Who is the target audience of the OP's calculations? To answer my own question, it's apparently folks that are considering the tradeoff between a close-in ticket paid in cash versus a standard award.
How many people are there who do this? Certainly not me.
In my 20+ years of earning and redeeming miles/points, I have never used them for a close-in redemption. Granted, I've been lucky to not need to use them for a family emergency (knock on wood) and stuff like that.
I have used all of mine for family vacations, and we always plan those several months out, trying to grab saver awards early, or gambling on getting them closer in. I've got to believe that the size of the audience who uses miles/points in this manner is much greater than the pool looking at the tradeoff the OP is investigating.
If I were the OP, and was interested in providing a service using this kind of data, I would focus on the type of tradeoff that provides the greatest value to the greatest number of people. I don't this tradeoff is it.