With 14 days remaining before selection day for the NCAA Division I Football Bowl Series, we decided to apply the Bradley-Terry model for identifying a ranking of the 128 NCAA Division I Football Bowl Series teams. All we considered for this model is whether a team won a particular match-up, and whether the location of the game (-1 for loser at home, +1 for winner at home, 0 for neutral game).
The maximum number of games played for each team at this point of the season is 11 games. Given the 128 teams, this means there are “127 choose 11” or 2,224,316,764,644,975 total possible schedules for each team. Ideally, we obtain at a minimum of “128 choose 2” or 8,128 games in order to apply a basic logistic regression model. Unfortunately there have been a total of 637 FBS vs. FBS games played all season. Thus the Bradley-Terry model will have an expected low r-square value when fit. In fact, the Bradley-Terry model fit gives us an r-square of 0.4909; which is relatively good for NCAA football.
Immediately we see that three of the top 4 are the same as the Top 4 teams vying for the football tournament: Clemson, Notre Dame, and Iowa. However, we have a vastly different team with Navy embedded as number 4 in our rankings. The reason for their high ranking is due to what we consider for rankings.
First, we do not consider the score of a game. Navy’s suffered a 17 point loss to Notre Dame; but it’s viewed the same as a 45 point loss as well as a 1 point loss in triple overtime. Second, we consider the location of the game. Losing at home is more important than losing on the road. Navy’s sole loss is at Notre Dame; the second highest ranked team on our rankings. Third, Navy has beaten several quality teams such as South Florida (43rd in our model; 40th according to AP), Air Force (31st AP, 36th Coaches, 34th ESPN; 76th ours…), and Memphis (26th in our model; rapidly tumbling in others but was once in the teens).
We find that the most underrated teams in our model are West Virginia and LSU. LSU is ranked 15th in our model, but lingers around 27th in the three major polls. West Virginia, ranked 14th in our model, is 6-4 and therefore is understandingly out of the top 40 for every poll. However, since we consider only wins and losses; West Virginia ranks high when you see their four losses: at Oklahoma (6th our model, 5th AP, 5th Coaches, 3rd ESPN), at TCU (9th our model, 15th AP, 16th Coaches, 17th ESPN), at Baylor (5th our model, 7th for all others), and home vs. Oklahoma State (7th our model, 9th AP, 10th ESPN and Coaches). As you can see, West Virginia doesn’t lose to slouches. Unfortunately, West Virginia’s biggest wins are against Texas Tech (who beat Arkansas) and Texas (who beat Oklahoma).
The most overrated team according to our model is North Carolina; ranked 11th across the three main polls but are settled in at 36th in our poll. North Carolina started the season with a loss to South Carolina (51st in our model; not ranked in top 40 in others). After that, North Carolina strung together 10 consecutive wins over unranked teams. In fact, the best ranking an opponent has is Pittsburgh (40th in our model, 27th AP, 30th Coaches, 26th ESPN). The other rankings of opponents are: 55th (Miami FL), 65th (Illinois), 68th (Georgia Tech), 70th (Duke), 71st (Virginia Tech), 72nd (Virginia), 89th (Wake Forest). None of the teams are considered in the top 40 for the AP, Coaches, and ESPN polls; therefore unranked. The other two wins? Non-FBS teams: North Carolina A&T and Delaware.
With a couple weeks remaining in the season, it will be interesting to see the late-season shake-ups.