Questions about chart difficulty
 

Does difficulty increase exponentially with speed? (If 1.1x is n times as tough as 1.0x, is 1.2x n^2 times as tough?) (or: if 150bpm jacks are m times as tough as 140bpm jacks, are 160bpm jacks m^2 times as tough?)

Precisely how does stamina have a general impact on ability to hit notes? How much does physical and mental fatigue come into it? Is fatigue also a thing that wears exponentially?

Given a speed of x bpm, at what speed f(x) is it so that x bpm jacks are as difficult as f(x) bpm one-hand trills? Can this generalize to other patterns?

Input from anyone and everyone is appreciated!

Re: Questions about chart difficulty
 

You'll have to define what you mean by 'difficulty' more precisely to answer any of those questions.

Re: Questions about chart difficulty
 

It's impossible to judge difficulty purely on speed or density of notes, imo. I don't think it's quite a linear factor, I think it would be approximately linear for low speeds but surely it must become exponentially harder at higher speeds - regardless, I feel like your skill level to play certain difficulties anyways is exponential (e.g. the difference between a SM 24 and 25 is bigger than a 14 and 15).

Like for example, a 140 bpm jack for 15 seconds might be harder than a 160 bpm jack for 5 seconds.

Honestly I don't think it's possible to simple scale difficulty by some function of rate, I think it would be better to recalculate difficulty with the higher bpm factored into the parsing algorithm.

EDIT: I'm presuming difficulty means difficulty to combo/combo with high accuracy.

Re: Questions about chart difficulty
 

Difficulty == skill needed to reliably hit a pattern (or whatever mina's definition was, that one)