Baseball Player Won-Loss Records
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Shared Credit

In many cases, it is not clear exactly who should get credit for a particular play. For example, pitchers and catchers share responsibility for Component 1 (basestealing) Player decisions. The allocation of Player decisions in these cases is done based on the relative skill level apparent by the relevant players.

The technique outlined here is used to divide responsibility between pitchers and catchers for Component 1 (basestealing) and Component 2 (wild pitches and passed balls) Player decisions, between pitchers and fielders for Components 5 (hits vs. outs), 6 (single vs. double vs. triple), and 7 (double plays), and between batters and baserunners for Components 7, 8 (baserunner outs), and 9 (baserunner advancements).

The division of Component 1 Player decisions between pitchers and catchers is used here as an illustration of the general technique.

1.    Basic Theory
How does one determine how to divide credit between pitchers and catchers for Component 1 (basestealing) Player decisions?

Let's begin by asking, what if somebody deserved no credit for a particular component of Player decisions but we allocated Player decisions to them anyway? For example, what if we assigned Component 1 Player decisions to the defensive team's right fielder? What would we expect Component 1 Player decisions to look like in that case? Essentially, we would expect every right fielder to have a Component 1 winning percentage of 0.500 plus or minus some random variation.

Suppose we were to try to predict a right fielder's Component 1 winning percentage over some time period based on his Component 1 winning percentage over some other time period. We would expect, in such a persistence equation, for there to be no predictive ability of this component.

Alternately, what would we expect Component 1 Player decisions to look like if we assigned them to players who had different levels of talent in terms of affecting the opponents' basestealing? In such a case, we would expect a player's Component 1 winning percentage to be equal to his "true" winning percentage (his "true-talent") plus or minus some random variation and for a player's Component 1 winning percentage over some time period to have significant predictive capacity over other time periods.

In other words, the extent to which a player's winning percentage at some point in time is predictive of his winning percentage at some other point is suggestive of the extent to which there is a true skill involved in a particular component. Based on this, Player wins and losses are allocated in proportion to the extent to which a player's winning percentage has predictive power.

2.    Mathematics
The basis for dividing shared Player decisions is Persistence Equations. I divide the plays that took place in a particular season into two pools: odd and even. To evaluate the persistence of skills, I then fit a simple equation which attempts to explain winning percentage by component on even plays as a function of the same factor for odd plays:

(Win %)Even = b*(Win %)Odd + (1-b)*(Win %)Baseline


where (Win %)Baseline represents a baseline toward which Component winning percentage regresses over time.

The coefficient b in the persistence equation measures the persistence of Component winning percentage between the two samples (even plays v. odd plays) and, hence, the extent to which Component winning percentage is a true "skill" for the relevant set of players being evaluated.

This equation is estimated using a Weighted Least Squares technique which weights observations by the harmonic mean of the number of games over which the even and odd winning percentages have been compiled squared.

3.    Complication: Controlling for the Talent of the Other Players Involved
Earlier, I identified a defensive team's right fielder as an example of a player for whom we would expect his Component 1 winning percentage to simply be randomly distributed. In fact, however, some of you might have seen a flaw in my example.

In 2004, the Montreal Expos allowed only 58 stolen bases on the season, while catching 41 opposing baserunners attempting to steal. Based on this, the Montreal Expos compiled a team-wide Component 1.1 (basestealing by runners on first base) winning percentage of 0.642. Of course, this means that Expos right-fielders would have a combined Component 1.1 winning percentage of 0.642, not 0.500, not because Expos right fielders had some innate ability to prevent the other team from stealing bases, but because they had the good fortune to be teammates with Brian Schneider, who amassed an unadjusted Component 1.1 winning percentage of 0.660 at catcher.

On the other hand, the 2002 New York Mets allowed 151 stolen bases against only 53 caught stealing, leading to a team-wide context-neutral Component 1.1 winning percentage of 0.428, due, in part, to the notorious problems of their catcher, Mike Piazza, who allowed 125 stolen bases (which led the National League) against 27 caught stealing in 121 games caught, for a context-neutral Component 1.1 winning percentage of 0.317.

Unfortunately, this problem with attempting to measure "true-talent" Component 1 winning percentage is not limited to outfielders, where we know that no such talent exists. In fact, on average, the context-neutral Component 1.1 winning percentage for Montreal Expos pitchers in 2004 was 0.642, not necessarily because Expos pitchers were particularly adept at holding runners on base, but, in large part, because Brian Schneider was their catcher. Yet, pitchers do have some ability here. The key is to separate the ability of Montreal Expos pitchers from the ability of Montreal Expos catchers.

The first step before one can accurately assess "true-talent" Component 1 winning percentages is to adjust player winning percentages for the context in which these percentages were amassed. Specifically, pitchers' Component 1 winning percentages are adjusted to control for the Component 1 winning percentages of their catchers, and catchers' Component 1 winning percentages are adjusted to control for the Component 1 winning percentages of their pitchers. Similar adjustments are done for all Components for which Player Game Points are to be shared.

This is done iteratively. First, pitchers' Component 1 winning percentages are adjusted to control for the Component 1 winning percentages of their catchers. This is done using the Matchup Formula.

After pitchers' winning percentages are adjusted based on catcher winning percentages, catcher winning percentages are then adjusted based on these newly-adjusted pitcher winning percentages. Ideally, one would probably prefer to continue the iterative process until all Component 1 winning percentages do not change between iterations. For computational simplicity, I simply repeated this process three more times for both pitchers and catchers.

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