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juni 30, 2004
Straffsparkar i fotboll och annan fotbollsmatematik
Apropå de många straffarna i fotbolls-EM.
Följande paper är en spelteoretisk modell av straffsparkar (ganska teknisk och har ännu inte luslästs):
P.A. Chiappori, S. Levitt, T. Groseclose: Testing Mixed Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer (PDF).
Abstract
This paper tests the predictions of game theory using penalty kicks in soccer. Penalty kicks are modelled as a variant on matching pennies in which both the kicker and the goalie choose one of three strategies: left, middle, or right. We develop a general model allowing for heterogeneity across players and demonstrate that some of the most basic predictions of such a model survive the aggregation necessary to test the model using real-world data, whereas others do not. We then present and test a set of assumptions su¢cient to allow hypothesis testing using available data. The model yields a number of predictions, many of which are non-intuitive (e.g. that kickers choose middle more frequently than goalies). Almost all of these predictions are substantiated in data from the French and Italian soccer leagues. We cannot reject the null hypothesis that players are behaving optimally given the opponent's play.
En av författarna till ovanstående paper, Steven Levitt, har skrivit andra skoj saker; tyvärr inte kostnadsfritt nedladdningsbara.
Ovanstående länkar: via Full Context
Lite mer efterforskningar ledde bl.a. till nedanstående om fotbollsmatematik
John Haigh, författare till boken Taking Chances: Winning With Probability, har skrivit några essäer om fotbollsmatematik.
Blast it like Beckham?. En spelteoretisk analys av straffsparkar, men ska nog ses som en introduktion till spelteori snarare än en vetenskaplig analys av straffsparkar.
On the ball innehåller däremot mer empiriska rön.
Om tiderna för målens läggande (som funderades kring i Optimering av fotbollstittande):
Data collected from professional soccer matches suggest strongly that the
times when goals are scored are fairly random, with two minor
modifications: more goals are scored, on average, in a given five-minute
period late in the game than earlier; and "goals beget goals" in the sense
that the more goals that have already been scored up to the present time,
the greater the average number of goals in the rest of the match. But
these two points are second order factors: by and large, the simple model
which assumes that goals come along at random at some average rate, and
irrespective of the score, fits the data quite well.
Om sannolikheten för ett lag att vinna matchen om det lägger första målet:
So in the Premiership, indeed most professional soccer, we expect a team
to win about 2/3 of the games in which it scores first, and draw about 1/5
of them. That offers the warm comfort that if your team scores first, it
should lose only about one time in seven. You can check the match outcomes
each week, and over a season, from information in the newspapers. Real
data do conform well to these proportions.
För övrigt är Plus Magazine en mycket intressant sajt för den som vill läsa denna typ av artiklar. Fler spelteoriartiklar från Plus Magazine finns här.
Några andra skrifter på samma tema:
Game Theory: Additional Topics, Shooting at the goalkeeper. Kort exempel.
Kicker/goalie = pitcher/batter
Professionals Play Minimax: Appendix (PDF),
Posted by hakank at juni 30, 2004 08:01 EM Posted to Statistik/data-analys