Volume 77, Number 3, February 2007
|Number of page(s)||5|
|Published online||24 January 2007|
Scaling in tournaments
Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
2 Department of Physics, Boston University - Boston, MA 02215, USA
Accepted: 8 December 2006
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 , and the stronger player wins with probability . 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, , decays algebraically with the number of players, N, as . Different decay exponents are found analytically for sequential dynamics, , and parallel dynamics, . 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.
PACS: 01.50.Rt – Physics tournaments and contests / 02.50.-r – Probability theory, stochastic processes, and statistics / 89.75.Da – Systems obeying scaling laws
© Europhysics Letters Association, 2007
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