Three years ago I fooled around with doing my own computer rankings of college football teams. I’ve decided to try it again, this time using some ideas from elementary kinetics.
The quality of each team is determined by its position on a line. Teams with better wins and better losses have a higher position than teams with worse wins and worse losses. All teams start out at position 0, and then move around the line based on the games they played, their scores of these games, and the quality/position of their opponents. This movement is modeled as follows:
- is the number of points that team i scored against team j.
- is the set of opponents that team i has played.
- is the quality and position of team i.
- is the velocity of team i
- is the drag coefficient, which dampens the oscillations in the system.
- is the net force being exerted on team i by its opponents. It is calculated by the following equation:
If is a small unit of time, then the velocity and position of team i are updated as follows.
From the starting position of all teams at 0, the system is allowed to run according to the above equations until it stabilizes within a certain tolerance.
Running the algorithm on the games played so far with and a stabilizes at iteration 2056. The full results can be found in this file. Below is a table of the top best fifty teams. Their positions have been scaled based such that the best team has a position of 100, and the worst 1-A team has a position of 0.
|13||Kansas St||4-3-0||77.79680508||38||Brigham Young||5-2-0||59.90100247|
|16||Penn State||6-2-0||71.18947026||41||Florida St||4-3-0||58.44603885|
|22||South Carolina||6-2-0||68.99577511||47||Miami FL||5-3-0||56.48983775|
Now how do we know these rankings are any good? There is no “right” way to rank teams. However, there are two things that I think every computer rating system should be able to roughly do: 1) sort out the divisions and 2) sort out teams based on records. This ranking does both of these, so I’d call it a success. I still need to work on balancing blow-outs and shut-outs. I think I’m currently giving the offenses too much control over the rankings.