How many of your simulations fell within the salary range and in the correct salary formula?
That's a good question. I don't know, since I didn't make a counter and just discarded everything not meeting the criteria. I think it should be something in the magnitude like 50-100 player generated to get one qualified.
You don't need to go through all this trouble though: the minimum TSP of a SF in that range is 31 and the maximum is 54. So yeah, if it was completely random you'd expect a TSP of around 43.
The 19yo however is probably incorrect, because the theoretical minimum for a 5.5k PF is 39, but the maximum is actually 80.
My assumption is that every skill is i.i.d. uniform distribution in the interval [1.0, 7.99] or [1.0, 8.99], but the TSP will not be a uniform distribution in the interval [10, 79.9] or [10, 89.9].
Here is a discrete version of the problem. Suppose you throw 10 identical 6-faced dices. Suppose you know that the sum of dices are >=40, what is the expected value of the sum of dices? The answer is indeed lower than 50.
Your estimation relies on the fact that the distribution of the TSP is symmetric within the range of the TSP, which is not guaranteed (although it seemed to be more symmetric than the dice situation above). So I would say that at most it is a reasonable estimation.
But anyway, I tried to emulate the total distribution, and hope it helps those who have different criteria when making their decision: some might be conservative and look at the 30% percentile, while some others may look into the extreme case and bet for the top 1% guy. Your call
