Hierarchical Bayesian Bradley–Terry for applications in Major League Baseball

Abstract

A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley–Terry model [5, 20], first studied by Zermelo in 1929 and rediscovered by Bradley and Terry in 1952. One obvious area of application for such a model is sporting events, and in particular Major League Baseball. With this in mind, we describe a hierarchical Bayesian version of Bradley–Terry suitable for use in ranking and prediction problems, and compare results from these application domains to standard maximum likelihood approaches. Our Bayesian methods outperform the MLE-based analogues, while being simple to construct, implement, and interpret.