College Football Rankings: Do the Computers Know Best?

Matrix-based Methods for College Football Rankings

College football season is one of the most popular and anticipated sports competitions in the United States. Many of the National Collegiate Athletic Association (NCAA) Division I-A football games are surrounded by enormous fan interest and receive extensive media coverage. They are attended by tens of thousands of spectators and are followed by millions through the media. As a result, success ...

Minimizing Game Score Violations in College Football Rankings

One metric used to evaluate the myriad ranking systems in college football is retrodictive accuracy. Maximizing retrodictive accuracy is equivalent to minimizing game score violations: the number of times a past game's winner is ranked behind its loser. None of the roughly 100 current ranking systems achieves this objective. Using a model for minimizing violations that exploits problem characte...

Robust Rankings for College Football

We investigate the sensitivity of the Colley Matrix (CM) rankings—one of six computer rankings used by the Bowl Championship Series—to (hypothetical) changes in the outcomes of (actual) games. Specifically, we measure the shift in the rankings of the top 25 teams when the win-loss outcome of, say, a single game between two teams, each with winning percentages below 30%, is hypothetically switch...

A Penalized Maximum Likelihood Approach for the Ranking of College Football Teams Independent of Victory Margins

We introduce a penalized maximum likelihood approach for ranking all NCAA Division 1-A college football teams. The model does not consider margin of victory and is based solely on win/loss data. Despite the simplicity, the model leads to rankings which exhibit greater agreement with expert opinion (i.e. AP and Coaches polls) than the models historically and currently used by the Bowl Championsh...

Do We Know What We Do not Know? A Response to Celine Bonnet