The Science of Who’s the Best

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?

There are many aspects to the debate, from the talent levels of the athletes, to the differing styles of play, questions of effort, substance vs. style, and so on.  But the one thing that college fans always point to is the unique thrills brought on by the single-elimination NCAA Tournament, as compared to the seven-game series of the NBA.

From an entertainment perspective, both formats have their merits.  A single-elimination tournament is more unpredictable, and upsets are more common.  A seven-game series presents an evolving chess match as the two teams get to know each other and rivalries are born.  And, for my money, the do-or-die atmosphere of a Game 7 offers even more drama than in a single-elimination tournament.  But the question of which format is more entertaining is largely a matter of personal taste.  (I would think that basketball fans would find something to appreciate in both levels of play, and I’m dumbfounded when I hear college fans declare the NBA unwatchable.  But that rant is beside the point.)

However, if you are looking at the tournament as a way to determine the best team, the research in this article confirms what is intuitively obvious: single-elimination tournaments are not the way to go.  The authors mention repeating the experiments (playing more games), or playing the games for longer until one team’s lead is large enough to guarantee that they are better to a certain degree of confidence.  I’d like to see them apply their methods to a 16-team tournament with 7-game series, and estimate the odds that the “best” team wins.  I’m sure it would be a lot higher than 28%.

But while basketball fans may not agree on the best method for deciding the best team, I think that we can all agree on the worst: college football’s BCS.

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