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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

Game Theory and The World Marathon Majors

By Benjamin Jones

The World Marathon Majors (WMM) Series Prize was enacted in 2006 as a million dollar prize handed out annually to the top man and woman competing at five of the most important marathons. This paper considers the motivations behind setting up this prize, as well as the theoretical rationale for its existence and whether the empirical data supports these results. We find that the game theory model supports the ideas that the World Marathon Majors organizers state as their goals in creating the prize, but at the same time, there is not much empirical support as of yet to support any quantifiable changes within marathoning in the past few years. The regressions do not produce statistically significant data for finishing times decreasing even though the world record has been broken three times in these races since the implementation of the WMM. This may be due to the small number of observations and the fact that the series is so new. However, there are other areas of interest, such as an increase in World Record-breaking times or an increase in overall publicity, that may justify such a lucrative prize for these races. These topics are not included within the regressions and could be an area for further study.


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Advisor: Curtis Taylor, Michelle Connolly | JEL Codes: C7, C73, L83 | Tagged: Game Theory, Marathon, Sports Economics, Tournament Theory


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