I have the prestiges, wins, losses, conference champ status, ct champ status, pi round, and nt round of every team in HD in a database, and can export as a spreadsheet and post a link if anyone is interested. I did this with D3 only because I know that baseline prestige should be irrelevant. I use the finishing prestige of the last 8 seasons of each program as the thing to predict (normalized to a numerical grade, so e.g. a C is 2.0), and the above variables as the predictors. This is a simple linear regression and I know I can do better, but this still accounts for 94.3% of the variance (adjusted R-squared, which accounts for over-fitting).
RPI is actually RPI rank divided by 300, and the coefficient is negative because a smaller ranking number is better. The CT champ coefficient is negative because the model is probably not very good, and possibly because winning the CT means absolutely nothing, above and beyond the other achievements of a team. I made separate indicator variables for each of the possible values of NT wins and PI wins, because I didn't want to make a guess about the functional form that the real model might take, e.g. NT wins squared or something like that. Lastly, you can see the coefficients decrease with the number of seasons back, which makes sense.
I also used the Lasso method for penalizing over-fitting, and finally rounded coefficients to the nearest tenths place. Here is how you interpret the following. A team which wins 2 NT games in the most recent season will, on average, have a prestige that is 2*0.3 + 2^2*(-0.04) = 0.44 better (about half a letter grade) than a team that makes the NT but wins 0 NT games, but is otherwise the same in every way. I have bolded the two lines I am using to make that calculation. This will be obscure to many of you, and even those of you that do statistical modeling will probably have some criticism, but that's fine I'm happy to revise the model based on your ideas.
Lastly, sometimes you get a negative number where you probably shouldn't, e.g. the very first one (CT Champ -0.08). Taken at face value, this would imply that, all things being equal, it is worse to win the CT than to not. I'm sure this is not true, so you should just interpret this as noise and assume it probably has no effect.
1 seasons ago: CT Champ -0.08
1 seasons ago: Conf Champ 0.1
1 seasons ago: Wins 0.44
1 seasons ago: NT 0.63
1 seasons ago: NT wins 0.3
1 seasons ago: NT wins^2 -0.04
1 seasons ago: PI 0.28
1 seasons ago: PI wins 0.03
1 seasons ago: PI wins^2 0.0
2 seasons ago: RPI -0.01
2 seasons ago: CT Champ -0.05
2 seasons ago: Conf Champ 0.03
2 seasons ago: Wins 0.15
2 seasons ago: NT 0.3
2 seasons ago: NT wins 0.18
2 seasons ago: NT wins^2 -0.02
2 seasons ago: PI 0.09
2 seasons ago: PI wins 0.03
2 seasons ago: PI wins^2 0.0
3 seasons ago: RPI -0.01
3 seasons ago: CT Champ -0.0
3 seasons ago: Conf Champ 0.01
3 seasons ago: Wins 0.07
3 seasons ago: NT 0.12
3 seasons ago: NT wins 0.09
3 seasons ago: NT wins^2 -0.01
3 seasons ago: PI 0.03
3 seasons ago: PI wins 0.0
3 seasons ago: PI wins^2 0.0
4 seasons ago: RPI 0.0
4 seasons ago: CT Champ 0.01
4 seasons ago: Conf Champ 0.0
4 seasons ago: Wins 0.02
4 seasons ago: NT 0.06
4 seasons ago: NT wins 0.06
4 seasons ago: NT wins^2 -0.01
4 seasons ago: PI 0.02
4 seasons ago: PI wins -0.0
4 seasons ago: PI wins^2 0.0
5 seasons ago: RPI 0.01
5 seasons ago: CT Champ -0.0
5 seasons ago: Conf Champ -0.0
5 seasons ago: Wins 0.0
5 seasons ago: NT 0.06
5 seasons ago: NT wins 0.05
5 seasons ago: NT wins^2 -0.01
5 seasons ago: PI 0.03
5 seasons ago: PI wins 0.0
5 seasons ago: PI wins^2 0.0
6 seasons ago: RPI 0.0
6 seasons ago: CT Champ 0.0
6 seasons ago: Conf Champ -0.0
6 seasons ago: Wins 0.0
6 seasons ago: NT 0.02
6 seasons ago: NT wins 0.03
6 seasons ago: NT wins^2 -0.01
6 seasons ago: PI 0.01
6 seasons ago: PI wins 0.0
6 seasons ago: PI wins^2 -0.0
7 seasons ago: RPI 0.0
7 seasons ago: CT Champ 0.0
7 seasons ago: Conf Champ -0.0
7 seasons ago: Wins 0.01
7 seasons ago: NT 0.01
7 seasons ago: NT wins 0.02
7 seasons ago: NT wins^2 -0.0
7 seasons ago: PI -0.0
7 seasons ago: PI wins 0.01
7 seasons ago: PI wins^2 -0.0
8 seasons ago: RPI 0.0
8 seasons ago: CT Champ 0.01
8 seasons ago: Conf Champ 0.0
8 seasons ago: Wins 0.0
8 seasons ago: NT 0.0
8 seasons ago: NT wins 0.02
8 seasons ago: NT wins^2 -0.0
8 seasons ago: PI 0.0
8 seasons ago: PI wins 0.01
8 seasons ago: PI wins^2 -0.0
9 seasons ago: RPI 0.01
9 seasons ago: CT Champ 0.01
9 seasons ago: Conf Champ 0.0
9 seasons ago: Wins 0.0
9 seasons ago: NT 0.01
9 seasons ago: NT wins 0.01
9 seasons ago: NT wins^2 -0.0
9 seasons ago: PI 0.0
9 seasons ago: PI wins 0.0
9 seasons ago: PI wins^2 0.0
10 seasons ago: RPI 0.0
10 seasons ago: CT Champ 0.0
10 seasons ago: Conf Champ 0.0
10 seasons ago: Wins -0.0
10 seasons ago: NT 0.01
10 seasons ago: NT wins 0.01
10 seasons ago: NT wins^2 -0.0
10 seasons ago: PI 0.0
10 seasons ago: PI wins 0.0
10 seasons ago: PI wins^2 -0.0