Friday, 19 February 2010

Short tournaments

Short tournaments are notoriously bad for choosing the best team. I read an article a few months ago on the likelihood that a soccer game will select the best team and the fact of the matter is that a single game isn't a very good experiment. (short summary) In light of this I've been thinking about the optimal setup for a very short tournament of the sort necessitated by the Winter Olympics, assuming we want the tournament to be maximally likely to "choose" the best team. The article considered, among other things, intransitivity as an indicator of the effectiveness as a game, i.e., if Team A beats Team B which beats Team C which beats Team A then we have an intransitivity. A lot of intransitivity suggests the games aren't very good at selecting winners.

I suspect the intransitivity will be lower in hockey, not because the games are better experiments but because the difference in relative ability is much greater between teams. But, there are also tiers of skill levels, I suspect. If we consider games between the top 5 or 6 teams in the tournament I suspect we'd see close scores and fairly high intransitivity. So, in a good tournament, I think the thing to do is to have early knockout of bad teams and allow for more games between the really good teams. I don't suspect that the best way to set up the tournament is to have a long round robin (3 games/team) after which zero teams are eliminated. If Norway loses 8-0 to Canada, they should immediately move to a consolation pool, the US shouldn't then be forced to waste time playing this team. But this tournament eliminates zero teams after the round robin, although they do give the top four teams a bye through one of the playoff rounds. It will have Russia and the US and Canada wasting a lot of time, three games, on potentially far lesser skilled teams and then move to single elimination games in the playoffs. I think it's a very poorly designed setup if our goal is to be able to crown the truly best team.

x-posted to blogspot.

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