The Physics ArXiv Blog recently discussed a paper on the statistical problem with soccer tournaments. In particular, the authors note the problem that there is only a 28% chance that the “best team” won the most recent World Cup. They also point to the presence of intransitive triplets, or rock-paper-scissors type relationships where team A beats team B beats team C, who then beats team A. They cite these results to support their claim that single-elimination tournaments, and soccer games in general are a bad experiment to determine the best team.
I don’t know much about soccer, but as a basketball fan, I’m not surprised to hear about the existence of these intransitive triplets. Sure, after an 82-game NBA season where every team plays each other at least twice, you can feel pretty confident about ranking the teams on a rough hierarchy. But three teams of roughly the same level can definitely have a rock-paper-scissors relationship because of different areas of strength.
More interesting, however is their claim about single-elimination tournaments, as it makes me think of the age-old debate that seems to come up every March: Which is better, NCAA or NBA basketball?