Catalyst: nice idea! but it's very difficult to measure that, no?
Degrees of freedom
Godspawn, what the hell is your problem? If you can't say anything nice about other users, then don't say it at all. You're not the forum police around here.

So 1. Nf3 would have less ddeg than 1. e4 even though Nf3 can transpose into many different openings?
EDIT: Oh I see. ddeg is intended to measure how quick development of pieces would be. Still, 'degrees of freedom' is a bit misleading for something like that.
Yeah, ddeg(1.Nf3) is only +2. Now, since it's highly transitional, ddeg will grow with subsequent 1.e4 or 1.d4.
I define the degree of freedom in a given position as the number of all possible moves. One of interesting parameters is the difference of degrees for white and black created by a move. I'll denote it by ddeg. It might be useful in the opening theory measuring the speed of development.
Example: In the initial position, there are 20 possible moves. The KP opening 1.e4 creates 10 additional moves (5 for white-square bishop, 4 for the queen, 1 for the knight and 1 for da king minus 1 for e-pawn). There are no restrictions for black. So ddeg(1.e4) = +10.
... to be continued