I don’t know crap about football. But I do recognize interesting algorithms when I see them, and this is some of the finest football-related math I’ve seen in some time: Two researchers at the University of Michigan have used network theory to design an alternative ranking system for college football.

Currently, inter-university football competition is a strangely balkanized affair. Unlike as with baseball or basketball, there is no single ranking for all teams; they’re broken into conferences, one of which is selected each year to be the “bowl” championship. But the problem here is that teams don’t get a chance to be evenly measured against one another. As the authors note in their paper (PDF here):

One often hears sports fans arguments of this form: “Although my team A didn’t play your team C this season, it did beat B who in turn beat C. Therefore A is better than C and would have won had they played a game.” (See Fig. 1.) In fact, this argument is usually articulated with less clarity than this and more beer, but nonetheless we feel that the general line of reasoning has merit.

So they essentially wrote a computer algorithm that would crunch game stats for the last couple of years and rank the teams according to precisely that idea: If A beats B and B beats C, A is thus superior to C, even if they never play. When they checked their results against the actual team results, they i) produced the funky graphic seen above, but more importantly, ii) found that their technique did a better job of predicting actual victors than the annual poll currently conducted by the Associated Press.

It’s Miller Time.

(Thanks to Samuel Arbesman for this one!)