I can't begin to tell you how many emails I received about not releasing a DUSHEE ranking last week and I heard your pleas and cries.
I started playing around with the methodology to respond to the large number of WTF teams this season. As discussed in the last post, I attecked this in two ways; 2) by deemphasizing statistical outliers (i.e., games that are significantly better or worse than the typical performance for a particular team and 2) emphasizing the strength of the opponent.
I'll confess I'm uneasy about these changes. One of the things I really liked about the DUSHEE method is it's simplicity. The changes I made add a lot of complexity. And I worry that I'm adding more abitrariness to the methodology. The only arbitrary choice I made in the past was how much to emphasize point differential over yardage. Now I'm raising shit to the third power and adding stuff to the point margin and not to the yardage margin and neither with a great deal of statistical validity. But it made the WTF teams go down in the rakings although not all of them and some of them not as much as you might expect. Bowling Green is still really high. Just not quite as high as before.
1) Deemphasizing Statistical Outliers
This is an issue where one or two really good or really bad games drive a particular team's ranking more than their typical performance. The poster child for this was West Virginia whose week 1 game against Georgia Southern was driving their ranking up disproportionately although TCU's performance against Kansas was another example on the other side of the performance scale.
To address this, I calculate the average point differential and yardage differential for each team and then the standard deviation across all the games for each. For each game, the point differential and yardage differential is compared to the team average and then divided by the standard deviation. That value is then raised to the 3rd power and added to the point/yardage differential. If the value is under one standard deviation, then it has negligible impact on the team's score. At three standard deviations, it will drive the performance score toward the mean by 9 points. So West Virginia's point differential against Georgia Southern dropped from a 58.6 to a corrected 46.1 prior to correction 2. TCU's yardage differential went from -30.1 to a corrected -21.5 prior to correction 2.
2) Emphasizing Strength of Opponent
This is an issue where teams with really weak or really strong schedules stretch the assumption that there is enough cross-correlation among teams to assume one team's "average" opponent is about the same as another team's "average" opponent. This seems to be less true than ever this year as DUSHEE highly rated teams who have feasted on blowing out their opponents in weak conferences. Keep in mind that if this change were made retroactively to MWC-era Frog teams, it would probably have a deleterious effect on those rankings.
The correction I've implemented here is to simply add the opponent's DUSHEE score to the point differential. So remember how TCU's score against Kansas benefitted from correction 1? Add in Kansas' DUSHEE score of -31.8 and TCU's corrected point differential falls to -53.3. However the same corrections provide big boosts to their Oklahoma and Baylor scores.
Now these two corrections had a big impact on most of the DUSHEE WTF teams, dropping Western Kentucky from 10 to 24, Appalachian State from 13 to 27, and Bowling Green from 8 to 16. Bowling Green wasn't impacted as much as one might think because DUSHEE had BGSU's SOS at 80th, not all that low when compared to Western Kentucky (113th) and Appalachian State (118th).
So the next DUSHEE ranking will include these changes.