24 de enero de 2007

Scaling in tournaments

E. Ben-Naim, S. Redner, F. Vazquez, EPL 77, 30005 (2007)

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.