A MARKOV-CHAIN APPROACH TO BASEBALL

Most earlier mathematical studies of baseball required particular mode ls for advancing runners based on a small set of offensive possibiliti es. Other efforts considered only teams viith players of identical abi lity. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a g iven model for runner advancement. Our method is limited only by the a vailable data and can use any reasonable deterministic model for runne r advancement when sufficiently detailed data are not available. Furth ermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method t o find optimal batting orders, run distributions per half inning and p er game, and the expected number of games a team should win. We also d escribe the application of our method to test whether a particular tra de would benefit a team.