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College Football Chain Reactions

Sam BurerFans of the Kansas State Wildcats probably don’t realize it, but their BCS hopes will be affected at least a little by this weekend’s University of Northern Iowa game against Western Illinois.

K-State, currently second in the BCS rankings, hasn’t played UNI this season, nor will it. But because of the way the computer generated portion of the BCS rankings work, the outcome of the Panthers game will have an impact on the Wildcats’ rankings. It works like this: K-State played Iowa State on Oct. 13 and won, 27-21. Iowa State played Iowa on Sept. 8 and won, 9-6. And Iowa played UNI on Sept. 15 and won, 27-16.

Because the computer rankings take into account not only each team’s wins and losses but the wins and losses of all the teams they played, it creates a kind of college football butterfly effect (it should be noted that the computers do not take into account margins of victory or on-field statistics, only wins and losses). So if UNI beats WIU this weekend, that will give UNI a stronger profile, which in turns gives Iowa a stronger profile, which gives Iowa State a stronger profile, and which finally improves K-State’s profile and the likelihood that they’ll play for the BCS national championship.

Sam Burer thinks this is kind of nuts. Burer, a management sciences professor in the University of Iowa’s Tippie College of Business, doesn’t think such inconsequential games should play such a prominent role in deciding the best teams in college football.

“Should games played between teams at the bottom of the heap have that much of an effect on what’s happening at the top?” says Burer. “The top rankings provided by computer systems should be more robust against the outcomes of inconsequential games.”

The idea that such an inconsequential game impacts the rankings has actually been borne out. In 2010, one of the computer programs used to determine the BCS rankings—the Colley Matrix—forgot to include in its final ranking the result of a football championship subdivision game between Western Illinois and Appalachian State. The game clearly had no direct impact on the BCS rankings because as FCS teams, neither qualify for the BCS. But thanks to the butterfly effect, forgetting to include that game had enough changes to actually have an impact.

The final BCS rankings had LSU ranked 10th and Boise State 11th. However, if the missing game had been added, the two schools would have switched places.

This, Burer points out, was a single game missing from just one of the six computer rankings the BCS uses, and that makes up just 6 percent of the BCS ranking (the other five computer rankings and two human polls make up the remaining 94 percent).

The issue with the Colley Matrix, Burer says, is that it gives equal weight to games between weaker teams, giving the UNI-WIU game an importance it does not deserve. His own formula works by also emphasizing each team’s wins and losses, but minimizes the butterfly effect by systematically changing the results of five games between weaker teams, comparing the results of each change, and devising a balanced ranking based on the comparisons.

“Our goal is to devise a ranking system whose top rankings are stable even if a ‘far away,’ inconsequential game happens to have a different outcome,” he says. “Our approach asks, ‘suppose the outcomes of just a few of the inconsequential games switched, but we do not necessarily know which ones.’”

Burer is compiling a ranking this season using his own matrix and comparing his results to the weekly BCS rankings. The BCS top five this week are Alabama, Kansas State, Notre Dame, Oregon, and LSU. The Burer top five, however, are Notre Dame, Kansas State, Alabama, Oregon, and Florida. (His ranking also includes Ohio State, which the BCS does not include because of its bowl ineligibility.)

He says his concept could eventually lead to improved rankings in other areas where head-to-head competition is not possible, such as chess, college and university rankings, or online searches.

Burer’s study, “Robust Rankings for College Football,” is published in the current issue of the Journal of Quantitative Analysis in Sports.

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