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— Where BTF's Members Investigate the Grand Old Game
Monday, September 16, 2002
Pitching XR: Dividing The Responsibility for Runs
How much is fielding worth?
Statistical analysts have been scratching their heads for years trying to determine how the responsibility for run prevention should be divided between pitching and defense. Pete Palmer and John Thorn, in The Hidden Game of Baseball, suggest that defense is about 12% of run prevention, because about 12% of runs (at that time) were unearned. Bill James, in developing the Win Shares method, uses a formula that assigns about 32.5% of the responsibility for run prevention to the defense. In his Defensive Translations that are published in Baseball Prospectus, Clay Davenport first removes events that cannot be affected by the fielders from his analysis, then assigns the defense responsibility for 70% of the remaining runs. Voros McCracken’s DIPS analysis suggests that differences between pitchers are small enough so that they can be ignored, and the defense can be assigned 100% of the responsibility for preventing runs on balls in play. In this case, the pitchers would be responsible only for runs that are scored (or prevented) as the result of those events that cannot be affected by the fielders - strikeouts, walks, HBP, and HRs.
We do have methods for estimating the impact of pitcher-specific events on run scoring - for example, Extrapolated Runs (XR). The formula for XR contains explicit weight for strikeouts, walks (including intentional walks), hit batsmen, and home runs. By using the XR formula, we can estimate the pitcher-specific contribution to XR - which I’ve called Pitching XR (PXR) - and use that as a starting point for dividing up the responsibility for run prevention between pitching and fielding.
Table 1. XR and Pitching XR, 9 Sep 2002
I’ve looked at this for several other recent seasons, and the range of performance has generally been about the same, with pitcher XR being close to 45% of total XR. That would suggest that, if we follow Voros’s approach and assume that pitcher contributions to run prevention from BIP can be ignored, the defenders are responsible for 55% of run prevention. If we instead use the Davenport model of dividing the responsibility for run prevention from balls in play as 70% fielding and 30% pitching, we then get an estimate that the fielders are responsible for about 38.5% of run prevention, closer to the 32.5% that James uses in Win Shares.
Voros’s research demonstrates that pitchers do not have a large impact on balls in play, and that therefore the fielders should assume more importance when most of the run scoring derives from balls in play. An approach based on pitching XR (or any similar RC method that allows separation of the impact of pitcher-specific events from the impact of fielder-affected events) balances the relative responsibilities of pitchers and fielders, especially before 1920, far better than an absolute percentage assignment such as James uses.
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