Okay so this has been posted elsewhere on the internets, but I don’t know if this has been addressed here.
The typical nomenclature is to use Hidden Killer in perma stealth backstab builds, and to use Executioner’s on other builds. This post is here to answer the question: Why? Hopefully from answering this question, we can have a better understanding of the two different traits and establish a guideline on how to effectively judge whether we should take one over the other in any given backstab build. So let’s get to it!
This is going to involve some basic math, but I’ll try to walk us through it as best as possible. For those who don’t care about the math, the formula is as follows:
b = (0.3 +a) / (0.6 + 1.2(a))
Where b = chance to crit; and a = crit% dmg increase.
Any b-value above the calculated value will mean to choose Executioner’s. Anything below this b-value will mean to choose Hidden Killer.
The expected damage (i.e. the damage that will occur most often) of any build follows this basic rule:
E = d(1 – b) + D(b)
Where:
Expected Damage = E
Non-crit damage = d
crit damage = D
increased % to crit damage = a
and percentage chance to crit = b
Also please note:
D = d(1.5 + a)
Plugging this into our E equation, we get:
E = d(1 – b) + d(1.5 + a)(b)
Now lets compare hidden killer expected damage to Executioner’s expected damage. First, we make some simple assumptions that we are only backstabbing (i.e. attacking from stealth) and the target is always below 50% health, holding all other variables equal:
Hidden Killer expected damage:
E = d(1.5 + a)
This is true since b = 1, or in other words 100%.
Executioner’s expected damage:
E = 1.2(d(1 – b) + d(1.5 + a)(b))
Basically multiply the expected damage by the multiplier of Executioner’s.
Now we set them equal to each other and solve for our crit chance:
d(1.5 + a) = 1.2(d(1 – b) + d(1.5 + a)(b))
simplifying will result to:
b = (0.3 + a) / (0.6 + 1.2a)
This equations says that the percentage chance to crit, where the damage of hidden killers and executioner’s is equal to each other, is when you take your crit% damage increase and do some maths to it.
As an example:
Say you have 50% increase to your crit damage. Then the crit percentage chance that will make hidden killer and executioner’s equal to each other will be:
b = (0.3 +0.5) / (0.6 + 1.2(0.5))
b = 2/3 = 66%
So at around 66% chance to crit, you will be indifferent between taking Hidden Killer or Executioner’s. Anything above this number, and Executioner’s will outperform Hidden Killer. Anything below this number, and Hidden Killer will outperform Executioner’s. Also, if you can breach this crit chance, then you will do more damage than if you use hidden killer with lower crit chance, regardless. This pushes us to establish some crit chance above a certain level.
Please note that, since we are dealing with assumptions, this number shouldn’t be treated as a specific value, only a general one. But to see why this number is a valid number, we look at a standard backstab build in spvp:
This build has a 53% dmg increase to crit. This means that the crit chance we need, to validate bringing Executioner’s, is 67%. At best, with side strikes, we can get 60% (65% with the off-chance you will be above 90% health). With fury, we get 80% – well above our threshold. So this merits bringing Executioner’s in this build. Fundamentally this highlights why there is an importance to bringing fury (Trickery V) in any backstab build with Executioner’s. Lets look at a typical perma-stealth build:
This build has a 58% dmg increase to crit. This means we need a crit chance of 68%.
The best we can get in this build is 54% with 5 minor in the crit line. If we chose to use 10 in trickery for trickery V, then we can push this value up to 69 – 74%. This would validate an Executioner’s, but to do this we lose out on better control of our heartseekers through blackpowder (acrobatics VI). So if we choose to have better control, we have to use Hidden Killer because we don’t have anything that will bump our crit chance past the threshold. This validates taking Hidden Killer.
I hope this helps others have some better foothold on how to choose ether trait. Of course this only applies if you have 30 in the crit line and running a backstab build, but I still hope it helps others.
(edited by Chicago Jack.5647)