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 datasets composed of a large number of penalty kicks mediate the behaviour of the players in \emph{different} games, and the properties of optimal mixed strategies cannot be tested directly because of \emph{aggregation bias}. In this paper we model the heterogeneous ability of players. We then test the hypothesis that differently talented players randomise over different actions. To this aim, we study a dataset that collects penalties kicked during shootout 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.