A Brief, Incomplete History of Replacement Level

Baseball Prospectus was kind enough to run a meta-sabermetric history piece written by me on the history of replacement level in sabermetric analysis. As you can imagine, it's not a topic that has generated a lot of responses, but the one person who has commented on the article so far seems to like it, and perhaps you will too.

End of Season Statistics 2012

The 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. The player spreadsheets are not ready yet, but I want to get the team stuff posted.

The data comes from a number of different sources. Most of the basic data comes from Doug's Stats, which is a very handy site, or Baseball-Reference. KJOK's park database provided some of the data used in the park factors, but for recent seasons park data comes from B-R. Data on pitcher's batted ball types allowed, doubles/triples allowed, and inherited/bequeathed runners comes from Baseball Prospectus.

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.

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.

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.

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.

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.

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:

A = H + W - HR - CS
B = (2TB - H - 4HR + .05W + 1.5SB)*.76
C = AB - H
D = HR
Naturally, A*B/(B + C) + D.

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:

iPF = (H*T/(R*(T - 1) + H) + 1)/2
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+.

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%.

In the calculation of the PFs, I did not get picky and take out “home” games that were actually at neutral sites, like the Astros/Cubs series that was moved to Milwaukee in 2008. I have also reset the NYN park factor due to park modifications; only 2012 data for the Mets is being considered.

There are also Team Offense and Defense spreadsheets. These include the following categories:

Team offense: Plate Appearances, Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Secondary Average (SEC), Walks 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) and ISO = SLG - BA).

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.

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:

1) BMR--wild pitches and passed balls per 100 baserunners = (WP + PB)/(H + W - HR)*100

2) mFA--fielding average removing strikeouts and assists = (PO - K)/(PO - K + E)

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)

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).

For all of the player reports, ages are based on simply subtracting their year of birth from 2011. 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, for which case 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.

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).

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.

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.

* 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.

* 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.

The formula for eRA is:

A = H + W - HR
B = (2*TB - H - 4*HR + .05*W)*.78
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
eRA = (A*B/(B + C) + HR)*9/IP

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%.

Now everything has a common denominator of PA, so we can plug into Base Runs:

A = e%H + %W
B = (2*(z*e%H + 4*%HR) - e%H - 5*%HR + .05*%W)*.78
C = 1 - e%H - %W - %HR
cRA = (A*B/(B + C) + %HR)/C*a

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.

In the past couple years I’ve presented a couple of batted ball RA estimates. I’ve removed these this year, 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.

Instead, I’m showing strikeout and walk rate, both expressed as per game. By game I mean not 9 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.

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):

PA = K + (3*IP - K)*x + H + W
Where x = league average of (AB - H - K)/(3*IP - K)

Then KG = K*Lg(PA/G) and WG = W*Lg(PA/G).

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?

%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.

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 am using RRA as the building block for baselined value estimates for all pitchers this year. I explained RRA in this article , but the bottom line formulas are:

BRSV = BRS - BR*i*sqrt(PF)
IRSV = IR*i*sqrt(PF) - IRS
RRA = ((R - (BRSV + IRSV))*9/IP)/PF

The two baselined stats are Runs Above Average (RAA) and Runs Above Replacement (RAR). RAA uses the league average runs/game (N) for both starters and relievers, while RAR uses separate replacement levels for starters and relievers. Thus, RAA and RAR will be pretty close for relievers:

RAA = (N - RRA)*IP/9
RAR (relievers) = (1.11*N - RRA)*IP/9
RAR (starters) = (1.28*N - RRA)*IP/9

All players with 300 or more 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).

I do not bother to include hit batters, so take note of that for players who do get plunked a lot. Therefore, PA are simply AB + W. Outs are AB - H + CS. BA and SLG you know, but remember that without HB and SF, OBA is just (H + W)/(AB + W). Secondary Average = (TB - H + W)/AB = SLG - BA + (OBA - BA)/(1 - OBA). I have not included net steals as many people (and Bill James himself) do--it is solely hitting events.

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. 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.

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. Anyway, RC = (TB + .8H + W + .7SB - CS - .3AB)*.322.

RC is park adjusted by dividing by PF, making all of the value stats that follow park adjusted as well. RG, the 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).

I have decided to switch to a watered-down version of Bill James' Speed Score this year; I only use four of his categories. Previously I used my own knockoff version called Speed Unit, but trying to keep it from breaking down every few years was a wasted effort.

Speed Score is the average of four components, which I'll call a, b, c, and d:

a = ((SB + 3)/(SB + CS + 7) - .4)*20
b = sqrt((SB + CS)/(S + W))*14.3
c = ((R - HR)/(H + W - HR) - .1)*25
d = T/(AB - HR - K)*450

James actually uses a sliding scale for the triples component, but it strikes me as needlessly complex and so I've streamlined it. I also changed some of his division to mathematically equivalent multiplications.

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:

HRAA = (RG - N)*O/25.5
RAA = (RG - N*PADJ)*O/25.5
HRAR = (RG - .73*N)*O/25.5
RAR = (RG - .73*N*PADJ)*O/25.5

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 the last ten years, but finally have done an update. 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.

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.

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".

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.

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.

The good news is that the two approaches are essentially equivalent; in fact, they are 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:

RAA = (6.957 - 4.5)*350/25.5 = +33.72

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:

RAA = (8 - 5.175)*350/25.5 = +38.77

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:

WAA = 33.72/9 = +3.75
WAA = 38.77/10.35 = +3.75

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 2010 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?

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.

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.

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).

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.

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".

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.

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.

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.

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).

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.

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.

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 work by Keith Woolner has shown that the replacement level hitting performance is about the same for every position, relative to the positional average.

