Tim Harford (The Undercover Economist) explains “what economics tells us about penalty kicks” in World Cup Game Theory:
In soccer, penalty kicks pit the goalkeeper against a lone striker in a mentally demanding contest. Once the penalty-taker strikes the ball, it takes 0.3 seconds to hit the back of the net — unless the goalkeeper can somehow get his body in the way. That is simply not enough time for the keeper to pick out the trajectory of the ball and intercept it. He must guess where the striker will shoot and move just as the ball is being struck. A keeper who does not guess correctly has no chance.Both striker and keeper must make subtle decisions. Let’s say a right-footed striker always shoots to the right. The keeper will always anticipate the shot and the striker would be better off occasionally shooting to the left—because even with a weaker shot it is best to shoot where the goalie isn’t. In contrast, if the striker chooses a side by tossing a coin, the keeper will always dive to the striker’s left: Since he can’t guess where the ball will go, best to go where the shot will be weak if it does come. But then the striker should start favoring his stronger side again.
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Game theory, applied to the problem of penalties, says that if the striker and the keeper are behaving optimally, neither will have a predictable strategy. The striker might favor his stronger side, of course, but that does not mean that there will be a pattern to the bias.The striker might shoot to the right two times out of three, but we cannot then conclude that it will have to be to the left next time.
Game theory also says that each choice of shot should be equally likely to succeed, weighing up the advantage of shooting to the stronger side against the disadvantage of being too predictable. If shots to the right score three-quarters of the time and shots to the left score half the time, you should be shooting to the right more often. But as you do, the goalkeeper will respond: Shots to the right will become less successful and those to the left more successful.
It turns out that real players do — intuitively — understand this:
Ignacio Palacios-Huerta, an economist at Brown University, found that individual strikers and keepers were, in fact, master strategists. Out of 42 top players whom Palacios-Huerta studied, only three departed from game theory’s recommendations — in retrospect, they succeeded more often on one side than the other and would have been better altering the balance between their strategies. Professionals such as the French superstar Zinédine Zidane and Italy’s goalkeeper Gianluigi Buffon are apparently superb economists: Their strategies are absolutely unpredictable, and, as the theory demands, they are equally successful no matter what they do, indicating that they have found the perfect balance among the different options. These geniuses do not just think with their feet.