The Rationality of Soccer Goalkeepers

(source: Flickr)

A study in the Journal of Economic Psychology analyzes soccer goalkeepers penalty decision-making: jump left, jump right, or stay in the center. Bar-Eli et al.'s study of

(... ) 286 penalty kicks in top leagues and championships worldwide shows that given the probability distribution of kick direction, the optimal strategy for goalkeepers is to stay in the goal's center.

The probability of stopping a penalty kick are the following:


Why do goalkeeper jump left of right, when the optimal nash-equilibirum strategy is is to stay in the goal's center? Because jumping is the norm, and thus

(...) a goal scored yields worse feelings for the goalkeeper following inaction (staying in the center) than following action (jumping), leading to a bias for action.

This study illustrates the tension between internal(subjective) and external (objective) rationality discussed in my last post: statistically speaking, as a rule for winning games, to jump is (externally) suboptimal; but given the social norm and the associated emotional feeling, jumping is (internally) rational. Note also how modeling the game is important for normative issue: two other studies, (Palacios-Huerta, 2003; Chiappori et al., 2002) concluded that goalkeepers play a rational strategy, but they supposed that shooter and goalkeeper had only two options, (kick/jump) left or right. Bar-Eli et al. added (kick/stay) in the center.


Reference

• Bar-Eli, M., Azar, O. H., Ritov, I., Keidar-Levin, Y., & Schein, G. (2007). Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology, 28(5), 606-621.
• Palacios-Huerta, I. (2003). Professionals Play Minimax. Review of Economic Studies, 70(2), 395-415.
  
• Chiappori, P., Levitt, S., & Groseclose, T. (2002). Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer. The American Economic Review, 92(4), 1138-1151.