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.

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.

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 4 runs a 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.

The specific positional adjustments I use are based on 1992-2001 data. There's no particular reason for not updating them; at the time I started using them, they represented the ten most recent years. I have stuck 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 (.94), while third base and center field are both neutral (1.01 and 1.02).

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.

One other note on this topic is that since the offensive PADJ is a proxy 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.

The reason I have taken this flawed path is because 1) it ties the position adjustment directly into the RAR formula rather then 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.

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.

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:

Alpha = (75*25.5/380 - 4.5)*380/25.5 = +7.94

Similarly, Bravo is at +2.65, and so the difference between them will be 5.29 RAR.

Using the flawed approach, Alpha's RAR will be:

(75*25.5/380 - 4.5*.73*.86)*380/25.5 = +32.90

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.

The downside to using PA is that you really need to consider park effects if you, 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.

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 valuation. 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).

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.

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.

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.

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").

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.

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 is 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.

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 ten 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.

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 Joe Mauer (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.

2012 Leagues

2012 Park Factors

2012 Teams

2012 Team Offense

2012 Team Defense

2012 AL Relievers

2012 NL Relievers

2012 AL Starters

2012 NL Starters

2012 AL Hitters

2012 NL Hitters

Playoff Meanderings

* I always like to write a little something about playoff odds. The playoff odds that I publish are not intended to be the most accurate. They incorporate only full seasonal team data, haphazardly thrown into a weighted average. They assume that win probabilities are constant from game to game. There are other nits I could pick, but those are the huge ones.

So why bother? The main goal is to once again make the point that attempting to predict playoff outcomes is largely a fool’s errand. This is probably an obvious point to anyone who reads this blog, but it is one that I feel compelled to come back to each October regardless.

The methodology here was to use my crude team ratings--based on estimated win ratio and adjusted for strength of schedule. I figured three sets of these--based on actual wins and losses, based on runs scored and allowed, and based on runs created and allowed. Then I combined them and built-in some regression to the mean, with no real rhyme or reason to the weighting (the win ratios fed into the rating are based 30% on actual record, 30% on R/RA, 20% on RC/RCA, and 20% on .500).

These then go into this spreadsheet, which calculates the probability of a team winning a playoff series using Log5 and an assumed home field winning percentage of .545 for a .500 team. First, here are the ratings for each of the playoff teams:



As you can see, the rating system still believes that the AL is superior to the NL (the overall AL rating is 106 versus 95 for the NL). Baltimore comes out better than I expected, and it is worth remembering that playing in the AL East means that their schedule was very tough (after the season, I’ll have a post with full rankings). You may be surprised to see Cincinnati so low, but they exceeded their expected W%s by a fair amount and along with St. Louis were the strongest teams in the weakest division, meaning they faced the easiest schedules in MLB.

Feeding those rankings through the playoff odds spreadsheet, here are the crude playoff probabilities:



I would suggest that Oakland and Washington are the teams that benefit the most from the crude nature of this approach. No team has much better than a 1 in 3 chance of winning the pennant, which is typical but completely out of line with the mainstream notions of anointing favorites. It should come as no surprise that the four wildcards rate as having the lowest odds, but it’s worth noting that the wildcards combined have a higher estimated probability of winning the World Series than the #3 seeds in each league.

Whichever team comes out of the wildcard game will be in decent shape, although as the media will remind you many times will be a bit disadvantaged in their starting pitching options for the Division Series. Here are each of the wildcard’s probabilities assuming they win the game (again, with no penalty for fatigue):



Collapse aside, Texas remains one of the strongest teams on paper. Atlanta compares favorably to Cincinnati or San Francisco, and both Baltimore and St. Louis have respectable chances (in fact, the Cards 8% is better than their 7% from a similar methodology last year).

* The 2-3 Division Series format is already being set up as a ready-made excuse for any of the higher seeded teams that lose. I’m not saying it’s the optimal format, but the importance of having the first two games at home can be overstated. Of course, the model I’m using here can’t account for any psychological effects, but there is no difference in the expected outcome of the series as long there are three home games scheduled.

Theoretically, assuming evenly matched teams in each game of a series, 37.5% of five-game series should go the distance and only 25% should be sweeps. But empirically, 41 five-game series since 1969 have been sweeps, while only 27 have gone the distance. Of course, those empirical results include teams that benefitted from jumping up 2-0 at home.

While the 2-3 format is not ideal, and offers the possibility of what I call a reverse home field advantage (the lower seeded team actually playing more home games), I don’t see any reason to accept it as an excuse. A couple of the higher seeded teams will probably lose, but that happens in typical seasons as well.

It’s also worth noting that a 2-3 format has been used before, most recently in 1995-96. In those two seasons, the cross-divisional matchups were pre-determined. In 1995 for example, the 100-44 Indians opened against the 86-58 Red Sox with two games at Jacobs Field and the final three games schedule for Fenway Park (Cleveland swept). Meanwhile, the 79-66 Mariners played the 79-65 Yankees. The 2-3 of 2012 may be a mild annoyance, but playoff formats have previously reached colossal levels of stupidity to which it can only aspire.

* For the last few years I have also expressed my playoff rooting preferences. There’s no reason why you should care, but it’s good to get it off my chest.

Would be happy if they win: Yankees, A’s, Reds, Nationals, Braves
Would be indifferent if they win: Rangers, Cardinals
Would be annoyed if they win: Orioles, Tigers, Giants

So expect a BAL/SF World Series (1.8% chance based on the crude odds).

