Wednesday, February 24, 2016
Bayesian Umpire
?Long (long, long) time Straight Arrow commenter GuyM has a sensational article over at BPro.
But why do umpires shift their error rates at all, unless it is to lend a helping hand to the underdog? The answer is, because they know (more or less) what’s coming. Umpires are changing their decision rule on close calls—“lean ball” vs. “lean strike”—based on the likelihood that the pitch will actually be a strike. With two strikes, they know the pitcher will usually throw outside the zone, and they know the hitter will typically swing at anything close—so guessing “ball” on any taken pitch is the percentage play. By adjusting their decision rule at each count to reflect their prior knowledge of the true distribution of pitches, they make better guesses and fewer mistakes. In short, umpires are Bayesian, not compassionate.