron saint of sad sack franchises Doris Kearns Goodwin are to believed was a level of baseball fan suffering unmatched and possibly comparable to the Battle of Stalingrad. Well, except for the initial two World Series winning streak--Boston won their first four World Series.<br /><br />The two Cleveland notes I have are negative, which is only because I have been thinking about them in conjunction with Game 7. One is how bad Yan Gomes was this season, creating just 1.9 runs per game over 262 PA, dead last in the AL among players with 250 or more PA. I did not understand Terry Francona's decision to pinch-run for Roberto Perez with the Indians down multiple runs in the seventh inning. He must have felt that a basestealing threat would distract Jon Lester, but given the inning and the extent of Cleveland's deficit, it basically ensured that Gomes would have to bat at some point. And bat he did, with the go-ahead run on first and two outs in the eighth against a laboring Chapman who had just coughed up the lead.<br /><br />Also costly was the decision to bring Michael Martinez in to play outfield in the ninth. That move made more sense given Coco Crisp's noodle arm, but to see Martinez make the last out was a tough pill to swallow (and had Martinez somehow reached base, Gomes would have followed). And don't even get me started on the intentional walks in the tenth inning.<br /><br />Also, it must be noted that Mike Napoli, who struggled in the postseason, was a very average performer in the regular season, creating 5.2 runs per game as first baseman. This is not intended as a criticism of Napoli, especially since I have been kvetching for years about the Indians inability to get even average production out of the corners. Napoli fit that need perfectly. But it felt as if the fans and media evaluated his performance as better than that (even limited strictly to production in the batter's box and not alleged leadership/veteran presence/etc.)<br /><br />* For various reasons, a few of the players who were in the thick of the NL MVP race a year ago and were surely considered favorites coming into this season had disappointing seasons. These three outfielders (Bryce Harper, Andrew McCutchen, Giancarlo Stanton) all wound up fairly close in 2016 RAR (28, 27, 23 respectively), yielding the MVP center stage to youngsters (Kris Bryant and Corey Seager), first basemen (Freddie Freeman, Anthony Rizzo, Joey Votto) and a guy having a career year (Daniel Murphy). <br /><br />More interestingly, those big three outfielders combined for 78 RAR--five fewer than Mike Trout.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-50643838578009704012016-11-16T17:16:00.000-05:002016-11-16T17:16:19.736-05:00Hypothetical Ballot: Cy YoungThere are no particular standout candidates for the Cy Young in either league, and I was tempted to open up this post by saying something like “Maybe it is a harbinger of things to come, as starting pitchers workloads continue to decrease and more managers consider times through the order in making the decision to go to the bullpen…we can expect more seasons like this, where no Cy Young contender really distinguishes himself.”<br /><br />And then I stopped and concluded, “You idiot, don’t you dare write that.” This is exactly the kind of banal over-extrapolation of heavily selected data that I rail against constantly. In the long run, is it possible that those factors could contribute to a dilution of clear Cy Young candidates, leaving voters to comb over a pack of indistinguishable guys pitching 180 innings a year? Entirely possible. Does that make 2016 the new normal? Of course not. Just last year, there was an epic three-way NL Cy Young race. This year, only an injury to Clayton Kershaw seems to have stood in the way of a historic season and Cy Young landslide.<br /><br />In the AL race, Justin Verlander had a 70 to 61 RAR lead over Chris Sale, with a pack of pitchers right behind them (Rick Porcello 59, Corey Kluber 58, Jose Quintana 57, Aaron Sanchez/JA Happ/Masahiro Tanaka 56). Convieniently, the first four in RAR also are the only pitchers who would also have 50 or more RAR based on eRA or dRA, with one exception. Verlander allowed a BABIP of just .261 and would so his dRA is 3.80, significantly higher than his 3.04 RRA. However, none of the others look better using dRA--all three are five to eight runs worse. So I go with Verlander for the top spot and Porcello second over Sale (he led the AL with a 3.14 eRA, and since we are talking about one run differences here, Bill James would at least want us to consider his 22-4 W-L record). I didn’t actually consider the W-L record, but he does rank just ahead of Sale if you weight RAR from actual/eRA/dRA at 50%/30%/20%, which has no scientific basis but seems reasonable enough. Again, there’s only a one RAR difference between Sale and Porcello, so using W-L or flipping a coin to order them is just as reasonable. I gave the fifth spot to Jose Quintana over Aaron Sanchez, and would not have guessed that Quintana had a better strikeout rate (8.1 to 7.8).<br /><br />This leaves out Zach Britton, who I credit with just 35 RAR. I remain thoroughly unconvinced that leverage bonuses are appropriate. Each run allowed and out recorded is worth the same to the final outcome regardless of what inning it comes in. The difference between starters and relief aces is that some of the games the former pitch could have been won or lost with worse or better performances, while relief aces generally are limited to pitching in close games. But the fact that Britton pitches the ninth doesn’t make his shutout inning any more valuable than the one Chris Tillman pitched in the fourth within the context of that single game. To the extent that Britton contributes more value on a per inning basis, it’s because he pitched in a greater proportion of games in which one run might have made a difference, not because that is more apparent for any particular game at the point at which Britton appears in it than it was when the starter was pitching. I have alluded to this viewpoint many times, but have never written it up satisfactorily because I’ve not figured out how to propose a leverage adjustment that captures it, without going to the extreme that value can only be generated by pitching in games your team wins. <br /><br />1. Justin Verlander, DET<br />2. Rick Porcello, BOS<br />3. Chris Sale, CHA<br />4. Corey Kluber, CLE<br />5. Jose Quintana, CHA<br /><br />In the NL, there were seven starters with 60 RAR and then a gap of four to Jake Arrieta, which makes a good cohort to consider for the ballot. Of this group, Tanner Roark and Madison Bumgarner at the bottom in terms of RAR and had high dRAs (4.17 and 3.87) which justify dropping them. <br /><br />That leaves Jon Lester (71 RAR), Kyle Hendricks (70), Max Scherzer (70), Johnny Cueto (65), and Clayton Kershaw (64). If you weight 50/30/20 as for the AL, all five are clustered between 60 and 64 RAR. This makes it tempting to just to pick Kershaw as he was much the best in every rate and narrowly missed leading the league in RAA despite pitching only 149 innings. <br /><br />Among the four who pitched full seasons, Scherzer ranks first in innings and third in RRA, eRA, and dRA. However, he pitched significantly more innings than the Cubs candidates--25 more than Lester and 38 more than Hendricks. Comparing him to Cueto, who pitched nine fewer innings, Scherzer leads in RRA by .09 runs, eRA by .13 runs, and trails in dRA by .09 runs. So for my money Scherzer provided the best mix of effectiveness and durability.<br /><br />All that’s left is a direct comparison of Scherzer to Kershaw, in which I think the innings gap is just too great without giving excessive weight to peripherals. The difference between Scherzer and Kershaw is 79 innings with a 3.62 RRA. To put it in 2016 performance terms, that makes Scherzer equivalent to Kershaw plus a solid reliever like Felipe Rivero or Travis Wood. That’s too much value for me to ignore looking at the gaudy (and they are gaudy!) rate stats:<br /><br />1. Max Scherzer, WAS<br />2. Jon Lester, CHN<br />3. Kyle Hendricks, CHN<br />4. Clayton Kershaw, LA<br />5. Johnny Cueto, SFphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-82190123462122375072016-11-16T09:37:00.000-05:002016-11-16T17:17:35.644-05:00Hypothetical Ballot: MVPYou could basically copy and paste the same thing for AL MVP every year, so I’ll try to keep it brief. My position is that wins are value, and 8 wins don’t count for more because the rest of your teammates were worth 50 than if the rest of your teammates were only worth 30. <br /><br />But the debate over the definition of value is not what I find most obnoxious about the Mike Trout-era MVP discussions. It’s easy enough to disagree on that point and move one. What is most bothersome is the way that people attempt to co-opt the sabermetric terms that sound sabermetric like “error bars” to push their own narratives.<br /><br />Let’s suppose that Player A is estimated to have contributed 87 RAR and player B is estimated to have contributed 80 RAR, and that the standard error is something like 10 runs. In this case, it certainly is inconclusive that player A was truly more valuable than player B. I would grant that player B would be a reasonable choice as MVP.<br /><br />But if you’re filing out your MVP ballot, *should* you put Player B ahead of Player A? It’s still quite likely that Player A was more valuable than Player B. To me, you need to have a good reason to put Player B ahead, particularly when the margin is “significant” but not beyond the “error bar”.<br /><br />Worse yet, though, is the attempt to twist oneself into a pretzel to make up those good reasons. The real gem going around, which you will see in comment sections and message boards, is that the error bars must be larger for Player A. Because you see, Player A’s park became a strong pitcher’s park right around when he arrived, and parks don’t change character like that (says someone who has never examined historical park factors). Because you see, Player A always leads the league in RAR, and by a wide margin--that just can’t be right. Player A is so consistently great in the metrics that the metrics must be wrong.