Does Divisional Play Lead to More Pennant Races?

A “pennant race” occurs in a sports league if the top two teams in a league finish within m̄ games of each other. We develop an analytical model that can be used to predict the probability that a sports league will have a pennant race. The model is then tested on data from the last 50 major league baseball seasons and is shown to do a remarkable job of predicting the number of pennant races that actually occurred. Finally, we give conditions which ensure that dividing a league of 2n teams into 2n-team divisions will increase the expected number of pennant races. As a corollary to this result we prove that the divisional structure which maximizes the expected number of pennant races must contain no divisions with 4 or more teams.