Scaling in tournaments

ELI BEN-NAIM; FEDERICO VAZQUEZ; SIDNEY REDNER

EUROPHYSICS LETTERS

EPL ASSOCIATION

Año: 2007 vol. 77 p. 30005 - 30005

0295-5075

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, 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^(-eta). Different decay exponents are found analytically for sequential dynamics, beta_seq=1-2q, and parallel dynamics, beta_par=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.