Single elimination competitionT. M. A. Fink1, 2, 3, 4, J. B. Coe1, 3, 4 and S. E. Ahnert5
1 INSERM U900, Curie Institute - Paris F-75248, France
2 CNRS UMR144, Curie Institute - Paris F-75248, France
3 Ecole des Mines de Paris, ParisTech - Fontainebleau, F-77300 France
4 London Institute for Mathematical Sciences - London W1K 2NY, UK
5 Theory of Condensed Matter, Cavendish Laboratory - Cambridge CB3 0HE, UK
received 12 January 2008; accepted in final form 1 August 2008; published September 2008
published online 15 September 2008
We study a simple model of competition in which each player has a fixed strength: randomly selected pairs of players compete, the stronger one wins and the loser is eliminated. We show that the best indicator of future success is not the number of wins but a player's wealth: the accumulated wealth of all defeated players. We calculate the distributions of strength and wealth for two versions of the problem: in the first, the loser is replaced; in the second, the loser is not. The probability of attaining a given wealth is shown to be path-independent. We illustrate our model with the popular game of conkers and discuss an extension to round-robin sports competition.
02.50.-r - Probability theory, stochastic processes, and statistics.
01.50.Rt - Physics tournaments and contests.
© EPLA 2008