Artículo
Randomness in Competitions
Fecha de publicación:
11/2012
Editorial:
Springer
Revista:
Journal of Statistical Physics
ISSN:
0022-4715
e-ISSN:
1572-9613
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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 N−−√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 N9/5, whereas traditional leagues require N3 games to fairly determine a champion.
Palabras clave:
Competition
,
Social Dynamics
,
Kinetic Theory
,
Scaling Laws
,
Algorithms
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IFLYSIB)
Articulos de INST.FISICA DE LIQUIDOS Y SIST.BIOLOGICOS (I)
Articulos de INST.FISICA DE LIQUIDOS Y SIST.BIOLOGICOS (I)
Citación
Ben-Naim, Eli; Hengartner, N. W.; Redner, Sidney; Vazquez, Federico; Randomness in Competitions; Springer; Journal of Statistical Physics; 151; 3-4; 11-2012; 458-474
Compartir
Altmétricas