Universal statistics of the knockout tournament.
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a power law with an exponent close to unity if the competitiveness is a stable quantity and a decisive factor to win a match. Otherwise, the distribution is found narrow. The existing observation of power law distributions in various kinds of real sports tournaments therefore suggests that the rules of those games are constructed in such a way that it is possible to understand the games in terms of the contestants' inherent characteristics of competitiveness.
Department of Physics, Pukyong National University, 608-737 Busan, Korea.
Seung Ki
SK
Baek
Il Gu
IG
Yi
Hye Jin
HJ
Park
Beom Jun
BJ
Kim
D054874:Athletic Performance / Q000502:physiology* / Q000706:statistics & numerical data*; D001363:Awards and Prizes; D003163:Competitive Behavior / Q000502:physiology*; D006801:Humans; D013177:Sports / Q000706:statistics & numerical data*