Disjointed Ramblings on the Indians' Managerial Vacancy

NOTE: I wrote this on Thursday and didn't expect the Indians to hire Acta over the weekend.

While the Indians have been searching for their next manager, it has been amusing to observe the reaction of non-analytical fans on message boards and talk radio. There are a large number of people who are furious at the prospect of Manny Acta becoming manager.

Let me digress for a moment by saying that I hope he gets the job. From everything I've read and heard from him, his outlook on the game is one that I can relate to. He says the right things about being open to analytics and his managing seems to reflect that. His bullpen usage seems to this distant observer to fall into the over-managing category, but I have to question how much of that was conviction and how much of that was trying to squeeze every possible advantage out of a bunch of lemons. In any event, I'm thoroughly unconcerned about his win-loss record in Washington, a franchise that was a basket case before he got there and maybe now with a new GM can finally right itself. (Acta bonus fact: He's the David Aardsma or Hank Aaron of big league managers--first all-time alphabetically.)

I say all of that, but if you asked me whether it was more likely, should Acta become Tribe skipper, that he would be considered a success or a failure when his tenure was over, I wouldn't hesitate: failure. It's a cliché, but it's a cliché with a lot of truth: managers are hired to be fired. Most of them get three or four years to turn around a team that was usually already in some sort of distress (or else they wouldn't have been in the market for a new manager at all) and fail to do so, often through no fault of their own.

I don't want to make it sound as if I think managers are unimportant--I certainly think they are less important than a lot of non-analytical observers believe they are, but I also am much more concerned about the identity of the GM and whether anyone can hit, pitch, and field. I do believe, however, that most of what really separates managers from one another are factors that we as outsiders cannot judge with any sort of accuracy--discipline, motivation, the makeup of their coaching staff, how well they interface with the GM, and the like. Those things may not turn the Royals into World Series contenders, but I believe they matter more than the usually small tactical differences between managers (there are exceptions of course, many of whom do not need to be named).

The amusing part is the ways that fans attempt to evaluate managers. The following is an incomplete listing of some of the criteria I see fans using:

1. Tactics: Of course, this is where your baseball worldview really comes into play. One man's genius is another man's moron on the tactical scale. While sabermetrics certainly has some insight to offer on this front, it's not as if you can just plug some variables into a formula and get a strategic rating.

2. Past success: Fans like it better when the prospective manager has won something. However...

3. Freshness: Other fans don't want a "retread" manager. Of course, there is no definition of what constitutes a retread versus a Proven Veteran (TM) manager. Bobby Valentine managed parts of fifteen seasons, compiling a .510 W%, two playoff appearances, and a pennant. Does that make him a proven winner, a proven mediocrity, a winner, a loser, or something else? Does his tenure in Japan count for anything?

4. Media image

These criteria often result in a bewildering mix of contradictory preferences. With the Phillies winning another pennant, there are now Tribe fans bemoaning that Charlie Manuel was once our manager. But how many of these folks were upset that he was fired? How many of them believed that he was a country bumpkin? How many of them really, honestly believe that he would have led the Indians to victory with the same players Eric Wedge was given, or that Wedge would have flopped with Chase Utley and Jimmy Rollins on his team?

My opinion of Charlie Manuel today is the same as it was the day he was fired by Cleveland: Nice guy. Presumably knows a lot about hitting. Makes a lot of inexplicable decisions while managing.

Since I think it's a pretty decent bet that Eric Wedge will be a manager again, I can't wait to see what will happen if he ever leads a team to a pennant. Near the end of his tenure, it was hard to find many Indian fans who had anything positive at all to say about the man (other than perhaps that he had class). I've written some tepid pro-Wedge stuff over the past year and only because no one reads this blog was I able to avoid being labeled as an apologist. Should he win, he will join Manuel as a tool with which to attack the organization--rather than as the cautionary tale about judging a manager on his record in one stop.

Anyway, to sum up my position:

1. Managers matter, but not as much as the average fan thinks they do.
2. Much of what distinguishes managers from one another is almost unknowable to outsiders.
3. I prefer a manager who is open to analysis and/or independently came to a similar view of baseball as the one I possess.
4. It's silly to think that because a manager didn't win during one job, he'll never win in another.
5. It's more likely than Manny Acta will be unceremoniously fired than that he will lead the Indians to a World Series. That doesn't mean he's a bad hire--I'd say that about anyone stepping into this position.

To really beat the dead horse that is the fourth point, try a thought experiment. Right down the names of 5-10 current managers that you think you'd like to have managing your team. It's a pretty decent bet that a lot of your picks have been fired at some point.

Suppose you'd chosen the eight managers who managed in the postseason this year:

Ron Gardenhire, MIN--first managerial position
Joe Girardi, NYA--fired by Florida, although not really for on-field performance
Mike Scioscia, LAA--first managerial position
Terry Francona, BOS--fired by PHI (285-363, .440)
Tony LaRussa, STL--fired by CHA (522-510, .506)
Joe Torre, LA--fired by ATL, NYN, STL (894-1003, .471), not extended by NYA
Charlie Manuel, PHI--fired/not extended by CLE (220-190, .537)
Jim Tracy, COL--fired by LA and PIT (562-572, .496)

IBA Ballot: Rookie of the Year

Disclaimer: Presented below is my ballot (and some justification) for one of the categories in the Internet Baseball Awards hosted at Baseball Prospectus. I’m just one person, and the whole point of having a vote like the IBA is to get a wide variety of (intelligent) perspectives, and so I will not feel in the list bit slighted if you don’t give a flip about this. You've been warned. Also, the RAA and RAR figures that will be cited are my own estimates, detailed here. Any Leverage Index, WPA, or UZR figures cited are from FanGraphs; any quality of opposition or baserunning figures are from Baseball Prospectus.

In the American League, there aren't many viable position player candidates for the award. The top ranking rookie in RAR is Nolan Reimold, but at +21 he doesn't rank very highly, and his fielding knocks him out of contention. Elvis Andrus moves up to +30 if UZR is taken at face value, which gets him on the ballot but not at the top. Gordon Beckham is second among position players at around +20. Had he played more, he would definitely be a contender.

