I was trying to compromise some.
When you compromise between a good solution and a bad solution, you still have a bad solution.
Just to clarify my goals.
My goals are to keep up schizo wave composition variety within a single wave, bump up average difficulty a good deal, maintain some consistency of difficulty between different waves, and bring in just enough of what makes mono-waves have such a high max difficulty without compromising variety within a single wave much.
Both of our ideas would bump up "practical" min difficulty, bump up "practical" max difficulty, bump up average difficulty a little, and keep pretty decent within a single wave variety.
My idea (using roles), compared to yours (using types), tries to bump up the min difficulty a bit more and keep up some within a single wave variety some, at the expense of not bumping up "practical" max difficulty as much. How average difficulty would compare between the two ideas is rather tricky to answer (see below)
It really depends on which attribute we want to maximize which one is the better choice.
Just to clarify, BOTH ideas would raise the "practical" max and average difficulties, so both ideas would make schizo waves more threatening. It's how much we care about the other variables that will influence the decision (and how much we care about smallish differences to the max difficulty, and the yet to be determined effects on max-difficulty)
However, there is a fundamental question:
Is, on average, (assume ratios have already adjusted for ship caps) how does the difficulty, the expected "practical" min, average, and "practical" max difficulties vary when facing 1/N ratio of N types of ships? (Note, the exact value will vary strongly with which types are used. Complicated matters is that the ship type selection are NOT independent events, especially in the "role" selection idea, making describing the expected distribution of these types even trickier.)
The issue is that the functions are not non-decreasing and not non-increasing. For example, average difficulty may go up from N=1 to 2, but go down from N=1 to 10, but stay the same from N=9 to 10 (not sure if any of these are true, but this is just an example of the kinds of effects that can crop up). This makes the shape of the curves complex, and we need to get a rough idea of where the "peaks and valleys" are in this curve before we can compare what the difference between our two ideas would be in the average case.
Plus, this assumes equal distribution (scaled for ship cap), which does not have to be true (like a bomber focused schizo wave, for instance), making things even more complicated.