Cleveland Manager Rant

I have considered myself a baseball fan first and a fan of any particular team for over a decade. I can’t pinpoint the exact moment at which this happened, but it’s been a while. I never regret this; college sports offer me plenty of opportunity for simple good v. evil, one team only fanaticism. I consider professional baseball too entertaining of a sport, one too amenable to rational analysis, to tie up much of my interest in a partisan stupor.

Still, I am a fan of the Indians, and I assume I will be until they move to Albuquerque in 2037. And so on Thursday evening, as I learned about Manny Acta’s firing, I vented a little bit on Twitter. The last time I had such a visceral reaction to a piece of Indians news, it was upon learning about the Ubaldo Jimenez trade.

The problem with being a fan first is that it makes one prone to that sort of off-the-cuff emotional reaction, whereas I’d much prefer to think for a while and then react. This is the more refined (albeit still tinted by the irrationality of fandom, poorly written and disjointed) version of that initial screed.

I always liked Manny Acta as the Indians manager. I supported his hiring, and I generally thought that he did a good job as manager from what I could tell. Of course, some of the most important duties of the manager are the things that, as an outsider, I cannot quantify and really can’t even get a good feel for--how he relates to players, how well he works with the front office and how he interacts with them on roster decisions, and the like. It’s certainly possible that Manny Acta is bad at these aspects of the job.

However, I reject the notion pushed by a contingent of Cleveland fans that Acta is a poor tactical manager from a sabermetric tactic. Again, this is an area that’s next to impossible to quantify--it's easy to pick some key categories on which managers have influence (like intentional walks, sacrifice hits, stolen base attempts, pitching changes, lineup construction) and mentally assign the manager a score based on rudimentary criteria (“intentional walks = bad”, “games led off by sub-.330 OBA hitters = bad”, etc.), but it’s difficult to develop a comprehensive evaluation even on these limited criteria. This is all complicated by the fact that some of our sabermetric tools have a margin of error comparable to the theoretical payoffs of alternative strategies, and that the manager always is working with more information than we have regarding the factors that could cause players’ abilities to deviate from our estimate of their true talent.

However, based on my general notion of baseball strategy and ability to process my observations, I have no overarching issues with the tactics employed by Manny Acta. Quite the opposite, in fact--I had less moments of confusion when watching Acta manage than I did with Mike Hargrove, Charlie Manuel, or Eric Wedge. Acta spoke intelligently about strategy in his media appearances and stayed true to his word as much as can be reasonably hoped for from a manager.

Of course, any manager is going to make isolated decisions that are puzzling. If cherry-picking just a few of these instances is enough to call for the skipper’s head, then I can guarantee you that it won’t take much more than a week into his replacement’s regime for a similar emotion to emerge. If you have to point to one specific choice in reliever usage, or one marginal young player that didn’t play enough for your taste, then I humbly suggest you don’t have much of a case. No, it doesn’t make sense to me either that Acta chose to use Vinny Rottino as a leadoff hitter (in one game!), but how many managers would have used Shin-Soo Choo as their leadoff hitters in over half of the team’s games? I’d suggest the latter is a much bigger deviation from the normal practice of managers, and one more amenable to sabermetric orthodoxy than the other is a departure.

In any event, Acta is gone now, making the more important question for Indians fans the matter of what this tells us about the people who run the organization. I don’t think it’s pretty. First, a quote from owner Larry Dolan:

“I fully support Chris' decision to make this change and am confident that he will lead a tireless search to find the right individual to lead the club to our ultimate goal of winning the World Series.”

Of course, this is typical owner-speak and reading into it is pointless. Still, the quote strongly implies that Dolan believes the single individual most responsible for winning the World Series is the manager. If the Indians could just find the right manager, they’d be fine.

Team president (and former GM, for the majority of Dolan’s ownership) Mark Shapiro tweeted:

“One of only levers u can pull w potential for broader change is the manager. Not easy but decision should indicate our desire to improve”

Left unsaid is what those levers are. And those levels have never been pulled. Since Dolan bought the team, the Indians have hired and fired three full-time managers: Charlie Manuel, Eric Wedge, and Manny Acta. They have fired zero general managers: Shapiro was promoted to president and his lieutenant Chris Antonetti took over after the 2010 season.

Manuel’s firing was a little different than those of Wedge and Acta--it came mid-season in the Indians first transition year between perennial contender and rebuilding. Manuel was not seen as a fit for the new paradigm, and so his attempt to force the issue by requesting an extension led to his dismissal.

Shapiro displayed a tremendous amount of loyalty to Wedge. It would have been easy to fire him after the failed attempt at contention in 2006, or the letdown on 2008 on the heels of 2007’s near pennant. But Shapiro stood by Wedge until after 2009, when a team that fancied itself a contender crashed and burned to 65-97.

The Indians’ fundamental problems, however, remain the same in 2012 when Acta was canned as they were in 2009 when Wedge was canned. The Indians possess a number of solid hitters at tough positions (Carlos Santana at catcher, Jason Kipnis at second, Asdrubal Cabrera at short), but gaping holes at the easiest positions (only Shin-Soo Choo was a good producer in the corners, and Travis Hafner’s perennial injuries have also held back the DHs). This is not a temporary problem--the Indians’ farm system has not produced a major league caliber 1B/LF since--Luke Scott? Sean Casey?

The Indians of 2009 and 2012 were also both woefully short on starting pitching. In 2009, the team had just traded CC Sabathia and Cliff Lee, so it was somewhat understandable. In 2012, though, those departures could not be blamed. The Indians ventured into 2012 with a rotation consisting of one pitcher who’d both pitched well and had good peripherals in the prior season (Justin Masterson). They had an enigmatic pitcher acquired at the cost of the organization’s top two pitching prospects (Ubaldo Jimenez); a veteran coming off a lousy season in the NL (Derek Lowe); a finesse righty who was below average in 2011 despite a league-leading 1.1 W/9 (Josh Tomlin); and a sinkerballer with an unremarkable minor league track record (Jeanmar Gomez).