That leaves the pitchers. Jeff Niemann, Rick Porcello, Ricky Romero, and Brad Bergesen all are at +30 or better. All of them have less impressive peripherals than actual run averages, which leaves me without a lot of justification for changing the RAR ordering listed above (Certainly the differences are small enough that you could justify making changes, so I don't mean to imply that you must rank them in that order. I just don't see anything that makes me want to do so.)

Some people may give Porcello a boost due to his age, but I do not take age into account when looking at Rookie of the Year. If it was an award for best future potential, then I would be looking at a very different set of candidates.

One name missing from my ballot that you'll surely see on many others is Brett Anderson. If you are of the school of thought that pitcher seasonal awards should be determined by DIPS school metrics, then Anderson is the best of the lot. If you don't, you'll note that his RA is nearly half a run higher than that of Romero, who has the highest of the four pitcher cohort defined above.

None of those players are my selection for the top spot, though. It is usually very difficult for a relief pitcher to crack one of my Cy Young ballots, and you can just about forget about MVP support entirely. However, I think that I tend to support more relievers for ROY than the mainstream media does. I believe this is because of my philosophy that the ROY should be for the rookie who provides the most value and that age is not a factor. Often rookie relievers are on the old side (Brad Ziegler last year), and even if they are young it would usually be a stretch to project them as having greater future value than a starter or a position player. Some people also may tend to write off the extra value relievers generate by pitching in high leverage situations in a ROY discussion because htey are looking for the best performance. Since I don't consider age and do consider leverage, I've reserved spots on my ballots for Ziegler (2008), Okajima (2007), Papelbon, Zumaya, and Saito (2006), and Street and Majewski (2005).

In that spirit, my choice this year is Andrew Bailey. Bailey was +31 RAR with strong peripherals (2.09 eRA and 3.09 dRA), and served as Oakland's closer for most of the season, going 26/30 in save opportunities and recording a 1.4 LI. While his LI was lower than that of many bullpen aces, it's still enough for me to edge him ahead of Niemann and into the top spot on the ballot. This is how I see it:

1) RP Andrew Bailey, OAK
2) SP Jeff Niemann, TB
3) SP Rick Porcello, DET
4) SS Elvis Andrus, TEX
5) SP Brad Bergesen, BAL

Moving on to the Neanderthal League (I promise I won't use that again when I discuss the Cy Young and MVP), I reluctantly have to support JA Happ for the award. Happ, at +49 RAR, has a ten run lead over any other NL rookie. So why am I reluctant about my choice? Simply, Happ's eRA is a full run higher than his RA and his dRA is another .7 runs higher still. I suspect that many sabermetriclly-inclined folks will dock him significantly for this, but I am always very cautious of doing so. Differences between RA and DIPS can be either due to "luck" (I'm using that word as a catch-all, not literally) or superior fielding support. If it's the latter, then I'm all for adjusting it away. If it's the former, then I'm not--and it is often a little of both.

Had Tommy Hanson been in the majors longer, he may have made it all a moot point, as he was outstanding over 128 innings of work, good enough to edge Randy Wells as the second most impressive rookie starter.

Among position players, Chris Coghlan seems to be getting some mainstream support, but he doesn't crack my ballot. Yes, he was +37 RAR, tying him with Andrew McCutchen, but his -10 UZR puts a big dent in that. Comparing Coghlan to McCutchen offensively, Coghlan hit .323 to McCutchen's .288, but McCutchen's edge in secondary average was .311 to .246. Put it all together, and they each created 6.3 runs per game. Coghlan played more, but he was a bad left fielder and McCutchen was an average center fielder according to UZR. It's not a particularly tough call for me.

Comparing McCutchen to his out of nowhere teammate Garrett Jones, Jones was certainly a better hitter on a rate basis, but he played in 26 less games, came to the plate 130 less times, and had a -6 UZR in right.

So I have it:

1) SP JA Happ, PHI
2) CF Andrew McCutchen, PIT
3) SP Tommy Hanson, ATL
4) SP Randy Wells, CHN
5) RF Garrett Jones, PIT

End of Season Statistics, 2009

Note: This is largely the same explanation as for the last two years.

For the past several years I have been posting Excel spreadsheets with sabermetric stats like RC for regular players on my website. I have not been doing this because I think it is a unique thing that nobody else does--Hardball Times, Baseball Prospectus, and other sites have similar data available. However, since I figure my own stats for myself anyway, I figured I might as well post it on the net.

This year, I am not putting out Excel spreadsheets, but I will have Google Spreadsheets that I will link to from this blog.  If you would prefer an Excel copy of the spreadsheets, all you have to do is change the end of the link from "=html" to "=xls".  What I wanted to do here is a quick run down of the methodology used. These will be added as they are completed; as I post this, there are none, but by the end of the week they should start popping up.

First, I should acknowledge that the primary data source is Doug’s Stats, and that park data for past seasons comes from KJOK’s park database. Baseball-Reference.com and ESPN.com round out the sources.

The general philosophy of these stats is to do what is easiest while not being too imprecise, unless you can do something just a little bit more complex and be more precise. Or at least it used to be. Then I decided to put my money where my mouth was on the matter of Base Runs for pitchers and teams and Pythagenpat. On the other hand, using ERP as the run estimator is not optimal--I could, in lieu of having empirical linear weights for 2009, use Base Runs or another approach to generate custom linear weights. I have decided that does not constitute a worthwhile improvement. Others might disagree, and that’s alright. I’m not claiming that any of these numbers are the state of the art or cannot be improved upon.

First, the team report. I list Park Factor (PF), Winning %, Expected Winning % (EW%), Predicted Winning % (PW%), Wins, Losses, Runs, Runs Allowed, Runs Created (RC), Runs Created Allowed (RCA), Runs/Game (R/G), Runs Allowed/Game (RA/G), Runs Created per Game (RCG), and Runs Created Allowed per Game (RCAG):

EW% is based on runs and runs allowed in Pythagenpat, with the exponent = RPG^.29. PW% is based on runs created and runs created allowed in Pythagenpat.

Runs Created and Runs Created Allowed are both based on a simple Base Runs formula. For the offense, the formula is:
A = H + W - HR - CS
B = (2TB - H - 4HR + .05W + 1.5SB)*.76
C = AB - H
D = HR
For the defense:
A = H + W - HR
B = (2TB - H - 4HR + .05W)*.78
C = AB - H (approximated as IP*2.82, or whatever the league (AB-H)/IP average is)
D = HR
Of course, these are both put together, like all BsR, as A*B/(B + C) + D. The only difference between the formulas is that I include SB and CS for the offense, but don’t want to waste time scrounging up stolen bases allowed for the defense.

