The math that could make UEFA's draw fair for every team
- A tight little cluster hidden in the 2025-26 Champions League draw shows why the “new format” needs one small tweak, and gives a beautiful excuse to talk about symmetric graphs.
- TL;DR: UEFA’s new league-phase format can accidentally produce small clusters of teams that play each other disproportionately often, hurting their collective chance of advancing all at once.
- A single symmetric graph on 36 vertices, C(36; ±{1, 4, 10, 17}), eliminates this risk provably.
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- A tight little cluster hidden in the 2025-26 Champions League draw shows why the “new format” needs one small tweak, and gives a beautiful excuse to talk about symmetric graphs.
- TL;DR: UEFA’s new league-phase format can accidentally produce small clusters of teams that play each other disproportionately often, hurting their collective chance of advancing all at once.
- A single symmetric graph on 36 vertices, C(36; ±{1, 4, 10, 17}), eliminates this risk provably.
Sources: Sariyuce