## Thursday, September 29, 2011

### Playoff Meanderings

I always like to put down some of my thoughts about the playoffs each year, but it’s a challenge to say anything even remotely close to being meaningful. Predicting the outcome of short series is folly (although I’ll engage in a little of this folly later), and you can read that anywhere. So I always try to come up with a different angle to illustrate why the playoffs are subject to such uncertainty.

I’ve certainly had some more interesting illustrations in the past; this one is pretty lame, but for some reason when it crossed my mind in August I thought it was a lot more interesting than I do now. What is the value of each playoff game or series in terms of a regular season game? In asking this, I’m not talking about the weight that should be applied to playoff performance for evaluating individual value, or any such thing...I’m just asking what the implied value is, given the assumption that the regular season standings carry over to the playoffs.

Of course, that’s not how it works--it's a clichÃ©, but every team starts every series out at 0-0. However, I’ll assume that regular season standings carry over (resetting with the start of each additional round to keep things manageable) and the playoff games are weighted in a manner such that at the end of the series, the team that wins the series has a better overall record than its opponent.

There are at least two different ways to approach this increasingly silly scenario, which will be best illustrated by example--treating the series outcome as a binary, or considering the games individually. Suppose that the Alphas enter a five-game division series with a record of 92-70 while their opponents the Betas are 90-72.

First, from the series outcome perspective, if the Alphas win, the series was unnecessary since the Alphas already led in the standings. If the Betas win, however, the series must be given a weight of a number of games such that adding that many wins to the Betas and losses to the Alphas give the Betas a better record. Leaving things in terms of whole games, the answer in this case is three. Giving the Betas three additional wins leaves them at 93-72; three additional losses for the Alphas would make them 92-73. The series could have gone three, four, or five games, making the effective value of those games equal to either 1, .75, or .6 regular season games.

You can also consider this from the game perspective, that is actually looking at the outcome of each game in the series rather than treating the series as a binary win or loss. If the Betas win the above series 3-0, this is pretty straightforward given the two game margin--treating playoff games as equivalent to regular season games leaves the Alphas 92-73 and the Betas 93-72. Suppose the Betas had been 88-74 instead of 90-72, though. In order to bring the Betas ahead of the Alphas (on a whole wins basis), they need five, so each win (and thus each game has to be worth) 5/3 = 1.67 times a regular season game. Now the Alphas have 3*1.67 + 70 = 75 losses and the Betas have 3*1.67 + 88 = 93 wins, so that the Alphas record is 92-75 and the Betas 93-74.

You can see that if the final margin of the series is 3-2 in favor of the Betas, the weight on each playoff game would have to be roughly four times that of a regular season game since the Betas only pick up one win when the playoff series is considered. A 4x weight brings the Alphas and Betas together at 100-82.

This is all just a silly digression, but given the assumptions it is a simple way to think about how the implied value of a playoff game compares to that of a regular season game.

Getting to the 2011 playoffs, let me offer some quick thoughts. I’ll leave the detailed handicapping to those who are better suited for it and also like quixotic quests. The marginal value of more in-depth analysis is limited, but if that’s what you seek, you won’t find it here.

The probabilities that follow assume nothing about home field advantage or pitching matchups, or even true talent for that matter. They are simply based on my crude team rankings, fueled by 25% actual W%, 25% expected W% (from R/RA), 25% predicted W% (from RC/RCA), and 25% from .500.

That formula is also arbitrary. The results should be fairly reasonable, but I’m also eager to disown at the same time, as something of a commentary on the futileness of the exercise...and most especially the bloviating that is done without any logic at all. I’m sure that there are many scribes across the country furiously writing about how certain teams have no chance, never learning the lesson that the differences between major league teams simply aren’t that great, especially after eight of the best have been selected from a 162 game sample.

This method considers all of the playoff teams to be in the top ten in MLB; only Boston (#3) and the Angeles (#8) are on the outside looking in. The Yankees, Phillies, and Rangers are near co-favorites to win it all; NYA and TEX are ranked about evenly, while PHI benefits from the weaker NL field and has the highest odds of winning a first round series and the pennant. Overall, the AL has an estimated 57% chance of winning the World Series. The most likely matchup in the Series is NYA/PHI (11%); the least likely is DET/STL (4%). The rankings imply that the worst playoff team (ARI) would beat the best playoff team (NYA) 43% of the time, which over 162 games is seventy wins. Strictly equating true probability to actual 2011 record, consider the odds that the Padres could win a seven game series against the Indians, and there is roughly the same likelihood of the Diamondbacks winning a seven game series against the Yankees.