<br /><br />The world is not worthy of Player A. Every week of Player A’s career is scrutinized by pseudo-sabermetricians who have deadlines to fill with their micro-analytical pablum, and who when they aren’t vulturing over Player A are busy writing extrapolating trends from blips in thirty-team samples to blame metrics for their own arrogance. Player A can’t win with the people who should be appreciating him--not in the sense that a fan might but exactly in the sense that a detached analyst would.<br /><br />I’m sure you’ve deduced by now that Player A is Mike Trout, and you may have guessed that Player B is Mookie Betts. Except those aren’t even my true estimates of their RAR, they’re what I would come up with their RAR if I took my hitting/position RAR + BP’s baserunning runs (for non-steals, since steals are incorporated in the first piece) + the average of each player’s BP FRAA, BIS DRS, and MGL UZR. In other words, if I didn’t regress fielding at all, which I don’t think is the correct position. When adding components together, if one (hitting) is more reliable than another (fielding), it doesn’t make sense to ignore that. In actually estimating RAR for the purpose of filling out a fake MVP ballot, I used 50% FRAA, 25% DRS, 25% UZR, and halved it. Then Trout is at 86 RAR, Betts 68, and Jose Alutve slides in between them at 71, which explains the top of my ballot.<br /><br />If anything, I think I may be generous to Betts, who needs all of his 8 baserunning runs and 11 “regressed” fielding runs to overcome 49 hitting RAR, which ranked just ninth in the league. Kyle Seager also made it onto my ballot on the strength of 8 fielding runs, and Francisco Lindor came close with 5 from baserunning and 10 from fielding. David Ortiz and Miguel Cabrera gave up 5 runs from non-hitting activities (or in Ortiz’s case, non-acitivty), which pushed them just off the ballot. Last year’s Player B, Josh Donaldson, was only a hair behind Betts, having another excellent season with 65 RAR and good-average fielding except in FRAA, which didn’t like his performance at all (-12).<br /><br />The AL starting pitchers lacked any standout Cy Young candidates, but made up for it by being tightly bunched, so four of the final six spots go to them:<br /><br />1. CF Mike Trout, LAA<br />2. 2B Jose Altuve, HOU<br />3. RF Mookie Betts, BOS<br />4. 3B Josh Donaldson, TOR<br />5. SP Justin Verlander, DET<br />6. 2B Robinson Cano, NYA<br />7. SP Rick Porcello, BOS<br />8. SP Chris Sale, CHA<br />9. SP Corey Kluber, CLE<br />10. 3B Kyle Seager, SEA<br /><br />In the NL, I think Kris Bryant is a pretty clear pick for the top spot. He was second in the league in RAR by just one run to Joey Votto, which he makes up with baserunning alone and pads with strong fielding runs (2, 10, 12). Anthony Rizzo seems to be the other top candidate in mainstream opinion, but he only ranks third among first baseman on my ballot. Rizzo, Freddie Freeman, and Joey Votto all had similar playing time, but both significantly outhit him (Rizzo 6.9 RG, Votto 8.2, Freeman 7.6). Rizzo makes up much of the ground on Votto with his glove, but Freeman is no slouch himself. <br /><br />Corey Seager got mixed reviews as a fielder (-8, 0, 11) so he falls just behind Freeman on my ballot. I’m quite certain I’ve never had brothers on both of my MVP top 10s in the same year, or any year. Daniel Murphy was third to Votto and Bryant in RAR, but his fielding reviews aren’t so mixed (-5, -11, -6), and even before considering that was actually just behind Max Scherzer in RAR. From there, it’s just a matter of mixing in the pitchers and noting that four Cubs are on the ballot:<br /><br />1. 3B Kris Bryant, CHN<br />2. 1B Freddie Freeman, ATL<br />3. SS Corey Seager, LA<br />4. SP Max Scherzer, WAS<br />5. 2B Daniel Murphy, WAS<br />6. SP Jon Lester, CHN<br />7. 1B Joey Votto, CIN<br />8. 1B Anthony Rizzo, CHN<br />9. SP Kyle Hendicks, CHN<br />10. SP Clayton Kershaw, LAphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-48422218417202677822016-11-09T20:08:00.002-05:002016-11-10T17:12:31.250-05:00Hypothetical Ballot: Rookie of the YearIt was a bad year for rookies in the AL, made more interesting by the very late arrival of Gary Sanchez. Most of the discussion about the award seems to center around whether it is appropriate to give it to Sanchez based on his brilliant 227 PA, and whether ROY should be a value award, a future prospect award, or some kind of ungodly hybrid of the two. My own approach is that it should be a value award--anyone who is a rookie should be eligible and my primary criteria is how productive they were in 2016, not how old they are, their prospect pedigree, how their team held down their service time, or the like. Only in a very close decision would I factor in those criteria. I understand why others might consider those factors, and why it makes a lot more sense to deviate from a value approach for ROY than for Cy Young or MVP. <br /><br />As such, I don’t consider Sanchez’s case to be particularly compelling. Yes, Sanchez was more productive on a rate basis than any AL hitter other than Mike Trout. Yes, the lack of a standout candidate in the rest of the league makes Sanchez all the more appealing. But Sanchez’s performance far outpaced both his prospect status and his minor league numbers (807 OPS in 313 PA at AAA this year, 815 across AA and AAA last year). If I was going to consider a shooting star exception, it would be for someone who checked all the boxes. I would much rather have Sanchez’s future than any of the other four players on my ballot, but in 2016 he fell in the middle in terms of value.<br /><br />With Sanchez out, the top of the ballot comes down to Michael Fulmer, who is the top non-Sanchez candidate in the popular discussion, and Chris Devenski. I watched a game in which Devenski pitched this year and was vaguely aware of his existence in subsequent box scores, but how effectively he was pitching completely escaped my attention until I put together my annual stat reports. Devenski pitched extremely well for Houston, mostly in relief (48 games, 5 starts) with a 1.80 RRA over 108 innings. His peripherals were strong as well (2.39 eRA and 2.79 dRA). <br /><br />Fulmer pitched 159 innings with a 3.41 RRA for 42 RAR versus Devenski’s 39. Fulmer’s peripherals were also reasonably strong (3.46 eRA, 4.02 dRA), and since this was a curious case I also checked Baseball Prospectus’ DRA, which attempts to normalize for any number of relevant variables (park, umpires, defensive support, framing, quality of opposition, etc.). Using DRA, Fulmer has a clear edge considering his quantity advantage (3.49 to 3.72).<br /><br />One thing my RAR figures oversimplify is pitcher’s roles--it is a binary reliever (with replacement level at 111% of league average) or start (replacement level 128% of league average). If I figured RAR using Devenski’s inning split to set his replacement level (83 innings in relief to 24 starting works out to 115% of league as the replacement level), his RAR would edge up to 41. It should be noted too that Devenski pitched decently in his five starts, averaging just under 5 innings with a 4.01 RA.<br /><br />I think the two are very close; this is a case where Fulmer’s status as a starter and a younger, better regarded prospect leave him just ahead for me. Even so, I assume Devenski will rank higher on my ballot than almost any submitted even for the IBAs.<br /><br />Filling out the bottom of the ballot, the only other legitimate hitting candidate, Tyler Naquin and his 26 RAR, was heavily platooned and fares poorly in defensive metrics. That leaves two A’s pitchers, one a starter and one a reliever. If I strictly followed RAR, I would actually have the latter (Ryan Dull) ahead of the former (Sean Manaea), and the peripherals don’t really help either’s case, but since they were so close I will vote here for prospect status.<br /><br />1. SP Michael Fulmer, DET<br />2. RP Chris Devenski, HOU<br />3. C Gary Sanchez, NYA<br />4. SP Sean Manaea, OAK<br />5. RP Ryan Dull, OAK<br /><br />The top of the NL ballot is easy, as Corey Seager is a legitimate MVP candidate and far outshines the rest of the rookies. There is a cluster of qualified candidates in the 30-40 RAR range who make up the rest of my ballot. Kenta Maeda gets the nod over Junior Guerra as top pitcher based on stronger peripherals, with apologies to Zach Davies, Tyler Anderson, and Steven Matz. Among hitters, Aledmys Diaz led in RAR with 37 to Trea Turner’s 34, but Diaz’s fielding metrics are bad (-9 FRAA, -3 DRS, -8 UZR) while Turner’s are…not as bad (-3, -2, -5). Both are credited with baserunning value beyond their steals by BP (2 runs for Diaz, 4 for Turner); when you add it up it’s very close, but I consider Turner’s age and the fact that he did it in 130 PA to put him ahead:<br /><br />1. SS Corey Seager, LA<br />2. SP Kenta Maeda, LA<br />3. SP Junior Guerra, MIL<br />4. CF Trea Turner, WAS<br />5. SS Aledmys Diaz, STLphttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com2tag:blogger.com,1999:blog-12133335.post-45932834202951355992016-10-07T12:25:00.000-04:002016-11-30T19:35:12.658-05:00End of Season Statistics, 2016The spreadsheets are published as Google Spreadsheets, which you can download in Excel format by changing the extension in the address from "=html" to "=xls". That way you can download them and manipulate things however you see fit. <br /><br />The data comes from a number of different sources. Most of the data comes from Baseball-Reference. KJOK's park database is extremely helpful in determining when park factors should reset. Data on bequeathed runners for relievers comes from Baseball Prospectus. <br /><br />The basic philosophy behind these stats is to use the simplest methods that have acceptable accuracy. Of course, "acceptable" is in the eye of the beholder, namely me. I use Pythagenpat not because other run/win converters, like a constant RPW or a fixed exponent are not accurate enough for this purpose, but because it's mine and it would be kind of odd if I didn't use it. <br /><br />If I seem to be a stickler for purity in my critiques of others' methods, I'd contend it is usually in a theoretical sense, not an input sense. So when I exclude hit batters, I'm not saying that hit batters are worthless or that they *should* be ignored; it's just easier not to mess with them and not that much less accurate. <br /><br />I also don't really have a problem with people using sub-standard methods (say, Basic RC) as long as they acknowledge that they are sub-standard. If someone pretends that Basic RC doesn't undervalue walks or cause problems when applied to extreme individuals, I'll call them on it; if they explain its shortcomings but use it regardless, I accept that. Take these last three paragraphs as my acknowledgment that some of the statistics displayed here have shortcomings as well, and I've at least attempted to describe some of them in the discussion below.