So How else can it be done?

© Copyright 2005, Paul Kislanko

On the subscriber mailing list for collegeBCS.com, a poster suggested "Shouldn't the polls evaluate a team on their entire year's body of work?" I replied that that we'd be expecting too much. As fans we come up with examples that make it look easy, but what that entails is really evaluating all teams in terms of how they've done against their opponents based upon how other teams have done against their opponents, and the combinatorics gets out of hand very quickly.

For the 2005 Division 1A football season there are 872,868 connections between the 119 teams as either opponent, opponent-opponent, or, well the longest paths are to opponents' opponents' opponents' opponents (more or less, there's one game that was postponed that might not be rescheduled). That's an average of about 124 comparisons for each of the 7,021 team-pairs.

Oh, and those numbers don't include 1AA opponents who played other 1AA teams that played other 1A teams. The comparisons get much harder when those are taken into account.

Now, that's daunting if not impossible for a human voter, but this is exactly what the computers are good at. So it should be possible to use them to come up with a top 25.

It may not be as easy as it appears at first glance. There are several classifications of rankings, and not all produce the same "kind" of ordered list. A predictive system that takes into account all games to date and all possible connections between teams may "predict" that a team would win against an opponent it's already lost to, for instance.

That is not necessarily a bad thing - there are many variables that can be different the next time the teams meet. For instance, in Jeff Sagarin's "Predictor" ranking, teams rated within the "home field advantage" value of each other are predicted to win or lose based upon game location - the rating itself can be used to order the list based upon neutral site game locations.

The ISOV is a combined Predictive/Retrodictive method that produces a base rating similar to Sagarin's, but it can't be treated the same way. Because the weighting factor for each game is not just margin of victory but "strength of victory"

SOV = MOV (Total Points)

the predictive part of the ISOV is not a linear relationship between team A's ISOV and team B's. It's a rational function that depends upon:

• Team A's ISOV with respect to team B's SOS, A's average points per game and B's average points allowed per game;
  and
• Team B's ISOV with respect to team A's SOS, B's average points per game and A's average points allowed per game.

To convert the ISOV list into an ordered ranking where the higher-ranked team would be predicted to beat every team ranked lower than it is simple. Just find the prediction for each pair of teams, pretend all 7,021 games were played, and then order the teams by winning percentage in the imaginary games.

This "theoretical winning percentage" is the probability that the team would win (on a neutral field) against a team selected at random from the 118 possible opponents. After week 12, the list looks like this (note that the TWP rank differs from the ISOV rank in several important cases):

Theretical Winning Percentage
21 Nov 2005 11:08:54 (US Central)

One of the things the (ISOV-based) TWP provides is a "degree of confidence" for the predictions. Since the value is the probability of beating a randomly chosen team, we can calculate the probability that the prediction team A will win over team B is correct is given by

Prob(A beats B) = P×(1-Q) (P×(1-Q)+Q×(1-P))

where P is TWP(A) and Q is TWP(B). For instance, the probability that Auburn would beat LSU on a neutral field is