crit chance/crit dmg

[Morphio]

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PREPARATE PARA EL AMAZING WALL OF TEXT

C = crit chance
D = crit damage boost (note, this means a boost ABOVE the standard 2 times base damage, for a normal, non-boosted crit).
B = base damage.

In this case, the average damage you do per attack is given by adding your normal base damage times the chance of NOT critting, plus the crit boosted damage times your chance of critting.
OR: average damage per attack = B * (1-C) + B*C*(2+D)

Since both the normal attacks, and critical attacks are dependent on your base damage, I'm going to throw that out for now too, to compare the different crit statistics.

So the average damager per attack normalized by the base damage (let's call this X) is given by: X = (1-C) + C*(2+D) = 1 - C + 2*C + C*D = 1 + C + C*D


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Now you may be wondering, how the heck is this useful? I now have a multivariable function that shows how my damage (averaged, normalized by base damage) depends on crit chance and crit damage boost, but how does that help me?

Well, what we really want to know is the RATE at which this function increases. For some small increase (say due to a rune, or a mastery, etc.) is it more effective to increase C, or D? Well to answer this question, we need the rate of change of this function. That's right, we gotta do some (basic) calculus now.

the rate of change (with respect to C) is:
dX/dC = 1+D
the rate of change (w.r.t. D) is:
dX/dD = C

So the more crit damage boost you have, the higher D is, the more important it is for you to raise the CHANCE of crit. Conversely, the higher a chance of crit you have, the higher C is, the more important it is to raise your crit DAMAGE boost.


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But the real question is, so far as runes go anyway, which is better? And we have to remember that all is not equal. We can either raise C by 20% or D by 50% if we totally stack our tier 3 runes one way or the other.

That is, when is the damage increase dX the same in both cases:
dX (from chance) = (1+D) * dC = dX (from damage) = C * dD (where dC and dD are the CHANGE caused by runes)

Lets look at a few examples. In all cases, dC = 20% = 0.2 and dD = 50% = 0.5

Presuming we start with no help whatsoever, C = 0 and D = 0 :
dX (from chance runes) = (1+0)*.2 = .2
dX (from damage runes) = 0*0.5 = 0

Ok this was obvious. If your chance to crit is 0%, then no amount of crit damage boost is going to help. At all. Ever.

But lets say you got a few useful items / masteries, and your crit chance is 20% already, but still no damage boost yet:
dX (chance) = (1+0)*.2 = .2
dX (damage) = .2*.5 = .1

So even if you already have 20% crit. It is still more effective to get MORE CRIT % than a crit damage boost.


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So where is the tipping point? At some point, crit damage boost is going to be better than a higher crit chance. When does this happen? We'll lets see. Let's find the very point where the damages from increasing chance, or boost damage, are equal to each other. This will be the tipping point.

Case 1: no crit damage boost
dX = (1+0) * .2 = C*.5 --> C=.4 = 40%
So if you have no masteries/runes/items to enhance your crit boost, then you need a 40% crit chance before crit damage boost runes (50%) are better than extra crit chance runes (20%).

Case 2: 10% crit damage boost from masteries
dX = (1+.1)*.2 = C*.5 --> C = 44%
If you put points into crit damage boost in masteries, you need to have > 44% crit chance before crit damage boost runes are better.


But let's face it. If you're even considering getting crit damage boost runes, you're probably playing a champion that will focus on getting infinity's edge ASAP, right? And you're going to put those points into the crit boost damage mastery. So what about this scenario?

Case 3: 10% crit damage from masteries and 50% boost from Infinity's Edge
dX = (1+.6)*.2 = C*.5 --> C = 64%
That's right, if you have infinity's edge, then only when you have a whopping 64% crit chance do crit damage boost runes (+50%) become MORE effective than extra crit chance runes (+20%).


las runas de crit dmg rinden solamente si tenes un minimo de 64% de crit y infinity edge asiq para el 95% de los champs del juego q no pasan de 40 con cualquier build NO sirven para nada

ty busque teorycraft sobre este tema y no encontre nada.
de donde lo sacaste?

[DrFlesh]

del foro del lol xD

[Bizantinolynx]

del foro del lol xD

LoL