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Abstract:
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Up to now, formal statistical analyses of the strike zone actually called by Major League Baseball umpires have modeled the probability that a pitch crossing the plate at a certain location is either called a strike or is called correctly. We present an approach that, in contrast, directly models geometric features (centroid, size, and shape) of the called strike zone (as determined by kernel density estimation). Our approach uses the morphometric technique of elliptic Fourier outline analysis, in which the outlines of called strike zones corresponding to various covariates of interest (e.g., handedness of the batter and pitcher and ball-strike count of the at-bat) are represented by truncated Fourier series expansions. The vectors of coefficients of these expansions may then be analyzed by a multivariate analysis of variance, in order to make inferences about covariate effects on geometric features of the called strike zone. Using PITCHf/x pitch tracking data from the 2014-2016 Major League Baseball seasons, we apply this methodology to discover some interesting effects of this type.
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