A Cayley graph could fix UEFA's unfair Champions League draw
UEFA's Champions League draw creates unfair clusters; a Cayley graph fixes it
The 2025-26 Champions League draw produced a tight cluster: Napoli, Benfica, Chelsea, Ajax, and Qarabağ play 9 of their 10 possible pairings, hurting their joint chances of advancing. This pattern recurs every season in UEFA's new league-phase format. The author shows how a symmetric graph on 36 vertices—a Cayley graph—can eliminate such dense clusters by design, requiring only a small tweak to the country rule for UCL/UEL and none for UECL.
The point isn’t that this specific draw was cursed; it’s somewhat above average in cluster density (roughly top 20% of comparable random draws we simulated), not statistically extreme. It’s that the format allows this.
- wjnc
It’s something I like (math and networks) on a subject I like (football) but the AI tone is so heavy I get turned off. It’s far beyond my load-bearing capacity.
(tldr - a subset of teams get paired dispropotionally often in UEFA Champions League when compared to random, lowering average points taken away and thus harming chances for this ingroup and increasing chances for the outgroup; it’s interesting stuff; the group differs per year)
- rsrsrs86
Impossible to read the slop wall and find the interesting bits. “Unusually” boring because “this distinction matters”
- jazzpush2
Shame, it's a cool idea, but the writing is so full of claudism's my mind skims over it completely.
Bit of an embarrassment to publish that as a published researcher, to be honest.