Ranking College Football Teams

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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.

Rank Team Record Position Rank Team Record Position
1 LSU 7-1-0 100 26 Oklahoma St 5-3-0 66.76833079
2 Ohio State 8-0-0 91.91770206 27 Georgia 5-2-0 66.26334342
3 Oregon 6-1-0 90.37649059 28 Texas Tech 6-2-0 64.5558861
4 Florida 5-2-0 89.98650034 29 Clemson 5-2-0 64.43963901
5 Kansas 7-0-0 88.56028599 30 Michigan 6-2-0 63.79715507
6 Oklahoma 7-1-0 88.16654584 31 UCLA 5-2-0 63.37091573
7 South Florida 6-1-0 84.70038249 32 Illinois 5-3-0 62.57093573
8 Arizona St 7-0-0 84.64538387 33 Colorado 4-4-0 62.11719707
9 Auburn 5-3-0 83.03292418 34 Vanderbilt 4-3-0 61.96470088
10 West Virginia 6-1-0 83.01792455 35 Washington 2-5-0 61.9359516
11 Kentucky 6-2-0 79.32176696 36 Boise St 6-1-0 60.91472713
12 Missouri 6-1-0 78.85427864 37 Georgia Tech 5-3-0 60.79973001
13 Kansas St 4-3-0 77.79680508 38 Brigham Young 5-2-0 59.90100247
14 Arkansas 4-3-0 74.74063148 39 Michigan St 5-3-0 58.60603485
15 Rutgers 5-2-0 72.42568936 40 Virginia 7-1-0 58.51728707
16 Penn State 6-2-0 71.18947026 41 Florida St 4-3-0 58.44603885
17 Cincinnati 6-2-0 70.9919752 42 Texas A&M 6-2-0 57.41231469
18 Southern Cal 6-1-0 70.60698483 43 Louisville 4-4-0 57.29856754
19 Alabama 6-2-0 70.55448614 44 Purdue 6-2-0 56.90607735
20 Texas 6-2-0 70.34324142 45 Maryland 4-3-0 56.90232744
21 Virginia Tech 6-1-0 69.73700657 46 Tennessee 4-3-0 56.70733232
22 South Carolina 6-2-0 68.99577511 47 Miami FL 5-3-0 56.48983775
23 California 5-2-0 68.80077998 48 Oregon St 4-3-0 56.1398465
24 Connecticut 6-1-0 67.81830454 49 Wake Forest 5-2-0 55.73110672
25 Boston College 7-0-0 67.52581185 50 Troy 5-2-0 54.97737557

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.

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This page contains a single entry by Reed A. Cartwright published on October 25, 2007 12:58 AM.

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