● Covered by 1 source · 1 reportLow impact1 negative
UEFA Champions League new format creates unfair team clusters, a Cayley graph could fix it
Key points
- New UCL format creates dense clusters of teams playing each other frequently.
- 2025-26 UCL has a 5-team cluster with 9 out of 10 possible pairings.
- A Cayley graph on 36 vertices can provably prevent these clusters.
- Fix requires a small tweak to country rules for UCL/UEL.
Problem with the New Champions League Format
UEFA's new Champions League format, implemented in 2024-25, has an unintended consequence: the formation of 'tight clusters' of teams. These clusters consist of a small group of teams that are scheduled to play against each other in a high percentage of their matches during the league phase. For example, in the 2025-26 UCL, Napoli, Benfica, Chelsea, Ajax, and Qarabağ are slated to play each other in nine out of ten possible pairings, creating a disproportionate number of internal matches within this group.
Prevalence of Clusters Across Competitions
This issue is not isolated to a single season or competition. The 2024-25 UCL season features a similar cluster with Bayer Leverkusen, Atlético Madrid, Feyenoord, RB Salzburg, and Sparta Prague playing each other in 9 of 10 possible matches. The Europa League (UEL) and Europa Conference League (UECL) also exhibit these dense clusters, though UECL's sparser structure (6 opponents per team) results in slightly less density. Every completed UCL/UEL season under the new format has produced at least one cluster with 8 or more internal matches.
Proposed Solution: A Symmetric Graph
To address this issue, a solution involving a specific symmetric graph has been proposed. A Cayley graph on 36 vertices, C(36; ±{1, 4, 10, 17}), can provably eliminate the risk of these dense clusters forming. Implementing this graph would require a minor adjustment to the country rule for the UCL and UEL, but no changes would be needed for the UECL.
Changes in UEFA Competition Structure
Prior to 2024-25, the Champions League featured 32 teams divided into 8 groups of 4, with each team playing 6 group-stage matches. The new format introduces a single 36-team 'league phase' where each team plays 8 different opponents. Teams are then ranked in a single table, with the top 8 advancing directly to the round of 16, teams ranked 9-24 entering a knockout playoff, and teams 25-36 being eliminated.
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Primary sources
GitHub alshedivat/al-folioReporting from
The new UEFA Champions League format, introduced in 2024-25, inadvertently creates small clusters of teams that play each other disproportionately often, potentially hindering their collective advancement. A proposed solution involves using a specific symmetric graph, C(36; ±{1, 4, 10, 17}), which would eliminate this risk with minor rule adjustments.