Hey all,
I have been messing around with the idea of a mysterious stranger who focuses on the gunslingers dead shot. In order to get some sense of comparison on damage and how much to hit and Cha bonus play into the damage I am trying to build a DPR formula for dead shot. Here is what I got so far. Correct me if I am wrong / missing something and definitely point out any thread that tried to do this (I didn't find any).
I am going to break the formula into 2 parts:normal damage and crit damage
Normal damage:
h1*(d+s)+ h2*d+ h3*d + ... + hn*d
h1->hn: Chance of hitting with each attack from first (h1) to last (hn)
d: average dice damage plus charisma modifier
s: static damage (includes all damage that isn't from weapon dice and charisma mod)
Critical damage:
f*(1-m^n)*(c*d+c*b)
f: chance to confirm critical hit
(1-m^m): this calculates the chance of getting one critical hit where m is the chance to not get critical hit and n is the total number of attacks you make
c: number of bonus multiples you get on a crit. x2=1, x3=2, x4=3
d: sum of normal damage calculation above
b: bonus damage from burst / thundering enchant
So in total DPR looks like this:
DPR = (h1*(d+s)+ h2*d+ h3*d + ... + hn*d) + f*(1-m^n)*(c*(h1*(d+s)+ h2*d+ h3*d + ... + hn*d)+c*b)
I know I know...way more complex than the standard dpr. Thats why I am asking for opinions and possible corrections.
DPR = (h1*(d+s)+ h2*d+ h3*d + ... + hn*d) + f*(1-m^n)*(c*(h1*(d+s)+ h2*d+ h3*d + ... + hn*d)+c*b)
The static damage (in bold) should actually be its own separate item in the normal damage calculation. Also, it shouldn't be in the crit calculation. However, I am trying to find a way to express that as an equation.
The point is that with a gunslinger, the chance for the static damage is pretty darn close to 1. So it may be a lot easier to just make it that rather trying to come up with the accurate equation that takes into account the changing chance of hitting with each shot.
DPR = (h1*d+h2*d+h3*d+hn*d+s) + f*(1-m^n)*(c*(h1*d+h2*d+h3*d+hn*d)+c*b)
EDIT: Got it.
the chance of hitting once and applying STATIC DAMAGE is 1-(1-h1)*(1-h2)*(1-h3)*(1-hn)
DPR = (h1*d+h2*d+h3*d+hn*d+(1-(1-h1)*(1-h2)*(1-h3)*(1-hn))*s) + f*(1-m^n)*(c*(h1*d+h2*d+h3*d+hn*d)+c*b)
That is officially ridiculous.