Penalty Shoot-Outs

Abstract

This article proposes a rule to determine the winner of a soccer match, which is different from the traditional penalty shoot-outs at the end of extra time. The author shows that games can be more attractive if penalties are shot before extra time and the outcome counts only if the tie is preserved during extra time. In general, this rule will promote offense by the team that loses the penalty shoot-outs, and it will promote defense by the team that wins the penalty shoot-outs. The author provides conditions on the marginal effect of offensive play in the probabilities of scoring and conceding a goal such that the proposed rule dominates the current one. Last, this study determines a class of functions that satisfies these conditions. More generally, the article shows how the ordering of tasks may affect the incentives to exert and allocate effort.