Abstract
Baseball teams face the problem of choosing a set of nine players to start in each game and of determining a sequence in which these nine players bat. The objective is typically to maximise the offensive capability of the team. In baseball, the payoffs associated with a slight statistical advantage can be huge. While these are difficult to quantify exactly, the multimillion dollar contracts with the players and the managers suggest that even a few more wins every year are significant. We model this problem of choosing the players and of determining their batting order as a problem of finding the longest simple cycle in a graph and demonstrate our methodology by proposing batting orders for the Florida Marlins. We also explain how our model can also be useful in quantifying the benefits of trading players and for predicting the outcome.