Scaling in Tournaments
| dc.creator | Ben-Naim, E. | |
| dc.creator | Redner, S. | |
| dc.creator | Vazquez, F. | |
| dc.date | 2006-07-26 | |
| dc.date | 2006-12-14 | |
| dc.date.accessioned | 2026-07-07T07:42:33Z | |
| dc.date.available | 2026-07-07T07:42:33Z | |
| dc.description | 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^(-beta). 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. | |
| dc.description | 5 pages, 1 figure, empirical study added | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0607694 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0607694 | |
| dc.identifier | Europhys. Lett. 77, 30005 (2007) | |
| dc.identifier | doi:10.1209/0295-5075/77/30005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122483 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Physics and Society | |
| dc.title | Scaling in Tournaments | |
| dc.type | text |