The 2011 Indians started the season 30-15, which was a lot of fun at the time, even for those of us who suspected it was but a mirage. But those 45 games have ultimately proved to be a disaster for the franchise. They transformed what was supposed to be a rebuilding season into an increasingly desperate attempt to cling to the lead in the AL Central. They goaded the front office into trading its two best pitching prospects for Ubaldo Jimenez. And even after the team stumbled to 80-82, those 45 games influenced the team’s expectations heading into 2012: they were contenders.

Regardless of intention, the Indians were either unwilling or unable to acquire additional talent to fill out the roster, and insisted that there was sufficient talent to contend, leaving Acta as the fall guy if the purported contender failed to contend.

The Shapiro regime has controlled the Indians for eleven seasons, and in that time they have managed to make the playoffs just once while playing in one of MLB’s weaker divisions. Assuming that they should have a 20% chance of winning and seasons are independent, there’s a 26% chance that could happen by chance, so it’s not inherently damning.

When I tweeted something to that effect (minus the binomial probability), I got a reply that simply said “Process != Results”. I was unfamiliar with the tweeter, so I’m not sure if it was serious or facetious. I’m inclined to think it’s the latter, as it sounds very much like the kind of sentiment that is often offered by what could be called the Cameron school of sabermetrics.

There is of course a great deal of truth in the statement; a process can be valid and yet produce poor results through decisions made on the basis of incomplete information, unforeseen events, chance, and other factors. But that doesn’t mean that actual results can be ignored, particularly as the sample becomes larger.

Of course, it’s easier to rationalize poor results when the process is in line with one’s ideological leanings (this is true for me as well, of course). It wasn’t long ago that Chris Antonetti was the darling of the organizational rankings crowd.
Some people believe that they possess enough insight about front offices to make ordinal rankings of their quality. I am not one of them--all I can do is lay out the facts as I see them:

* The Indians can generally be classified in the upper tier of publically open to sabermetrics organizations, which is certainly a plus from where I sit

* Shapiro’s Indians have drafted poorly. The most recent Indians first rounder to establish a solid major league career is Jeremy Guthrie (2002). The most recent to have one with the Indians is CC Sabathia (1998). The jury is still out on several recent picks, although if Alex White or Drew Pomeranz is productive, it will be with another organization.

* The Indians have done a great job of trading for players either in the minors or very early in their major league careers. Cliff Lee, Grady Sizemore, Asdrubal Cabrera, Travis Hafner, Carlos Santana, Shin-Soo Choo, Michael Brantley, Chris Perez, Coco Crisp, and Justin Masterson are examples. But it’s much harder to find contributors drafted or signed by the Indians--Jhonny Peralta, Fausto Carmona, Jason Kipnis, Rafael Betancourt, Rafael Perez, Vinny Pestano? (Neither of these lists is comprehensive by any means, but I think thye are representative of the whole).

I don’t think that questioning the efficacy of the current organization at developing talent based on an eleven year fallow is excessively “results-oriented”.

With respect to the next managerial hire, I tend to think it won’t matter much. The organization will not win until it can develop more players, regardless of who is managing them. I’m hoping that Terry Francona’s interest is real and not simply a courtesy to Shapiro, but I doubt that is the case. While I don’t think Francona would be a silver bullet, his tenure in Boston doesn’t raise any obvious red flags. But Francona figures to be the default #1 candidate for any openings, and it’s difficult for me to believe that he would choose Cleveland over other options.

Sandy Alomar appears to have the inside track otherwise, and there’s very little evidence as to what type of manager he would be. There is plenty of evidence that Indians fans will welcome him as 90s nostalgia grows more powerful, and while that may be a plus from a PR perspective, it can be obnoxious for someone who was never a particular fan of Alomar the player. And heaven forbid the fans start talking about Omar Vizquel.

Playoff Probabilities

I am not a fan of the two wildcard playoff format, but my protestations were not considered and so it will soon be upon us. One thing I meant to do look at eventually was how the second wildcard would impact the probability of teams of a certain presumed strength winning in the playoffs. I’ve never gotten around to it, so I’m pretty much forced to look into it now or forever hold my peace.

The model that I will use to discuss this is admittedly simplified. It makes assumptions that are clearly simpler than reality:

* Teams have a constant strength from game to game. Even the strictest believer in baseball games as an expression of random chance disagrees with this as the identity of the starting pitcher obviously matters.

* Game outcomes are completely independent of one another. While game outcomes are largely independent, the argument for independence is weakened in the playoffs where decisions about how to manage the game (particularly pitcher usage) are clearly influenced by the status of the series.

* Home field advantage is uniform for all teams.

With these assumptions (along with others that have gone unstated), it is easy to construct a model of a playoff series. If one ignores home field advantage, the binomial distribution makes it very easy. That is the way I’ve approached these problems in the past, but I’ve decided to consider home field advantage and make the computations a tad more arduous this time (Of course, as you incorporate HFA into analysis of playoff series, you realize how inconsequential it is barring some intangible psychological force).

I have set up an (excessively) clumsy spreadsheet to do the math. The spreadsheet allows you to enter the playoff teams in order of seeding (i.e. A1 is the AL #1 seed down to N5, the NL’s second wildcard, with the National League assumed to have home field advantage--if the AL does, just enter the AL teams as N1-5 and the NL teams as A1-5) and enter a strength rating for each team (in the form of a win ratio as I use here). It then calculates the probability of each potential playoff series and their outcomes. The probability of each series outcome is figured on the other tabs, and if you are so inclined you could alter the home field pattern for each round. You can also enter the average W% for the home team. I’ve set this to .573, which is the World Series average for 1922-2008. The regular season average is usually around .540, so I think this is a fairly generous assumption in terms of strength of HFA.

