Baseball Player Won-Loss Records
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Component 2: Wild Pitches, Passed Balls

In the second step of calculating Player Wins and Losses, baserunners, pitchers, and catchers are given credit and blame for either advancing (allowing) or failing to advance by (preventing) wild pitches or passed balls.

1.    Calculation of Component 2 Player Game Points
Credits/debits for wild pitches and passed balls (and the occasional case of a baserunner being thrown out trying to advance on a wild pitch or passed ball) are calculated simply as the change in Win Probability resulting from the change in the base/out situation (and the score, if appropriate). Component 2 is also where credit is given to batters for successfully reaching base on a dropped third strike.

The probability of a wild pitch or passed ball is calculated based on the league-wide percentage of times such an event occurred given a particular baserunner/out state – that is, 24 probabilities are calculated, one for each base-out state (note, in this case, non-zero probabilities in bases-empty situations refer to incidences of the batter reaching base safely on a dropped third strike). Unique probabilities are calculated for each league-season. As an example, average probabilities for the entire Retrosheet Era (1921 - 2017) are shown below.

Outs Baserunners WP/PB
0 0 0.0%
0 1 1.9%
0 2 2.2%
0 3 1.6%
0 1-2 2.1%
0 1-3 2.1%
0 2-3 1.5%
0 1-2-3 1.4%
1 0 0.1%
1 1 1.9%
1 2 2.3%
1 3 1.6%
1 1-2 2.2%
1 1-3 2.1%
1 2-3 1.4%
1 1-2-3 1.4%
2 0 0.1%
2 1 1.8%
2 2 2.1%
2 3 1.6%
2 1-2 2.0%
2 1-3 2.1%
2 2-3 1.5%
2 1-2-3 1.4%


As with stolen bases, credit is also given for not throwing wild pitches or committing passed balls. The net win probability in the absence of any wild pitch or passed ball is calculated as follows. The overall win probability is equal to the weighted average of the win probability with and without wild pitches, i.e.,

WinProb = Prob(WP)•WinProbWP + (1-Prob(WP)) •WinProbnoWP

where Prob(WP) is the probability of a wild pitch (or passed ball), which, as noted above, is base-out dependent. The Win Probability in the absence of a wild pitch (or passed ball), WinProbnoWP, can then be calculated as follows:

WinProbnoWP = [1/(1-Prob(WP))]•(WinProb – Prob(WP)•WinProbWP)

The net effect on Win Probability, then, of no wild pitch or passed ball during a plate appearance will simply be the difference: WinProbnoWP – WinProb.

Offensively, wild pitches, passed balls, and the lack thereof, are credited to baserunners. Defensively, the credit for these things is shared by pitchers and catchers. This is one of several cases where credit may be shared by different players. The basic process whereby this credit is divided is described elsewhere. The specific division of defensive Component 2 Player Game Points is presented next.

2.    Division of Component 2 Game Points Between Pitchers and Catchers
As explained elsewhere, Component 2 Player Games are divided between pitchers and catchers based on the extent to which player winning percentages persist across different sample periods.

One measure of the extent to which a particular factor is a skill is the extent to which a player’s winning percentage persists over time. To evaluate the persistence of skills, I fit a simple persistence equation which modeled Component 2 winning percentage on even-numbered plays as a function of Component 2 winning percentage on odd-numbered plays:

(Component 2 Win Pct)Even = b•(Component 2 Win Pct)Odd + (1-b)•(WinPct)Baseline

where (WinPct)Baseline represents a baseline winning percentage toward which Component 2 winning percentages regress over time.

Equations of this type were fit for Component 2 Player Game Points for pitchers and catchers. Separate equations were estimated for each base. The results for these equations are shown below. A brief explanation of these variables follows.

