How can an elimination tournament favor a weaker player?

Abstract

This work shows that balanced elimination tournaments with eight or more players cannot guarantee that weaker players are not favored. We present a procedure that obtains a matrix of pairwise winning probabilities for each possible seeding of the players, which favors a weaker player over a stronger player and identifies those players.

The effects of draw restrictions on knockout tournaments

“…Interestingly, the data align with the assumption of strong stochastic transitivity of the pairwise winning probability matrix, that is, if a team 𝑥 is stronger than another team 𝑦, then 𝑥 defeats any third team with a higher probability than 𝑦. This property is often used in the probabilistic analysis of knockout tournaments (Arlegi, 2022;Arlegi and Dimitrov, 2020;Hwang, 1982;Horen and Riezman, 1985;Schwenk, 2000). If the two clubs have the same type, the probability of winning is assumed to be 0.5.…”

League competitions and fairness

“…The strong versions impose that a league-type competition should fulfill the property for every possible assignment of the players, while the weak forms only require that the property be fulfilled for at least one such assignment. The effect of these weak versions of the axioms was also studied in Arlegi and Dimitrov (2020) and Arlegi (2022). However, the analysis in these works is set within the framework of elimination-type competitions (knockout tournaments) which is completely different from the model of league-type competitions we develop and study in the current paper.…”

Eleme Turnuvalarında Seribaşı Eşlemelerinin Sayılması ve Sayımlanması

“…Öncül sayılabilecek çalışmalarda, bazı niceliksel koşulları sağlayan seribaşı eşlemeleri aranmış ve az sayıda yarışmacısı olan turnuvalar için bu şartları sağlayan bazı seribaşı eşlemeleri belirlenmiştir [1][2][3][4]. Takip eden çalışmalardan bir kısmında seribaşı eşlemelerinin etkileri gerçek turnuva örnekleri üzerinde matematiksel olarak incelenirken [5][6][7][8][9], diğer bir kısmında da bir seribaşı eşlemesinin neden ve nasıl diğerlerinden daha iyi olduğunu belirten aksiyomatik kriterler ortaya konmuş, bu kriterleri sağlayan seribaşı eşlemeleri önerilmiştir [10][11][12][13][14][15][16][17]. Ancak, bildiğimiz kadarıyla, kombinatorik bir problem olan seribaşı eşlemelerinin sayımlanması için bir algoritma sunulmamıştır.…”