Grynberg
06-16-2015, 07:21 AM
I was a bit bored the other day so I tried to calculate the average critical chance with expose weakness. I'm not bad at math but the cumulative increase made the probability calculations hurt my head. So I went the easy way and made a small java program that took every critical profile from 0-20 to 20-20 and made ~1 million hits with expose weakness mechanics.
From the data I got the equasion of: 0.157x^2 + 0.561x + 0.282 where x is the weapon critical chance and belongs to [0.00;1.00]. The correct graph is as follows:
http://i284.photobucket.com/albums/ll6/karli_grynberg/expose_zpsfzekm2h9.png
Lets take a swashbuckler with expose weakness, light pick and improved critical. Light pick is 20-20, Swashbuckler increases that to 19-20 and IC increases it to 17-20. That's a probability of 0.2 (20%) to hit a critical. 0.157*0.2^2 + 0.561*0.2 + 0.282 = 0.4005. In this case Expose weakness increases your average critical chance from 20% to 40.05%
You can see from the equation that the smaller critical ranges benefit more from Expose Weakness. For example
1. Someone with a 20-20 profile (0.05 or 5% chance) gets his critical chance upped to 31.04% which is a whooping 26,04% increase in critical chance.
2. Someone with rapier/IC/celestial champion with a critical profile 13-20 (0.4 or 40%) gets an average critical chance of 53.15%. That's only a 13.15% increase.
After this I started looking at the critical multipliers and how all this increases the average damage.
I split the critical damage multiplier into three ranges:
1. Damage that's not multiplied (didn't crit)
2. Damage that's multiplied with normal critical multiplier (crits normally)
3. Damage that's multiplied with an increased multiplier (hits 19-20 and has overwhelming critical or stuff from legendary dreadnaught)
C - Critical chance (from 0.05 to 0.4 usually), M - critical multiplier that applies to every critical. N - critical multiplier that applies from 19-20 (overwhelming for example)
Critical damage bonus D = 1-C (1. part) + (C-0.1)*M (2. part) + 0.1*(M+N) (3. part) = C*(M-1) + 1 + 0.1*N
The only weapon that has a different critical profile in swashbuckling, is the light pick. Lets see how the average critical damage bonus compares to the other weapons. The only critical bonus we assume the character must have is Improved Critical (and who doesn't). All the other critical bonuses are left into variables x, m and n.
a) All swashbuckler weapons (18-20/x3)
C = 0.157x^2 + 0.561x + 0.282, M = y
D(R) = (0.157x^2 + 0.561x + 0.282)*(y-1) + 1 + 0.1*N
b) Light pick (19-20/x4)
C = 0.015(x-0.1)^2 + 0.561(x-1) + 0.262 = 0.157x^2 + 0.5296x + 0.2359, M = y+1
D(P) = (0.157x^2 + 0.5296x + 0.2359)*y + 1 + 0.1*N
Let's make an assuption that light pick always yields more critical bonus damage then rapiers. So we can write
D(P) - D(R) > 0 =>
(0.157x^2 + 0.5296x + 0.2359)*y + 1 + 0.1*N - (0.157x^2 + 0.561x + 0.282)*(y-1) + 1 + 0.1*N > 0 =>
y < (0.157*x^2 + 0.561*x + 0.282)/(0.0341*x+0.0461) where x belongs to section [0.00;1.00], replacing the equation on the right with Z and calculating the new limits.
y < Z where Z belongs to section [6,115;12,469] (it's a pretty linear equation)
Y was the base critical modifier of a swashbuckler weapon and it's always less then 6 so our initial assumption was correct and we can safely assume that D(P) - D(R) > 0 or D(P) > D(R). On similar conditions, light pick will yield better critical damage bonus on average.
