Randomness in Competitions

摘要: We study the effects of randomness on competitions based an elementary random process in which there is a finite probability that weaker team upsets stronger team. apply this model to sports leagues and tournaments, compare theoretical results with empirical data. Our shows single-elimination tournaments are efficient but unfair: number games proportional teams N, weakest wins decays only algebraically N. In contrast, leagues, where every plays other team, fair inefficient: top \(\sqrt{N}\) remain contention for championship, while becomes champion exponentially small. also propose gradual elimination schedule consists preliminary round championship round. Initially, play small games, subsequently, few qualify This algorithm efficient: best high scales as N9/5, whereas traditional require N3 fairly determine champion.