Minimax on the Gridiron: Serial Correlation and Its Effects on Outcomes in the National Football League

Abstract

We examine whether the predictions of minimax in zero-sum games holds under highly incentivized conditions with highly informed informed decision makers. We examine data from 3455 National Football League (NFL) games from the 2000 season through the 2012 season. We categorize every relevant play as either a rush or a pass. We find that, despite the predictions of minimax, the pass-rush mix exhibits negative serial correlation. In other words, given the conditions of the play, teams employ an exploitable strategy in that play types alternate more frequently than implied by an independent stochastic process. We also find that the efficacy of plays are affected by previous actions and previous outcomes in a manner that is not consistent with minimax. Our analysis suggests that teams could profit from more clustered play selections, which switch play type less frequently. Our results are consistent with the explanation that teams excessively switch play types in order to not be perceived as predictable.