Scaling in Tournaments

Abstract

We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q ≤ 1/2, and the stronger player wins with probability 1−q. The loser is eliminated. Extremal statistics of the initial distribution of player strengths governs the tournament outcome. For a uniform initial distribution of strengths, the rank of the winner, x∗, decays algebraically with the number of players, N , as x∗ ∼ N −β . Different decay exponents are found analytically for sequential dynamics, βseq = 1 − 2q, and parallel dynamics, βpar = 1 + ln(1−q) ln 2 . The distribution of player strengths becomes self-similar in the long time limit with an algebraic tail. Our theory successfully describes statistics of the US college basketball national championship tournament.

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Cite this paper

@inproceedings{BenNaim2006ScalingIT, title={Scaling in Tournaments}, author={E. Ben-Naim and Sidney Redner and Francisco V{\'a}zquez}, year={2006} }