Modeling the Performance of a Baseball Player's Offensive Production

• Main Author: Smith, Michael Ross
• Format: Others
• Published: BYU ScholarsArchive 2006
• Subjects: baseball; Hierarchical Bayes; Gibbs sampler; Metropolis-Hastings; Statistics and Probability
• Online Access: https://scholarsarchive.byu.edu/etd/362; https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1361&context=etd

This project addresses the problem of comparing the offensive abilities of players from different eras in Major League Baseball (MLB). We will study players from the perspective of an overall offensive summary statistic that is highly linked with scoring runs, or the Berry Value. We will build an additive model to estimate the innate ability of the player, the effect of the relative level of competition of each season, and the effect of age on performance using piecewise age curves. Using Hierarchical Bayes methodology with Gibbs sampling, we model each of these effects for each individual. The results of the Hierarchical Bayes model permit us to link players from different eras and to rank the players across the modern era of baseball (1900-2004) on the basis of their innate overall offensive ability. The top of the rankings, of which the top three were Babe Ruth, Lou Gehrig, and Stan Musial, include many Hall of Famers and some of the most productive offensive players in the history of the game. We also determine that trends in overall offensive ability in Major League Baseball exist based on different rule and cultural changes. Based on the model, MLB is currently at a high level of run production compared to the different levels of run production over the last century.