Universal statistics of the knockout tournament
نویسندگان
چکیده
منابع مشابه
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 fou...
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We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimato...
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Balanced knockout tournaments are one of the most common formats for sports competitions, and are also used in elections and decision-making. We consider the computational problem of finding the optimal draw for a particular player in such a tournament. The problem has generated considerable research within AI in recent years. We prove that checking whether there exists a draw in which a player...
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This paper provides nested sets and vector representations of knockout tournaments. The paper introduces classification of probability domain assumptions and a new set of axioms. Two new seeding methods are proposed: equal gap seeding and increasing competitive intensity seeding. Under different probability domain assumptions, several axiomatic justifications are obtained for equal gap seeding....
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Sumner’s universal tournament conjecture states that any tournament on 2n−2 vertices contains any directed tree on n vertices. In this paper we prove that this conjecture holds for all sufficiently large n. The proof makes extensive use of results and ideas from a recent paper by the same authors, in which an approximate version of the conjecture was
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ژورنال
عنوان ژورنال: Scientific Reports
سال: 2013
ISSN: 2045-2322
DOI: 10.1038/srep03198