Explanation of the rankings
The idea of this ranking system is a little bit different from how the human polls operate. Voters and fans all tend to argue about who is the best team, but we all seem to agree there are some caveats. For instance, consider a team that lost three of its first four games on fluke plays to solid opponents but won the last eight games by huge margins while playing in the SEC. We might think that would be the best team in the sense that they would be the hardest to beat right now. But clearly they don't deserve to play in the national championship because they have three losses.
So the point of the first paragraph is to say that we don't really have a concrete definition of what we are looking for when we rank the teams as humans. Most people seem to agree that it has something to do with this idea of the best team. My computer ranking system does not really take this approach at all. There are several general themes to the raking system.
- The rankings should be based entirely on what has happened on the field this season.
- The rankings should indicate who has had the best entire season.
- The rankings must include all the games played by all the teams.
- The rankings should use a methodology that gives an indication of which team would be the most likely to have the best record in a hypothetical season in which all teams played each other exactly once.
A lot of things come out of this set of rules. Based on the first point, there cannot be any preseason rankings. Also the rankings would be trivial after one game played. In theory a full set of rankings could be compiled after two games, but games are not scheduled that way. In practice I don't even try to calculate the rankings until the fourth or fifth week of games has been completed. The second point raises a bit more controversy. Because the idea is that the rankings are a measurement of the entire season, the difference between an early-season loss and a late-season loss is either trivial or nonexistant.
I think the third point is critical, but if nothing else it makes the rankings a lot more fun to look at. Because lots of FBS teams play one FCS team in a season, and lots of FCS teams play at least one Division II team, and Division II teams sometimes play Division III teams who often play NAIA teams, the ranking system should really include all 700+ college football teams—even if the goal is only to rank the FBS teams. A ranking system that misses an Appalachian State win over Michigan is missing something really important. In case you are wondering about even bigger jumps, I have seen an FBS team (Western Kentucky) play an NAIA team (West Virginia Tech) in 2007.
Now the fourth point gets down to what the ranking system actually does, since I have spent a lot of time saying what it does not do. The whole problem with our silly college football system in this country is that there are a lot of teams (120 in FBS) that only play a few games per season (about 12.2 before the bowls). To make things worse, some teams have far easier schedules than others. If teams all played each other exactly once, we'd have no need for all the debate (consider the NFL, for instance, in which every team plays about half of the other teams). So the goal of this system is to estimate probabilities about what would happen in such a hypothetical season.
Estimating what would actually happen is obviously impossible, but we can use a few tricks to at least set some odds. The rankings at the end of such a season would be determined quite simply by wins and losses (since each team had the same schedule). By definition, this ranking would be the one ranking such that the minimum number of upsets happened during the season. In this case by "upset" I mean simply that a lower-ranked team beat a higher-ranked team. Those two sentences are a little hard to parse, but if you think about it for a while, it will make sense.
Since such a season is not what we get as fans, we need to come up with a proxy for this ranking. In order to do that we would need to establish a ranking of the teams that minimizes the probability of upsets in the next game. We will have to use a system more sophisticated than wins and losses in this case because a 5-0 Division III team is not likely to beat a 2-2 FBS team. To do this what you need is a probability pairing between each team and the other 722 teams. This means 261003 pairings. That's kind of a ludicrous amount of numbers to keep track of, but there's a simple way to make all those pairings easy to calculate. All we have to do is give a numeric value to each team, and then the pairing is just the difference of these two numbers. For example, if Team A has a score of 4.57, and Team B has a score of 3.46, then Team A would be favored if the two teams played tomorrow. The values of the scores are not important except to order the teams. If we multiplied every team's score by 2, it would not affect anything.
The only remaining aspect is to come up with a way to calculate these "scores" for each team. The way that I have chosen to do this is by saying the games that already happened are indistinguishable from the hypothetical future games. So the current "scores" are determined such that the games that have already been played has the fewest upsets&mspace;actually, it ranks the teams so that the existing games had the lowest "upset value." This just means that bigger upsets count for more than small upsets.
Since the team "scores" are an estimate of how likely each team is to win these hypothetical future games, the teams with the highest scores would win the most games. Thus, the scores calculated based on the games that have already been played become the Dalle Rankings based on the current schedule.