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Optimal Lineups in Penalty Kick Shootouts: An Empirical and Theoretical Investigation

By Lucas Hubbard

The purpose of this paper is to determine how teams should order their lineups in a five-man penalty kick shootout. We begin with a theoretical investigation of how comparative advantages for certain players in stressful situations will create clear, optimal lineup strategies for managers to emulate. Then, we analyze the performance of shooters in all professional men’s international shootouts thus far. We observe a number of factors that affect the player’s success rate—most notably, shooting in a high-pressure situation, shooting in a World Cup, and shooting against a more experienced goalkeeper all negatively impact the player’s success rate. Interestingly, we see a diminishing effect of the adverse response to high-pressure as the shooters are more experienced: inexperienced players suffer a statistically significant adverse response, while average and experienced players show no adverse response to high-pressure. We conclude with a simulation based on the empirical values that suggests teams should place their worst high-stress players (their inexperienced players) in the earlier shootout slots, as those are guaranteed to be of a low-stress variety. Conversely, players who perform relatively well under high-stress should be placed in slots 3-5, which are more likely to be of the high-stress variety. We observe the proportion of shootouts that end after a certain number of kicks, and we conclude that if coaches are able to identify their best high-stress kickers, the first team’s best kicker should kick in either round 4 or 5, while the second team’s best kicker should kick in either round 3 or 4. Finally, we see that the structure of the shootout provides an inherent advantage to the first team to shoot in shorter shootouts and an inherent advantage to the second team in longer shootouts. We recommend the ABBA ordering strategy put forth by Palacios-Huerta as a way to prevent this systemic inequality.

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Advisor: Attila Ambrus, Kent Kimbrough | JEL Codes: C7, C79 | Tagged: Game Theory, Optimality, Penalty Kicks, Soccer

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