“The rules should be designed to guarantee fairness in all cases” – this is what Dr László Csató thinks about football, the favourite sport of many of us and this opinion is also reflected in his book on the subject. In mid-October, the associate professorof the Institute of Operations and Decision Sciences (IODS) at the Corvinus University of Budapest presented his e-book “Paradoxes in the Rules of Sports Competitions”, published by Typotex Publishing House.
Why is it so important to make the rules of sport as fair as possible? Csató says that there is little difference between an unfair rule and a fair rule, that with minimal changes and the help of mathematics you can make the rule good, so why not do it.
Dr. László Csató, research fellow and researcher at HUN-REN SZTAKI, associate professor at Corvinus, noticed in 2017 that in the 2018 World Cup European qualifiers, certain circumstances may lead to defeat being beneficial for certain teams. After studying the literature, he soon realised that other researchers had already discovered this, but he felt that this should not discourage him from studying the issue in depth. Paradoxes in the rules of sports competitions is the outcome of five years of work and can be downloaded free of charge from the Typotex website (after registration).
What should de done about interrupted matches?
The author said that the book also dealt with the championships during Covid that had already started but could not be completed because of the pandemic. It is interesting that different sports have used different methods. This type of problem had arisen much earlier, i.e. what to do with unfinished games, and Árpád Élő, the Hungarian-born American physicist, proposed the use of the so-called Elo scores, primarily in chess, but since then they have also been used in other sports. This method takes into account the relative skills of the competitors. For example, after Covid, the Hungarian Handball Federation decided to cancel the year’s season and delegated the previous year’s players to the international cup competitions, which of course led to a lot of injustice.
According to Csató, it is very important that the strength of the opponents should count in the case of round robin matches that are not completed for whatever reason, and the axiom-based method can lead to a fairer ranking. The author believes that unfinished tournaments may still occur in the future for any reason, so he recommends in his book that decision-makers in sports, given the many good mathematical-statistical methods available, should choose and fix in advance the rules that will be used in truncated tournament scenarios.
Who should shoot first?
For football fans, it is always very exciting when a penalty shoot-out takes place after extra time in a tournament. In his book, Csató also examines in detail how penalty shootouts could be made fairer. Under the current rules, the toss of a coin is used to decide which team can choose whether to take the penalty first or second. There is also a lively debate in professional circles about who is in a better position, the first or second team to take the penalty, depending on the ability of the opposing goalkeeper. In any case, there is a lot of psychological pressure on the penalty takers, as the fate of the match could depend on them. The author believes that by using different mathematical methods, it is possible to find a solution that could make penalty shootouts fairer than the current rules. This problem is also present in other sports (hockey, field hockey), and in politics, too, where order can play an important role: in the US presidential debates, candidates are given 2-2 minutes to talk about an important issue. The order – who speaks first – can also influence viewers’ opinions and ultimately the outcome of the election.
At the book launch, Csató also talked about how to organise a 24-team football tournament. In many tournaments there are 6 groups of four, with teams of unequal strengths in them. in 2026, the football World Cup will be played with 48 teams, so there will be a lot of matches, and the rules of the tournament are not yet known.
The human and economic consequences must also be taken into account
The book also discusses the fact that it is not always worthwhile for a team to win a match because of the avialability of more than one qualification options. It is possible for a team to qualify for a football tournament in more than one way, but the question is who then receives the resulting freed up place. It could be the case that it is not even worthwhile for a team to win in a group stage match, which is a bad “incentive”, as better rules could motivate teams to play well.
Finally, teams also receive financial support based on their performance. Csató has shown that if bad regulations are applied for a long time, they will lead to problems sooner or later. This could have the effect of limiting the amount of financial support (many thousands of euros) that a team can receive. “The rules must therefore be constructed in such a way as to guarantee justice in all cases,” the author said. He added that certain sports matches can sometimes have serious consequences: ethnic conflicts, deaths (the number of heart attacks can be linked to penalty shoot-outs), and the national team can also affect stock markets.
At the presentation, the author thanked those who helped him during his research: Zsombor Szádoczki and Csaba Ágoston Kolos, Head of the Department of Operations Research and Actuarial Sciences at Corvinus.
Afterwards, Zsombor Szádoczki Assistant Lecturer (IODS) spoke about his research on the ranking of women tennis players. The co-authored study was published in the Journal of the Operational Research Society. The authors have compiled a sort of perpetual ranking of women tennis players who have occupied the top spot at some point between 1973 and 2022, based on the official rankings of the Women’s Tennis Association (WTA). 28 such players were found. As Szádoczki said, the top two are Serena Williams and Steffi Graf. They worked with different mathematical methods and calculations, which was necessary because some tennis players have never played each other, some have played each other only once and some have played each other 80 times. (A previous article has already given a detailed account of this research project.)