This paper formalizes the game between the goalkeeper and the kicker at the time of a penalty kick in soccer. The likelihood of a goal/save depends on the kicker's shot direction, intensity, and precision. We model those characteristics as functions of the agent's decisions: They can either “wait and see” some signals about the opponent's move or instead choose to “precommit” to a particular action. For a group of professional players, we calibrate our model using data from 1,083 penalty kicks and find their optimal strategy at the time of the event. We compare those predictions with the data and conclude that these players’ behavior was not always optimal. Deviations from optimal play are particularly frequent for the goalkeepers in our sample.
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