Quick Spell Speed Question

[JackFross]

Going from 5% to 6% is an increase of 0.51% of base damage, 0.49% increase of adjusted damage
Going from 20% to 21% is an increase of 0.81% of base damage, 0.72% increase of adjusted damage

Crit hit rate has increasing proportional returns, similar to spell speed.

They specifically said "If crit didn't increase crit damage" - you then just responded by saying "but because it buffs crit damage" which seems to ignore the comment that was made.

Maths below the cut.

Regardless, yeah. It's clearly NOT diminishing, as Waliel said:
If your crit is such that you have a 5% crit rate base, you deal 150% damage on a crit. Thus, adjusted base damage is:
100 x (.05*1.5 + .95*1) = 102.5

Increasing it to 6% (and thus Crit damage to 151%):
100 x (0.06*1.51 + .94*1) = 103.06

Difference: 103.06 - 102.5 = 0.56 -> 0.56/102.5 = 0.546% increase in damage

And similar calculations for 20% (165%) -> 21% (166%):
100 x (0.20*1.65 + .80*1) = 113
100 x (0.21*1.66 + .79*1) = 113.86

Difference: 113.86 - 113 = 0.86 -> 0.86/113 = 0.761% increase

However, if you get rid of the crit rate increasing crit damage, the crit mod is always 1.5. If we plug this into the above formulas, we can actually solve everything. Consider x to be the current crit rate as a percentage. Below, I solve to find the net change in potency that is gotten when increasing the critical hit rate by 1%:

net change = [ 100 x (((x+1)/100)*1.5 + ((1-(1+x))/100)) ] - [ 100 x ((x/100)*1.5 + ((1-x)/100)) ] -> simplify:
net change = [ 1.5(x+1) - x ] - [ 1.5x + 1 - x ]
net change = [ .5x + 1.5 ] - [ .5x + 1 ]
net change = .5x - .5x + 1.5 - 1 = 0.5

Considering the fact that, as your crit rate increases, the expected potency of each hit, adjusted for crit, increases as well, even with constant crit damage percentage, the fact that you have a constant rate of change (rather than variable) leads to a pretty clear picture as to why what Waliel said is completely accurate.

tl;dr: Waliel is right.
With crit damage, 20-21% gives a buff of 0.761% whereas 5-6% gives a buff of 0.546%.
But if crit damage were NOT increased by crit, both the gain from 20-21% and from 5-6% give the same static buff to net potency, resulting in a higher percentage gain for 5% to 6%.


What they were saying (and are NOT wrong about) is that increasing Crit is NOT double dipping. You get good gains from the boost to crit damage which clash with the diminishing returns on crit rate. Thankfully, the bigger gain from the damage outweighs the diminishing effect of boosted rates to make it an overall increasing growth curve.