Definitions and General Information
The official definition of Wilson's College Football Performance Rating is:
A team's rating is the average of its opponents' ratings plus 100 for a win or minus 100 for a loss. Wins that lower the rating and losses that raise the rating count one twentieth as much as the other games. Post-season games count double.
The official definition of the Wobus Rating is:
Each team's rating equals its number of relevant wins, minus its number of relevant losses, plus the sum of the ratings of its relevant opponents, all divided by one more than its number of relevant opponents. ("Relevant" means the opponent's rating is within 1.0 of the team in question.)
Non-Mathematical Explanation ("How the heck are you doing this?")
A team's rating is based on its number of wins and losses in games played to date. Further, each team's rating is adjusted based on the ratings of the opponents they play--thus, each team's rating is partially dependent on their strength of schedule. (The formulas above are the ones used to determine the ratings.) A computer program produces all the teams' ratings at once; since we don't initially know how strong each opponent is, the definition is used over and over again until the ratings settle down.
Somewhat More Mathematical Explanation
Each team is assigned a "default" initial rating (the division rating in Wilson's system; for Wobus, all games are treated as "relevant" for the "0th" iteration). The program then iterates over all teams (i.e., calculates a rating for every team), and uses the ratings from the previous iteration as the first guess. The ratings will eventually converge (see Colley's explanation for a more eloquent discussion of rating system convergence); Wilson's system usually does so within about 1000 iterations, Wobus within about 100. As the season progresses, the two methods produce very similar results (correlations > 0.98).
Basic Premises of a Rating System, and some General Thoughts
As in any system, the premise here is: points are awarded for winning, and taken away for losing.
See the page by John Wobus for a good discussion of computer ratings vs. human polls, as well as discussion of the "RPI" used in college basketball. A comprehensive list of college football ratings is available from David Wilson.
Ratings are based solely upon who beat whom:
I make no claim that either of these statistical methods is superior to the other, or to the appropriateness of their use. I believe there is a better way to seed (and perhaps even determine) playoff teams, but I dare say that Alabama is well over a decade away from moving to a system like this (even though a number of states already use computer rankings exclusively to determine playoff teams).