The yellow cells are where the user should input custom data. I’ve not provided full documentation for every step as I doubt anyone will actually use this spreadsheet, but if you do and have any questions I will be happy to expound on the documentation. The spreadsheet can be accessed here (change html at the end to xls to download in Excel format).

In the post linked above, I looked at the winning percentages for all playoff teams and theoretical second wildcards for 1995-2010. I’m going to use these averages to set up a theoretical “typical” playoff scenario, and see how the probability of each team advancing to certain round varies with and without the second wildcard team. Using the actual W%s without adjustment to represent the strength of the teams is wrong for a couple of reasons, most notably that some regression is needed to estimate true quality and that no adjustment has been made for the unbalanced schedule, which is a big concern when performing interleague comparisons (and a smaller but still present concern for intraleague comparisons). However, exaggerating the differences in quality between teams will produce a liberal estimate of the differences between playoff formats, which may not be terrible for the sake of discussion. Also note that I’ve not made any adjustment for the fact that under the old format, the wildcard could be matched up with the #2 seed if the #1 seed came from their division.

Here are those average W%s and the resulting CTR (simply W%/(1 - W%) in this case) for each seed:



To rehash that earlier post, much of my antipathy towards the second wildcard and the fetishization of division titles is on display here. The AL wildcard has typically been one of the strongest playoff teams, while the wildcard in both leagues has a better average record than the third division winner. If MLB is hellbent on allowing a fifth team into the playoffs, then I would propose making the playoff between the two qualifying teams with the worst record rather than the two that failed to win their division. This complaint is water under the bridge at this point, though.

First, let’s run through the playoffs with a standard home field advantage (I’m using .543) and just one wildcard:



Now the same scenario, but with a special increased playoff HFA of .573. The last column is the marginal number of World Series victories per 1000 seasons relative to the .543 HFA assumption:



Remember, I’ve given the National League World Series HFA, so the NL teams get more of a boost from assuming a stronger HFA than do the AL teams. The NL picks up 9.6 World Series victories per 1000 seasons as a result of this stronger HFA assumption.

More relevant to the point of this post, here is the effect of adding the second wildcard to the mix. Again, let me emphasize that I’m assuming that there is no difference in expected W% from game-to-game. This is particularly relevant for the wildcard teams as one of the purported benefits of the extra playoff is that it will put the winner at a disadvantage entering the Division Series in terms of pitcher availability, since they will clearly have an incentive to use their best available pitching in the wildcard game. I’m not saying that you shouldn’t attempt to model this and other game-to-game factors when assessing playoff probabilities--but doing so complicates the exercise considerably. Instead, think of what I’m doing here as simply an analysis of the format itself rather than the consequences of that format upon the teams. These probabilities are based on the .573 HFA assumption. The last column is the marginal number of World Series victories per 1000 seasons relative to the single wildcard:



Keeping in mind that this analysis is not a true comparison of the previous format to the current one as it doesn’t account for the wildcard being unable to face a divisional opponent in the Division Series, this actually makes me feel a little better about the two wildcard formats, as it increases the probability of the best teams (#1 and #2 seeds, although the AL wildcard is generally in that class as well) winning the World Series. #1 seeds get an easier Division Series matchup by getting the second wildcard roughly 40% of the time. Obviously the #5 seed benefits the most, going from out of the picture to being a long shot. Equally obviously, the first wildcards take a huge hit.

The interesting result is the decrease in W% for the #3 seed, the reason for which is not immediately obvious. The cause is the increased likelihood of facing the #1 seed in the LCS (and the increased likelihood of facing the other league’s best teams in the World Series).

Still, the effects on the division winners’ odds are relatively small, not much different than the difference in assuming that the typical player HFA is .03 wins greater. The brunt of the impact is felt by the first wildcard.

Meanderings

* There is always some grumbling about September roster expansion, and the supposed ills it inflicts on the game, but it seems to have reached a fever pitch in September 2012. There are a lot of calls for some kind of reform, whether it involves severely curtailing the practice or (most popularly) forcing a manager to declare 25 active players at the start of every game.

I don’t have a problem with roster expansion, myself--my preference would be to keep the status quo. I will also admit to not having read all of the pieces that have been written about this, so it is quite possible that someone has prominently beaten me to the punch with the following suggestion. Rather than having the manager declare a 25 man active roster, why not simply limit the manager to using 25 players in a particular game?

Such a rule would give a manager in-game flexibility that would be absent in the case of a pre-declared scratch list. In a close game, he would be free to use extra players in situational roles. In a blowout, he would be able to use his mop up relievers and get young players into the game. But he would not be able to use any more players than he could during the rest of the season.

There are a couple of drawbacks to this rule that come to mind. One is that 25 players is still an increase over the number that is typically deployed during the rest of the season, even in fairly unusual cases. The four excess starting pitchers usually are excluded from game action, especially in the American League. I’d argue that this is a good thing--it allows for some additional substitutions while preventing abuse, but if one is concerned about any change in the behavior of managers, it’s a valid criticism.

The other is a logistical issue rather than a baseball issue, but it would be a little harder to keep track of. Announcers would be completely bewildered as a team approached the substitution limit, and while the omnipresent lineup cards should be sufficient for managers and umpires to keep up, it’s not hard to imagine some confusion arising.