R/G, RA/G, RCG, and RCAG are all calculated straightforwardly by dividing by games, then park adjusted by dividing by park factor. 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.

Next, we have park factors. 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 (unshown) 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 1- (1-iPF)*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 also offer a league report, for which some explanation is necessary. 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.

Next is the relief pitchers report. 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 2009. 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.

Anyway, for relievers, the statistical categories are Games, Innings Pitched, Run Average (RA), Relief Run Average (RRA), Earned Run Average (ERA), Estimated Run Average (eRA), DIPS-style estimated Run Average (dRA), Guess-Future (G-F), Strike Zone ERA (szERA), Inherited Runners per Game (IR/G), Inherited Runs Saved (IRSV), hits per ball in play (%H), Runs Above Average (RAA), and Runs Above Replacement (RAR).

All of the run averages are park adjusted with the exception of szERA. RA is R*9/IP, and you know ERA. Relief Run Average subtracts IRSV from runs allowed, and thus is (R - IRSV)*9/IP; it was published in By the Numbers by Sky Andrecheck. eRA, dRA, %H, and RAA will be explained in the starters section.

Guess-Future is a JUNK STAT. G-F is A JUNK STAT. I just wanted to make that clear so that no anonymous commentator posts that without any explanation. It is just something that I have used for some time that combines eRA and strikeout rate into a unitless number. As a rule of thumb, anything under 4 is pretty good. I include it not because I think it is meaningful, but because it is a number that I have been looking at for some time and still like to, despite the fact that it is a JUNK STAT. JUNK STATS can be fun as long as you recognize them for what they are. G-F = 4.46 + .095(eRA) - .113(KG), where KG is strikeouts per 9 innings. JUNK STAT JUNK STAT JUNK STAT JUNK STAT JUNK STAT

Inherited Runners per Game 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 or what have you. I think it’s mildly interesting, so I include it.

Inherited Runs Saved is the difference between the number of inherited runs the reliever allowed to score, subtracted from the number of inherited runs an average reliever would have allowed to score, given the same number of inherited runners. I do not park adjust this figure. Of course, the way I am doing it is without regard to which base the runners were on, which of course is a very important thing to know. Obviously, with a lot of these reliever measures are superfluous if you have access to WPA and LI data and the like.

IRSV = Inherited Runners*League % Stranded - Inherited Runs Scored

Runs Above Replacement is a comparison of the pitcher to a replacement level reliever, which is assumed to be a .450 pitcher, or as I would prefer to say, one who allows runs at 111% of the league average. So the formula is (1.11*N - RRA)*IP/9, where N is league runs/game. Runs Above Average is simply (N - RRA)*IP/9. Note that RAR compares the reliever to a replacement-level pitcher, while RAA compares him to an average pitcher regardless of role, not to an average relief pitcher.

On to the starting pitchers. The categories are Wins, Losses, Innings Pitched, Run Average, ERA, eRA, dRA, KG, szERA, G-F, %H, Neutral W% (NW%), Quality Start% (QS%), RAA, and RAR.

The run averages (RA, ERA, eRA, dRA) are all park-adjusted except for szERA, simply by dividing by park factor.

eRA is figured by plugging the pitcher’s stats into the Base Runs formula above (the one not including SB and CS that is used for estimating team runs allowed), multiplying the estimated runs by nine and dividing by innings.

dRA is a DIPS method (which of course means that Voros McCracken is the true developer), using Base Runs as the run estimator. This is overkill, since a DIPS estimator like FIP will work just fine, but I decided to use Base Runs wherever I could this year. To find, it first estimate PA as IP*x + H + W, where x = Lg(AB-H)/IP. Then, find %K (K/PA), %W (W/PA), %HR (HR/PA), and BIP% = 1- %K - %W - %HR. Next, find estimated %H (which I will just call %H for the sake of this explanation, but it is not the same as the %H displayed in the stats. That is the pitcher’s actual rate, (H-HR)/(estimated PA-W-K-HR)) as BIP%*Lg%H.


Then you use BsR to find the new estimated RA:

A = %H + %W
B = (2*(%H*Lg(TB-4*HR)/(H-HR) + 4*%HR) - %H - 5*%HR + .05*%W)*.78
C = 1 - %H - %W - %HR
D = %HR

dRA = (A*B/(B+C) + D)/C*25.2/PF

Yes, it's true that pitchers do have some control over their BABIP, and presenting a DIPS run average here is in no way intended to deny that fact. Even if there was no insight to DIPS whatsoever, though, I still think that a DIPS run average would be an interesting freak show statistic, as it only considers the three true outcomes. To restate my point, even if Voros' insight has no analytical utility (and I don't think anyone worth listening to has staked out such an extreme position), it would still be worth some kicks to ignore defense-influenced events.

szERA is a Tango Tiger creation which uses only the difference between strikeouts and walks per PA to estimate ERA. I have not used actual PA here but instead have estimated PA as (IP*x + H + W) as in dRA above, giving this formula for szERA (which is not park-adjusted):

szERA = 5.4 - 12*(K-W)/(IP*x + H + W)

Neutral Winning Percentage is the pitcher’s winning percentage adjusted for the quality of his team. It makes the assumption that all teams are perfectly balanced between offense and defense, and then projects what the pitcher’s W% would be on an average team. I do not place a lot of faith in anything based on wins and losses, of course, and particularly not for a one-year sample. In the long run, we would expect pitchers to pitch for fairly balanced teams and for run support for an individual to be approximately the same as for the pitching staff as a whole. For individual seasons, we know that things are not going to even out.

I used to use Run Support to compare a pitcher’s W% to what he would have been expected to earn, but now I have decided that is more trouble than it is worth. RS can be a pain to run down, and I don’t put a lot of stock in the resulting figures anyway. So why bother? NW% = W% - (Mate + .5)/2 + .25, where Mate is (Team Wins - Pitcher Wins)/(Team Decisions - Pitcher Decisions).

