Here's a brief description of how I computed the 2009 college football ratings.

Each team initially starts with a rating of 0. An iterative procedure is used where a team's rating is increased by (average margin of victory - average expected margin of victory). The average margin of victory is just their points minus their opponents points divided by the number of games played. The average expected margin of victory is the average of the difference between a team's rating and their opponents rating (both adjusted for home field advantage).

This procedure is equivalent to solving the linear system given by

N_ir_i-\Sigma_{j\in\{opponents of i}}r_j=\Sigma_{k=1}^N_im_i^k+(R_i-H_i)A

where N_i is the number of games played by team i, R_i is the number of road games, H_i is the number of home games, r_i is the rating, and m_i^k is the margin of victory in the k-th game for team i, and A is the home field advantage.

Since I released the 2009 college football rankings, I've changed my algorithm a bit. The equivalent linear system is now

N_ir_i-\Sigma_{j\in\{opponents of i}}r_j=\Sigma_{k=1}^N_if(m_i^k)+(R_i-H_i)A

where f is a function. The function f is chosen via an optimization procedure and varies depending on the sport/league. The goal is to optimize the predictive ability. I'm also planning to incorporate a "best linear unbiased estimator" to further improve the predictive ability.

Daniel O'Malley / omalled AT purdue DOT edu