<br /><br />The League spreadsheet is pretty straightforward--it includes league totals and averages for a number of categories, most or all of which are explained at appropriate junctures throughout this piece. The advent of interleague play has created two different sets of league totals--one for the offense of league teams and one for the defense of league teams. Before interleague play, these two were identical. I do not present both sets of totals (you can figure the defensive ones yourself from the team spreadsheet, if you desire), just those for the offenses. The exception is for the defense-specific statistics, like innings pitched and quality starts. The figures for those categories in the league report are for the defenses of the league's teams. However, I do include each league's breakdown of basic pitching stats between starters and relievers (denoted by "s" or "r" prefixes), and so summing those will yield the totals from the pitching side. The one abbreviation you might not recognize is "N"--this is the league average of runs/game for one team, and it will pop up again.<br /><br />The Team spreadsheet focuses on overall team performance--wins, losses, runs scored, runs allowed. The columns included are: Park Factor (PF), Home Run Park Factor (PFhr), Winning Percentage (W%), Expected W% (EW%), Predicted W% (PW%), wins, losses, runs, runs allowed, Runs Created (RC), Runs Created Allowed (RCA), Home Winning Percentage (HW%), Road Winning Percentage (RW%) [exactly what they sound like--W% at home and on the road], Runs/Game (R/G), Runs Allowed/Game (RA/G), Runs Created/Game (RCG), Runs Created Allowed/Game (RCAG), and Runs Per Game (the average number of runs scored an allowed per game). Ideally, I would use outs as the denominator, but for teams, outs and games are so closely related that I don’t think it’s worth the extra effort.<br /><br />The runs and Runs Created figures are unadjusted, but the per-game averages are park-adjusted, except for RPG which is also raw. Runs Created and Runs Created Allowed are both based on a simple Base Runs formula. The formula is:<br /><br />A = H + W - HR - CS<br />B = (2TB - H - 4HR + .05W + 1.5SB)*.76<br />C = AB - H<br />D = HR<br />Naturally, A*B/(B + C) + D.<br /><br />I have explained the methodology used to figure the PFs before, but the cliff’s notes version is that they are based on five years of data when applicable, include both runs scored and allowed, and they are regressed towards average (PF = 1), with the amount of regression varying based on the number of years of data used. There are factors for both runs and home runs. The initial PF (not shown) is:<br /><br />iPF = (H*T/(R*(T - 1) + H) + 1)/2<br />where H = RPG in home games, R = RPG in road games, T = # teams in league (14 for AL and 16 for NL). Then the iPF is converted to the PF by taking x*iPF + (1-x), where x = .6 if one year of data is used, .7 for 2, .8 for 3, and .9 for 4+. <br /><br />It is important to note, since there always seems to be confusion about this, that these park factors already incorporate the fact that the average player plays 50% on the road and 50% at home. That is what the adding one and dividing by 2 in the iPF is all about. So if I list Fenway Park with a 1.02 PF, that means that it actually increases RPG by 4%. <br /><br />In the calculation of the PFs, I did not get picky and take out “home” games that were actually at neutral sites.<br /><br />There are also Team Offense and Defense spreadsheets. These include the following categories:<br /><br />Team offense: Plate Appearances, Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Walks and Hit Batters per At Bat (WAB), Isolated Power (SLG - BA), R/G at home (hR/G), and R/G on the road (rR/G) BA, OBA, SLG, WAB, and ISO are park-adjusted by dividing by the square root of park factor (or the equivalent; WAB = (OBA - BA)/(1 - OBA), ISO = SLG - BA, and SEC = WAB + ISO).<br /><br />Team defense: Innings Pitched, BA, OBA, SLG, Innings per Start (IP/S), Starter's eRA (seRA), Reliever's eRA (reRA), Quality Start Percentage (QS%), RA/G at home (hRA/G), RA/G on the road (rRA/G), Battery Mishap Rate (BMR), Modified Fielding Average (mFA), and Defensive Efficiency Record (DER). BA, OBA, and SLG are park-adjusted by dividing by the square root of PF; seRA and reRA are divided by PF.<br /><br />The three fielding metrics I've included are limited it only to metrics that a) I can calculate myself and b) are based on the basic available data, not specialized PBP data. The three metrics are explained in this post, but here are quick descriptions of each:<br /><br />1) BMR--wild pitches and passed balls per 100 baserunners = (WP + PB)/(H + W - HR)*100<br /><br />2) mFA--fielding average removing strikeouts and assists = (PO - K)/(PO - K + E)<br /><br />3) DER--the Bill James classic, using only the PA-based estimate of plays made. Based on a suggestion by Terpsfan101, I've tweaked the error coefficient. Plays Made = PA - K - H - W - HR - HB - .64E and DER = PM/(PM + H - HR + .64E)<br /><br />Next are the individual player reports. I defined a starting pitcher as one with 15 or more starts. All other pitchers are eligible to be included as a reliever. If a pitcher has 40 appearances, then they are included. Additionally, if a pitcher has 50 innings and less than 50% of his appearances are starts, he is also included as a reliever (this allows some swingmen type pitchers who wouldn’t meet either the minimum start or appearance standards to get in).<br /><br />For all of the player reports, ages are based on simply subtracting their year of birth from 2016. I realize that this is not compatible with how ages are usually listed and so “Age 27” doesn’t necessarily correspond to age 27 as I list it, but it makes everything a heckuva lot easier, and I am more interested in comparing the ages of the players to their contemporaries than fitting them into historical studies, and for the former application it makes very little difference. The "R" category records rookie status with a "R" for rookies and a blank for everyone else; I've trusted Baseball Prospectus on this. Also, all players are counted as being on the team with whom they played/pitched (IP or PA as appropriate) the most. <br /><br />For relievers, the categories listed are: Games, Innings Pitched, estimated Plate Appearances (PA), Run Average (RA), Relief Run Average (RRA), Earned Run Average (ERA), Estimated Run Average (eRA), DIPS Run Average (dRA), Strikeouts per Game (KG), Walks per Game (WG), Guess-Future (G-F), Inherited Runners per Game (IR/G), Batting Average on Balls in Play (%H), Runs Above Average (RAA), and Runs Above Replacement (RAR).<br /><br />IR/G is per relief appearance (G - GS); it is an interesting thing to look at, I think, in lieu of actual leverage data. You can see which closers come in with runners on base, and which are used nearly exclusively to start innings. Of course, you can’t infer too much; there are bad relievers who come in with a lot of people on base, not because they are being used in high leverage situations, but because they are long men being used in low-leverage situations already out of hand.<br /><br />For starting pitchers, the columns are: Wins, Losses, Innings Pitched, Estimated Plate Appearances (PA), RA, RRA, ERA, eRA, dRA, KG, WG, G-F, %H, Pitches/Start (P/S), Quality Start Percentage (QS%), RAA, and RAR. RA and ERA you know--R*9/IP or ER*9/IP, park-adjusted by dividing by PF. The formulas for eRA and dRA are based on the same Base Runs equation and they estimate RA, not ERA.<br /><br />* eRA is based on the actual results allowed by the pitcher (hits, doubles, home runs, walks, strikeouts, etc.). It is park-adjusted by dividing by PF.<br /><br />* dRA is the classic DIPS-style RA, assuming that the pitcher allows a league average %H, and that his hits in play have a league-average S/D/T split. It is park-adjusted by dividing by PF.<br /><br />The formula for eRA is:<br /><br />A = H + W - HR<br />B = (2*TB - H - 4*HR + .05*W)*.78<br />C = AB - H = K + (3*IP - K)*x (where x is figured as described below for PA estimation and is typically around .93) = PA (from below) - H - W<br />eRA = (A*B/(B + C) + HR)*9/IP<br /><br />To figure dRA, you first need the estimate of PA described below. Then you calculate W, K, and HR per PA (call these %W, %K, and %HR). Percentage of balls in play (BIP%) = 1 - %W - %K - %HR. This is used to calculate the DIPS-friendly estimate of %H (H per PA) as e%H = Lg%H*BIP%.<br /><br />Now everything has a common denominator of PA, so we can plug into Base Runs:<br /><br />A = e%H + %W<br />B = (2*(z*e%H + 4*%HR) - e%H - 5*%HR + .05*%W)*.78<br />C = 1 - e%H - %W - %HR<br />cRA = (A*B/(B + C) + %HR)/C*a<br /><br />z is the league average of total bases per non-HR hit (TB - 4*HR)/(H - HR), and a is the league average of (AB - H) per game.<br /><br />In the past I presented a couple of batted ball RA estimates. I’ve removed these, not just because batted ball data exhibits questionable reliability but because these metrics were complicated to figure, required me to collate the batted ball data, and were not personally useful to me. I figure these stats for my own enjoyment and have in some form or another going back to 1997. I share them here only because I would do it anyway, so if I’m not interested in certain categories, there’s no reason to keep presenting them.