Continuing with my review of BCS computer rating systems, the 4th of the 6 systems in my series is Dr. Peter Wolfe’s ratings.
On his site, Wolfe only gives a brief explanation:
We rate all varsity teams of four year colleges that can be connected by mutual opponents, taking note of game locations….The method we use is called a maximum likelihood estimate. In it, each team i is assigned a rating value πi that is used in predicting the expected result between it and its opponent j, with the likelihood of i beating j given by:
πi / (πi + πj)
The probability P of all the results happening as they actually did is simply the product of multiplying together all the individual probabilities derived from each game. The rating values are chosen in such a way that the number P is as large as possible.
First thing to note is that Wolfe rates all teams from FBS through Division III and even NAIA. He includes all games between any two varsity teams at any level. Other systems, like Sagarin, only rate Division I teams. Some only rate the FBS teams. I am not sure any one method is more “right” than the others, but it is odd that the BCS allows different systems to rate different sets of teams.
On to the meat of the rating system, Wolfe uses a “maximum likelihood estimate”. But don’t fret, this is just a mathematically fancy way of saying that he is trying to find the ratings for each team that best explain the game results that we see. According to his formula, the likelihood of team i beating team j is calculated simply as the rating of team i divided by the sum of the two teams’ ratings. For example, let’s take Wolfe’s top two ranked teams: Oklahoma St. and Alabama. Oklahoma St. has a rating of 9.126, while Alabama comes in at 9.038. Thus, Oklahoma St. is 9.126 / (9.126 + 9.038) = 9.126 / 18.164 = 50.2% likely to beat Alabama. And against a weaker team like, say, Utah St. (rating of 3.749), Okie State would be 70.9% likely to win.
So what Wolfe’s ratings do is use some mathematical formulas to find the ratings that best explain the game results so far this season. This is a sound way of computing ratings. One thing that remains unclear, however, is how location of games is included. Wolfe does note that the system looks at all games “taking note of game locations”. However, he does not say how they do this.
One last note. Thanks to Austin Link who commented on my Anderson & Hester ranking and shared a link to something similar he did last year. On there, Austin notes with regard to the Wolfe ratings that “one problem is that under that method all undefeated teams should have infinitely high ratings. Since this doesn’t happen he presumably includes some limiting factor, but it’s likely sort of arbitrary, reducing the mathematical rigorousness.” Since undefeated teams are so important in BCS ratings–much more so than any other rating system I have seen (what other rating system is almost solely concerned with undefeated teams?!)–how Wolfe deals with this is actually very important.
Wolfe’s ratings are very solid. The only two questions are (1) how does he deal with game locations? and (2) how does he deal with undefeated teams, since all should theoretically have infinite ratings? Overall, Wolfe’s ratings seem to be a worth addition to the BCS computer ratings, though (as with most of these systems) it would be nice to see full methodology to provide a more rigorous review of their quality.