Game Theory in Soccer

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Tim Harford explains why to be good in soccer you’ve to be a master strategist;

“The answer comes from a wartime collaboration between economist Oskar Morgenstern and mathematician John von Neumann. They produced a “theory of games” which, applied to this problem, says the strategy of the striker and the keeper cannot be predicted. 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.

Von Neumann and Morgenstern also say 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. 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.

Von Neumann and Morgenstern did not produce game theory to help footballers: they believed it could illuminate anything from pay negotiations to waging war. The trouble is that for these applications the wrinkles of reality always obscure whether ordinary people actually follow the strategies that game theory predicts they should. Yet penalty taking is different. The objective is simple, the variables easy to observe, and the results immediate.

Ignacio Palacios-Huerta, an economist at Brown University, found that individual strikers and keepers were, in fact, master strategists. Out of 42 top players that Palacios-Huerta studied, only three departed from game theory recommendations. Professionals such as the Brazilian Rivaldo 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 between the different options. These geniuses do not just think with their feet.”

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This page contains a single entry by Paul published on June 18, 2006 4:28 PM.

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