Any Class Heavy Melee Dps With And Without Sorcery

This is a section of a document I've made and that's going to become a bigger thread later on, but as I felt like this subject is big enough I thought I'd make a quick small thread about it.
As it happens you can get a fairly good estimate of the average DPS a certain melee build will output with consideration to Quake, which is typical for heavy melee builds. The formulas I've managed to get are as follows:

For any class except archer:
Average DPS = D x A { 1 + [ 3.15 / (N+1) ] }
Average DPS including Sorcery = D x (10/7) x A { 1+ [ 4.15 / (N+1) ] }

Only for Archer:
Average DPS = D x A [ 1 + (4.5 / N) ]
Average DPS including Sorcery = D x (10/7) x A [ 1+ (5.928 / N) ]

D = the damage of a single melee hit.
A = the attack speed's numerical value, i.e hits per second
N = hits required to charge up quake.

Spoiler: Known information

the attack speed values and hits required to charge up quake for each of the different attacks speeds are:

• Super fast - 4.3 Hits / Second, 22 Hits to charge up quake
• Very fast - 3.1 Hits / Second, 16 hits to charge up quake
• Fast - 2.5 Hits / Second, 13 hits to charge up quake
• Normal - 2 Hits / Second, 11 hits to charge up quake
• Slow - 1.5 Hits / Second, 8 hits to charge up quake
• Very Slow - 0.83 Hits / Second, 5 hits to charge up quake
• Super Slow - 0.51 Hits / Second, 3 hits to charge up quake

Note that the attack speeds are theoretical values, which are used for spell damage calculations. Currently these are also the values used for melee damage calculations, but the actual values present in-game are slightly lower, especially for the faster attack speeds, and deviate between classes, so expect slightly lower damage output.

Although the title says Heavy Melee DPS, you can calculate the average DPS with accountability for quake for any attack speed using this formula, However, Using quake instead of Courage on melee builds is usually not favorable for the faster attack speeds except for some Rawstack or Cancelstack builds.

Spoiler: Explanations to the derivation of the formulas

Needless to say that if any of the formulas are wrong, just point out which and why and I'll gladly correct what's needed.