Post date: Sep 27, 2010 6:31:31 PM
I have always had trouble trying to come up with a good solution to the problem of FBS (I-A) teams losing to FCS teams. I don't find the wins over FCS teams that problematic, because it hurts the team in question to be denied the increased winning percentage that would have occurred with a win over another FBS team instead. That is considered when points are added to the winning FBS team as the last step in calculating the initial rating (see below for what that means) and final rating. Also, the least numerically significant type of game is a win against a lesser opponent, FCS or FBS. The differences between FCS wins are usually hundredths of a point, when there are almost 5 full points separating the best teams from the worst at the end of the season.
Addressing the losses is that manner was unsatisfactory because by adding a loss, that loss was not as bad as it should have been depending on how good the FBS strength of schedule was. For example, if it were a loss by a Sun Belt team whose best opponent was 50th, there wasn't much of a problem there, but if it were a team of an automatic-qualifying conference with a decent overall schedule, adding the loss was less significant. Most of the problem was in rating this FBS team as an opponent, because I think the final ratings had adequate adjustments, but small problems are magnified when "win chain" (team A beat team B, who beat team C) opponents are considered on multiple levels. It was also too much of a subjective judgment on what a "fair" penalty was. An equitable inverse number is not as easy to conceive and would probably get into the type of math that I designed my rating system to avoid.
Anyway, what I have done is, by employing the number I came up with to translate FCS results into FBS results, is to add in the FCS opponents as losses. I have to use that number since their SoS is not independently calculated. It changes a 5-5 record to something like 2-13. If it were an FCS team with a win over an FBS team (probably a bad one, certainly on the day they played that team) and 5 losses, I think that's about the correct correlation. The opponent's winning percentage for FCS opponents' opponents is simply the winning percentage that FCS teams in general have against FBS teams. I will add in the actual opponents' opponents' winning percentage for FBS teams. Earlier in this process, I may not have bothered, but there are too many FCS teams that have more than one FBS opponent at this point.
I realize this doesn't perfectly differentiate the quality of the FCS opponents, but it's enough to ensure losing to an Appalachian St. doesn't hurt as much as losing to an Idaho St., for example. I do understand that just like in FBS (or arguably even more so) going undefeated in one conference can be drastically different from going undefeated in another, but I've made sure to limit the harm done by any loss to what is appropriate for one week. It's hard to tell the difference between a FBS team who can't beat anyone else and an FCS team who can't beat anyone else. For the better FCS teams, I have made sure they're not rated any more highly than a mediocre FBS team (slightly better than average if the FCS team goes undefeated in the FCS and beats one or more good FBS teams as well). This is based on observations over years of looking at on-field results and computer ratings, even ones that attempt to integrate all the divisions into one formula.
Speaking of which, I doubt that even the BCS ratings have come up with an ideal solution in the framework of their ratings anyway. I know that Wes Colley, for example, groups together several FCS opponents into one "team" and rates that team as an opponent. From my own calculations, it seems there is no way to fully consider the difference in opponents from one division to the next. We do not have a representative sample of how good one division is compared to another. There are both very good and very bad FCS teams who (their coaches and administrators anyway) choose not to play FBS teams and both very good and very bad FBS teams who choose not to play FCS teams. At any rate, I have a full day job, and I have no input into who makes these big bowl games, so it's enough to enter in all the FBS results without trying to come up with a more complex system for the FCS teams. My ratings are a balance between saving time and being fair. These goals often coincide (I honestly used to stay up nights worried about whether I was fair in my ratings and would change them as one week progressed toward the next...it's just too hard for me to filter out bias and establish a fair assessment of 120 teams without the objective number-crunching which is the basis of these ratings), but where they do not, I believe I have struck a reasonable balance between the two.