I can hear what some of you are thinking. "Gasp!" you say. "You have taken the venerated formula that is DUSHEE and changed it? What right do you have?!?!"
I know. But here at DUSHEE headquarters, we strive for perfection.
What I've changed is relatively minor, and will make the "Score" for each team more useful. With the change, the DUSHEE score can be used not only to judge relative value, but also to estimate point spreads or how many points better is one team than another team ON AVERAGE. (Key emphasis, that.)
In the past, I calculated a Point Differential (PD) and a Yardage Differential (YD). I scaled the PD to be worth 2X the YM (arbitrarily) and then "normalized" the top Score to 100. For all the gory details in the methodology, see the very first post in this blog.
The negative to this is 1) the Score in of itself didn't really mean anything in real football terms (e.g., it didn't tell you how many points a team was better than another) and 2) the Score was only of value for that season; you couldn't compare teams from different seasons or eras. I had little cheats to get around those problems, but rather than keep those cheats hidden, I figured, why not incorporate them into the DUSHEE Score.
So here's what I've changed. If you plot the YD (on the y-axis) vs. the PD (on the x-axis) for all of the teams in the FBS, you get something that looks like this:
You can see that with some variation, the correlation between the two is pretty linear and in a given year usually varies between 6 and 7 yards per point. So if a team has a PD of 10 points, we would expect them, if they were a "normal" team, to have a YD around 65. But since most of the teams do not fall exactly on that "normal" line, I choose to "correct" their PD based on how much their YD deviates from this "normal" 6.5 yards per point.
So I take the teams actual PD, multiply it by the slope of that line in the chart above (6.5 in our example) and get an "expected" YD. I subtract it from the team's actual YD and then divide that value by some multiple (call this multiple the CF for correction factor) of the slope (6.5) to get a "corrected" PD, which is then added to the team's real PD to get the new DUSHEE score.
If I use a CF of 1, then the team's YD is all of the DUSHEE Score; the PD is basically ignored. As CF goes up, PD is emphasized more over YD.
Right now, I've arbitrarily chosen 3 as the CF. That gives PD an effective 3:1 emphasis over YD. Since the number of games is still relatively small and the spread in the data is higher than it will be at the end of the season, the value of CF is pretty important. Changing from 3 to 2 will make a pretty substantial difference in the rankings. As the season goes on and we collect more data, the impact of changing the CF will decrease.
So with this change, you can view the "Score" as the corrected "points better/worse than average" for each team. Ascore of zero means you are squarely average.
One other change that I'm considering but can't implement yet is eliminating the highest and lowest PD and YD for each team from the calculation. One potential weakness of this methodology is rewarding teams giving teams too much credit for being able to put up a lot of points on weak teams. I'm still not sure whether this is the right thing to do; I know some other computer polling techniques do it. Right now, there aren't enough data points to be throwing some out. But we'll look at the impact of this as we near the season's end.
And with that, the inaugural 2014 DUSHEE ranking ...