As far as my personal rooting interests go, New York and Tampa Bay are my top two choices, followed by Milwaukee and St. Louis. I would be happy to see any of those teams win, have no particularly strong feelings about Arizona or Detroit, and be mildly disappointed if it’s Philadelphia or Texas. But there are no White Sox in this group.

## Tuesday, September 20, 2011

### A Quick Look at Negro League W-L Records

I wrote this about a year ago and wasn’t sure if I’d ever post it. With the recent publication of some Negro League data at Seamheads, I figured I’d better post it now before it became completely dated. The data I used was compiled by Chris Cobb and posted on the Hall of Merit site, with John Holway's research as his source data.

I need to admit upfront that I know very little about the Negro Leagues. My knowledge level of the Negro Leagues peaked at about age eleven when I read Only the Ball Was White, and has only gone downhill since then. That is one of the reasons for this post--as a (very limited) education for me on the great pitchers of the Negro Leagues.

I am going to be applying the Netural Win-Loss record approach introduced by Rob Wood, which I have written about several times. It is a way to contextualize a pitcher's W-L record using only the win-loss record of the pitcher's team. This post applies it to several Negro League pitchers.

The basic idea behind Wood's approach is that an average team's deviation from .500 is due in equal parts to their offense and defense. The portion of a team's deviation from .500 that arises from the defense (with the exception of relievers in the pitcher's game and fielders) doesn't do anything to increase a pitcher's expected W% in reality, but if you compare his W% directly to that of his teammates', he will suffer for it.

The formula is simple and linear; instead of comparing a pitcher to his team's W% when he does not get a decision (Mate), the comparison is to the average of Mate and .500. The neutral W% is easy to figure:

NW% = W% - Mate/2 + .25

From NW%, one can figure Neutral Wins and Losses:

NW = NW%*(W + L), NL = W + L - NW

It is also very easy to combine NW% and the number of decisions into wins above some baseline. Wins Above Team is traditionally defined as wins above .500:

WAT = (NW% - .5)*(W + L)

I also use Wins Compared to Replacement, with the assumption that a replacement level starter will have a .380 W%:

WCR = (NW% - .38)*(W + L)

There are a number of weaknesses to the Neutral W-L approach, and there are a number of additional complications that arise when applying it to the Negro League data. This is an incomplete list of the methodological issues that are present even when looking at major league data:

* It does not isolate performance when the pitcher actually pitches; some will receive lousy run support despite pitching for good offensive teams.

* While the approach assumes that the team is balanced between offense and defense, this is not always the case. It is a decent assumption for a pitcher's entire career, but there are still going to be cases in which a pitcher is predominantly on teams skewed one way or the other. Those on offensive teams will benefit unfairly in the metric, while those who are on teams with otherwise strong starting pitching staffs will be hurt.

* All of the problems with the definition and concept behind pitcher wins and losses themselves are still present

With respect to the Negro League results included in this post, the data I have used was compiled by Chris Cobb and posted on the Hall of Merit site, with John Holway's research as his source data. Among the problems that arise from the data:

* The records themselves are incomplete (missing seasons, team records only published for half seasons, etc.) and sometimes contradictory (individual totals that don't add up to the team total, etc.) These kind of errors exist even in major league data from the period, so it's no surprise that they are present in the more chaotic, less-organized Negro League data.

To deal with the gaps in the specific data I used, if I couldn't find the team's record, I assumed that they were .500 when the pitcher in question's decisions were removed. If a pitcher split time between teams and there was no breakdown of his W-L record with the two teams provided, I used the average of the two team's record. For seasons in which Cobb did not include the team's record and I had to look it up from another source, I used the ESPN Baseball Encyclopedia. In that case, if the team's record was only available for a half-season, I assumed that the full season record was double the half-season record.

* I only used the results from domestic Negro League games. The world of the Negro Leagues encompassed a lot more than that; players went to the Caribbean to play, teams barnstormed extensively, played games against major league opponents, etc. Limiting the analysis to league games makes it workable, but it does omit a lot of relevant performances.

In this regard the Negro Leagues were similar to the early NA/NL days, in which the league schedule constituted only a small fraction of total games played, and independent teams often compared favorably to league opponents.

