2006-06-24 09:35

Football+Maths

If you have read the past 5 posts, you saw it was coming, right? ;-)

Via Slate here's a paper applying game theory to penalties:

http://www.econ.brown.edu/fac/ipalacios/pdf/professionals.pdf

The conclussion (and they made me retype this, because of stupid DRM):

The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a one-shot two-person zero-sum game. The results of the tests are remarkably consistent with equilibrium play in every respect: (i) winning probabilities are statistically identical across strategies for players; (ii) players' choices are serially independent. The tests have substantial power to distinguish equilibrium play from disequilibrium alternatives. These results represent the first time that both implications of von Neumann's Minimax theorem are supported under natural conditions.

In human:

  • Players are pretty good at making decisions according to game theory
  • Game theorists call that good

However (this I am making up as I go)...

  • A well kicked penalty is a goal, because there are places the keeper simply can't reach in time.
  • Since there is a winning strategy, it makes no sense to apply minimax: there is a global maximum (yes, I know, it makes sense, you just need to consider missing the goal as the chance of failure, then it is not a winning strategy... and I am not going to read the 21-page paper to see if he thought about it).

Of course the winning strategy (strong kicks to the top angles of the goal) is impractical for mere humans. All the more reason to consider RoboCup the most important tournament for the future.

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