Optimal batting orders in run-limit-rule baseball: a Markov chain approach

Abstract

Amateur baseball contests, particularly those involving young players, often feature a run limit, which establishes a maximum number of runs that may be scored in a half-inning of play. Although conventional wisdom can be used for designing the batting order under standard baseball rules, the composition of the optimal lineup under run limit is still unclear, and the best batting order could differ significantly from the traditional ordering. In this paper, we consider the impact of run limits on the design of the optimal batting order, by developing a Markov chain model for calculating the expected number of runs scored (ENRS) under 3- and 5-run limits. We apply this model to both a high-quality and a lower-quality team, using the data from the 2011 Little League World Series, and illustrate the effect of run limit on the ENRS and the optimal batting order.