The Colley-Thurston Matrix

This past college football season I spent time developing a ranking system that would give good results, but still be based in some sort of mathematics.  One of the rankings I have followed in the past is the Colley Matrix Ranking.  It only takes into consideration the win-loss record of a team, and the schedule each team has played.  By storing this information in a matrix, it can simultaneously solve for a ranking of all the college football teams.

I decided to modify this approach, by incorporating the scores of each game.  One would think that if it was a close game, where a team lost by only one point, the two teams are actually fairly evenly matched, as opposed to a 42-point blowout, where the winning team is clearly much better than the losing team.  I also decided to curve the point differential, using the natural logarithm function.  This makes the difference between a 3-point loss and a 6-point loss more important than the difference between a 42-point loss and a 45-point loss.

The final rankings from the Colley-Thurston Matrix can be found here.  I'm looking forward to keeping track of this again next season.