E. Ben-Naim et al 2007 EPL 77 30005 doi:10.1209/0295-5075/77/30005
Scaling in tournaments
E. Ben-Naim1, S. Redner2 and F. Vazquez1,2
Show affiliationsWe 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, 
. 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
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02.50.-r Probability theory, stochastic processes, and statistics
- Subjects
- Dates
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Issue 3 (February 2007)
Received 26 July 2006, in final form 8 December 2006
Published 24 January 2007
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Scaling in tournaments
E. Ben-Naim et al 2007 EPL 77 30005
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