* Everyone has an opinion on Stephen Strasburg. I don’t, really--I certainly agree with the principle of being cautious with pitchers, particularly young pitchers, those who have prior injury histories, and those of extraordinary talent--all three of which fit Strasburg. What I do have an opinion about is the intestinal fortitude of Mike Rizzo and anyone else who took responsibility for the final decision. I consider it a pretty bold stance to take, given that there is almost no outcome in which they do not receive heavy criticism.

If Washington fails to win the World Series, the question of how they might have performed with Strasburg will be raised incessantly. Even a quick sweep in the Division Series in which one win would have not stemmed the tide will not get them off the hook, because psychological factors will be raised (“Strasburg could have won game one and completely changed the momentum”, “The Nationals players would have been more confident with Strasburg available”, etc.) And if they lose a seven game World Series in which Edwin Jackson gets roughed up a couple of times--well, if I was Rizzo, I’d consider hiring a food taster at that point. So far I’ve only discussed the 2012 on-field consequences. A bigger outcry will come if Strasburg gets hurt again, particularly if it’s in the next two years.

What’s remarkable about this decision is the near certainty with which it will be judged as a failure by mainstream observers. Perhaps my imagination is too limited, or my faith in sound reasoning on behalf of mainstream observers artificially low, but it’s difficult for me to imagine a scenario in which the shutdown is considered to be a success. The odds are very good that Washington will not win it all, with or without Strasburg. Steven Strasburg is quite unlikely to have an injury-free career. The takeaway for me is that Rizzo must really believe he’s made the right call.

* I am an unabashed supporter of the World Baseball Classic, so I’m taking it as my duty to update you about the upcoming qualifying tournaments. The existence of these has largely gone unremarked upon.

For the first time, four spots in the sixteen team field will be up for grabs. The twelve countries that won games in the 2009 WBC are automatic qualifiers (Japan, Korea, China, United States, Mexico, Italy, Netherlands, Dominican Republic, Venezuela, Cuba, Australia, and Puerto Rico). The first two qualifiers open up next week.

The qualifiers are four-team double elimination tournaments, the format of which will be familiar to those who watched the 2009 WBC or follow the NCAA Tournament. In Jupiter, FL, South Africa will play Israel and Spain will play France. In Regensburg, Germany, Canada will play Great Britain and Germany will play the Czech Republic. In November, the other two spots will be decided. In Panama City, Panama will play Brazil and Colombia will play Nicaragua. In Taipei City, the Philippines will play Thailand and Taiwan will play New Zealand.

Handicapping these tournaments is silly (after all, the Netherlands beat the Dominican Republic twice in the 2009 WBC). Speaking broadly without knowledge of the actual makeup of the teams, there are clear favorites in the Germany and Taiwan qualifiers, as Canada and Taiwan are much stronger baseball nations than the second-tier European and Asian countries, respectively.

The other two are fairly wide open. WBC rules allow people who could be but are not citizens of a country to play, which allows Israel access to Jewish players. Israel will be managed by Brad Ausmus, and faces a very weak field, so they may be the favorite. Panama played in the first two WBCs without much success. Colombia and Nicaragua have both produced their share of major leaguers, and even Brazil now has their own big leaguer in Yan Gomes.

Just to provide a general sense of how the participating countries have performed in recent international tournaments, here is each country’s rank in the IBAF World Rankings divided by qualifier. (These rankings don’t do justice to countries with strong baseball that don’t field teams in many international tournaments such as the Dominican Republic, and obviously are based on tournament results and don’t tell one anything about the quality of WBC team being fielded. Nonetheless, it’s kind of fun to look at--and it’s even more fun to look at the full ranking list, which includes countries such as Bolivia, Myanmar, and New Caledonia, which I had to look up on Wikipedia. Also note that the top-ranked non-participant, Netherlands Antilles, is included with the Netherlands for the WBC):



It is also worth noting that the IBAF website states that it will now bestow the title of world champion on the WBC winner rather than the soon to be defunct World Cup winner.

Sabermetric Generations

Allow me the indulgence of going meta-sabermetric here. I don't really like doing that, as this is the point at which you are writing about sabermetrics itself rather than baseball, and baseball is a heckuva lot more interesting than sabermetrics. However, I think there are some things about the field that those of us who fancy ourselves as sabermetricians should consider. This post is a half-developed missive on some of those things.

My basic premise here is that sabermetric people can be divided into three generations--not perfectly, of course, but as a general classification. I say "people" because I don't want to make it about who is or is not a "sabermetrician" (Do you have to publish your own run estimator to be a sabermetrician? Write a blog? Do any research at all?), but just about people who would consider themselves to be either practitioners or consumers of sabermetric research, or both.

These three generations are not defined strictly by age, but rather by when you came of age as a saberperson (or how, but the when and the how elements are very closely related). My three groups are:

1. Pioneers--This is by far the most restrictive group, as it only includes those who actually did pioneering sabermetric research (whether they called it by that name or not). Earnshaw Cook, George Lindsey, Pete Palmer, Bill James, and the like are the pioneers.

2. Second Wave--These are the folks who came to sabermetrics largely through the work of the pioneers--reading the Baseball Abstract or The Hidden Game or various SABR publications or The Diamond Appraised, and the like. They may or may not have gone on to become researchers themselves; they may just be consumers of research. It is also possible that their own inquisitiveness led them to sabermetrics without a firm push from Bill James or another pioneer, but they still came onto the scene after the work of the pioneers had been published. Many, many people fall into this group, and even listing a few would be foolish. I consider myself in this group although I also share a few traits with the third group, as I explained before.

