An investigaton of umpire performance using PITCHf/x data via longitudinal analysis

Abstract

Baseball has long provided statisticians a playground for analysis. In this report we discuss the history of Major League Baseball (MLB) umpires, MLB data collection, and the use of technology in sports officiating. We use PITCHf/x data to answer 3 questions. 1) Has the proportion of incorrect calls made by a major league umpire decreased over time? 2) Does the proportion of incorrect calls differ for umpires hired prior to the implementation of technology in evaluating umpire performance from those hired after? 3) Does the rate of change in the proportion of incorrect calls differ for umpires hired prior to the implementation of technology in evaluating umpire performance from those hired after? PITCHf/x is a publicly available database which gathers characteristics for every pitch thrown in one of the 30 MLB parks. In 2002, MLB began to use camera technology in umpire evaluations; prior to 2007, the data were not publicly available. Data were collected at the pitch level and the proportion of incorrect calls was calculated for each umpire for the first third, second third, and last third of each of the seasons for 2008-2011. We collected data from retrosheet.org, which provides game summary information. We also determined the year of each umpire’s MLB debut to differentiate pre- and post-technology hired umpires for our analysis. We answered our questions of interest using longitudinal data analysis, using a random coefficients model. We investigated the choice of covariance structure for our random coefficients model using Akaike’s Information Criterion and the Bayesian Information Criterion. Further, we compared our random coefficients model to a fixed slopes model and a general linear model.