<br /><br />Instead, I’m showing strikeout and walk rate, both expressed as per game. By game I mean not nine innings but rather the league average of PA/G. I have always been a proponent of using PA and not IP as the denominator for non-run pitching rates, and now the use of per PA rates is widespread. Usually these are expressed as K/PA and W/PA, or equivalently, percentage of PA with a strikeout or walk. I don’t believe that any site publishes these as K and W per equivalent game as I am here. This is not better than K%--it’s simply applying a scalar multiplier. I like it because it generally follows the same scale as the familiar K/9.<br /><br />To facilitate this, I’ve finally corrected a flaw in the formula I use to estimate plate appearances for pitchers. Previously, I’ve done it the lazy way by not splitting strikeouts out from other outs. I am now using this formula to estimate PA (where PA = AB + W):<br /><br />PA = K + (3*IP - K)*x + H + W<br />Where x = league average of (AB - H - K)/(3*IP - K)<br /><br />Then KG = K*Lg(PA/G) and WG = W*Lg(PA/G).<br /><br />G-F is a junk stat, included here out of habit because I've been including it for years. It was intended to give a quick read of a pitcher's expected performance in the next season, based on eRA and strikeout rate. Although the numbers vaguely resemble RAs, it's actually unitless. As a rule of thumb, anything under four is pretty good for a starter. G-F = 4.46 + .095(eRA) - .113(K*9/IP). It is a junk stat. JUNK STAT JUNK STAT JUNK STAT. Got it?<br /><br />%H is BABIP, more or less--%H = (H - HR)/(PA - HR - K - W), where PA was estimated above. Pitches/Start includes all appearances, so I've counted relief appearances as one-half of a start (P/S = Pitches/(.5*G + .5*GS). QS% is just QS/(G - GS); I don't think it's particularly useful, but Doug's Stats include QS so I include it.<br /><br />I've used a stat called Relief Run Average (RRA) in the past, based on Sky Andrecheck's article in the August 1999 By the Numbers; that one only used inherited runners, but I've revised it to include bequeathed runners as well, making it equally applicable to starters and relievers. I use RRA as the building block for baselined value estimates for all pitchers. I explained RRA in this article, but the bottom line formulas are:<br /><br />BRSV = BRS - BR*i*sqrt(PF)<br />IRSV = IR*i*sqrt(PF) - IRS<br />RRA = ((R - (BRSV + IRSV))*9/IP)/PF<br /><br />The two baselined stats are Runs Above Average (RAA) and Runs Above Replacement (RAR). Starting in 2015 I revised RAA to use a slightly different baseline for starters and relievers as described here. The adjustment is based on patterns from the last several seasons of league average starter and reliever eRA. Thus it does not adjust for any advantages relief pitchers enjoy that are not reflected in their component statistics. This could include runs allowed scoring rules that benefit relievers (although the use of RRA should help even the scales in this regard, at least compared to raw RA) and the talent advantage of starting pitchers. The RAR baselines do attempt to take the latter into account, and so the difference in starter and reliever RAR will be more stark than the difference in RAA.<br /><br />RAA (relievers) = (.951*LgRA - RRA)*IP/9<br />RAA (starters) = (1.025*LgRA - RRA)*IP/9<br />RAR (relievers) = (1.11*LgRA - RRA)*IP/9<br />RAR (starters) = (1.28*LgRA - RRA)*IP/9<br /><br />All players with 250 or more plate appearances (official, total plate appearances) are included in the Hitters spreadsheets (along with some players close to the cutoff point who I was interested in). Each is assigned one position, the one at which they appeared in the most games. The statistics presented are: Games played (G), Plate Appearances (PA), Outs (O), Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Runs Created (RC), Runs Created per Game (RG), Speed Score (SS), Hitting Runs Above Average (HRAA), Runs Above Average (RAA), Hitting Runs Above Replacement (HRAR), and Runs Above Replacement (RAR).<br /><br />Starting in 2015, I'm including hit batters in all related categories for hitters, so PA is now equal to AB + W+ HB. Outs are AB - H + CS. BA and SLG you know, but remember that without SF, OBA is just (H + W + HB)/(AB + W + HB). Secondary Average = (TB - H + W + HB)/AB = SLG - BA + (OBA - BA)/(1 - OBA). I have not included net steals as many people (and Bill James himself) do, but I have included HB which some do not.<br /><br />BA, OBA, and SLG are park-adjusted by dividing by the square root of PF. This is an approximation, of course, but I'm satisfied that it works well (I plan to post a couple articles on this some time during the offseason). The goal here is to adjust for the win value of offensive events, not to quantify the exact park effect on the given rate. I use the BA/OBA/SLG-based formula to figure SEC, so it is park-adjusted as well.<br /><br />Runs Created is actually Paul Johnson's ERP, more or less. Ideally, I would use a custom linear weights formula for the given league, but ERP is just so darn simple and close to the mark that it’s hard to pass up. I still use the term “RC” partially as a homage to Bill James (seriously, I really like and respect him even if I’ve said negative things about RC and Win Shares), and also because it is just a good term. I like the thought put in your head when you hear “creating” a run better than “producing”, “manufacturing”, “generating”, etc. to say nothing of names like “equivalent” or “extrapolated” runs. None of that is said to put down the creators of those methods--there just aren’t a lot of good, unique names available. <br /><br />For 2015, I refined the formula a little bit to:<br /><br />1. include hit batters at a value equal to that of a walk<br />2. value intentional walks at just half the value of a regular walk<br />3. recalibrate the multiplier based on the last ten major league seasons (2005-2014)<br /><br />This revised RC = (TB + .8H + W + HB - .5IW + .7SB - CS - .3AB)*.310<br /><br />RC is park adjusted by dividing by PF, making all of the value stats that follow park adjusted as well. RG, the Runs Created per Game rate, is RC/O*25.5. I do not believe that outs are the proper denominator for an individual rate stat, but I also do not believe that the distortions caused are that bad. (I still intend to finish my rate stat series and discuss all of the options in excruciating detail, but alas you’ll have to take my word for it now).<br /><br />Several years ago I switched from using my own "Speed Unit" to a version of Bill James' Speed Score; of course, Speed Unit was inspired by Speed Score. I only use four of James' categories in figuring Speed Score. I actually like the construct of Speed Unit better as it was based on z-scores in the various categories (and amazingly a couple other sabermetricians did as well), but trying to keep the estimates of standard deviation for each of the categories appropriate was more trouble than it was worth.<br /><br />Speed Score is the average of four components, which I'll call a, b, c, and d:<br /><br />a = ((SB + 3)/(SB + CS + 7) - .4)*20<br />b = sqrt((SB + CS)/(S + W))*14.3<br />c = ((R - HR)/(H + W - HR) - .1)*25<br />d = T/(AB - HR - K)*450<br /><br />James actually uses a sliding scale for the triples component, but it strikes me as needlessly complex and so I've streamlined it. He looks at two years of data, which makes sense for a gauge that is attempting to capture talent and not performance, but using multiple years of data would be contradictory to the guiding principles behind this set of reports (namely, simplicity. Or laziness. You're pick.) I also changed some of his division to mathematically equivalent multiplications.<br /><br />There are a whopping four categories that compare to a baseline; two for average, two for replacement. Hitting RAA compares to a league average hitter; it is in the vein of Pete Palmer’s Batting Runs. RAA compares to an average hitter at the player’s primary position. Hitting RAR compares to a “replacement level” hitter; RAR compares to a replacement level hitter at the player’s primary position. The formulas are:<br /><br />HRAA = (RG - N)*O/25.5<br />RAA = (RG - N*PADJ)*O/25.5<br />HRAR = (RG - .73*N)*O/25.5<br />RAR = (RG - .73*N*PADJ)*O/25.5<br /><br />PADJ is the position adjustment, and it is based on 2002-2011 offensive data. For catchers it is .89; for 1B/DH, 1.17; for 2B, .97; for 3B, 1.03; for SS, .93; for LF/RF, 1.13; and for CF, 1.02. I had been using the 1992-2001 data as a basis for some time, but finally updated for 2012. I’m a little hesitant about this update, as the middle infield positions are the biggest movers (higher positional adjustments, meaning less positional credit). I have no qualms for second base, but the shortstop PADJ is out of line with the other position adjustments widely in use and feels a bit high to me. But there are some decent points to be made in favor of offensive adjustments, and I’ll have a bit more on this topic in general below.<br /><br />That was the mechanics of the calculations; now I'll twist myself into knots trying to justify them. If you only care about the how and not the why, stop reading now. <br /><br />The first thing that should be covered is the philosophical position behind the statistics posted here. They fall on the continuum of ability and value in what I have called "performance". Performance is a technical-sounding way of saying "Whatever arbitrary combination of ability and value I prefer".<br /><br />With respect to park adjustments, I am not interested in how any particular player is affected, so there is no separate adjustment for lefties and righties for instance. The park factor is an attempt to determine how the park affects run scoring rates, and thus the win value of runs.