Identifying the best strategy for soccer penalty success: A predictive model for optimising behavioural and biomechanical trade-offs.

Success in a soccer penalty can be the difference between winning and losing matches. The outcome is determined by a complex interaction between the shooter and goalkeeper, whose performances are constrained by biomechanical trade-offs. To overcome these performance constraints, each player has a range of available strategies. Shooters can kick at different speeds, affecting accuracy, while goalkeepers can move at various times (leave-times), affecting the time available to move and the probability they move in the correct direction. Previous models of penalty success ignore such trade-offs and how they interact to influence the outcome. Here, we present a model that accounts for shooting inaccuracy to predict the probability of success for all shooting strategies, defined as any combination of: shot speed, position where the shooter aims, shooter footedness, and kicking technique (side-foot or instep). To estimate the probability of success each shooting strategy is matched against all possible goalkeeper leave-times, considering the probability each leave-time is chosen. We test the model against an average goalkeeper and a goalkeeper who tends to move later. Against the average goalkeeper, aiming on the ground toward the centre of the goal is optimal; however, against a late moving goalkeeper, aiming on the ground to the extremities of the goal is effective, with the optimal target in the horizontal dimension dependent on shot speed, kick technique, and footedness. Coaches could use this model to identify their best penalty takers and each players' optimal shooting strategy against either the average goalkeeper or a specific goalkeeper.