Statistical accuracy pp and speed scaling formulas

[Fr0stium]

Please see this document that details the changes of this proposal: https://docs.google.com/document/d/19KyQ7pd9HjFcbMVK_DlljOpFnN4mt_AN-GqJRbzz25M/edit?usp=sharing

In short, we estimate the player's unstable rate, assuming they tap with a mean hit error of 0 and their taps are normally distributed, and use that to generate accuracy pp and scale speed pp. The purpose of the change is to fix the issues with accuracy pp detailed in the document.

This change requires MathNet.Numerics, a math package that provides us with some functions that aren't present in the standard Math library, particularly the error function and the inverse error function.

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SR/PP sheet: https://docs.google.com/spreadsheets/d/1t4r_abJfWD9MHncVIKZ3c_bx_NsX30cOH2oxNrgIq04/edit
As of 16963a5

[joseph-ireland]

The change to strain time cap in speed.cs and the accuracy changes seem orthogonal. IIRC the intent of that cap is to stop easily double-tappable notes from contributing a lot to speed pp.

In the PP calculation, there isn't enough information about note spacing, so there's no way to have the same effect. Your accuracy change will affect all maps with the same OD equally: both 230bpm death streams and 380bpm doubles.

[apollo-dw]

The change to strain time cap in speed.cs and the accuracy changes seem orthogonal. IIRC the intent of that cap is to stop easily double-tappable notes from contributing a lot to speed pp.

That specific change was related to nerfing streams faster than the OD hitwindow, which was deemed necessary if changing speed cap stuff. Not necessarily doubletaps. I haven't looked into great detail for the changes proposed here yet, but @emu1337 could clarify whether this proposal removes the need for that nerf in the Speed skill