Rank college football teams quantitatively; no input from human opinion or previous seasons, only wins and losses.
College football has only a single-round (one-game) play-off to determine a national champion. This game is the Bowl Championship Series (BCS) National Championship game held each year since 1998. The BCS was introduced to allow the best two teams to play each year, whether or not their conference affiliations would otherwise place them in different bowl games, as had happened several times in the 1990s.
The difficulty arises, of course, in selecting the two teams to play in the BCS Championship game. The BCS recognized that the media poll and the coaches' poll should be important components of the ranking system, but also recognized the emergence of computer rankings as reliable indicators of team quality. As such, the BCS created a hybrid ranking system which used both human polls and computer rankings. Since 1998, several changes to the weighting of these factors (as well as a laundry list of other numerical quantities, such as total losses), have been added or removed from the final ranking computation. Importantly, in 2005, the system was revised to a very simple weighting of 2/3 human, 1/3 computers, with no other adjustments. The only other change is that a few computer rankings have been replaced with others ones regarded as more reliable. In 2001, the Colley Matrix rankings were introduced to the BCS as one of the official computer rankings.The Colley Matrix ranking system has a philosophy that record should be paramount, as it is with almost all other sports in seeding their play-offs (NFL, MLB, NHL, etc.) College football, with its one-game play-off, should be no different. However, college football differs from most other sports in that the number of games played by each team is very small relative to the number of teams (12 vs. 119). Furthermore, there is great disparity between the best teams and the worst teams. Therefore, a 10-2 team that has played only weak opponents may have much less to recommend it than an 8-4 team in a strong conference. As such, a correction for strength-of-schedule (SOS) must be made.
The Colley Matrix method accounts for SOS by adjusting the wins of each team to an effective number of wins based on the quality of its opponents. The adjustment is made again, based on the new, effective record of the opponents, and again, and again, until further adjustment no longer changes the effective win numbers. Somewhat curiously, a simple linear solution to this infinite recursion presents. This linear solution allows the entire process to be written as a single matrix equation that can be solved very rapidly with standard numerical methods (hence, the Colley Matrix).
Since 2001, the Colley Matrix rankings have agreed with the consensus computer rankings of #1 and #2, and, as such, represent a stable and reliable choice for the BCS. Moreover, the rankings agree surprisingly well with the media and coaches' polls, which bestows greater credibility to both the computers and the humans.