Bayesian locally optimal design of knockout tournaments

Glickman, Mark E.

doi:10.1016/j.jspi.2007.09.007

Cited by 29 publications

(18 citation statements)

References 26 publications

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“…A criterion often optimized is the probability of the true best player winning the final game (e.g. [12,26]). Second, pairwise comparisons in a tournament have no cost.…”

Section: Onementioning

confidence: 99%

Active exploration for learning rankings from clickthrough data

Radlinski

Joachims

2007

Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

112

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We address the task of learning rankings of documents from search engine logs of user behavior. Previous work on this problem has relied on passively collected clickthrough data. In contrast, we show that an active exploration strategy can provide data that leads to much faster learning. Specifically, we develop a Bayesian approach for selecting rankings to present users so that interactions result in more informative training data. Our results using the TREC-10 Web corpus, as well as synthetic data, demonstrate that a directed exploration strategy quickly leads to users being presented improved rankings in an online learning setting. We find that active exploration substantially outperforms passive observation and random exploration.

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“…A criterion often optimized is the probability of the true best player winning the final game (e.g. [12,26]). Second, pairwise comparisons in a tournament have no cost.…”

Section: Onementioning

confidence: 99%

Active exploration for learning rankings from clickthrough data

Radlinski

Joachims

2007

Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

112

View full text Add to dashboard Cite

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“…Numerous statistical and simulation studies aim at comparing tournament designs. Glickman (2008) assumes only partial information about competitors' relative rankings and develops Bayesian locallyoptimal design of adaptive knockout tournaments to maximize the probability that the best team advances to the next round. Recently, Glickman and Hennessy (2016) have extended this approach in order to identify the overall best team in fixed knockout tournament brackets.…”

Section: Remarkmentioning

confidence: 99%

What a fairer 24 team UEFA Euro could look like

Guyon

2018

JSA

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In 2016, for the first time, the UEFA European Championship gathered 24 men's national teams. It consisted of a group stage made of 6 groups of 4, followed by a knockout stage starting with the round of 16. We critically examine a number of flaws in the design of the knockout bracket that was used by UEFA: group advantage, lack of win incentive, and arbitrary choices. We suggest two fairer procedures that satisfy the balance and group diversity constraints but eliminate group advantage and significantly increase win incentive, hence interest, in the group stage. The suggested procedures use a global ranking of the 16 teams qualified to the knockout stage based on their performance during the group stage. They apply to any tournament consisting of a round robin stage made of 6 groups of 4, followed by a knockout stage. UEFA has decided to keep the 2016 format for Euro 2020, but has used our work to modify the knockout bracket so as to minimize group advantage.

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“…There are a number of ways for carrying out seeding and these seeding policies are described next. Various studies have been carried out in the past to explore seeding, but this has been done only in the context of a KO tournament, see for example the work of Hwang (1982), Appleton (1995), Schwenk (2000), Marchand (2002) and Glickman (2008). We extend this work to various structures and systematically compare seeding policies.…”

Section: Tournament Design and Competitive Balancementioning

confidence: 99%

A numerical study of tournament structure and seeding policy for the soccer World Cup Finals

Scarf

Yusof

2010

Statistica Neerlandica

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Tournament outcome uncertainty depends on: the design of the tournament; and the relative strengths of the competitors -the competitive balance. A tournament design comprises the arrangement of the individual matches, which we call the tournament structure, the seeding policy and the progression rules. In this paper, we investigate the effect of seeding policy for various tournament structures, while taking account of competitive balance. Our methodology uses tournament outcome uncertainty to consider the effect of seeding policy and other design changes. The tournament outcome uncertainty is measured using the tournament outcome characteristic which is the probability P q,R that a team in the top 100q pre-tournament rank percentile progresses forward from round R, for all q and R. We use Monte Carlo simulation to calculate the values of this metric. We find that, in general, seeding favours stronger competitors, but that the degree of favouritism varies with the type of seeding. Reseeding after each round favours the strong to the greatest extent. The ideas in the paper are illustrated using the soccer World Cup Finals tournament.

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Bayesian locally optimal design of knockout tournaments

Cited by 29 publications

References 26 publications

Active exploration for learning rankings from clickthrough data

Active exploration for learning rankings from clickthrough data

What a fairer 24 team UEFA Euro could look like

A numerical study of tournament structure and seeding policy for the soccer World Cup Finals

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