Krueger’s Round Robin Rankings

The Round Robin Rankings (RRR) system is different from others currently in use. Rather than use the seasonal performance to directly determine the rankings, I use the results to calculate an offensive and defensive strength of a team. Each team is then matched against all other division IA teams to determine the likely winner. The overall rating is based upon these simulated games and determines the resultant ranking.

How offensive and defensive strengths are determined.

I assume the points scored are determined by the teams offensive strength times the opponents defensive strength times the average score of all teams this season (adjusted for the average values for the strengths).

Sab = AverageScore * OffenseA * DefenseB / 0.49

Using results from this season the offensive and defensive strengths for each team are determined by a golden section search centered around 1.5 with an intial step size of 0.5. After 17 steps the range is nearly zero to nearly 3.000.

This system cannot easily differentiate between a team that dominates a weak but otherwise competitive conference and one that dominates a tough conference. The non-conference games do have some effect, but these are buffered by the relative multitude of conference games. This may be considered a weakness, but who can really say a team like 1998’s undefeated Tulane is not on par with the other top programs in the country that year. The strength of conference is rather subjective when considering a dominant team. A similar argument applies to inept teams. Was the 1998 South Carolina team (1-10) only bad relative to the "tough" SEC conference or would they have looked inept in any conference? A not so impressive win over terrible Ball State and losses to a weak Clemson team and surprisingly good Marshall don’t give much indication.

How the overall rating is determined.

I match each team against all other division IA schools and determine the outcome of each game. Again, I assume the score is a product of the offensive and defensive strengths of each opponent. This time, I adjust the average score by dividing by 3. This corrects for the fact that a touchdown is a little over two scores and a field goal is only 1 score. Using Bill James’ Pythagorean theorem, I postulate that the odds of a team winning a given game are determined by Sab²/(Sab²+Sba²). As others have noted, this accounts for the increased likelihood of winning a low scoring game with a two score differential compared to a high scoring game with the same scoring differential. If team A would beat Team B 70% of the time, then Team A adds 0.7 to its overall rating and team B adds 0.3 to its overall rating. The maximum overall rating is 115 if a team would absolutely beat all other teams. The minimum overall ranking is 0 if a team has no chance to beat any other team.

Please send your comments to krueger@engr.sc.edu