<br /><br />I apply the park factor directly to the player's statistics, but it could also be applied to the league context. The advantage to doing it my way is that it allows you to compare the component statistics (like Runs Created or OBA) on a park-adjusted basis. The drawback is that it creates a new theoretical universe, one in which all parks are equal, rather than leaving the player grounded in the actual context in which he played and evaluating how that context (and not the player's statistics) was altered by the park.<br /><br />The good news is that the two approaches are essentially equivalent; in fact, they are precisely equivalent if you assume that the Runs Per Win factor is equal to the RPG. Suppose that we have a player in an extreme park (PF = 1.15, approximately like Coors Field pre-humidor) who has an 8 RG before adjusting for park, while making 350 outs in a 4.5 N league. The first method of park adjustment, the one I use, converts his value into a neutral park, so his RG is now 8/1.15 = 6.957. We can now compare him directly to the league average:<br /><br />RAA = (6.957 - 4.5)*350/25.5 = +33.72<br /><br />The second method would be to adjust the league context. If N = 4.5, then the average player in this park will create 4.5*1.15 = 5.175 runs. Now, to figure RAA, we can use the unadjusted RG of 8:<br /><br />RAA = (8 - 5.175)*350/25.5 = +38.77<br /><br />These are not the same, as you can obviously see. The reason for this is that they take place in two different contexts. The first figure is in a 9 RPG (2*4.5) context; the second figure is in a 10.35 RPG (2*4.5*1.15) context. Runs have different values in different contexts; that is why we have RPW converters in the first place. If we convert to WAA (using RPW = RPG, which is only an approximation, so it's usually not as tidy as it appears below), then we have:<br /><br />WAA = 33.72/9 = +3.75<br />WAA = 38.77/10.35 = +3.75<br /><br />Once you convert to wins, the two approaches are equivalent. The other nice thing about the first approach is that once you park-adjust, everyone in the league is in the same context, and you can dispense with the need for converting to wins at all. You still might want to convert to wins, and you'll need to do so if you are comparing the 2015 players to players from other league-seasons (including between the AL and NL in the same year), but if you are only looking to compare Jose Bautista to Miguel Cabrera, it's not necessary. WAR is somewhat ubiquitous now, but personally I prefer runs when possible--why mess with decimal points if you don't have to? <br /><br />The park factors used to adjust player stats here are run-based. Thus, they make no effort to project what a player "would have done" in a neutral park, or account for the difference effects parks have on specific events (walks, home runs, BA) or types of players. They simply account for the difference in run environment that is caused by the park (as best I can measure it). As such, they don't evaluate a player within the actual run context of his team's games; they attempt to restate the player's performance as an equivalent performance in a neutral park.<br /><br />I suppose I should also justify the use of sqrt(PF) for adjusting component statistics. The classic defense given for this approach relies on basic Runs Created--runs are proportional to OBA*SLG, and OBA*SLG/PF = OBA/sqrt(PF)*SLG/sqrt(PF). While RC may be an antiquated tool, you will find that the square root adjustment is fairly compatible with linear weights or Base Runs as well. I am not going to take the space to demonstrate this claim here, but I will some time in the future. <br /><br />Many value figures published around the sabersphere adjust for the difference in quality level between the AL and NL. I don't, but this is a thorny area where there is no right or wrong answer as far as I'm concerned. I also do not make an adjustment in the league averages for the fact that the overall NL averages include pitcher batting and the AL does not (not quite true in the era of interleague play, but you get my drift). <br /><br />The difference between the leagues may not be precisely calculable, and it certainly is not constant, but it is real. If the average player in the AL is better than the average player in the NL, it is perfectly reasonable to expect the average AL player to have more RAR than the average NL player, and that will not happen without some type of adjustment. On the other hand, if you are only interested in evaluating a player relative to his own league, such an adjustment is not necessarily welcome.<br /><br />The league argument only applies cleanly to metrics baselined to average. Since replacement level compares the given player to a theoretical player that can be acquired on the cheap, the same pool of potential replacement players should by definition be available to the teams of each league. One could argue that if the two leagues don't have equal talent at the major league level, they might not have equal access to replacement level talent--except such an argument is at odds with the notion that replacement level represents talent that is truly "freely available".<br /><br />So it's hard to justify the approach I take, which is to set replacement level relative to the average runs scored in each league, with no adjustment for the difference in the leagues. The best justification is that it's simple and it treats each league as its own universe, even if in reality they are connected.<br /><br />The replacement levels I have used here are very much in line with the values used by other sabermetricians. This is based both on my own "research", my interpretation of other's people research, and a desire to not stray from consensus and make the values unhelpful to the majority of people who may encounter them.<br /><br />Replacement level is certainly not settled science. There is always going to be room to disagree on what the baseline should be. Even if you agree it should be "replacement level", any estimate of where it should be set is just that--an estimate. Average is clean and fairly straightforward, even if its utility is questionable; replacement level is inherently messy. So I offer the average baseline as well.<br /><br />For position players, replacement level is set at 73% of the positional average RG (since there's a history of discussing replacement level in terms of winning percentages, this is roughly equivalent to .350). For starting pitchers, it is set at 128% of the league average RA (.380), and for relievers it is set at 111% (.450). <br /><br />I am still using an analytical structure that makes the comparison to replacement level for a position player by applying it to his hitting statistics. This is the approach taken by Keith Woolner in VORP (and some other earlier replacement level implementations), but the newer metrics (among them Rally and Fangraphs' WAR) handle replacement level by subtracting a set number of runs from the player's total runs above average in a number of different areas (batting, fielding, baserunning, positional value, etc.), which for lack of a better term I will call the subtraction approach.<br /><br />The offensive positional adjustment makes the inherent assumption that the average player at each position is equally valuable. I think that this is close to being true, but it is not quite true. The ideal approach would be to use a defensive positional adjustment, since the real difference between a first baseman and a shortstop is their defensive value. When you bat, all runs count the same, whether you create them as a first baseman or as a shortstop. <br /><br />That being said, using "replacement hitter at position" does not cause too many distortions. It is not theoretically correct, but it is practically powerful. For one thing, most players, even those at key defensive positions, are chosen first and foremost for their offense. Empirical research by Keith Woolner has shown that the replacement level hitting performance is about the same for every position, relative to the positional average.<br /><br />Figuring what the defensive positional adjustment should be, though, is easier said than done. Therefore, I use the offensive positional adjustment. So if you want to criticize that choice, or criticize the numbers that result, be my guest. But do not claim that I am holding this up as the correct analytical structure. I am holding it up as the most simple and straightforward structure that conforms to reality reasonably well, and because while the numbers may be flawed, they are at least based on an objective formula that I can figure myself. If you feel comfortable with some other assumptions, please feel free to ignore mine.<br /><br />That still does not justify the use of HRAR--hitting runs above replacement--which compares each hitter, regardless of position, to 73% of the league average. Basically, this is just a way to give an overall measure of offensive production without regard for position with a low baseline. It doesn't have any real baseball meaning. <br /><br />A player who creates runs at 90% of the league average could be above-average (if he's a shortstop or catcher, or a great fielder at a less important fielding position), or sub-replacement level (DHs that create 3.5 runs per game are not valuable properties). Every player is chosen because his total value, both hitting and fielding, is sufficient to justify his inclusion on the team. HRAR fails even if you try to justify it with a thought experiment about a world in which defense doesn't matter, because in that case the absolute replacement level (in terms of RG, without accounting for the league average) would be much higher than it is currently. <br /><br />The specific positional adjustments I use are based on 2002-2011 data. I stick with them because I have not seen compelling evidence of a change in the degree of difficulty or scarcity between the positions between now and then, and because I think they are fairly reasonable. The positions for which they diverge the most from the defensive position adjustments in common use are 2B, 3B, and CF. Second base is considered a premium position by the offensive PADJ (.97), while third base and center field have similar adjustments in the opposite direction (1.03 and 1.02).