When Data Lies: Finding Optimal Strategies for Penalty Kicks with Game Theory

Relying on raw conversion rates for penalty kicks can be misleading because it ignores the strategic interaction between the kicker and goalkeeper. This scenario is better modeled as a two-player, zero-sum game using game theory, where the optimal approach is a mixed strategy known as a Nash equilibrium. Using a dataset of Premier League penalties, an empirical payoff matrix is constructed to calculate these equilibrium strategies for both players. The analysis reveals that kickers behave close to optimally, but goalkeepers deviate by not staying in the center often enough, which artificially inflates the observed success rate of central shots.