Likewise, I include Quality Start Percentage (which of course is just QS/GS) only because my data source (Doug’s Stats) includes them. As for RAA and RAR for starters, RAA = (N - RA)*IP/9, and RAR = (1.25*N - RA)*IP/9.

For hitters with 300 or more PA, I list Games (G), Plate Appearances (PA), Outs (O), Batting Average (BA), On Base Average (OBA), Slugging Average (SLG), Runs Created (RC), Runs Created per Game (RG), Secondary Average (SEC), Speed Unit (SU), 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. I have not included net steals as many people (and Bill James himself) do--it is solely hitting events.

For the last two season, the park adjustment method I’ve used for BA, OBA, SLG, and SEC has been based on the same principle as the “Willie Davis method” introduced by Bill James in the New Historical Baseball Abstract. The idea is to deflate all of the positive offensive events by a constant percentage in order to make the new runs created estimate from those stats equal to the park adjusted runs created we get from the player’s actual stats. I based it on the run estimator (ERP) that I use here instead of RC.

However, this year I have decided that this is really not necessary. One can obtain similar results by just using the square root of park factor, and while the Willie Davis method is clever and elegant, it's still an approximation that has its accuracy constrained by the accuracy of the run estimator itself. The square root adjustment is much quicker and again, the results will be similar.

Next up is Runs Created, which as previously mentioned is actually Paul Johnson’s ERP. 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).

Speed Unit is my own take on a “speed skill” estimator ala Speed Score. I AM NOT CLAIMING THAT IT IS BETTER THAN SPEED SCORE. I don’t use Speed Score because I always like to make up my own crap whenever possible (while of course recognizing that others did it first and better), because some of the categories aren’t readily available, and because I don’t want to mess with square roots. Anyway, it considers four categories: runs per time on base, stolen base percentage (using Bill James’ technique of adding 3 to the numerator and 7 to the denominator), stolen base frequency (steal attempts per time on base), and triples per ball in play. These are then converted to a pseudo Z-score in each category, and are on a 0-100 scale. I will not reprint the formula here, but I have written about it before here. I AM NOT CLAIMING THAT IT IS BETTER THAN SPEED SCORE. I AM NOT CLAIMING THAT IT IS AS GOOD AS SPEED SCORE.

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 1992-2001 offensive data. For catchers it is .89; for 1B/DH, 1.19; for 2B, .93; for 3B, 1.01; for SS, .86; for LF/RF, 1.12; and for CF, 1.02.

How do I deal with players who split time between teams? I assign all of their statistics to the team with which they played more, even if this means it is across leagues. This is obviously the lazy way out; the optimal thing would be to look at the performance with the teams separately, and then sum them up.

You can stop reading now if you just want to know how the numbers were calculated. The rest of this post will be of a rambling nature and will discuss the underpinnings behind the choices I have made on matters like park adjustments, positional adjustments, run to win converters, and replacement levels.

First of all, the term “replacement level” is obnoxious, because everyone brings their preconceptions to the table about what that means, and people end up talking past each other. Unfortunately, that ship has sailed, and the term “replacement level” is not going away. Secondly, I am not really a believer in replacement level. I don’t deny that it is a valid concept, or that comparisons to replacement level can be useful for answering certain questions. I just don’t believe that replacement level is clearly the correct baseline. I also don’t believe that it’s clearly NOT the correct baseline, and since most sabermetricians use it, I go along with the crowd in this case.

The way that reads is probably too wishy-washy; I do think that it is PROBABLY the correct choice. There are few things in sabermetrics that I am 100% sure of, though, and this is certainly not one of them.

I have used distinct replacement levels for batters, starters, and relievers. For batters, it is 73% of the league RG, or since replacement levels are often discussed in these terms, a .350 W% (at least using a conventional Pythagorean exponent of two). For starters, I used 125% of the league RA or a .390 W%. For relievers, I used 111% of the league RA or a .450 W%. I am certainly not positive that any of these choices are “correct”. I do think that it is extremely important to use different replacement levels for starters and relievers; Tango Tiger's work on reliever replacement level convinced me of this (he actually uses .380, .380, .470 as his baselines). Relievers have a natural RA advantage over starters, and thus their replacements will as well.

Now, park adjustments. Since I am concerned about the player’s value last season, the proper type of PF to use is definitely one based on runs. Given that, there are still two paths you can go down. One is to park adjust the player’s statistics; the other is to park adjust the league or replacement statistics when you plug in to a RAA or RAR formula. I go with the first option, because it is more useful to have adjusted RC or adjusted RA, ERA, etc. than to only have the value stats adjusted. However, given a certain assumption about the run to win converter, the two approaches are equivalent.

Speaking of those RPW: David Smyth, in his Base Wins methodology, uses RPW = RPG. If the RPG is 9.4, then there are 9.4 runs per win. It is true that if you study marginal RPW for teams, the relationship is not linear. However, if you back up from the team and consider things in league context, one can make the case that the proper approach is the simple RPW = RPG.

Given that RPW = RPG, the two park factor approaches are equivalent. Suppose that we have a player in an extreme park (PF = 1.15, approximately like Coors Field) 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 are 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. If we convert to WAA (using RPW = RPG), 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. This is another advantage for the first approach: since after park adjusting, everyone in the league is in the same context, there is no need to convert to wins at all. Sure, you can convert to wins if you want. If you want to compare to performances from other seasons and other leagues, then you need to. But if all you want to do is compare Ryan Howard to Adrian Gonzalez to Joey Votto, there is no need to convert to wins. Personally, I think that stating something as +34 is a lot nicer than stating it as +3.8, if you can get away with it. None of this is to deny that wins are not the ultimate currency, but runs are directly related to wins, and so there is no difference in conclusion from using them if the RPW is the same for all players, which it is for a given league season coupled with park adjusting runs rather than context.

Finally, there is the matter of position adjustments. What I have done is apply an offensive positional adjustment to set a baseline for each player. A second baseman’s RAA will be figured by comparing his RG to 93% of the league average, while a third baseman’s will compare to 101%, etc. Replacement level is set at 73% of the estimated average for each position.

So what I am doing is comparing to a “replacement hitter at position”. As Tango Tiger has pointed out, there is really no such thing as a “replacement hitter” or a “replacement fielder”--there are just replacement players. Every player is chosen because his total value, both hitting and fielding, is sufficient to justify his inclusion on the team. Segmenting it into hitting and fielding replacements is not realistic and causes mass confusion.

