Effects of pitch location and count on professional baseball umpires' ball-strike decisions.

In baseball, home plate umpires' perceptual-cognitive skills are tested with each pitch as they are required to judge, with accuracy, whether the ball passed through the imaginary region above home plate known as the strike zone. Home plate umpires must visually track the flight of a pitched ball as it leaves the pitcher's hand and travels over the home plate region in order to accurately determine whether a pitch should be called a strike or ball. Umpires must also contend with pitchers' tactics in which pitches are routinely delivered with unpredictable movements, at varying speeds, and to areas that may be difficult for batters to reach. As a result, umpires may be prone to making occasional errors. This study applied literature related to judgment and decision making among expert sport performers to the professional baseball umpire population. Using generalized linear mixed modeling with secondary data generated by the PITCHf/x pitch tracking system, umpires' ball--strike decisions were measured along the course of the 2013 season. Emphasis was placed on accounting for the effects of pitch location and ball--strike count on umpires' accuracy in making ball--strike decisions. During the 2013 MLB season, umpires were responsible for deciding the outcome of approximately 149 pitches per game on average. Results indicate umpire accuracy rates range from 90% to 95%. Results from a fully-unconditional generalized linear mixed model suggest approximately 0.05% of variability observed in pitch outcomes can be attributed to home plate umpires. To test for the effects of pitch location and ball--strike count on the probability of umpires' accuracy in judging pitch outcomes, a multilevel model with interactions between fixed and random effects was estimated. Results indicate predicted probabilities of accurate umpire decisions for pitches located in the inner region of the strike zone appear to be noticeably lower compared to predicted probabilities of accurate umpire decisions for pitches located in the middle or outer regions. Specifically, pitchers appear to be at a distinct disadvantage, compared to when the ball--strike count is either neutral or favors the batter.