Commenced in January 2007
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Modeling Football Penalty Shootouts: How Improving Individual Performance Affects Team Performance and the Fairness of the ABAB Sequence

Authors: Pablo Enrique Sartor Del Giudice


Penalty shootouts often decide the outcome of important soccer matches. Although usually referred to as ”lotteries”, there is evidence that some national teams and clubs consistently perform better than others. The outcomes are therefore not explained just by mere luck, and therefore there are ways to improve the average performance of players, naturally at the expense of some sort of effort. In this article we study the payoff of player performance improvements in terms of the performance of the team as a whole. To do so we develop an analytical model with static individual performances, as well as Monte Carlo models that take into account the known influence of partial score and round number on individual performances. We find that within a range of usual values, the team performance improves above 70% faster than individual performances do. Using these models, we also estimate that the new ABBA penalty shootout ordering under test reduces almost all the known bias in favor of the first-shooting team under the current ABAB system.

Keywords: Football, penalty shootouts, Montecarlo simulation, ABBA.

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[1] IFAB. Laws of the game - 2016/17., June 2016.
[2] Tim McGarry and Ian M. Franks. On winning the penalty shoot-out in soccer. Journal of Sports Sciences, 18(6):401–409, 2000. PMID: 10902675.
[3] Jose Apesteguia and Ignacio Palacios-Huerta. Psychological pressure in competitive environments: Evidence from a randomized natural experiment. American Economic Review, 100(5):2548–64, December 2010.
[4] Steven J. Brams and Mehmet S. Ismail. Making the rules of sports fairer. SSRN Electronic Journal, 2016.
[5] UEFA. Penalty shoot-out trial at UEFA final tournaments, May 2017.
[6] Pablo Regent and Pablo Sartor. La cultura como desventaja deportiva (Culture as a competitive disadvantage). Revista de Negocios IEEM, XX(3):34–45, June 2017.
[7] Andrew Anthony. On penalties. Yellow Jersey Press, May 2001.
[8] Federico Echenique. ABAB or ABBA? The arithmetics of penalty shootouts in soccer. Technical report, California Institute of Technology, 2017.