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.

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.

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. If you feel comfortable with some other assumptions, please feel free to ignore mine.

One other note here 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. For example, shortstops have a PADJ of .86. If we assume that an average full-time player makes 10% of his team’s outs (about 408 for a 162 game season with 25.5 O/G) and the league has a 4.75 N, the average shortstop is getting an adjustment of (1 - .86)*4.75/25.5*408 = +10.6 runs. However, I am distributing it based on player outs. If you have one shortstop who makes 350 outs and another who makes 425 outs, then the first player will be getting 9.1 runs while the second will be getting 11.1 runs, despite the fact that they may both be full-time players.

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 probably be to use defensive innings--set the full-time player to X defensive innings, figure how Derek Jeter’s innings compare 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.

Given the inherent assumption of the offensive PADJ that all positions are equally valuable, once we have a player’s RAR, we should account for his defensive value by adding on his runs above average relative to a player at his own position. If there is a shortstop out there who 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 we have 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.

It is with some misgivings that I publish “hitting RAR” at all, since I have already stated that there is no such thing as a replacement level hitter. It is useful to provide a low baseline total offensive evaluation that does not include position, though, and it can also be thought of as the theoretical value above replacement in a world in which nobody plays defense at all, yet players are still selected with defensive ability in mind. Imagine that you had to pick a team thinking you were going to play baseball as usual, but right before the game was about to start and your lineup was set, you found out that a third party was going to man the field for both teams I realize that scenario is contrived and absurd, but there is utility in having a measure that compares a player to a low baseline without bringing fielding into the mix.

The DH is a special case, and it caused a lot of confusion when my MVP post was linked at BTF once. Some of that confusion has to do with assuming that any runs above replacement methodology is the same as VORP from the Baseball Prospectus. Obviously there are similarities between my approach and VORP, but there also key differences. One key difference is that I use a better run estimator. Simple, humble old ERP is, in my opinion, a superior estimator to the complex MLV. I agree with almost all of the logic behind MLV--but using James’ Runs Created as the estimator to fuel it is putting lipstick on a pig (this is a much more exciting way of putting it in the 2008 context, don’t you think?).

The big difference, though, as it relates to the DH, is that VORP considers the DH to be a unique position, and 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, hitting as a DH is harder than hitting as a position player, etc. Anyway, the exact procedure for VORP is propriety, but it is apparent that they use some sort of average DH production to set the DH replacement level. This makes the replacement level for a DH lower than the replacement level for a first baseman.

A couple of the aforementioned nimrods took the fact that VORP did this and assumed that my figures did as well. What I do is evaluate 1B and DH against the same replacement RG. 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 on their own. Contrary to what the chief nimrod thought, this is not “treating a 1B as a DH”. It is “treating a 1B as a 1B/DH offensively”.

It is true, however, that this method assumes 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, despite what the nimrods might think--the only necessary adjustment is to take the DHs down a notch. The simple fact of the matter is that first baseman get higher RAR figures by being pooled with the DHs than they would otherwise.

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 Kevin Youkilis (who sees significant time at a tougher position than his primary position), and unduly boost a player like Victor Martinez (who logs 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.

2009 Park Factors

2009 Leagues

2009 Teams

2009 AL Relievers

2009 NL Relievers

2009 AL Starters

2009 NL Starters

2009 AL Hitters

2009 NL Hitters

Playoff Musings

For the sake of discussion, let's assume that we can estimate a team's true W% by taking 40% of their actual W%, 20% of their EW%, 20% of their PW%, and 20% of .500. Let's also assume that there is no quality difference between the NL and AL, no home field advantage, and that all games are independent of one another with the probability of a given outcome constant across games. This will allow us to estimate the quality of the playoff teams as follows:





We can couple this with the binomial distribution (since we assumed independence a constant W%) to figure the probability of each team winning the Division Series, and then the LCS and World Series (P(DS) is the probability that a team will win the Division Series, and so on):




Why am I doing this? It's obvious that while these estimates might be reasonable, they are could be improved fairly easily. We know there's a home field advantage, we could incorporate the actual pitching matchups, we could come up with a better combination of the various W%s--or better yet, we could look at projections for the team's actual personnel rather than using aggregate season W%s. So why bother, especially when you can find playoff odds reports elsewhere on the net that do take some of those factors into account?

As I said, they're a reasonable starting point without getting more involved. For the rest of the piece I will treat them as more than that, for the sake of discussion. More importantly, though, they illustrate what sabermetricians usually mean if they say something like "the playoffs are a crapshoot". The most lopsided first round matchup still yields a one-in-three chance for the underdog, and no team has a greater than 40% or less than 10% chance to win the pennant.

In fact, the source of a lot of the differences is the uneven first round matchups between NYA/MIN and LA/STL. Here are the probabilities of each team winning the World Series given that they make it out of the first round:




Here the probabilities range only from 16 to 36%. The Cardinals move ahead of the Phillies and Rockies; their first round matchup with the NL's top team drags down their chances, but if they get past LA, they are the strongest remaining team in the senior circuit.

Suppose that for some reason the Phillies' place in the playoffs (including seeding--obviously they would actually play the Dodgers and not the Rockies, but that's besides the point) was taken by the Nationals. What would the probabilities look like in that case? Washington was last in the majors with a crude strength estimate of .408--plugging that in produces these results:




Even the Nationals have a 1:4 chance of advancing to the LCS, benefiting from the five-game series. It gets tougher in the two seven game series, but they again have a roughly 1:5 chance of winning that series should they get to either one. Even looking at the playoffs as a whole, Washington has a 1% chance to win the World Series given these assumptions.

1 in 100 may not sound like a lot, but considering that they were the worst team in MLB, it's not that bad. Do you think the average mainstream media member would give them a 1% chance in that scenario? Do you think they'd say they had a 25% chance to beat Colorado in a division series?

I'd have to guess that, no, they wouldn't. I could be wrong, but it seems as if the public in general is far too confident in their ability to project the results of the postseason. If you can't state with more than 80% certainty that the Nationals wouldn't advance past the Dodgers, then what can you say with that kind of confidence?

This is all just a long way of saying that I avoid making predictions about the playoffs. I don't think that I'm smart enough to tell you anything with a high enough certainty level to even make it worthwhile. So instead I offer anti-analysis, something completely personal and not entirely rational--my rooting interests.

