David P. Daniels
Abstract: Do Major League Baseball umpires call balls and strikes solely in response to pitch location? We analyze all regular season calls from 2009 to 2011—over one million pitches—using non-parametric and structural estimation methods. We find that the strike zone contracts in 2-strike counts and expands in 3-ball counts, and that umpires are reluctant to call two strikes in a row. Effect sizes can be dramatic: in 2-strike counts the probability of a called strike drops by as much as 19 percentage points in the corners of the strike zone. We structurally estimate each umpire's aversions to miscalling balls and his aversions to miscalling strikes in different game states. If an umpire is unbiased, he would only need to be 50% sure that a pitch is a strike in order to call a strike half the time. In fact, the average umpire needs to be 64% sure of a strike in order to call strike three half the time. Moreover, the least biased umpire still needs to be 55% sure of a strike in order to call strike three half the time. In other words, every umpire is biased.Contrary to their formal role as unbiased arbiters of balls and strikes, umpires are biased by the state of the at-bat when deciding whether a pitch intersects the strike zone.