  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,
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.