I am definitely rooting for the Yankees to win the World Series. First, they have Nick Swisher, who is my favorite player in the game. Second, I actually like George Steinbrenner, and I would love to see him win another championship. Third, I would love to see A-Rod silence the critics that have attempted to brand him as a choker (although even a superlative performance throughout the playoffs by A-Rod would not make that meme disappear completely). Fourth, when the Yankees win there is always a hue and cry from the crowd that constantly wrings its hands about competitive balance, and I really don't agree with their position at all and am amused by their lamentations. Cold and petty? You betcha.

The Red Sox also offer the competitive balance angle, as well as a front office that is easy to root for. I've never been an Angel fan in the past, but Bobby Abreu has always been one of my favorite players and Chone Figgins leading the league in walks doesn't hurt. I also have to admit to being a little partisan towards the AL due to the DH issue. Albert Pujols alone is enough to make the Cardinals likeable, and I have no real problems with the other NL clubs. So:

1. Yankees
2. Cardinals
3. Red Sox
4. Angels
5. Rockies
6. Phillies
7. Dodgers
8. Twins

What I'm really rooting for though is some competitive series and compelling games (although I don't know how likely it is that the drama of the AL Central playoff will be topped). There hasn't been a six-game World Series since 2003, so that would be a great place to start.

More Mundane Comments on the Playoff Structure

In the previous post I briefly mentioned my dislike of the five-game series format currently used in the Division Series and formerly used in the LCS. But what is the real difference between a five and seven game series? If we make some simple assumptions about team quality, how often will the better team win a series of X length? Common sense tells us that the longer the series, the more likely the better team will win, but let's attempt to quantify that. (Actually, it's not attempting, since given the assumptions that I will make, the answers are simple probability, and it's also tough to classify it as an "attempt" since many people have done it before).

First, let's start with the assumptions:

* each game result is independent of the other games in the series (this assumption is likely weaker for the post-season than for the regular season, as the series status has a great influence on how the manager approaches the game, particularly with regards to pitcher usage).

* there is no home field advantage

* the probability of a win for the teams is the same from game-to-game--we are not making any allowances for the aforementioned home field advantage, the identity of the starting pitcher, etc.

With these assumptions in place, we can use the binomial and geometric distributions and the principles behind them to crudely model series of X length. Throughout the rest of the piece, I will refer to "better" or "correct" outcomes. Please understand that I am using these terms in conjunction with the stated assumptions--we know the precise probability of each team winning, and therefore we absolutely know which team is better and ideally will win the series. Obviously, in real life situations we do not know with certainty which team is better. Which is the point--if a playoff format does a poor job of rewarding the better team when we are certain about its identity, it will be even less efficient at that task when we don't know which team is better.

First, let's look at the probability of a team winning the series, given that it is of X length. This can be done with the binomial distribution. For example, for a seven-game series, we simply add up the probability that a given team will win all seven games (even though they will not all be played), six out of seven, five out of seven, and four out of seven. This is the probability that they will win the series.

I will present the probabilities for each interval of .01 in W% between .51 and .65. I have limited the range because realistically in playoff series we will rarely see matchups in which one team is a heavy favorite over the other. The most unbalanced realistic playoff matchup would pit a .700 team against a .500 team, with an expected W% of .700. And that is assuming that the team's sample W%s are their true talent W%s, which would be unlikely for a .700 team. Again, these W%s are the expectations for a single game between the two teams.

I figured the probabilities for series ranging in length from one to fifteen games. I went up to fifteen games because fifteen games was the actual length of the World's Series in 1887, even if the series was not treated with the full championship reverence of today's World Series:



I bolded the 53% line because I'm going to use it as the "average" playoff series--I realize this table is tough to read with fifteen different scenarios. The explanation for why I chose that particular W% is explained below--it's not profound by any stretch (*).

One takeaway from this chart is how silly it is when folks talk about locks to win a playoff series. Even in a situation in which one team has a 65% chance to win each game (which is a big mismatch in the playoffs--a .500 team against a 105 win team or a 90 win team against a 112 win team using Log5), that team only has an 80% shot at winning a seven-game series. Even if you more than double the series length to fifteen games, there's still an 11.3% chance of an upset.

When sabermetrically-inclined people say that the playoffs are a crapshoot, this is the kind of thing they're generally talking about. It's not that you have no way of knowing which team is better or estimating the degree to which they are, it's just that even in a case where you have clear superiority, the short length of the series makes an upset quite feasible.

It was quite amusing during the Roy Halladay sweepstakes to hear commentators talk about how the Phillies were a lock to win the pennant if they got Halladay. Just like it was amusing to read about how the Cubs were going to march right through the weak NL to the pennant last year, or how the Tigers were going to trounce the Cardinals in the World Series. I wish I knew one-twentieth as much about baseball as those folks think they know.

Let's express that table in a more useful form by showing the marginal probabilities for each extension of series length. For example, the team that wins 51% of their games will win a one-game playoff 51% of the time. Expanding to a three game playoff will lead to them winning 51.5% of the time, an increase of .5%. If we expand to a five game playoff, they will win 51.9% of the time, an additional increase of .4%. This will enable us to see the benefit to lengthening series in terms of ensuring the better team wins:




As you can see, the added benefit starts diminishing quickly and for the normal range, essentially levels out after you make the move to seven games. Of course, these are the marginal outcomes, so longer series are still "better"...but less so with every additional pair of games.

Since the marginal benefit levels off after lengthening to seven games (for the nearly even matchups at least--the more lopsided matchups continue to show significant increases), it seems like as good of a point as any at which to stop.

Of course, I have approached this solely from the perspective of encouraging correct outcomes. This is not the goal of a league--if it was, there would be no need for any kind of playoffs at all. The league is going to act in a way so as to maximize its profits. Which is well and good, but I am examining this from the personal perspective of what I'd like to see and/or what will produce the best outcomes.

There is one thing that overlaps between my perspective and the economic interests of the owners, and that is the desire for a competitive series. Close series encourage higher ratings, and longer series means more ticket revenue. For a fan, there's nothing more exciting that a decisive game for the world championship after a hard fought series. While I have a strong preference for better outcomes, I can't completely suppress the desire for a winner-take-all finale.

