Asymmetric Predictability and Cognitive Competition in Football Penalty Shootouts

Sports provide powerful demonstrations of cognitive strategies underlying competitive behavior. Penalty shootouts in football (soccer) involve direct competition between elite players and absorb the attention of millions. The penalty shootout between Germany and England in the 1990 World Cup semifinal was viewed by an estimated 46.49% of the UK population. In a penalty shootout, a goalkeeper must defend their goal without teammate assistance while an opposing series of kickers aim to kick the ball past them into the net. As in many sports, the ball during a penalty kick often approaches too quickly for the goalkeeper to react to its direction of motion; instead, the goalkeeper must guess the likely direction of the kick, and dive in anticipation, if they are to have a chance of saving the shot. We examined all 361 kicks from the 37 penalty shootouts that occurred in World Cup and Euro Cup matches over a 36-year period from 1976 to 2012 and show that goalkeepers displayed a clear sequential bias. Following repeated kicks in the same direction, goalkeepers became increasingly likely to dive in the opposite direction on the next kick. Surprisingly, kickers failed to exploit these goalkeeper biases. Our findings highlight the importance of monitoring and predicting sequential behavior in real-world competition. Penalty shootouts pit one goalkeeper against several kickers in rapid succession. Asymmetries in the cognitive capacities of an individual versus a group could produce significant advantages over opponents.

[1]  Jeffrey M. Woodbridge Econometric Analysis of Cross Section and Panel Data , 2002 .

[2]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[3]  A. Williams,et al.  Please Scroll down for Article Ergonomics Anticipation and Visual Search Behaviour in Expert Soccer Goalkeepers Anticipation and Visual Search Behaviour in Expert Soccer Goalkeepers , 2022 .

[4]  S. L. Lima,et al.  Randomness, chaos and confusion in the study of antipredator vigilance. , 1998, Trends in ecology & evolution.

[5]  Ofer H. Azar,et al.  Do soccer players play the mixed-strategy Nash equilibrium? , 2011 .

[6]  Jeffrey M. Wooldridge,et al.  Solutions Manual and Supplementary Materials for Econometric Analysis of Cross Section and Panel Data , 2003 .

[7]  Steven D. Levitt,et al.  Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer , 2002 .

[8]  Student BELIEF IN THE LAW OF SMALL NUMBERS , 1994 .

[9]  Uta Frith,et al.  Theory of mind , 2001, Current Biology.

[10]  Steven D. Levitt,et al.  Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League , 2009 .

[11]  P. Latham,et al.  References and Notes Supporting Online Material Materials and Methods Figs. S1 to S11 References Movie S1 Optimally Interacting Minds R�ports , 2022 .

[12]  Axel Cleeremans,et al.  Dissociating the effects of automatic activation and explicit expectancy on reaction times in a simple associative learning task. , 2006, Journal of experimental psychology. Learning, memory, and cognition.

[13]  G. Goldenberg,et al.  Components of Random Generation by Normal Subjects and Patients with Dysexecutive Syndrome , 1993, Brain and Cognition.

[14]  Michael F. Land,et al.  From eye movements to actions: how batsmen hit the ball , 2000, Nature Neuroscience.

[15]  Daeyeol Lee,et al.  Ubiquity and Specificity of Reinforcement Signals throughout the Human Brain , 2011, Neuron.

[16]  M. Siegal,et al.  Neural systems involved in 'theory of mind' , 2002, Nature Reviews Neuroscience.

[17]  Ignacio Palacios-Huerta,et al.  Psychological Pressure in Competitive Environments: Evidence from a Randomized Natural Experiment , 2008 .

[18]  Colin Camerer,et al.  A Cognitive Hierarchy Model of Games , 2004 .

[19]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[20]  Ignacio Palacios-Huerta Professionals Play Minimax , 2003 .

[21]  D. Barraclough,et al.  Reinforcement learning and decision making in monkeys during a competitive game. , 2004, Brain research. Cognitive brain research.

[22]  Claudio J. Tessone,et al.  How Random Is Social Behaviour? Disentangling Social Complexity through the Study of a Wild House Mouse Population , 2012, PLoS Comput. Biol..

[23]  Bo E. Honoré,et al.  Panel Data Models: Some Recent Developments , 2001 .

[24]  J. Krakauer,et al.  Inside the brain of an elite athlete: the neural processes that support high achievement in sports , 2009, Nature Reviews Neuroscience.

[25]  Peter Ayton,et al.  The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness? , 2004, Memory & cognition.

[26]  Eizo Akiyama,et al.  Chaos in learning a simple two-person game , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Jane F. Banfield,et al.  Medial prefrontal activity predicts memory for self. , 2004, Cerebral cortex.

[28]  Steven P. Abney,et al.  Bootstrapping , 2002, ACL.

[29]  Blair T. Johnson,et al.  The self-reference effect in memory: a meta-analysis. , 1997, Psychological bulletin.

[30]  C. Frith,et al.  Functional imaging of ‘theory of mind’ , 2003, Trends in Cognitive Sciences.

[31]  A. Williams,et al.  Please Scroll down for Article Journal of Sports Sciences Visual Search, Anticipation and Expertise in Soccer Goalkeepers Visual Search, Anticipation and Expertise in Soccer Goalkeepers , 2022 .

[32]  R. Tibshirani,et al.  An Introduction to the Bootstrap , 1995 .

[33]  R. Adolphs Cognitive neuroscience: Cognitive neuroscience of human social behaviour , 2003, Nature Reviews Neuroscience.

[34]  G. S. Tune RESPONSE PREFERENCES: A REVIEW OF SOME RELEVANT LITERATURE. , 1964, Psychological bulletin.

[35]  W. A. Wagenaar Generation of random sequences by human subjects: A critical survey of literature. , 1972 .

[36]  U. Böckenholt,et al.  Bootstrapping: applications to psychophysiology. , 1989, Psychophysiology.