* I am way out of my area of knowledge, but even I feel comfortable asserting that the NeL pitching rotations looked more like the early majors then the contemporary majors. Pitchers got a higher percentage of their team's decisions, reducing the sample size from which Mate is drawn and weakening the assumption that the other pitchers are average. I have also read that teams would purposefully match their aces against one another to create gate attractions, whereas our normal assumption is that teams will try to match their pitchers up in whatever manner creates the highest number of expected wins.

* The league structure was less stable from year-to-year, which makes it harder to compare NeL pitchers from one time period to the other. For twentieth-century major league pitchers, we can be confident that, regardless of when they pitched, that they were facing the highest level of competition available (with the obvious exception of the players locked out of the majors due to their skin color). We also know that they pitched in seasons of roughly equal length, and so their career records represent a fair sample of their performance at different ages.

We don't have that confidence when dealing with the NeL data. For example, Satchel Paige gets no credit for 1935 here, but the adjacent seasons of 1934 and 1936 appear to be among his best. Then he gets no credit for 1937-39, as he was not pitching in official league games. You will see that Paige doesn't come out as impressively as might be expected in the career totals, but the gaps in league play might well be the major cause.

* I have listed WCR figures using a .380 replacement level, but in actuality I have no idea where the NeL replacement level should be set.

From all of the caveats, it may seem as if I am declaring the NW-L statistics to be useless. That is not my intention; I simply don't want to oversell them or fail to acknowledge their biases. Many of the issues with the NW-L records are issues that would arise with any statistical analysis of Negro League pitchers. Consider what a logistical nightmare it would be to try to look at runs allowed, needing innings, and league averages, and park factors.

As sabermetricians we all know the flaws of pitcher W-L records, but there are a few benefits. Among them is the ease in determining them, at least if complete games are the norm. All you need to know is who the starting pitcher was and which team won the game, and you've got it. No need for box scores or play-by-play. No need for park factors or league averages--the average in every league and every park for all of time is .500.

These useful properties are most useful when dealing with incomplete data, and we can refine them further by incorporating team record and producing NW-L. Are the results perfect? Absolutely not. Are they likely to give us a better indication of the quality of these pitchers than raw W-L record or uncontextualized ERAs? I say yes.

The pitchers for whom data was available were: Chet Brewer, Dave Brown, Ray Brown, Bill Byrd, Andy Cooper, Leon Day, Willie Foster, Leroy Matlock, Satchel Paige, Dick Redding, Bullet Joe Rogan, Hilton Smith, Smokey Joe Williams, and Nip Winters.

Since I am out of my area of knowledge when discussing the Negro League stars, I'm not going to make a lot of comments--I'll leave interpretation up to the reader. Here are the actual career W-L records for the pitchers, along with Mate. The list is sorted by career wins above .380:

Only one of the pitchers had a worse record than that of his teams (Chet Brewer). If one figures Wins Above Team by the traditional method, Brewer would rate as a below-average pitcher. It's far more likely, though, that a pitcher with a .591 W% regarded as an excellent pitcher was in fact an excellent pitcher. The fact that his teams played .624 baseball without him indicates that they probably had above-average pitching, which while good for the team did absolutely nothing to increase Brewer's expected W%. Brewer still takes a hit, of course, when neutralizing his record by the Wood approach, but is assumed to be an above-average performer.

Here are the career neutral W-L records for the pitchers, sorted by WCR:

Here is a link to the spreadsheet containing the complete yearly breakdowns for each pitcher. You can see exactly what I inputted and which seasons I didn't have team records for (you'll see blanks in the TW and TL columns):

Again, this is obviously a very incomplete examination of the careers of a limited number of Negro League stars, and I certainly would not advocate placing too much stock in the results.

## Monday, September 12, 2011

### Scoring Self-Indulgence, pt. 5: Baserunner Advances

Last time I covered my scoring codes to recognize a batter reaching base; this time I’ll discuss what I record once he gets there. I’ll start with advances made by the runner independent of the actions of a subsequent batter on his team--things like stolen bases and advancing on wild pitches. Most of the codes that follow are pretty straightforward. In each case, I’ll show the advance as a runner going from first to second, but the same concepts apply to advancing to third and scoring. In each case, I’ll assume that the batter reached first by being hit by a pitch.

