Game theory and the art of the penalty

Slate Magazine explains why English penalty-takers should stop thinking with their feet:

"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 might sound strange that at this point any choice will do, but it is analogous to saying that if you are at the summit of the mountain, no direction is up.
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."

Unfortunately, the English problem is not so much a question of decision-making about left or right, more a propensity to balloon the ball over the bar. This is not a strategy likely to succeed.