Lessons from economists

One of the most important findings of the increasing literature on soccer and economics is that players behave in penalty kicks as if they were using a mixed strategy Nash Equilibrium. That means first that they behave as if randomizing, that is, as if instead of choosing kicking to one side or the other, what they choose is a probability distribution, like choosing between tossing a coin, playing the roulette or any other random device, before kicking the ball (and the goalkeeper, before diving). In addition, they randomize in an optimal way, given the choice of the rival. It turns out that this was proved by the Basque economist Ignacio Palacios-Huerta, who compiled an amazing data set with hundreds of penalty kicks. The data set is so rich, that he offers it to football teams, summarizing patterns of kickers and goalkeepers. One of the first to use the advice from Palacios-Huerta were Chelsea FC in the penalty shoout-out of the Champions League Final in 2008. But Chelsea lost. Then the same economist prepared a report for The Netherlands for the final of the 2010 World Cup, but then Iniesta scored that goal in the extra time, making the penalty shoot-out unnecessary. Some say that, although Palacios.Huerta claims that he did not advise The Netherlands in 2014, the Dutch players still kept some of the wisdom they received from previous reports by Palacios-Huerta. But by now it was common knowledge that they had received this advice (and the advice had been publicized in the book "Soccernomics"), so that their rivals could adjust accordingly. As a result, perhaps Argentina, but not Costa Rica, outsmarted them and reached the final, so that The Netherlands had to fight for the third place. But who is happier, the winner of the game for the third place, or the loser of the final? In any case, it is not clear that players do benefit from the advice of the economists. The work of Palacios-Huerta shows that players are extremely rational when they kick penalties, but the way to be rational is to keep the other player guessing, that is, randomizing. If you advise someone who is randomizing he may stop doing so. So there is an air of a paradox in Palacios-Huerta, the person who discovered that players optimally randomize, recommending them to follow patterns. But at least in 2008 the advice failed to deliver.