Does player specialization predict player actions? Evidence from penalty kicks at FIFA World Cup and UEFA Euro Cup

Penalty kicks are analysed in the literature as 'real life experiments' for assessing the use of rational mixed strategies by professional players. However, each penalty kick cannot be considered a repetition of the same event because of the varying background conditions, in particular the heterogeneous ability of different players. Consequently, aggregate statistics over data sets composed of a large number of penalty kicks mediate the behaviour of the players in <italic>different</italic> games, and the properties of optimal mixed strategies cannot be tested directly because of <italic>aggregation bias</italic>. In this article, we model the heterogeneous ability of players. We then test the hypothesis that differently talented players randomize over different actions. To achieve this aim, we study a data set that collects penalties kicked during shoot-out series in the last editions of FIFA World Cup and UEFA Euro Cup (1994--2012) where kickers are categorized as specialists and non-specialists. The results support our theoretical predictions.