Dale Zimmerman - Colloquium Speaker
The strike zone is an important feature of the game of baseball and is rigorously defined by its Official Rules. It is widely recognized, however, that umpires make mistakes in calling pitches as strikes (and balls) and may even adhere to a strike zone somewhat different than that prescribed by the rule book. This "called strike zone" is the object of interest in this presentation; in particular we are interested in making inferences about its geometric attributes (centroid, size, shape, orientation) and determining the degree to which its geometry deviates from the rule-book prescription, in an overall sense and in various game situations. We achieve these aims using the morphometric technique of elliptic Fourier outline analysis, in which the outlines of called strike zones, as determined by kernel discriminant analysis, are represented by a pair of truncated Fourier series expansions, and then the vectors of coefficients of these expansions are subjected to standard techniques of multivariate analysis such as MANOVA. Using PITCHf/x data comprising more than one million called pitches from the 2014-2016 Major League Baseball seasons, we apply this methodology to characterize the geometry of the called strike zone and investigate the effects that various game situation covariates, such as handedness of the batter and pitcher and the ball-strike count, have on it. We find several interesting, statistically and practically significant effects, some well-known and some not.