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WC 2006: Game theory and PKs
2006-06-24 23:44
by Bob Timmermann

Tim Hartford, the Undercover Economist, examines how game theory and penalty kicks intersect.

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.

How game theory explains Henrik Larsson is something for people smarter than me.

2006-06-25 00:11:04
1.   Ravenscar



I was possessed by the state of Minnesota.

2006-06-25 00:21:57
2.   Ken Arneson
no theory
will stand up to the breathless gasp
of a man, choking
in the clutch
2006-06-25 09:23:58
3.   das411
Now now Ken, that is for the "Game Theory and ARod" thread :)

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