Play calling strategies during football games are extremely important to the success of a team. In the past, coaches and players have subjectively determined the plays to call based on past experiences, personal biases, and various observable factors. This research quantifies these decisions using game theoretic techniques; updating optimal decision policies as new information becomes available during a game. A decision maker changes his perceived optimal strategy based on the information known about the opponent's strategy at the time of the decision. Additionally, utility theory is used to capture the different risk preferences of the decision makers. Furthermore, we use design of experiments and response surface methodology to optimize the risk strategies of each decision maker. By exploring the interaction of two football teams' risk preferences, optimal risk strategies can be suggested in the form of a varying mixed strategy. The techniques presented can be utilized in a precursory analysis to forecast different decisions a coach or player may encounter throughout the game, during a game to optimize each play called, or as a posterior analysis technique to dissect the decisions made and determine the effectiveness of the plays called. The procedures are easily transitioned to rapidly assist football teams or other sports teams in making better decisions through quantitative modeling and statistical analysis. A numerical example is presented to demonstrate the usefulness of the solution approach.