So, given the underlying assumptions of this post, let's look at the probabilities of a decisive game, given a series of X length. This is done with the geometric distribution, and I have included the formula (**) because I think many fewer people are familiar with it than the binomial distribution--just speaking for myself, I know the binomial function by heart but have to look up the geometric function just to be safe:



A five-game series with a fairly normal matchup will produce a game five about 37% of the time; a seven-game series about 30% of the time. So for a roughly 1% increase in the likelihood of the better team winning, you give up decisive games in 7% of your series.

The next step, moving from a seven-game series to a nine-game series, would result in roughly the same increase in the likelihood of the better team winning while sacrificing another 4% of series without a grand finale.

All told, it shouldn't be too surprising that the probabilities here can be read to suggest that MLB has correctly identified the series lengths that provide the best combination of practicality, uncertainty of outcome, and producing desired outcomes. The extra benefit in terms of desired outcomes from expanding to longer series is relatively small, and is offset by a larger percentage drop in the expected proportion of series with decisive games.

Finally, let's take a look at the potential value of home field advantage in a five-game series. I previously looked at World Series HFA (i.e. seven-game series), and the same principles will apply here. I have not looked at the empirical data in this case and will only be discussing theoretical results.

First, we can use the geometric distribution to calculate the percentage of series that are expected to go X games, assuming that each game is a 50/50 proposition (in other words, not considering HFA):



Just as is the case for a seven-game series, the probability of a full-length series and one short of it are equal. This makes logical sense, of course; in order to create this situation the first three games must have produced a 2-1 series. There is a 50% chance that the team that has already won two wins, ending the series and a 50% chance that the team behind forces a decisive game.

Unlike a seven-game series, it is impossible for the team with on-paper home field advantage to play more road games than home games, as the format is 2-2-1 (Obviously, I'm talking about the current format; I'm aware that it was sometimes different in the past). Theoretically, on-paper home field advantage results in a true home field advantage 62.5% time, and the other 37.5% of the time there is no HFA for either team.

In order to add HFA into the mix, we need to identify all the possible series sequences, which I will not reproduce here. Suffice it to say that from the perspective of the winning team, there is one series sequence that produces a three-game series (WWW), three that produce a four-game series (WWLW, WLWW, and LWWW), and six that produce a five-game series.

I will assume a home field W% of .573, which is the empirical World Series statistic. I believe that the "true" parameter is likely lower, for reasons discussed in the earlier post, but I'll use the sample statistic for the sake of discussion. Retaining the assumptions of evenly matched teams and independent game outcomes, the probability of the team with on-paper HFA winning a five-game series is 52.66%, compared to a 52.31% chance in a seven-game series. So HFA is theoretically more important in a shorter series (no surprise, but we've estimated the degree).

It should also be noted that we would expect the empirical home field advantage in a five-game series to be even stronger because in those series, the on-paper advantage usually goes to the team with the better record. The same applies to LCS games, but not to the World Series as on-paper home field advantage is chosen without regard to the specific teams competing.

That's it, except for the asterisked digressions.

(*) There is no particularly compelling reason to use 53% as a default W%; I just wanted a line that you could focus on that was reasonably telling, because the whole table is a bit much.

Anyway, I chose 53% because in the World Series (for 1923-2008 with a few years excluded), empirically the mean W% of the team with the better record has been .635, and the team with the lesser record has a mean of .594. Regressing 30% to .500, this results in .595 and .566. Log5 tells us that a .595 team should beat a .566 team 53% of the time. And there you are.

(**) The geometric distribution gives the percentage of time a certain number of failures (x) occur before a certain number of successes (r) occur for a binomial process. In the case of a baseball series, r is the number of wins for the victor in a series (3 for a five-game series, 4 for a seven-game series, etc.), x is the number of wins for the series loser (in a five-game series with a decisive games, x = 2; for a seven-game series with a decisive game, x = 3). We also need to know the probability of a success (P), and calculate the number of combinations using the combination function C(x + r - 1, x).

To find the probability of a decisive game for the series as a whole (with either team winning), we need to do a calculation for each team, which is why the results are summed below--one for the winner and one for the loser. Let G be the number of games in a full length series, W the number of wins for the winning team in such a series, L the number of losses for the losing team in such a series, and P the probability of one of the team winning an individual game. Then the probability of a decisive game is:

C(G - 1, L)*P^W*(1 - P)^L + C(G - 1, L)*P^L*(1 - P)^W

For example, the probability of a seventh game in a series (G = 7) in which one team has a 55% chance of winning each game (P = .55) is (W is 4 and L is 3, of course):

C(6, 3)*(1-.55)^3*.55^4 + C(6,3)*.55^3*(1-.55)^3 = 30%

One other thing to note is the expected number of games in a series. This is found by taking summing G*P(G) for all possible series outcomes. So in a five game series, the expected number of games is:

3*P(3 games) + 4*P(4 games) + 5*P(5 games)

Reverting to the assumption that each game is a 50/50 proposition, the expected number of games in a five-game series is 4.125. The expected number of games in a seven-game series is 5.8125. You can see that there are diminishing returns going on; despite lengthening the possible length of the series by two games, our expectation is that the actual number of games will only increase by 1.6875 games.

The probability of a decisive game hints at this as well, but this is another way you could attempt to quantify the real observed benefit of lengthening a series.

I'll Probably Regret This, But What the Heck?

I have always vowed never to be the old fogey who doesn't know anything about new technology, and yells "get off my lawn", and talks about how he walked eight miles to school uphill...well, you get the idea, and I'm sure you've vowed the same thing. It's an easy thing to say when you're young or middle aged, and probably a lot harder to actually do when you're older.

In any event, I'm really not old enough to worry about it yet, but just in case, I decided to start a Twitter. It's not going to be very interesting, and so far I've just been using it to snark, which is not the nicest side of me or anyone else. But it's nice to have an outlet for quick thoughts and non-baseball things (although a lot of my comments--I will not give and in and call them tweets--will be about baseball). Any real sabermetric content will continue to be posted here, so even if for some reason you find this worth reading, you won't be missing anything by not reading the twitter feed.

