Fair draws for group rounds in sport tournaments

We propose two draw systems for the group round of sport tournaments where there are some geographical and/or seeding restrictions. One of the systems, related to the equal-sum partition problem, is "perfect, " since it yields perfectly balanced groups. The other system, which uses the classical scheme of extracting teams from pots, is heuristic and gives results where the groups have very similar scores. We apply our results to Federation Internationale de Football Association (FIFA) Soccer World Cups and show that our proposals are much better than the FIFA system and also outperform other recently developed systems

The restricted group draw problem in sports tournaments: a detailed case study

Many sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Since finding an allocation of the teams that satisfies the established criteria is non-trivial, UEFA has adopted a procedure based on a random draw assisted by the computer to indicate the group(s) available for the drawn team. It is shown how this mechanism is connected to generating permutations, and a straightforward modification is proposed to increase the excitement of the draw. The consequences of draw restrictions are investigated through the case study of the European Qualifiers to the 2022 FIFA World Cup. We assess the probability of an obscure situation that threatens the transparency of the draw and quantify the departure of the UEFA mechanism from an evenly distributed random draw among all feasible allocations.Comment: 18 pages, 4 figures, 2 table

The UEFA Champions League seeding is not strategy-proof since the 2015/16 season

Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the most prestigious annual European club football tournament, the UEFA (Union of European Football Associations) Champions League, is shown to violate this requirement since the 2015/16 season. In particular, if the titleholder qualifies for the first pot by being a champion in a high-ranked league, its slot is given to a team from a lower-ranked association, which can harm a top club from the domestic championship of the titleholder. However, filling all vacancies through the national leagues excludes the presence of perverse incentives. UEFA is encouraged to introduce this policy from the 2021-24 cycle onwards.Comment: 11 pages, 1 figure, 1 tabl

Hogyan számszerűsíthető az ösztönzéskompatibilitás? Esettanulmány a sport világából

Minden sportbajnoksággal szemben alapvető elvárás a versenyzők megfelelő ösztönzése. A csalásbiztosságot az irodalom jellemzően bináris fogalomként kezeli, amely akadályozza az ösztönzéskompatibilitás és más kedvező tulajdonságok közötti átváltás feltárását. A cikk a csalás elleni védelem sérülésének számszerűsítésére tesz kísérletet a 2022-es labdarúgó-világbajnokság európai selejtezőjének példáján keresztül. Szimulációval becsüljük meg az eredményes manipuláció valószínűségét, majd megmutatjuk, hogy a csoportkör sorsolásához adott újabb korlátozó feltételek segítségével lényegében megszüntethető a hibás ösztönzés problémája. Ajánlásunk egyszerű, könnyen elfogadható, és nem növeli a szabályok bonyolultságát. Eredményeink révén javítható a sportbajnokságok igazságossága

A short comparative study on modified Duckworth-Lewis methods.

In this paper, the Duckworth-Lewis-Stern (DLS) and Duckworth-Lewis-McHale-Asif (DLMA) methods of revising targets for a team batting in second innings in an interrupted Limited Overs International Cricket (LOI), are examined for fairness. The work discusses four significant points: flexibility, intuition, simplicity, and goodness-of-fit of the two mentioned methods. The research findings have shown that the DLMA method is better in every aspect than the DLS method. Further, the data of 1764 ODI matches played during 2004-2021 to investigate the compatibility of the DLMA for high run-scoring One-Day International matches. The results show that DLMA is compatible to the situation of the well-above run-scoring situation

A paradox of tournament seeding

A mathematical model of seeding is analysed for sports tournaments where the qualification is based on round-robin contests. The conditions of strategyproofness are found to be quite restrictive: if each team takes its own coefficient (a measure of its past performance), only one or all of them should qualify from every round-robin contest. Thus the standard draw system creates incentives for tanking in order to be assigned to a stronger pot as each team prefers to qualify with teams having a lower coefficient. Major soccer competitions are shown to suffer from this weakness. Strategyproofness can be guaranteed by giving to each team the highest coefficient of all teams that are ranked lower in its round-robin contest. The proposal is illustrated by the 2020/21 UEFA Champions League.Comment: 23 pages, 3 table

A simulation comparison of tournament designs for the World Men's Handball Championships

The study aims to compare different designs for the World Men's Handball Championships. This event, organised in every two years, has adopted four hybrid formats consisting of knockout and round-robin stages in recent decades, including a change of design between the two recent championships in 2017 and 2019. They are evaluated under two extremal seeding policies with respect to various outcome measures through Monte-Carlo simulations. We find that the ability to give the first four positions to the strongest teams, as well as the expected quality and outcome uncertainty of the final is not necessarily a monotonic function of the number of matches played: the most frugal format is the second best with respect to these outcome measures, making it a good compromise in an unavoidable trade-off. A possible error is identified in a particular design. The relative performance of the formats is independent of the seeding rules and the competitive balance of the teams. The recent reform is demonstrated to have increased the probability of winning for the top teams. Our results have useful implications for the organisers of hybrid tournaments.Comment: 28 pages, 13 figures, 4 table

How to design a multi-stage tournament when some results are carried over?

The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used in handball and other sports, are shown to be incentive incompatible in the sense that a team can be strictly better of by not exerting full efort in a game. Historical examples are presented when a team was ex ante disinterested in winning by a high margin. We propose a family of incentive compatible designs. Their main characteristics are compared to the original format via simulations. Carrying over half of the points scored in the previous round turns out to be a promising policy