Abstract:Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the first comparison of them by analysing the most prominent example of four-team round-robin competitions, the group stage of the FIFA World Cup. We show that both methods are highly relevant in practice: all (four) deterministic and (six) probabilistic match types occurred in the 2014 and 2018 FIFA World Cups, respectively. The probabilistic model, which accounts for the relative benefits of attacking and defending, provides deeper insights; for instance, the competitive matches from the deterministic approach can be of any of the six probabilistic types. Finally, the probabilistic framework is used to quantify and decompose the impact of the main reforms introduced for the 2026 FIFA World Cup: the expansion to 48 teams, as well as the modified qualification and tie-breaking rules.
| Comments: | 22 pages, 4 figures, 6 tables |
| Subjects: | Physics and Society (physics.soc-ph); General Economics (econ.GN); Optimization and Control (math.OC); Applications (stat.AP) |
| MSC classes: | 62P20, 90-10, 90B90, 91B14 |
| Cite as: | arXiv:2605.25610 [physics.soc-ph] |
| (or arXiv:2605.25610v1 [physics.soc-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25610 arXiv-issued DOI via DataCite (pending registration) |
From: László Csató [view email]
[v1]
Mon, 25 May 2026 09:08:25 UTC (26 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。