Colley Matrix, one of six computer rankings that help to rate BCS hopefuls.
Colley started his rankings in the mid-1990s, while studying astrophysics at Princeton. Computer rankings were growing in popularity, and Colley, a longtime football fan, had reservations about their effectiveness. He began playing around with a few models of his own, including the one that would become the Colley Matrix, a comparative system that relies on wins, losses, and schedule strength.
“You could do different things – throw in margin of victory, offensive points, defensive points-allowed – but I settled on the system I’m currently using because it did about as well as any other and it was by far the simplest,” Colley says.
In the fall of 1998, Colley started posting his weekly rankings on a website at Harvard, where he was working as a postdoctoral researcher. Without making much of an effort to promote his system, Colley found a following – drawing “five times as many hits as any other website at the Center for Astrophysics,” he recalls – and after the 2000 season, the BCS contacted him, asking to include his ranking in the group of computer ratings that account for one third of the BCS formula.
Though Colley’s methodology is not related to astrophysics, or to his current field of modeling and simulation, he has taken an academic approach to the process, publishing a detailed explanation of how his results are calculated on his website. “Anybody who knows linear algebra and wants to type in all the 700-and-some-odd games can reproduce my rankings,” he says.
Colley’s approach is unique among the BCS computer ratings – the other five view their formulas as proprietary information – and earlier this year, his transparency left him open to criticism when one missing game score caused an error in his ratings and a subsequent error in the overall rankings of two top-20 teams.
“As a scientist, I’m happy that people are out there checking me and that we get it right in the end – and we did get it right in the end,” Colley says. “So it’s sort of a victory for science, even if it’s sort of embarrassing for the BCS.” In the future, Colley plans to download scores from six different sources and compare them to insure that no scores are omitted.
While computer ratings have been seen as a way to counteract the biases of human voters, this season’s findings were closely aligned: All six computer programs and both of the human polls rated Auburn No. 1 and Oregon No. 2. Colley is impressed by that agreement, given the number of variables involved.
“After all, my system is just linear algebra,” he says. “You think, ‘Gosh, a single algebraic equation can mimic, reasonably well, the collective wisdom of 60 coaches and 50 experts in the Harris Poll?’ It’s pretty remarkable.”