Should I stay or should I go? Optimal decision making in penalty kicks - Berger, R. (Institut für Soziologie, Ludwig-Maximilians-Universität München, 2009)
Bar-Eli et al. (2007, hereafter BE) conclude that goalkeepers in football suffer from an action bias that preserves them from optimally playing in penalty kicks. Particularly, they are thought to jump too often to the sides and to stay too seldom in the centre. This bias is explained by a norm that goalkeepers should jump to the sides in order to minimize their mental costs when failing to stop the ball. Because in this case at least they have done something instead of just watching how the kicker converts the penalty. We show that these conclusions are wrong using the data set of BE, the data set of the criticized Chiappori et al. (2002), an own data set consisting of 1043 penalty kicks from the German Bundesliga and data of the likewise criticized Palacios-Huerta (2003). The crucial mistake of BE consists of modeling the strategic interaction between the players as if it was a parametric decision. A game theoretic analysis that takes into account the middle as an option shows that goalkeepers on average behave astoundingly close to their optimal choices. Therefore, the action bias BE identify in an enquiry of goalkeepers actually is a rule of thumb that helps the goalies to maximise the chance of stopping the penalty kick. Finally, it is shown that players are not only rational in choosing their sides in a sole penalty kick but also in a series of kicks.