Too boring, didn't read
1. Expose weakness increased critical range can be calculated with 0.157x^2 + 0.561x + 0.282 where x is the critical range and belongs to range [0.00;1.00]. A weapon with a critical chance of 0.2 (17-20) becomes 0.4005 (roughly 13-20)
2. Exposed weakness yields better results for weapons with smaller critical ranges.
3. Light pick gives better average critical damage then every other swashbuckler weapon.
4. Balizarde disagrees.
From the data I got the equasion of: 0.157x^2 + 0.561x + 0.282 where x is the weapon critical chance and belongs to [0.00;1.00]. The correct graph is as follows:
http://i284.photobucket.com/albums/ll6/karli_grynberg/expose_zpsfzekm2h9.png
Lets take a swashbuckler with expose weakness, light pick and improved critical. Light pick is 20-20, Swashbuckler increases that to 19-20 and IC increases it to 17-20. That's a probability of 0.2 (20%) to hit a critical. 0.157*0.2^2 + 0.561*0.2 + 0.282 = 0.4005. In this case Expose weakness increases your average critical chance from 20% to 40.05%
You can see from the equation that the smaller critical ranges benefit more from Expose Weakness. For example
1. Someone with a 20-20 profile (0.05 or 5% chance) gets his critical chance upped to 31.04% which is a whooping 26,04% increase in critical chance.
2. Someone with rapier/IC/celestial champion with a critical profile 13-20 (0.4 or 40%) gets an average critical chance of 53.15%. That's only a 13.15% increase.
After this I started looking at the critical multipliers and how all this increases the average damage.
I split the critical damage multiplier into three ranges:
1. Damage that's not multiplied (didn't crit)
2. Damage that's multiplied with normal critical multiplier (crits normally)
3. Damage that's multiplied with an increased multiplier (hits 19-20 and has overwhelming critical or stuff from legendary dreadnaught)
C - Critical chance (from 0.05 to 0.4 usually), M - critical multiplier that applies to every critical. N - critical multiplier that applies from 19-20 (overwhelming for example)
Critical damage bonus D = 1-C (1. part) + (C-0.1)*M (2. part) + 0.1*(M+N) (3. part) = C*(M-1) + 1 + 0.1*N
The only weapon that has a different critical profile in swashbuckling, is the light pick. Lets see how the average critical damage bonus compares to the other weapons. The only critical bonus we assume the character must have is Improved Critical (and who doesn't). All the other critical bonuses are left into variables x, m and n.
a) All swashbuckler weapons (18-20/x3)
C = 0.157x^2 + 0.561x + 0.282, M = y
D(R) = (0.157x^2 + 0.561x + 0.282)*(y-1) + 1 + 0.1*N
b) Light pick (19-20/x4)
C = 0.015(x-0.1)^2 + 0.561(x-1) + 0.262 = 0.157x^2 + 0.5296x + 0.2359, M = y+1
D(P) = (0.157x^2 + 0.5296x + 0.2359)*y + 1 + 0.1*N
Let's make an assuption that light pick always yields more critical bonus damage then rapiers. So we can write
D(P) - D(R) > 0 =>
(0.157x^2 + 0.5296x + 0.2359)*y + 1 + 0.1*N - (0.157x^2 + 0.561x + 0.282)*(y-1) + 1 + 0.1*N > 0 =>
y < (0.157*x^2 + 0.561*x + 0.282)/(0.0341*x+0.0461) where x belongs to section [0.00;1.00], replacing the equation on the right with Z and calculating the new limits.
y < Z where Z belongs to section [6,115;12,469] (it's a pretty linear equation)
Y was the base critical modifier of a swashbuckler weapon and it's always less then 6 so our initial assumption was correct and we can safely assume that D(P) - D(R) > 0 or D(P) > D(R). On similar conditions, light pick will yield better critical damage bonus on average.
Too boring, didn't read
1. Expose weakness increased critical range can be calculated with 0.157x^2 + 0.561x + 0.282 where x is the critical range and belongs to range [0.00;1.00]. A weapon with a critical chance of 0.2 (17-20) becomes 0.4005 (roughly 13-20)
2. Exposed weakness yields better results for weapons with smaller critical ranges.
3. Light pick gives better average critical damage then every other swashbuckler weapon.
4. Balizarde disagrees.