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 characteristics found in college football, I found that all previous ranking systems generated violations that were at least 38 percent higher than the minimum. A minimum-violations criterion commonly would have affected the consensus top five and changed participants in the designated national championship game in 2000 and 2001-but not in the way most would have expected. A final regular season ranking using the model was perhaps the best prebowl ranking published online in 2004, as it maximized retrodictive accuracy and was nearly the best at predicting the 28 bowl winners.