A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics

Abstract

Numerous statistics have been proposed to measure offensive ability in Major League Baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are the most reliable or consistent. We address this issue by using a hierarchical Bayesian variable selection model to determine which offensive metrics are most predictive within players across time. Our sophisticated methodology allows for full estimation of the posterior distributions for our parameters and automatically adjusts for multiple testing, providing a distinct advantage over alternative approaches. We implement our model on a set of fifty different offensive metrics and discuss our results in the context of comparison to other variable selection techniques. We find that a large number of metrics demonstrate signal. However, these metrics are (i) highly correlated with one another, (ii) can be reduced to about five without much loss of information, and (iii) these five relate to traditional notions of performance (e.g., plate discipline, power, and ability to make contact)