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So curiosity about how the BCS works, combined with repeated frustration over advancing whatever team I was playing in NCAA 2002, led me to think about how I could try and do better. I was wondering what the team ratings would look like if one basically extended the 'strength of schedule' calculation (which takes into account the win-loss scores of both the opponents and the opponents' opponents) by a few branches and built a directed graph. A team's fitness score could be calculated by walking the graph and assigning points to a team based on how many teams it can reach in one step (direct victories), how many in two steps (beaten by teams you've beaten), three steps, etc. To prevent a team with a 13-2 record from scoring higher than a comprable team with a 12-0 record, also execute another round in which the team is penalized for direct losses, 2nd order losses, etc.
Basically, I wanted to see if I could do any better than Wes Colley's BCS-approved Matrix method. I believe in his basic contention that only win-loss ratios should be counted, and Margin of Victory not taken into account, but I don't like the fact that the inputs to a Colley Matrix don't explicitly show whether a team has beaten or lost any specific other team on its play list--the only thing we know about a team in Colley's method is what other teams it has played, and its overall win-loss ratio.

Anyway, enough with the details, let's see some results. As the season continues, I'll update this page with weekly tallies of my own rankings and also Colley's method. I decided to stick with ratios as follows. I'm not particularly standing by them, they're just the first things that came to mind. One TODO is to get my program to the point where I can test to see if there are any better ways to distribute poitns. But for this season at least, it looks like the ratios are going to be just straight halving: 

Order Win:     1     2     3     4     5
Score:         1     .5    .25   .125  .0625

2002-2003 Season
Week 5
Week 6

Okay, it looks like the simple harmonic method is not the way to go, because Week 7 moves the Badgers up to second place after a loss to Penn State. Maybe UW's oppnents had some good weeks, but I doubt it should make that much of a difference. Looks like I need to do some analyzing of better ratios soon.

Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Week 15
A new bit of information for Week 16. The number of total upsets at the end of each ranking list is the number of games in the season in which a team with a lower ranking beat a team with a higher ranking. For week 16, this means that out of 744 total games, both conference and non-conference, my ranking system predicted 127 games incorrectly, and Colley's system predicted 101 games incorrectly. Doing some futzing with the coefficient numbers, I found that the simple halving method was not the most optimal, and with basic exponential decay, the best way to put the numbers seems closer to quartering each generation rather than halving. I'll have to do some more fiddling in the off-season.
Also, my system disagrees with Colley's on who the national champion is--I say Ohio State, his says Miami. I guess we'll see in January.

Vindication! After most other computer rankers put Miami ahead of Ohio state, and most pundits predicted a win for Miami, Ohio State justified their First place ranking on the morning of January 3 with a squeaked out win in double overtime (why yes, all the ref's calls did seem fair, why did you ask?). The final ranking of all teams is here.

I found it interesting that my system was a lot more stable than Colley's--The single Ohio State win over Miami changed the final ranking order of much fewer teams under my system, and the reshuffling of teams under the Colley system caused an increase by one in the number of ranking upsets over his season. I'm not sure how good or bad that makes my ranker. Also, I'm a little worried about how much higher Ohio State ended up than Miami, leading by almost 6 and a half points coming into the Fiesta bowl. Judging by the game, these scores really should have been a lot closer.

Finally, there were more ties than I thought there would be. On the third, Tennessee, TCU and Kentucky were in a three-way tie for 30th place, and Navy was tied with UTEP for 113th. In the final rankings, the top 25 cannot avoid a tie, with Pittsburgh and Boston College tied for 20th place. Tennessee drops out of the 30th place contest because of its loss to a loser to Miami, but TCU and Kentucky are still tied. And Navy and UTEP are still tied down at the bottom. I suppose that will be another thing I'll have to fix. I suspect I can fix it by making sure that none of my score levels can be divided into a higher number, but that does not fix the problem in the theoretical sense. More work needed, I guess.