Modelling Strategies in Sports

Abstract

This paper presents a model that examines sports teams’ strategic choices about the extent of offense/defense to adopt in competing with other teams. The mathematical formulation adopted permits the derivation of a team’s optimal strategy under different game scenarios (current score and time left to play), and team characteristics (playing at home or away, and each team’s quality). A novel feature of the model is that teams can choose a strategy at several moments in the game, thereby incorporating a comprehensive dynamic element. The National Hockey League is used as an application. Optimal coaching behavior is derived in this setting, and the impact of rule changes is assessed. The study found that removing the overtime period, disproportionally increasing the rewards for a win, or removing the point that is currently awarded to the team that loses the shootout at the end of overtime, would all lead to the adoption of more offensive strategies during the game. That outcome is aligned with higher fan interest and team revenue.