3. Internet generation--These are people who have come to sabermetrics in the last 10-15 years and may have done so without ever reading the work of the pioneers. Their interest in sabermetrics is young enough to have been fueled by reading the work of second wavers (or of course their own inquisitiveness). A typical path to sabermetrics for a member of the Internet generation would have been to read Rob Neyer. From there, they sought out BP or Bill James.

Before I use these classifications to make a point, I need to issue a couple of disclaimers. The first is that I am not an evangelist for sabermetrics. I don't go to the airport and hand out flowers, or go to people's doors and hand them tracts. I don't really care if you are interested in sabermetrics or not, and I don't tailor my writing to appeal to folks who are on the fence.

So when I express my concern about something below, it's not borne out of any fear of what overzealous internet posters will do the reputation of sabermetrics or anything like that; it is simply out of an ordinary desire for intelligent and factual discourse.

The second disclaimer is that this is not a get off my lawn post. As I stated in the piece linked above, I straddle the fence between the second wave and the internet generation, and while I might wish to place myself in the former group, you could make a reasonable case that I am in fact a member of the latter group. No group is inherently better or worse than any other; this post is about certain negative traits of some members of the internet generation, but there are many positive things that can be said about the internet generation.

The third disclaimer is that this whole matter of putting saberpeople into groups and then describing those groups is obviously dangerous for the same reason that forming any sort of artificial groups of people is. So it should go without saying that I am not claiming that all members of a generation share certain characteristics or behave exactly the same way.

My concern is about the fact that with the wealth of information available today, particularly through sites like Baseball-Reference, Fangraphs, and StatCorner, it has become quite possible for members of the internet generation of saberpeople to cite statistics without really understanding them at all. Of course, second wavers also had this ability, but it wasn't so instantaneous. You had to wait for new books to be published in the spring or you had to go through the trouble of figuring statistics yourself.

Of course, there are many members of the internet generation who do fantastic research, develop their own statistics, or figure stats themselves. They are not who I am talking about. I am talking about the subset of folks who don't do their own research, don't endeavor to truly understand what the numbers mean, and yet still talk about them authoritatively.

With sabermetrics prominent on the internet baseball scene, it is much easier to learn about the field. This is on the whole a very welcome improvement, but it is also easier for people to get indoctrinated into sabermetric principles without fully understanding them. There is a sabermetric-brand of conventional wisdom which can be just as misleading as the conventional wisdom of the traditionalists when it is wielded by an individual who has not done his own legwork, but has simply read it or told it and believed it to be true.

The ubiquity of sabermetric ideas in online discussions of baseball makes it quite possible for members of the internet generation to be introduced to sabermetrics almost simultaneously to the moment at which they become serious baseball fans. This pretty much happened to me as recounted in the earlier linked post, although it was primarily through printed works of pioneers rather than through the internet. That being the case, I can't criticize this path of discovery. However, I do think that there might be a critical thinking advantage to having first accepted the conventional wisdom, gradually looking at it skeptically, and then having those questions reinforced by the discovery of sabermetrics. Today it is quite feasible for young baseball fans to skip the conventional wisdom altogether and jump right into sabermetric ideas.

A specific example of the kind of thing I'm talking about is the notion that any pitching statistic like ERA that does not incorporate DIPS principles is worthless, and that only FIP or tRA or a similar metric is appropriate. The problem is not with the truth that ERA has a lot of biases which have often been overlooked, or that FIP is a better predictor of future performance. The problem comes when a relatively good measure like ERA (and one that measures actual runs allowed, which are unquestionably important if not wholly attributable to the pitcher) is thrown in the dustbin as if it is no more useful or telling than Batting Average or raw RBI count, and that anyone who even considers it is classified as a dinosaur.

In defending ERA, I am not saying that it is inherently wrong to come to the conclusion that FIP or Metric XYZ is not the best tool for measuring pitcher performance--just that it is wrong to reflexively come to that conclusion, and that sometimes the advocates of such a position can take on a zealous tone. This tone often echoes that of reflexive anti-sabermetric screeds.

You may be thinking to yourself that I am attacking a strawman, and that no one actually thinks like that. I didn't quote/link anyone specifically, because singling out message board posters is not the point of this discussion--but sentiments of this sort are out there.

This is where my admission that this post is half-developed becomes painfully clear, because I really don't have anything to offer about what can or should be done about this (given that I am not a sabermetric evangelist, my developed answer would most likely be centered around the premise that individuals are responsible for their own rhetoric). At this point, it will devolve into a paean to do-it-yourself sabermetrics.

There are now at least four large-scale implementations of WAR floating out there--Rally/Baseball-Reference, Fangraphs, BP's WARP, and the Baseball Gauge's WAR. As a result, people will sometimes wonder why sabermetrics can't have a meeting of the minds, hash out all of the differences, and produce one unified version of WAR that can be presented to the wider world.

There are a number of reasons why I think this is a bad idea (the danger of presenting any one metric as *the* uberstat; the legitimate uses of alternate baselines, run estimators, park factors, league adjustments, position adjustments, and all of the other components that go into WAR; the notion that consensus is a positive for its own sake), but that's irrelevant, because it will never happen. The hypothetical moment that it did happen would prove Gary Huckaby right--sabermetrics would be dead. Enforcing standardization for problems in which the answer is often subjective would discourage innovation and discredit alternate views on the question of ability v. value (among others).

Additionally, the existence of one version of WAR, widely accepted and presumably published by major websites, would in my estimation do more to discourage people from figuring their own statistics than anything else in the history of the field--more that Total Baseball or Baseball-Reference or Fangraphs. If you were a new convert to sabermetric thinking, and were told that there was one metric that was the best and was freely available, what would be your most likely reaction?

1) Awesome, this sabermetrics thing is not nearly as complicated as all of the screeds suggested it would be.