<br /><br />Another flaw is that the PADJ is applied to the overall league average RG, which is artificially low for the NL because of pitcher's batting. When using the actual league average runs/game, it's tough to just remove pitchers--any adjustment would be an estimate. If you use the league total of runs created instead, it is a much easier fix.<br /><br />One other note on this topic is that since the offensive PADJ is a stand-in for average defensive value by position, ideally it would be applied by tying it to defensive playing time. I have done it by outs, though.<br /><br />The reason I have taken this flawed path is because 1) it ties the position adjustment directly into the RAR formula rather than leaving it as something to subtract on the outside and more importantly 2) there’s no straightforward way to do it. The best would be to use defensive innings--set the full-time player to X defensive innings, figure how Derek Jeter’s innings compared to X, and adjust his PADJ accordingly. Games in the field or games played are dicey because they can cause distortion for defensive replacements. Plate Appearances avoid the problem that outs have of being highly related to player quality, but they still carry the illogic of basing it on offensive playing time. And of course the differences here are going to be fairly small (a few runs). That is not to say that this way is preferable, but it’s not horrible either, at least as far as I can tell.<br /><br />To compare this approach to the subtraction approach, start by assuming that a replacement level shortstop would create .86*.73*4.5 = 2.825 RG (or would perform at an overall level of equivalent value to being an average fielder at shortstop while creating 2.825 runs per game). Suppose that we are comparing two shortstops, each of whom compiled 600 PA and played an equal number of defensive games and innings (and thus would have the same positional adjustment using the subtraction approach). Alpha made 380 outs and Bravo made 410 outs, and each ranked as dead-on average in the field.<br /><br />The difference in overall RAR between the two using the subtraction approach would be equal to the difference between their offensive RAA compared to the league average. Assuming the league average is 4.5 runs, and that both Alpha and Bravo created 75 runs, their offensive RAAs are:<br /><br />Alpha = (75*25.5/380 - 4.5)*380/25.5 = +7.94<br /><br />Similarly, Bravo is at +2.65, and so the difference between them will be 5.29 RAR.<br /><br />Using the flawed approach, Alpha's RAR will be:<br /><br />(75*25.5/380 - 4.5*.73*.86)*380/25.5 = +32.90<br /><br />Bravo's RAR will be +29.58, a difference of 3.32 RAR, which is two runs off of the difference using the subtraction approach.<br /><br />The downside to using PA is that you really need to consider park effects if you do, whereas outs allow you to sidestep park effects. Outs are constant; plate appearances are linked to OBA. Thus, they not only depend on the offensive context (including park factor), but also on the quality of one's team. Of course, attempting to adjust for team PA differences opens a huge can of worms which is not really relevant; for now, the point is that using outs for individual players causes distortions, sometimes trivial and sometimes bothersome, but almost always makes one's life easier.<br /><br />I do not include fielding (or baserunning outside of steals, although that is a trivial consideration in comparison) in the RAR figures--they cover offense and positional value only). This in no way means that I do not believe that fielding is an important consideration in player evaluation. However, two of the key principles of these stat reports are 1) not incorporating any data that is not readily available and 2) not simply including other people's results (of course I borrow heavily from other people's methods, but only adapting methodology that I can apply myself).<br /><br />Any fielding metric worth its salt will fail to meet either criterion--they use zone data or play-by-play data which I do not have easy access to. I do not have a fielding metric that I have stapled together myself, and so I would have to simply lift other analysts' figures. <br /><br />Setting the practical reason for not including fielding aside, I do have some reservations about lumping fielding and hitting value together in one number because of the obvious differences in reliability between offensive and fielding metrics. In theory, they absolutely should be put together. But in practice, I believe it would be better to regress the fielding metric to a point at which it would be roughly equivalent in reliability to the offensive metric.<br /><br />Offensive metrics have error bars associated with them, too, of course, and in evaluating a single season's value, I don't care about the vagaries that we often lump together as "luck". Still, there are errors in our assessment of linear weight values and players that collect an unusual proportion of infield hits or hits to the left side, errors in estimation of park factor, and any number of other factors that make their events more or less valuable than an average event of that type. <br /><br />Fielding metrics offer up all of that and more, as we cannot be nearly as certain of true successes and failures as we are when analyzing offense. Recent investigations, particularly by Colin Wyers, have raised even more questions about the level of uncertainty. So, even if I was including a fielding value, my approach would be to assume that the offensive value was 100% reliable (which it isn't), and regress the fielding metric relative to that (so if the offensive metric was actually 70% reliable, and the fielding metric 40% reliable, I'd treat the fielding metric as .4/.7 = 57% reliable when tacking it on, to illustrate with a simplified and completely made up example presuming that one could have a precise estimate of nebulous "reliability").<br /><br />Given the inherent assumption of the offensive PADJ that all positions are equally valuable, once RAR has been figured for a player, fielding value can be accounted for by adding on his runs above average relative to a player at his own position. If there is a shortstop that is -2 runs defensively versus an average shortstop, he is without a doubt a plus defensive player, and a more valuable defensive player than a first baseman who was +1 run better than an average first baseman. Regardless, since it was implicitly assumed that they are both average defensively for their position when RAR was calculated, the shortstop will see his value docked two runs. This DOES NOT MEAN that the shortstop has been penalized for his defense. The whole process of accounting for positional differences, going from hitting RAR to positional RAR, has benefited him.<br /><br />I've found that there is often confusion about the treatment of first baseman and designated hitters in my PADJ methodology, since I consider DHs as in the same pool as first baseman. The fact of the matter is that first baseman outhit DH. There are any number of potential explanations for this; DHs are often old or injured, players hit worse when DHing than they do when playing the field, etc. This actually helps first baseman, since the DHs drag the average production of the pool down, thus resulting in a lower replacement level than I would get if I considered first baseman alone.<br /><br />However, this method does assume that a 1B and a DH have equal defensive value. Obviously, a DH has no defensive value. What I advocate to correct this is to treat a DH as a bad defensive first baseman, and thus knock another five or so runs off of his RAR for a full-time player. I do not incorporate this into the published numbers, but you should keep it in mind. However, there is no need to adjust the figures for first baseman upwards --the only necessary adjustment is to take the DHs down a notch. <br /><br />Finally, I consider each player at his primary defensive position (defined as where he appears in the most games), and do not weight the PADJ by playing time. This does shortchange a player like Ben Zobrist (who saw significant time at a tougher position than his primary position), and unduly boost a player like Buster Posey (who logged a lot of games at a much easier position than his primary position). For most players, though, it doesn't matter much. I find it preferable to make manual adjustments for the unusual cases rather than add another layer of complexity to the whole endeavor.<br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTx0u-bQq7GnOtN5unnamnLvZC1HStFfdC6d_AVKlCmJs6FOdTwUW38UKV-HSH8snOsKLC2DLN9xLzh/pub?output=html">2016 League</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vThHXXja4xS09RQU0uiE4tVqFrmLaTQtWdruQFTOGFHLWAExR3qYqSkaPJHdxLcRUuWENO9sGp3SWFY/pub?output=html">2016 Park Factors</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vRX5dvFQC9StbBGY0BSlWB_1Qm5o_4ymSLlH08G6s07Gdk1NEgS24pvx2GQdas2btNpCOx9bxWiR9Xm/pub?output=html">2016 Team</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vR3m7ngJuypTCPI4tK29sNBF2yaClQ6_VFzXvN_Kn-y1IA0mRVwoyADMLjsw80E5slxWbPkY_mzcQDi/pub?output=html">2016 Team Offense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQDOlHF5ngXGQbgm0MM8E-aSR-nop9YvvjKCvqgtB6AQnnFhC5U-DxBvfmHw6KLxFKEWbdnbaU5-j-N/pub?output=html">2016 Team Defense</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQv-CQK53k1TDpb9s7zh8gnaOp1UGdksziO2a4NBN8tlVVC8PbXn1j0ZJtJTcsuXCOJtm4_8YMGPK20/pub?output=html">2016 AL Relievers</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQMOXnt5pCacy1GyXF6G2tNO6wMPD6LvbKn8MjwDecGT6vt6XVlcHS7X6jL6wjW16FuvsZX_qjHebtu/pub?output=html">2016 NL Relievers</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTkzqnrl6w5MUZcV2EaIa_JwG9ls3VrgKstseaUiETHeLEXYeGnf83Ch1czIbXb9Tdbz80FBeD-zEe7/pub?output=html">2016 AL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vT_E8TdNPucO6h4G0AJ0jGUYtdGscb-GWFOdg8ccKOVqnqSE2QAK8-TGRhF3CKOpHItWL8Uqog2QKXH/pub?output=html">2016 NL Starters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vTkkqgGoKrhCbfx6znCXdD-UCeuutewHrPsM1LRBrX10kY-EYbYDasgydP2w10NkX1-wp9zNB1C-Hi3/pub?output=html">2016 AL Hitters</a><br /><br /><a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQRjjuduaroa8t2NWa-RCVvChODXV3WXGwQ_q3JuWxGxy30WRPQw4G8DJrfGSetqRdyDNS23Bn6vvmp/pub?output=html">2016 NL Hitters</a>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com5tag:blogger.com,1999:blog-12133335.post-58207053178455302912016-10-03T18:58:00.000-04:002016-10-03T18:58:06.541-04:00Crude Playoff Odds--2016These are very simple playoff odds, based on my <a href="http://walksaber.blogspot.com/2016/01/crude-team-ratings-2015.html">crude rating system</a> for teams using an equal mix of W%, EW% (based on R/RA), PW% (based on RC/RCA), and 69 games of .500. They account for home field advantage by assuming a .500 team wins 54.2% of home games (major league average 2006-2015). They assume that a team's inherent strength is constant from game-to-game. They do not generally account for any number of factors that you would actually want to account for if you were serious about this, including but not limited to injuries, the current construction of the team rather than the aggregate seasonal performance, pitching rotations, estimated true talent of the players, etc.