Abstract

Among the many mathematical ranking systems published in college football, the method used byWes Colley is notable for its elegance. It involves setting up a matrix system in a relatively simple way, then solving it to determine a ranking. However, the Colley rankings are not particularly strong at predicting the outcomes of future games. We discuss the reasons why ranking college football teams is difficult, namely weak connections (as 120 teams each play 11–14 games) and divergent strengths-of schedule. Then, we attempt to extend this method to improve the predictive quality, partially by applying margin-of-victory and home-field advantage in a logical manner. Each team's games are weighted unequally, to emphasize the outcome of the most informative games. This extension of the Colley method is developed in detail, and its predictive accuracy during a recent season is assessed.

Many algorithmic ranking systems in collegiate American football publish their results online each season. Kenneth Massey compares the results of over one hundred such systems (see [9]), and David Wilson's site [14] lists many rankings by category. A variety of methods are used, and some are dependent on complex tools from statistics or mathematics. For example, Massey's ratings [10] use maximum likelihood estimation. A few methods, including those of Richard Billingsley [3], are computed recursively, so that each week's ratings are a function of the previous week's ratings and new results. Some high-profile rankings, such as those of USA Today oddsmaker Jeff Sagarin [12], use methods that are not fully disclosed, for proprietary reasons.