A Markov Chain Approach to Baseball

Most earlier mathematical studies of baseball required particular models for advancing runners based on a small set of offensive possibilities. Other efforts considered only teams with players of identical ability. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a given model for runner advancement. Our method is limited only by the available data and can use any reasonable deterministic model for runner advancement when sufficiently detailed data are not available. Furthermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method to find optimal batting orders, run distributions per half inning and per game, and the expected number of games a team should win. We also describe the application of our method to test whether a particular trade would benefit a team.