<br /><br />I say “generally” since this year, the team I am a fan of (Cleveland) lost two key starting pitchers, and I wanted to account for that in the ratings. While other teams have injuries of note as well, I did not consider those. This approach is basically being as conservative as reasonably possible in estimating the Indians strength. Using a runs allowed approach (and not adjusting for bullpen support and park factor because I haven’t had time to dig into the numbers yet) Carlos Carrasco and Danny Salazar combined for about 5.9 WAR, which over 161 games is a .037 hit to the Indians’ W%. Of course, the real impact is not necessarily equal to the WAR impact; generic replacements don’t apply and the impact of starting pitchers in the playoffs can be muted. Still, this adjustment is better than nothing. I should also note that not park adjusting is mildly conservative since Cleveland tends to be a pitchers park.<br /><br />Knocking .037 points off of Cleveland’s three W% metrics, the resulting CTRs are:<br /><br /><a href="https://3.bp.blogspot.com/-HfC0lNWx4F4/V_Lh-zwURWI/AAAAAAAACSw/gGpKk9Mj9w4pZBVf76aBJM6PR5Y1eWyoACLcB/s1600/podds16a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-HfC0lNWx4F4/V_Lh-zwURWI/AAAAAAAACSw/gGpKk9Mj9w4pZBVf76aBJM6PR5Y1eWyoACLcB/s400/podds16a.jpg" width="400" height="392" /></a><br /><br />One thing to note here is just how good Boston is assumed to be; they were excellent in the W% estimators. The Cubs were even better in each of those metrics their 103 wins would suggest, but the Red Sox close the gap on strength of schedule, 104 to the Cubs’ 93 (implying that Boston’s average opponent would have a .528 W% against Chicago’s average opponent). With the injury adjustment the Indians are the weakest team on paper, but not so much so that they have significantly lower odds (last year, the Mets at 104 were the lowest-rated team and we know how that worked out).<br /><br />Wildcard odds are the least useful, since it is the round where pitching matchup has the biggest effect:<br /><br /><a href="https://4.bp.blogspot.com/-76t18ErSxC4/V_LiFOLEKII/AAAAAAAACS0/G3qrLzW_Pj4_TBVtBsjjL8ZKtxqSyOHaACLcB/s1600/podds16b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-76t18ErSxC4/V_LiFOLEKII/AAAAAAAACS0/G3qrLzW_Pj4_TBVtBsjjL8ZKtxqSyOHaACLcB/s400/podds16b.jpg" width="400" height="79" /></a><br /><br />Since we’re assuming the home team wins 54.2%, there’s very little difference in assumed strength in these two matchups (of course, the Mets suffer from even more extreme pitching maladies than do the Indians).<br /><br />In the charts that follow, “P” is the probability that the series occurs; P(H win) is the probability that the home team wins should the series occur; and P(H) is the probability that the series occurs and that the home team wins [P*P(H win)].<br /><br />LDS:<br /><br /><a href="https://3.bp.blogspot.com/-TUtFAh_O7EQ/V_LiJaw48JI/AAAAAAAACS4/0fs1GEu-V0kb1U6-tlTVGlQhTdoAEB9kACLcB/s1600/podds16c.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-TUtFAh_O7EQ/V_LiJaw48JI/AAAAAAAACS4/0fs1GEu-V0kb1U6-tlTVGlQhTdoAEB9kACLcB/s400/podds16c.jpg" width="400" height="107" /></a><br /><br />My guess, based on no calculations but including my inherent knowledge of the team’s statistical records and characteristics, was that Cleveland would have a 45% chance against Boston. So strike one for homerism there. Texas/wildcard figures will be the closest DS matchup on paper, although I’m most eager to see WAS/LA (other than the Indians, of course).<br /><br />LCS:<br /><br /><a href="https://4.bp.blogspot.com/-87vihVjNJs0/V_LiNbf4m6I/AAAAAAAACS8/2cMb9ROzrlQH5R75UnnCrj4YtPkhIU_SACLcB/s1600/podds16d.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-87vihVjNJs0/V_LiNbf4m6I/AAAAAAAACS8/2cMb9ROzrlQH5R75UnnCrj4YtPkhIU_SACLcB/s400/podds16d.jpg" width="400" height="197" /></a><br /><br />You’ll note that the Cubs have a higher probability against stronger teams than they do in the NLDS thanks to the extra games. Cubs/Dodgers is the most lopsided potential LCS, while Dodgers/Mets is the closest.<br /><br />World Series:<br /><br /><a href="https://3.bp.blogspot.com/-z2wnlByqHWU/V_LiToIIsLI/AAAAAAAACTA/-xSHUQ7WlA8fjlO8UDRM7QSljXF529CkwCLcB/s1600/podds16e.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-z2wnlByqHWU/V_LiToIIsLI/AAAAAAAACTA/-xSHUQ7WlA8fjlO8UDRM7QSljXF529CkwCLcB/s400/podds16e.jpg" width="400" height="395" /></a><br /><br />The AL is favored in 13 of the 25 possible matchups, but 13 of 20 that don’t involve Chicago. It doesn’t help the stronger circuit that it’s two highest seeds have the two lowest CTRs in the field.<br /><br />Putting it all together:<br /><br /><a href="https://4.bp.blogspot.com/-zSRNBbfqFhI/V_LiXSFwcwI/AAAAAAAACTE/KkFsVEin6qMVXWCqJQOa9dVrXt7voyaQACLcB/s1600/podds16f.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-zSRNBbfqFhI/V_LiXSFwcwI/AAAAAAAACTE/KkFsVEin6qMVXWCqJQOa9dVrXt7voyaQACLcB/s400/podds16f.jpg" width="400" height="233" /></a><br /><br />This gives the NL a 51.1% chance to win, a 84% chance of an outcome I like, a 79% chance of an outcome I really like, and a 7.9% chance of an outcome that would be the best thing that’s ever happened in baseball. Plus a 100% of being a better outcome than 2015.phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-84746637124777206112016-07-28T23:21:00.000-04:002016-07-28T23:21:18.457-04:00Great Moments in CBSSports Box Scores<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-h0Le3a2xvDQ/V5rLoQz1jJI/AAAAAAAACSc/NxNkzbUGrxoi66YiZWgt_4Jhu7C2188QgCLcB/s1600/cbs1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-h0Le3a2xvDQ/V5rLoQz1jJI/AAAAAAAACSc/NxNkzbUGrxoi66YiZWgt_4Jhu7C2188QgCLcB/s400/cbs1.jpg" width="400" height="91" /></a></div>phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0tag:blogger.com,1999:blog-12133335.post-18729486958101539202016-07-26T07:51:00.000-04:002016-07-26T07:51:02.528-04:00The Willie Davis Method and OPS+ Park FactorsThis post is going to lay out the math necessary to apply the so-called "Willie Davis method" of Bill James to his Runs Created and to Base Runs. The last three posts have explained how you can use it with Linear Weights. This is offered in the interest of comprehensiveness, should you decide that you’d like to fiddle with this stuff yourself. <br /><br />The Willie Davis method as explained by Bill James is based on the most basic RC formula, (H + W)*TB/(AB + W). You could use one of the technical RC versions too, of course, but then you would introduce the problem of what to do with all of the ancillary categories that are included in those versions. A minor modification that would help matters is to give a weight to walks in the B factor (which is simply TB in the basic version), but James has never done that as it would complicate the basic version and mess up all of the neat little RC properties like OBA*SLG*AB = runs. <br /><br />While I tried to emphasize that I wouldn’t take any of the results from the linear weight translations too seriously, the output of the Willie Davis method is actually used by Sean Forman to calculate OPS+ at baseball-reference.com. So while James used it in the vein that I advocate, Forman uses it to park-adjust the most-looked at total offensive statistic at his site. For this reason, I’ll compare park-adjusted OPS+ figured by his method to what I would do later in the post.<br /><br />To apply the Willie Davis method to RC, first define a = 1 + W/H, b = TB/H, and outs as AB-H. You also need to calculate New RC, which I will abbreviate as N. That is just regular RC times the adjustment factor you are using (in a park case, if the PF is 1.05 then N is RC*1.05). Then this relationship holds:<br /><br />N = (a*H)*(b*H)/(a*H + Outs)<br /><br />This can be manipulated into a quadratic equation:<br /><br />abH^2 - NaH - N*Outs = 0<br /><br />And then we can use the quadratic equation to solve for H, which we’ll call H’:<br /><br />H' = (Na + sqrt((Na)^2 + 4ab(N*Outs)))/(2ab)<br /><br />The adjustment factor for all of the basic components (S, D, T, HR, W with outs staying fixed) is simply H'/H. So we multiply the positive events by H'/H and the result is a translated batting line.<br /><br />Since we have applied this type of approach to RC and LW, we might as well do it for Base Runs as well. Allow me to start with this particular BsR equation, published some time ago by David Smyth:<br /><br />A = S + D + T + W<br />B = .78S + 2.34D + 3.9T + 2.34HR + .039W<br />C = AB - H = outs<br />D = HR<br /><br />BsR is of course A*B/(B + C) + D, and New BsR (N) is BsR*adjustment factor. To write everything in terms of singles, let’s define a, b, and c (of course, I didn’t realize until after I wrote this that a, b, and c are terrible abbreviations in this case, but I already had them in my spreadsheet and it would have been a real pain to change everything):<br /><br />a = (S + D + T + W)/S <br /><br />b = (.78S + 2.34D + 3.9T + 2.34HR + .039W)/S<br /><br />c = HR/S<br /><br />Then we need to solve for S' (the new number of singles) in this equation:<br /><br />aS'*bS'/(bS' + Outs) + cS' = N<br /><br />This results in a quadratic equation just as the RC approach does, and it can be solved:<br /><br />S' = (Nb - cOuts + sqrt((cOuts - Nb)^2 + 4(NOuts)(ab + bc)))/(2*(ab + bc))<br /><br />S'/S is then the multiplier for all of the positive events.