In the spirit of this week’s earlier post on going for it on fourth down in football, here’s an example of using economics in real football (soccer to Americans). For those who lack the good taste and sophistication to follow the beautiful game, penalty kicks involve a one-on-one contest where a shooter tries to score against the goalkeeper from a distance of twelve yards.
Anticipating how your opponent will act is critical. If you are the keeper, if you can accurately predict the direction of the shot (to the right/left or down the middle), you have substantially increased your odds of stopping the shot. In these types of situations, game theory predicts that players will use mixed strategies in which they randomize over their possible actions in order to remain unpredictable.
In a 2003 paper in the Review of Economic Studies, economist Ignacio Palacios-Huerta studied over 1,400 penalty kicks in professional soccer games (so, here’s a guy who is essentially getting paid to watch sports highlight shows!). He found that professional players could indeed behave randomly. Their decisions showed no correlations with prior outcomes, prior decisions they had made, or prior decisions of the opponent. They appeared to be able to generate random sequences, an act that is usually quite difficult for people to accomplish (try it yourself at Mike Shor’s game theory web site.)