Talk:Ashe/@comment-26941996-20151201052118/@comment-26941996-20151201052441

The math was bothering me with Ashe's chance to crit with a single Q-empowered autoattack, so I figured I'd do some maths.

"y" variable is the chance to crit at least once over a single Q-empowered autoattack, since it calculates crit 5 individual times per autoattack.

"x" variable stands for crit chance as a decimal:

y=1-(1-x)^5

So why is this important? Well, if your crit chance is 0% or 100%, it doesn't help you at all. Your Q-empowered autoattack will have a 0% or 100% chance to crit at least once during a single autoattack, respectively.

However: this is where things get OP. If your crit chance is 20%:

y=1-(.8)^5 = 1-.32768 = .67232 OR approximately 67% chance to crit once in a single Q-empowered autoattack, up from 20% with an unempowered autoattack.

Since I can't exactly graph something down here in the comments section, I figured I'd make a table with a change in 'x' (standard chance to crit) at 10%. This table is at the top.

So, when does crit chance peak its usefulness in Q-empowered autoattacks? Simple Calculus incoming!!

We derive to find y-prime, denoted as y'  (yes, with a cute little apostrophe (uguu~)):

y'= -5(1-x)^4(-1) = 5(1-x)^4      BY 'CHAIN RULE.'

Suppose that we can define 'peak usefulness' where the original function's slope equals 1: where 5(1-x)^4=1

Which is around x=0.331. Ergo, the usefulness of crit chance in calculating Q-auto's chance to crit at least once peaks around 33% before beginning to fall off super duper hard. This is stated in the TL;DR.