College football ranking system

Following links, I came across a network-based mathematical algorithm for ranking college football teams. Basically, it seeks to extend wins to teams that the losing team has beaten, etc. so you know that since Notre Dame beat Michigan and Michigan beat Michigan State, then Notre Dame is better than Michigan State (wait a minute, didn’t they play head to head?). Anyway, it’s kind of interesting to consider. The problem with all this kind of stuff is that nobody can really be objective. Otherwise, you’d have to rank ND #2 right behind USC after yesterday’s improbable loss. Dad, you might even be able to understand the math.

PatrickRecommendations10/16/05 1 comments


Dad • 10/16/05 11:34 PM:

I don’t intend to spend any significant time trying to “understand” the linked ranking system, although it looks like pretty much matrix algebra. (I have always hated that, but it isn’t particularly difficult.) This system can be ostensibly objective because it uses a single parameter to adjust the weighting of various interactions (direct win, indirect win, etc.) The factor could be determined (and agreed upon) based on past years and then applied to this year. I suspect that, if done, this, like any other “system” would just become the starting point for arguments.

In thinking about the recent ND/USC game, it’s hard to imagine a game any closer than that one. Yet, it goes down as a 3 point loss for ND. Human raters can factor in (in some fuzzy way) the fact that the game was really up for grabs and could have gone either way. (Maybe one could take the margin of victory and multiply by the fraction of game time that you held this margin. By this measure, USC won by 3 points x 3 sec/3600 sec of game time = 0.0025.) Or maybe you could factor in quarterly scores (did you win all quarters? did you empty the bench? How early was the game decided?)

I think ND will preserve it’s ranking or possibly even go up slightly on the basis that they almost beat the #1 team. But what do I know?

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