<br /><br />So we have three different approaches based on three different run estimators to accomplish the same task. Which one should be used? Unfortunately, there’s no good empirical way to test these approaches; the entire point of having them is to make estimates of equivalent value under different conditions…i.e. conditions that did not occur in reality.<br /><br />However, I think it should be self-evident that the quality of the model from which the estimate is derived says a lot about its value. I don’t need to beat that horse again, but it is well-known that Basic RC is not a very good estimator when applied to individuals, which is exactly what we are doing here.<br /><br />It would also follow that the Linear Weights-based approach should be marginally better than the Base Runs-based approach since BsR should not be applied directly to individuals. Since BsR is better constructed than RC, though, the discrepancies shouldn’t be as bothersome.<br /><br />I am going to use the three approaches to derive park-adjusted BA, OBA, and SLG for the 1995 Rockies. In all of the calculations, I am using a 1.23 park factor for Coors Field. The unshaded columns are the players’ raw, unadjusted numbers; the pink columns are adjusted by the RC approach, orange by the ERP approach, and yellow by the BsR approach:<br /><br /><a href="https://1.bp.blogspot.com/-Ron6elJXZHE/V2MzhqCBxiI/AAAAAAAACRw/ahq6HNkzoV4krhq-4Ux8pu12omKtIoYpwCLcB/s1600/post4a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-Ron6elJXZHE/V2MzhqCBxiI/AAAAAAAACRw/ahq6HNkzoV4krhq-4Ux8pu12omKtIoYpwCLcB/s400/post4a.jpg" /></a><br /><br />From eyeballing the numbers, I’d say that there is a strong degree of agreement between the ERP and BsR estimates, with the RC estimates as the outliers. As mentioned above, this is along the lines of what I would have expected to see, as both ERP and BsR are better models of the run scoring process than RC. That the ERP and BsR results are close should not come as a surprise, as both estimators give similar weight to each event.<br /><br />Using RC results in a less severe park adjustment for most players. Why is this? My guess is that it is because RC, with it’s well-known flaw of overvaluing high-end performance, naturally needs to draw down the player’s OBA and SLG less then ERP or BsR to still maintain a high performance. In other words, RC overestimates Larry Walker’s run contribution to begin with, and since the problem only gets worse as OBA and SLG increase, it doesn’t take that that big of a change in OBA or SLG to reduce run value by X%.<br /><br />As I mentioned earlier, I think it is worth looking at the Willie Davis method closely since some sources (particularly Baseball-Reference) use it for serious things like park-adjusting OPS+. This is in contrast to the position of its creator, Bill James, who presented it more as a toy that yields a rough estimate of what an equal value performance would look like in a different environment.<br /><br />So, here are the OPS+ figures for the 1995 Rockies figured seven different ways. Let me note off the bat that I am using OBA = (H + W)/(AB + W); for this reason and the fact that I am using my own Coors PF, we should not anticipate exact agreement between these OPS+ results and the ones on Baseball-Reference. The league OBA in the 1995 NL was .328, and SLG was .408, so the basic formula for OPS+ is:<br /><br />OPS+ = 100*(OBA/.328 + SLG/.408 - 1)<br /><br />The first column of the table, "unadj" uses the player’s raw stats with no park adjustment. The second column, "trad", reflects the traditional method of figuring OPS+ used by Pete Palmer in <u>The Hidden Game of Baseball</u>, <u>Total Baseball</u>, and the <u>ESPN Baseball Encyclopedia</u>: simply divide OPS+ by the runs park factor (1.23) in this case.<br /><br />The third column, "sqrt", adjusts OBA and SLG separately by dividing each by the square root of park factor, and uses these adjusted figures in the OPS+ formula above (*). The fourth column, "reg", uses the runs factor to estimate an OPS+ park factor based on a regression equation that relates OPS+ to adjusted runs/out (this is covered in the digression as well).<br /><br />Finally there are three shaded columns, which use the translated OBA and SLG results from RC, ERP, and BsR respectively as the inputs into the OPS+ equations:<br /><br /><a href="https://4.bp.blogspot.com/-yAbIILRkK9U/V2Mz2iJ6S0I/AAAAAAAACR4/YOz_XSlcqo45EqYr-uXT4CPYYmzyRbcDACLcB/s1600/post4b.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-yAbIILRkK9U/V2Mz2iJ6S0I/AAAAAAAACR4/YOz_XSlcqo45EqYr-uXT4CPYYmzyRbcDACLcB/s400/post4b.jpg" /></a><br /><br />What can we see from this? The traditional approach is more severe than any of the Willie Davis approaches, while the square root approach is a pretty good match for the Willie Davis approaches. Thus, I suggest that the best combination of ease and accuracy in calculating OPS+ is to divide OBA and SLG by the square root of park factor, then plug the adjusted OBA and SLG into the OPS+ equation.<br /><br />Of course, I should point out that 1995 Coors Field and its 1.23 park factor is one of the most extreme cases in the history of the game. For run of the mill environments, we should expect to see little difference regardless of how the park adjustments are applied, and so I am NOT saying that you should disregard the OPS+ figures on Baseball-Reference (although I do wish that OPS+ would be pushed aside in favor of better comprehensive rate stats). On the other hand, though, I see no reason to use a complicated park adjustment method like the Wille Davis approach when there are much easier approaches which we have some reason to believe better reflect true value.<br /><br />(*) I shunted some topics down here into a digression because it covers a lot of ground that I’ve covered before and is even drier than what is above. And a lot of sabermetricians are sick and tired of talking about OPS, and I don’t blame them, so just skip this part if you don’t want to rehash it.<br /><br />As I’ve explained <a href="http://walksaber.blogspot.com/2008/01/beating-dead-horse-pt-1.html">before</a>, OPS+ can be thought of as a quick approximation of runs/out. Some novice sabermetricians are surprised when they discover that OPS+ is adjusted OBA plus adjusted SLG minus one rather than OPS divided by league OPS. And it’s true that the name OPS+ can be misleading, but it is also true that it is a much better metric. One reason is that OPS/LgOPS does not have a 1:1 relationship with runs/out; it has a 2:1 relationship. If a team is 5% above the league average in OPS, your best guess is that they will score 10% more runs. So the OPS/LgOPS ratio has no inherent meaning; to convert it to an estimated unit, you would have to multiply by two and subtract one.<br /><br />The other reason why OPS+ is superior is that it gives a higher weight to OBA. It doesn’t go far enough--the OBA weight should be something like 1.7 (assuming SLG is weighted at 1), while OPS+ only brings it up to around 1.2--insufficient, but still better than nothing.<br /><br />Anyway, if you run a regression to estimate adjusted runs/out from OPS+, you find that it’s pretty close to a 1:1 relationship, particularly if you include HB in your OBA. I haven’t though, and so the relationship is something like 1.06(OPS+) - .06 = adjusted runs/out (again, it should be very close to 1:1 if you calculate OPS+ like a non-lazy person). The "reg" park adjustment, then, is to substitute the park factor for adjusted runs/out and solve for OPS+, giving an OPS+ park factor:<br /><br />OPS+ park factor = (runs park factor + .06)/1.06<br /><br />The slope of the line relating OPS+ to runs/out is not particularly steep, and so this is an almost negligible adjustment--for Coors Field and its 1.23 run park factor, we get a 1.217 OPS+ park factor.<br /><br />Now a word about the traditional runs factor v. the individual square root adjustments. Since OPS+ is being used as a stand-in for run creation relative to the league average, I would assume that the goal in choosing a park adjustment approach is to provide the best match between adjusted OPS+ and adjusted runs/out. It turns out that if you figure relative ERP/Out for the ’95 Rockies players, the results are fairly consistent with the ERP/BsR translated OPS+. Thus, I am going to assume that those are the “best” adjusted OPS+ results, and that any simple park adjustment approach should hope to approximate them.<br /><br />As a consequence, the square root adjustments to OBA and SLG look the best. Why is this? I’m not exactly sure; one might think that since OPS+ is a stand-in for relative runs/out, we should expect that the best adjustment approach once we already have unadjusted OPS+ is to divide by park factor. Yet we can get better results by adjusting each component individually by the square root of PF. OPS+ is far from a perfect approximation of relative runs/out, though, so it may not be that surprising that applying OPS+ logic to park factors is not quite optimal either.<br /><br />Interestingly, the justification for the square root adjustment can be seen by looking at Runs Created in its OBA*SLG form. While OBA*SLG gives you an estimate of runs/at bat, not runs/out, it is of course related. If you take OBA/sqrt(PF)*SLG/sqrt(PF) you get OBA*SLG/(sqrt(PF)*sqrt(PF)) = OBA*SLG/PF<br /><br />It is quite possible that there is a different power you could raise PF to that would provide a better match for our ERP-based OPS+ estimates, but getting any more in-depth would defeat the purpose of having a crude tool. In fact, I think that adjusting OPS+ by the Willie Davis method goes too far as well. Regardless, I would be remiss if I didn’t again emphasize that the 1995 Rockies are an extreme case, and so while the differences between the approaches may appear to be significant, they really aren’t 99% of the time.<br />phttp://www.blogger.com/profile/18057215403741682609noreply@blogger.com0