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.Comment: 16 pages, 14 figure
