David Wilson has written some code to produce football rankings. "It was inspired by the rating system used in Chess," he writes. In fact, it's similar to the system used by the U.S. Chess Federation to deal with previously unrated players. I've used his code to produce ratings based on a system more closely patterned on the system for rated players. I may go into more detail on this in the future — for those who read C, I've included my "rate.c", mostly taken from David Wilson's "rate.c" — but, for those in the know, I'll mention here that the ratings are Elo ratings in which each team's winning percentage is calculated with an extra win and an extra loss included. (100 points is a ratio of "e"; multiply by 4/ln(10) to get something more nearly like what the US Chess Federation uses.) Something clearly has to be done to encourage undefeated (and winless) teams' ratings to converge, and while a full game on each side may seem a bit much, I feel good about it. To the right of the ratings in "byrating.txt" is a record of wins and losses only in upsets; e.g., Notre Dame has "2 3", denoting that it beat 2 teams listed above it in the rankings, and lost to 3 teams listed below it.

Some differences between the ratings I produce and those Wilson produces: beating a bad team will never hurt you with my ratings, as they will (slightly) with Wilson's; an undefeated team, in Wilson's ratings, will find its rating based heavily on that of the best team it played, while mine may be less impressed if you play a single good team and more if there are three or four comparable near-best teams; big upsets are more attenuated in my system (losing to a really bad team will, broadly speaking, only hurt you twice as much as losing to a team of about your calibre, where in Wilson's ratings it can swamp the rest of your season). And so on.

There should follow a general discourse on the fact that, using no score information, there's only so much one can say about an undefeated team; indeed there might should follow a general rant about the BCS thus handicapping its computers in the very sector of their ratings that has been given the greatest importance, viz. the top of the ratings. Of course, such rant should also probably be mitigated by the observation that the purpose is to win games, not roll up large margins, and perhaps the rant should be directed at atheletic directors who construct weak schedules. Even that point, though, falls to the fact that Utah's schedule, for example, was put together at a time that Air Force and BYU could have been expected to be better than they were, Texas A&M and North Carolina were not fluff teams, and nobody at Utah could really have been expected to foresee that their team would go through that entire schedule and a BCS bowl game without winning by less than two touchdowns. It's a real shame they didn't get a better opponent for the bowl game, to tell us how good they were.