For every advancement that occurs during the course of a plate appearance, I record both the lineup slot of the batter at the plate and the pitch on which the event occurs (or which pitches it is between if applicable). The pitch is indicated by the same letter used in the batter’s box, except in lower case--the first pitch of a PA is “a”, the second pitch is “b”, etc.

There are several exceptions. If the last pitch (which is never given a letter in the batter’s scorebox) is labeled “lp”. If an event happens before the first pitch of a plate appearance, I use “bfp”. Finally, if an event occurs between pitches, it is labeled “a!”, where ! is replaced by the pitch letter for the last pitch before the event. Suppose the event occurs between pitches two and three of the plate appearance; in this case, the pitch code for the event is “ab”, because the second pitch (b) was the last one thrown. “ab” can be read as “after b”.

The code for a stolen base is the obvious “SB”. If it occurred on the third pitch of a plate appearance taken by the #6 batter in the lineup, the scoring would be:

As you can see from the example, the pitch information is written above the advancement symbol, in smaller type.

Wild pitches and passed balls are separated by a distinction I’d wipe out of the rule book if given the chance, but I do record them differently: “WP” and “PB” are the obvious codes. In the examples, the wild pitch occurs on the last pitch to the #6 batter, and the passed ball occurs on the first pitch to the #2 hitter:

The code for a balk is “BK”; this one comes between the third and fourth pitches to the cleanup hitter:

I don’t like the scoring distinction between a stolen base and defensive indifference, but I do make note of it on my scoresheets because SB is such a common category, and it’s easier to keep track of the ones that are really scored as steals and add in fielder’s indifference if one chooses than it is to try to divine after the fact what the scoring was. I refer to it as Fielder’s Indifference (FI), because it is a subset of fielder’s choice by definition, and the symbol seems more consistent. This one occurs on the sixth pitch to the #5 hitter:

A runner could advance on an error between pitches, which almost always would be a throwing error. If the pitcher throws the ball away on a pickoff attempt before the first pitch to the #2 hitter, the scoring looks like this:

Sometimes, the extra bases are gained before the batter-runner becomes a runner; that is, on the same play on which he reaches base. Suppose a batter dribbles a hit to the pitcher, but in his haste to make the play, the pitcher hurls the ball down the right field line, allowing the batter to move up to second. The scoring looks like this:

If there is no additional information included with the notation, it is assumed that the advance occurred on the same play as the on-base event. The other common way a batter-runner moves up is when he is able to advance on a throw to another base made in an attempt to retire another runner. In this example, the batter singles to right, then advances to second on a throw home. The code “ATx” means advanced on throw, with x standing in for the base to which the throw is made (2 for second, 3 for third, and H for home):

I have yet to touch on the means by which most bases are gained: advances on plays initiated by subsequent batters. I mark these by writing and circling the batting order position of the batter responsible in the quadrant of the runner’s scorebox corresponding to the base he wound up at. Suppose the runner from first advances to third on a play initiated by the #7 hitter. I would score it:

If the runner scores, then I use a box instead of a circle, so that it’s easy to distinguish how many runs a team has scored. In this case, the runner who moved to third a player initiated by the #7 hitter ends up scoring on a play initiated by the #9 hitter:

A runner can also score due to an event not initiated by another batter. The most common is scoring on a wild pitch. In this example, the runner from third scores on a wild pitch, with the wild pitch coming on the second pitch to the #9 hitter:

As you can see, I allow the box that indicates a run scored to vary in shape and size as appropriate to allow the necessary space for recording the event.

Sometimes, the event that advances the baserunner occurs while the ball is in play, but referring to the relevant batter’s scorebox will not note how the advancement occurred. Suppose that there is a runner on first, and the batter singles to right, advancing the runner to second. Then the right fielder boots the ball, allowing both to move up one base (the batter-runner to second and the runner to third). In this case, I would simply record the appropriate batter number circled in the runner’s third base quadrant. The batter’s scorebox will include the error by the right fielder, imply that it occurred during his plate appearances, and thus imply that the single plus the error enabled the runner to advance from first to third.

However, there are also cases in which the runner advances but the batter stays put. Suppose that the same play occurs as described above, except the batter-runner (who happens to be the #4 hitter) stops at first base. Now I would score the runner’s advancement as:

In this case, the use of a small circled 4 above the error indicates that the error occurred during the PA of the cleanup hitter.