The number n is the number of players over whom the equation was estimated, that is, who accumulated any Player wins and/or losses on both odd- and even-numbered plays. The value R2 measures the percentage of variation in the dependent variable (WinPctEven) explained by the equation (i.e., explained by WinPctOdd). The numbers in parentheses are t-statistics. T-statistics measure the significance of b, that is, the confidence we have that b is greater than zero. The greater the t-statistic, the more confident we are that the true value of b is greater than zero. Roughly, if the t-statistic is greater than 2, then we can be at least 95% certain that the true value of b is greater than zero (given that certain statistical assumptions underlying our model hold). The value of (WinPct)Baseline, the baseline winning percentage toward which winning percentages regress over time, is set equal to 0.500 by construction.
note: To be precise, I estimate unique Persistence Equations for every season, which use all of my data in all of these equations, but weight the data based on how close to the season of interest it is. The equations shown here weight each season equally.

Persistence of Component 2 Winning Percentage: Batter as Baserunner (ability to reach on dropped third strike)
 
Pitchers:  n = 34,465, R2 = -0.0531
WinPctEven = (95.81%)•WinPctOdd + (4.19%)•0.5000 (522.3)
 
Catchers:  n = 7,714, R2 = -0.0468
WinPctEven = (38.93%)•WinPctOdd + (61.07%)•0.5000 (37.38)
In terms of preventing batters from reaching first base on a dropped third strike, Component 2 win percentage is highly significantly persistent for both pitchers and catchers, albeit far more so for pitchers. The percentage of Component 2 Player decisions associated with the batter (i.e., associated with dropped third strikes) (Component 2.0) which are attributed to pitchers is set equal to the pitcher persistence coefficient (95.8%) divided by the sum of the persistence coefficients for pitchers and catchers (95.8% +38.9%). This leads to 71.1% of Component 2.0 decisions being allocated to pitchers and 28.9% of Component 2.0 decisions allocated to catchers.

Persistence of Component 2 Winning Percentage: Baserunner on First Base
 
Pitchers:  n = 38,317, R2 = 0.1370
WinPctEven = (64.41%)•WinPctOdd + (35.59%)•0.5000 (163.7)
 
Catchers:  n = 8,074, R2 = 0.0749
WinPctEven = (31.78%)•WinPctOdd + (68.22%)•0.5000 (29.66)
For baserunners on first base, Component 2 win percentage is also significantly persistent for both pitchers and catchers, with 67.0% of Component 2.1 decisions allocated to pitchers and 33.0% of Component 2.1 decisions allocated to catchers.

Persistence of Component 2 Winning Percentage: Baserunner on Second Base
 
Pitchers:  n = 37,863, R2 = 0.0278
WinPctEven = (69.95%)•WinPctOdd + (30.05%)•0.5000 (185.0)
 
Catchers:  n = 7,991, R2 = 0.0395
WinPctEven = (27.19%)•WinPctOdd + (72.81%)•0.5000 (25.14)
Persistence in wild pitches and passed balls is significant here for both pitchers and catchers. This persistence is much stronger as well as much more significant for pitchers, to whom 72.0% of Component 2.2 decisions are allocated, than for catchers, to whom 28.0% of Component 2.2 decisions are allocated.

Persistence of Component 2 Winning Percentage: Baserunner on Third Base
 
Pitchers:  n = 36,492, R2 = -0.0910
WinPctEven = (77.72%)•WinPctOdd + (22.28%)•0.5000 (245.9)
 
Catchers:  n = 7,824, R2 = -0.0076
WinPctEven = (22.94%)•WinPctOdd + (77.06%)•0.5000 (20.78)
The results for baserunners on third base are similar to the earlier results. Component 2.3 decisions are allocated 77.2% to pitchers and 22.8% to catchers.

Overall, Component 2 Player Game Points account for 1.3% of total Player Decisions, a percentage that has remained fairly stable over the 97 years for which I have estimated Player won-lost records so far.

Component 2 leaders can be found here.

All articles are written so that they pull data directly from the most recent version of the Player won-lost database. Hence, any numbers cited within these articles should automatically incorporate the most recent update to Player won-lost records. In some cases, however, the accompanying text may have been written based on previous versions of Player won-lost records. I apologize if this results in non-sensical text in any cases.

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