Talk:Ashe/@comment-26941996-20151201052118

TL;DR cause maths:  if Ashe's crit chance is 20%, activating her Q makes    approximately 67% chance to crit  (apply Essence Reaver and Empowered Slow from Frost Shot) at least once in a single Q-empowered autoattack, up from 20% with an unempowered autoattack.

The usefulness of crit chance peaks at 33% in Q-empowered autoattacks before beginning to fall off hard.

Chance to crit during a standard autoattack |  Chance to crit once or more during a Q-autoattack

                                                        0% |  0%

                                                      10% |  41%

                                                      20% |  67.2%

                                                      30% |  83.2%

                                                      40% |  92.2%

                                                      50% |  96.9%

                                                      60% |  99%

                                                      70% |  99.8%

                                                      80% |  ~100.0%

                                                      90% |  ~100.0%

                                                    100% |  100% END TL;DR

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. This is stated in the TL;DR.