2) Darnit, I was hoping to find the unified theory of everything myself.

3) Darnit, I can't believe I don't get to try to figure out how to use a slide rule, or make a spreadsheet, or do SQL coding, or however these saberwhatevers get their results.

There is a lot of value in figuring your own sabermetric statistics, even by just applying other people's metrics. There's no better way to learn about the inputs and how they are combined than by actually walking through the process yourself.

At one time, in order to have up-to-date access to sabermetric stats, you pretty much had no choice but to figure them yourself. This resulted in a waste of a lot of man-hours of sabermetricians, but it also meant a group of people that were better informed about the construction and therefore the objectives and philosophy of the metrics they were using. The easy availability of statistics today is a great boon to the field, to be sure, and it is particularly great for serious practitioners who already have a good understanding of metric construction. I am not a luddite--the downside of a potentially less-informed average consumer of sabermetrics does not outweigh the benefits--but it also should serve as an impetus for transparency in computational explanations and for continuing reminders of the why in addition to the numerical results themselves.

Ballpark Thoughts

My apologies to anyone who reads the title of this post and expects to read a discussion of some arcane aspect of estimating park factors. On Saturday I visited Great American Ball Park in Cincinnati for the first time for the Cubs/Reds doubleheader. I am by no means a well-traveled fan when it comes to attending MLB stadiums--GABP raises my lifetime count to five (Jacobs Field, Municipal Stadium, PNC Park, Tropicana Field). What follows are some random thoughts (and snark at the expense of my southern neighbors):

* I expected to be underwhelmed by the ballpark. I can’t point to any particular influence, but I thought that the general consensus on GABP was that it was not on par with the best of the new parks.

Having only been to four of the current parks, I can’t place GABP on a grand continuum, but given my lowered expectations, I was quite impressed. For the day game, I purposefully bought a ticket in the very last row of the stadium behind home plate. My main motivation was shade, but it offered a great opportunity to take in the park from the bird’s eye view. For the second game, I sat in the right field moon deck, which was useful because it provided the opposite orientation.

The Ohio River and the hills of Kentucky provide nice scenery for those facing the outfield. While the park is not situated close enough to the field to allow for splash hits, the river is certainly quite prominent in the view past right field, and the lack of a second or third deck in right field leaves the scenery largely unimpeded.

Those looking towards left field have a much less interesting view--the left field bleachers and the basketball arena block any view. The impediment of the arena validates the decision to leave right field open, as otherwise you wouldn't be able to see much beyond the park from any perspective.

From the outfield perspective, you mostly just have a view of the stadium. Most of the skyline is obscured, with the top of the (surprise) Great American building the highlight. The PNC “power stacks” are a bit of an annoyance from these seats--not because they block the view (they’re behind you) but because you can feel the heat from the napalm or whatever exactly it is that they shoot off. This would be a plus at a cold April game, but is annoying otherwise.

Of course, all this talk about the view misses the primary point of visiting a stadium, which is to watch the ballgame and not the scenery.

* The silliness of the attempt to manufacture a “game day experience” is by no means unique to GABP nor to MLB, but in my limited experience Cincinnati takes the cake. One of the most annoying features added at Jacobs Field over the last few seasons are way too cheery “hosts” who appear on the scoreboard, going around the park and telling you about all the exciting and fun things to do at the park. GABP has these as well, so I was edified about the pre-game concert featuring a band doing a particularly bland cover of the Black Crowes’ version of “Hard to Handle”, about the Big Red Machine exhibit at the Reds Hall of Fame (the Reds “dominated baseball in the 70s”...I’m sure the A’s really felt dominated), and various other distractions.

The Reds also feature an extraordinary number of mascots. There are four. One is Gapper, the generic fuzzy monster that almost every team has a version of. The next is Mr. Red, a giant baseball head who manages to look much more menacing than Mr. Met. Then there is Mr. Redlegs, the old time giant baseball head (you can tell by his taste in mustaches) who appears to cheat at the mascot race (only conducted on the scoreboard, which is a plus). Finally, there is Rosie the Red, easily the most creepy mascot in history.

Prior to the day game (the night game was not as bloated), there were three first pitches (a logical conundrum), a kid yelling “play ball”, an honorary captain, and a delivery of the official game ball to the mound. Many traditional religious services have less ceremony.

Again, none of this is unique to Cincinnati, but I’ve previously been fortunate to not encounter so much of it at once.

* For the night game, the first 20,000 fans received a 1995 replica hat with Barry Larkin’s #11 on the side. The good people of Cincinnati really wanted to ensure that they received their hats. The lines to get into the ballpark before the gate opened were very long. I wasn’t quite ready to go into the park yet (I like getting there early, but ninety minutes is a little much for me), but I bowed to the inevitable and got in line to ensure that I too would receive a 1995 Reds hat.

* Two things struck me about the area surrounding the ballpark. The first was the pandhandlers. Now maybe I don’t go to the right (wrong) places, but in the two cities I am most familiar with (Cleveland and Columbus), the panhandlers are not nearly as sophisticated. All of the Cincinnati pandhandlers stand there with cardboard signs displaying their sob stories.

The other is scalpers, or more precisely, the lack thereof. Apparently, Cincinnati has fairly strict (and thus asinine) laws against selling tickets above face value. Surely this is still happening, but it is clearly done more discretely than it is around Jacobs Field or Nationwide Arena.

* Along the river, there are a set of columns which have plaques on each side. These comprise the Steamboat Hall of Fame. Spoiler alert: Many of the steamboats in the Steamboat Hall of Fame met unpleasant demises.

* Charging admission to your team’s Hall of Fame is almost as pretentious as pretending that your team was established in 1869 when it was actually established in 1882.