Received wisdom in baseball takes it as a given that it is an advantage have the last turn at bat in a baseball game. This belief is supported, implicitly or explicitly, by an argument that the team on offense benefits by knowing with certainty the number of runs it must score in the final inning. Because the discrete nature of plays in baseball lends itself naturally to a model of a baseball contest as a zero-sum Markov game, this hypothesis can be tested formally. In a model where teams may employ the bunt, stolen base, and intentional walk, there is no significant quantitative advantage conferred by the order in which teams bat, and in some cases batting first may be of slight advantage. In practice, the answer to the question may be determined by actions more subtle than previously considered, such as the extent to which the defensive team can influence the distribution of run-scoring by pitch selection or fielder positioning.