Larry Corcoran's New Tombstone

There is a nice story from the New Jersey Star-Ledger about some firefighters who have raised money to erect a headstone for Larry Corcoran. Corcoran, for those of you who don't know much about nineteenth century and haven't read any of my 1876-1881 NL series, was an outstanding pitcher for the Chicago White Stockings (today's Cubs). He was the first pitcher to toss three no-hitters, the ace of Chicago's 1880-82 pennant winning teams, and IMO the most valuable pitcher in the NL in 1880.

This is certainly a nice gesture, and it's always nice to see overlooked nineteenth century ballplayers get their due. However, they may have wanted to run the design by someone before going ahead with it...

h/t: SavoyBG at Baseball Fever

Mundane Comments on the Playoff Structure

Believe it or not, this is a post filled with opinions. The underlying assumption is that if you are not interested in my opinion, you will not read, and so I’m not going to go around and apologize for giving my opinion in what follows.

The current MLB playoff system is bizarre from a certain standpoint, as the number of teams vary from division to division, even within the same league. It is apparent that teams from different divisions do not have equal likelihoods of making the playoffs (and therefore winning the pennant or the World Series) due to this structure, even if one assumes that all teams are equally likely to win each game.

In fact, if you grant me another assumption, that there is no home field advantage (I would add a balanced schedule, but since we have assumed that all teams are equal, we really don’t care--your opponents are .500 even if you play the Dodgers in all 162 games) in the playoffs, it is relatively simple to calculate the chances of a team from each division reaching certain goals.

Using the AL East as the example, there are five teams in the division; each team therefore has a 1/5 chance of winning the division title. 4/5 of the time, they will not win the division and thus will be in competition for the wildcard. There are fourteen teams in the American League, three of which will win division titles, so they are competing against eleven teams for the wildcard, and are expected to win with probability 1/11. The probability of making the playoffs is straightforward:

P(Playoffs|AL East) = (1/5) + (4/5)*(1/11) = 7/22

Since we have assumed equality amongst team and no home field advantage in the playoffs, the probability of winning the pennant is simply:

P(Pennant|AL East) = P(Playoffs|AL East)*(1/4) = (7/22)*(1/4) = 7/88

And the probability of winning the World Series is just as simple:

P(World Series|AL East) = P(Pennant|AL East)*(1/2) = (7/88)*(1/2) = 7/176

The probabilities for the other divisions can be figured similarly, and converting to four place decimals (overkill, I know, but I feel bad about killing all the nice fractions), this is what you get:



I realize that I am not telling you anything you couldn’t figure out for yourself.

One thing to note here is that the difference between playing in the AL and the NL is not too much of an issue as long as the divisions are of equal size. An AL East team can expect an extra playoff appearance every 89 years and another world title every 714 years compared to its NL East counterpart. This isn’t really worth worrying about IMO, and since the AL was at a similar disadvantage between 1977 and 1992, it only seems fair in a way.

The real issue lies in the divisions of different sizes, not the fact that the leagues are different sizes. An AL West team can expect to make the playoffs 32 times in a century, while an AL East or Central team will make the playoffs 27 times. Of course, there are so many other factors at play (after all, teams are not perfectly balanced as we have assumed) that you may not find this particularly troublesome.

The gap between the two extreme divisions, the AL West and the NL Central, is pretty extreme. Nine extra playoff trips and one extra world title per century seems inherently problematic for my money.

It would be nice if you could balance the two issues (more teams in the division making a division win less likely, more teams in the league making a wildcard less likely) by putting the larger division in the smaller league, but of course it is only because the league is larger that a division must be larger.

Assuming that expansion to thirty-two teams is inevitable (and I believe it is, although any guess on the timeframe would be me blowing smoke), and that the two league structure will endure (no need to start a civil war here), what should the divisions look like when it happens? As a side note, it certainly appears as if there will be no expansion prior to 2015, which will make the period from 1998-whenever the longest period of non-expansion in the expansion era (surpassing 1977-1993).

What I would suggest is two eight-team divisions in each league, with the wildcards being the two non-winners with the best record. In fact, I would like to see such a structure right now, with the difference being that the AL divisions would each have seven teams. Larger divisions are my preference as they increase the probability of the best teams making the playoffs.

However, the entirety of American pro sports history shows a trend towards smaller divisions over time. I did not check thoroughly, but I do not believe that any of the four major leagues have ever reduced the number of divisions. Certainly baseball has not, going from no division to two divisions in 1969 to three divisions in 1994. Football has gone from two to three to four, and hopefully will serve as a cautionary tale for baseball.

After all, in the NFL, it is relatively common for 8-8 teams to win one of the four-team divisions; in 2008, the Cardinals and the Chargers both pulled this off, and while it was unusual to have two such cases in one season, individual occurrences are not particularly uncommon.

For the NFL, the issue of having two good teams in one of the divisions while a mediocre team wins another division is blunted by the presence of two wildcards. But still, something just feels wrong about having the 11-5 Patriots on the outside looking in while the Chargers are in. Any divisional format will occasionally result in teams with better records being left out, but the tiny divisions increase the odds.

For baseball, unless the playoffs were expanded, you don’t have a lot of choices. You can have:

1) 4 4-team divisions, no wildcard
2) the NL model of 2 5-team divisions plus a 6-team division, 1 wildcard
3) 2 8-team divisions, two wildcards
4) one big league

While this is certainly a matter of personal taste, option four is the clear winner to me, while option three is the most attractive that would have a prayer of being implemented.

As an aside, I find the phenomenon of increasing numbers of divisions as time has marched on somewhat puzzling. Travel times and expenses should have made smaller divisions and unbalanced schedules most appealing early in the history of leagues, not now. The universality and as of yet unrelenting nature of the trend could be explained in a few ways. The most generous explanation is that fans like the excitement generated by more, smaller divisions, and the leagues are just giving their customers what they want. I find this preference odd, as an 8-8 team winning a four-team division does not seem any more exciting to me than a 9-7 team beating out another 9-7 team for a wildcard spot. But it may well be there the cachet that goes with winning a division as opposed to winning a wildcard justifies the system economically.

It may be so, but the reasoning behind it is completely foreign to me. In the small division race, you have to beat out just three other teams. In the wildcard race, you have to beat out thirteen other teams (admitted they are all teams with lesser records than at least one other team in the league and possibly as many as three). Still, I’m not impressed by being a division champion if all that entails is beating out three other teams.