Outline analyses of the called strike zone in Major League Baseball

Abstract

We extend statistical shape analytic methods known as outline analysis for application to the strike zone, a central feature of the game of baseball. Although the strike zone is rigorously defined by Major League Baseball's official rules, 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. Our methods yield inference on geometric attributes (centroid, dimensions, orientation and shape) of this "called strike zone" (CSZ) and on the effects that years, umpires, player attributes, game situation factors and their interactions have on those attributes. The methodology consists of first using kernel discriminant analysis to determine a noisy outline representing the CSZ corresponding to each factor combination, then fitting existing elliptic Fourier and new generalized superelliptic models for closed curves to that outline and finally analyzing the fitted model coefficients using standard methods of regression analysis, factorial analysis of variance and variance component estimation. We apply these methods to PITCHf/x data comprising more than three million called pitches from the 2008-2016 Major League Baseball seasons to address numerous questions about the CSZ. We find that all geometric attributes of the CSZ, except its size, became significantly more like those of the rule-book strike zone from 2008-2016 and that several player attribute/game situation factors had statistically and practically significant effects on many of them. We also establish that the variation in the horizontal center, width and area of an individual umpire's CSZ from pitch to pitch is smaller than their variation among CSZs from different umpires.

A Multidisciplinary Perspective on Publicly Available Sports Data in the Era of Big Data: A Scoping Review of the Literature on Major League Baseball

“…We also observed that a research team with the same authors, well-versed in manipulating massive baseball data like PITCHf/x, published two studies in the same year. One applied a forward stepwise multiple regression model to investigate the pitching success, which is measured by fielding independent pitching (FIP), considering the relevance to pitch selection, ball speed, ball movement, release location, variation in pitch speed, variation in ball movement, and variation in release location (Zimmerman et al, 2019). The other examined the changes in pitching-performance characteristics across nine innings of MLB games using pitch type, speed, ball movement, release location, and strike-zone data to compare with the pitcher’s FIP (Guss et al, 2018).…”

“…In this study, a total of 10 papers were categorized as performance evaluations (Table 2), with eight of them using PITCHf/x data and three using massive pitch data over 1 million. The study with the largest amount of data is Zimmerman et al (2019), which uses more than 3 million called pitches from the 2008 to 2016 seasons to analysis the called strike zone (CSZ), to examine the performance of umpire. The second one is Mills (2017), which also studied the CSZ with 2.47 million pitch-level observations in the 2008 to 2014 regular seasons.…”

The causal effect of a timeout at stopping an opposing run in the NBA

“…Deshpande and Evans (2020) use non-parametric Bayesian analysis and imputation methods to track how completion probability evolves through receivers' routes in the National Football League (NFL). In addition to player movement analyses, Zimmerman et al (2019) apply outline analysis to make inference on the geometric attributes of the called strike zone in Major League Baseball (MLB). Furthermore, a larger comparison of team strength within and competitiveness across sports leagues is estimated using Bayesian state-space modeling in Lopez et al (2018).…”