Play Calling Strategy in American Football: A Game-Theoretic Stochastic Dynamic Programming Approach

Abstract

This manuscript presents a model to assist in the determination of optimal American football play selection for first down and goal situations. A game theoretic approach is embedded within a stochastic dynamic programming formulation, resulting in a mixed strategy satisfying the ex-ante declared objective of maximizing the probability of scoring a touchdown. The methodology provides a quantitative framework to a problem that impacts on team performance and addresses a gap in the literature concerning the application of quantitative methods to sports.