Simulation and Optimization of Penalty Kicks and Shooting Probability Based on Monte Carlo Method

Abstract

Abstract Since there are few models that specialize Penalty kicks probability or shooting accuracy, this research innovatively uses the Monte Carlo method to simulate the situation of real football penalty kicks and shooting. Unifrom random generator and normal random generator are both used to better simulate the real situation, and finally the most suitable distribution model is chosen from these two distributions. Since the existence of goalkeepers is considered in a real football competition, this simulation experiment also divides the goalkeeper’s actions into 5 types, and the corresponding probability of each action is also considered. Finally, specific shooting probability is collected from the Premier League in 2021 to compare with our simulated situation to obtain the most accuracy model. By comparing with real probability, I finally confirm the appropriate model and the goalkeeper’s action probability. Similarly, the Monte Carlo method can also simulate some other real situations to determine the most suitable model.