After watching years of football games, I am always left feeling that either team could have scored another touchdown or that either team got lucky and scored a touchdown they didn’t deserve.  The BSC also acknowledged this and moved to get the margin of victory removed from their polls.  However, this over rewards teams who just barely won. Rather, close games indicate teams that are of equal or near-equal strength.  The other argument against margin of victory is that blowouts are over-rewarded. By computing the odds of winning through a power number and a Pythagorean of the score, the effect of blowouts is merely to distinguish that the winner is superior.  If the score is only used as an approximate and is adjusted to allow an additional score by either team, then the ratings should also avoid the difficulty in ranking teams in close games.  The details of the method are given below.

Here is a brief summary of how the ratings are determined.

1. Assume that the odds of winning a game are described by a Pythagorean calculation of the games score:           
2. Compute a window of the odds by adding 7 points to A’s actual score and then by adding 7 points to B’s actual score.  (saying that either team could have reasonably scored another touchdown and PAT).
3. Determine the odds of winning based on a probability number:
4. subtract the odds computed in 3 from that computed in 1 and square the result
5. If the odds computed in 3 are outside the range computed in 2 ten multiple 4 by five. Else multiply by one.
6. Minimize the sum of the computations in 5 for all games simultaneously.
7. This is aided by making a variable substitution such that _{, which results in 3 being  and has the benefit of w being unbounded. Then minimization can be done via a Jacobean (Newton-Raphson) iteration.}

Some side notes:

• Home field advantage: Because I only use the score as approximate, it is not necessary to account for home field advantage.  Other models that do so only attribute 2 -3 points for home field.  Since the scores are considered to be within 7 points of a reasonable value, the home field advantage can manifest itself without explicit determination.
• Divisional Strength: Most methods of computing divisional strength are ad hoc adjustments.  Meaning that they are not necessarily based on a model of how the strength between teams is determined, but added to avoid the instances when a team dominates their conference but the teams in that division were dominated by teams outside the conference as well.  Obviously, the challenges of playing in a major conference are tougher than playing in a small conference.  However, without actual game results, there is no means of discerning if the weakness of the conference yielded the dominance of a good team, or if the team was great and would have dominated any conference.  Likewise, is a poor team in a good conference really better than a poor team in a poor conference?  All the data simply says the team was easily beaten by all opponents.  For this reason, I do not attempt to adjust for conference strength. This can lead to disputable results, but any adjustments would make the results equally disputable.
• Is this a predictive model? The nature of a computer ranking model is to determine which team is better when the two haven’t played (or when they have played, but the result was not consistent with the other games played). Thus, all ranking models are predictive regardless of if they attempt to determine the score of a future game or simply run a formula based on past performance.  Given this, I will argue that computer ranking schemes that attempt to make accurate predictions of future outcomes are better than those which take a more simplistic and retrospective approach. 
• Problems with computer ranking models:  Almost every computer ranking schemes limit their input to the final outcome and possibly the home team.  This assumes that the team ability is constant from game to game throughout the season.  There is no account for weather effects, key injuries, unique weaknesses in certain philosophies that certain opposing philosophies are designed to exploit, luck, etc.  With such limited input, we should not expect the rankings to be all that precise.  I would say that it can distinguish a great team form a good team from a poor team from a terrible team.  The exact ranking is not able to be determined with such limited input.  To account for all factors would require precise simulation of every possible game several times.  Even advanced game simulations (think Playstation games) are limited in their accuracy to reproduce the different play calling options and outcomes.  So, a ranking scheme presented here or elsewhere is not accurate.  They are reasonable in that they produce a ranking that completely accounts for all inputs equally.  There are approximately 1400 division 1A football games each season.  To learn enough to properly evaluate all of them would be a daunting task for any human.  In light of this, computer rankings give a good starting point to the rue ranking and this can be balanced with some thoughtful analysis on the part of humans.
• NCAA Division 1A playoffs vs. the current bowl system: The current bowl system acts as a 2 team playoff with rewards for nearly every team with a wining season. This works well in terms of scheduling and interest.  How many teams would have a large following through several rounds of a playoff system? Would the fans of teams that were no longer involved care about the playoffs?  Would a better champion be determined?  I’d like to address this last question.  If two great teams play, the odds of one winning are likely limited to 60%, maybe 75% if the team is that awesome.  So, the better team can always be upset if it plays a quality opponent.  If more games are played against quality opponents then the chance that the strongest team is the champion is reduced.  This is why the NCAA basketball tournament can have frequent Cinderella stories.  You may argue: If the team won then it was truly the stronger team.  That may or may not be true.  If you watch a game, you can often argue that luck, bad officiating, or a single botched play caused the score to be in favor of the opposing team.  If these are real factors, then the strongest team does not always win.  So, a playoff does not produce a better champion.  It does reduce the opportunity to argue the merit of the champion because it at least won a series of games. I would prefer to use the season as a playoff culminating in a championship game with other good teams getting to go to bowl games.  I’ll post more details on this at a later date.  Given the choice of a playoff system or a bowl system, I am very happy with the bowl system and hope that it is retained.