Randomness in Competitions

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and compare the theoretical results with empirical data. Our model shows that single-elimination tournaments are efficient but unfair: the number of games is proportional to the number of teams N, but the probability that the weakest team wins decays only algebraically with N. In contrast, leagues, where every team plays every other team, are fair but inefficient: the top $\sqrt{N}$ of teams remain in contention for the championship, while the probability that the weakest team becomes champion is exponentially small. We also propose a gradual elimination schedule that consists of a preliminary round and a championship round. Initially, teams play a small number of preliminary games, and subsequently, a few teams qualify for the championship round. This algorithm is fair and efficient: the best team wins with a high probability and the number of games scales as $N^{9/5}$, whereas traditional leagues require N^3 games to fairly determine a champion.Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144, arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/061221

Spartan Daily, May 12, 2008

Volume 130, Issue 56https://scholarworks.sjsu.edu/spartandaily/10482/thumbnail.jp

Spartan Daily, May 12, 2008

Volume 130, Issue 56https://scholarworks.sjsu.edu/spartandaily/10482/thumbnail.jp

The Cowl - v.78 - n.15 - Feb 13, 2014

The Cowl - student newspaper of Providence College. Volume 78 - No. 15 - February 13, 2014. 32 pages

Sacred Heart University Magazine, Volume 3, Issue 2

Highlights: Channels of peace: Sacred Heart\u27s campus ministry -- Judy Ann Riccio is SHU\u27s first female athletic director -- Canine Cognition Lab -- Untitled Othello Project -- SHU\u27s sororities and fraternities lead by example -- Chess Club -- Seeing beneath the surface, by Gina Pribaz: Tomas Koeck \u2722, senior in the School of Communication, Media & the Arts (SCMA) -- Better by design, by Steve Neumann: Tolga Kaya leads SHU\u27s fledgling computer engineering program -- All-in on ice, by William Meiners: Building underway for The Martire Family Arena -- Now. Listen. Here, by Will Mayer, Psy.D.: The last few years have been a challenge for everyone -- Spirit: Sports -- From the archive: 1967 commencement pprocession photo

What\u27s News At Rhode Island College

https://digitalcommons.ric.edu/whats_news/1389/thumbnail.jp