*theorycrafting*without on-paper damage calculation? :p

I have no idea, that's why I ask you, L.O.L... Anyways let's jump right in.

#### The Base Damage

The people who followed the update posts of

*Carbine Studios*over all those years know how the damage on*skills*is - or might be - calculated and what role*Assault Power*plays here.
According to

*balancing patches*a percentage of*assault power*is changed and a value which increases with the*level*is changed. If we say these are the only values and when experimenting with the last*patch values*comparing it with the numbers on the tool-tips we can assume the following formula for*assault abilities*:
baseDamage = assaultPower * skillAssaultPowerMod + levelStatRate * yourLevel

Higher skill tiers increase the skillAssaultPowerMod and the levelStatRate

Higher skill tiers increase the skillAssaultPowerMod and the levelStatRate

Now, this is a little bit old but

*Mortar Strike*on*Base Tier*the inner*AoE*(Area of Effect) hits with 29.77 per*level*and 94.02% of*Assault Power*.
So let's assume we have 17765

*Assault Power Rating*and of course we're*level*50.
17765

*Assault Power Rating*equals*17765 / 4 = 4441.25 Assault Power.*
So for our

*base damage*calculation:
baseDamage =

*4441.25 * 0.9402 + 29.77 * 50*
That's about 5664.16 damage.

#### Critical Hit Chance & Severity

*Critical hit chance*is, as the name says, the chance to hit harder.

*Severity*is how hard you hit. By default, the

*severity*is 150% (So a 50% damage increase compared to normal hits). The way I figured out how to calculate these both is by trial and error, but I'm gonna explain it a little bit.

No

*critical hit chance*, but a lot of*severity*. 0%*chance*vs 300%*severity*.*If you have no critical hit chance you won't ever hit harder, so you'll have no damage increase here.*

All hits are

*critical*, but no*severity.*100%*chance*vs 100%*severity*.*Even if each of your attacks hits critically if your critical hits don't hit harder your damage doesn't increase.*

Okay, if all of our attacks are

*critical*and*severity*doubles our damage. 100%*chance*vs 200%*severity*.*What happens? Our damage is doubled. As simple as it is.*

Now if we

*critically hit*every second time and still double the damage on a*critical hit*. 50%*chance*vs 200%*severity.**Surprise. On average we get a 50% damage increase. So with half the critical hit chance, we deal half the damage increase from severity on average.*

It doesn't take much to make the last step here but if you haven't got a feeling for math what happens here is:

criticalHitChance * criticalhitSeverityThe damage increase occurs

*critical hit chance*of the time and also we do 100% of our damage always. Keeping this in mind we get:(1 + criticalHitChance * (criticalHitSeverity - 1))

So applying

*critical hit chance*and*severity*to our damage calculation:
damage = baseDamage * (1 + (criticalHitChance * (criticalHitSeverity - 1))

Example:

We have a 48%

*critical hit chance*, 268%*critical hit severity*and the same damage as before.
damage = 5664.16 * (1 + 0.48 * (2.68 - 1))= ~10231.74

#### Multi-Hit Chance & Severity

*WildStar*has a stat called

*multi-hit chance*and

*multi-hit severity*. If your

*multi-hit chance*triggers the

*severity*of your previous damage is applied to the enemy a second time. This works exactly like

*critical hit chance*and

*severity*but our

*multi-hit severity*is much lower.

So we have:

multiHitChance * multiHitSeverity

However, compared to

So we keep this and add it to our formula like this:

*critical hit chance*if*multi-hit*does not occur we don't have*multi-hit*damage. If the*multi-hit*chance is zero we don't do any**additional**damage.So we keep this and add it to our formula like this:

damage = baseDamage * (1 + criticalHitChance * (criticalHitSeverity - 1)) + baseDamage * (multiHitChance * multiHitSeverity)

With our previous stats of 48%

*critical hit chance*, 268%*critical hit severity*, 31%*multi-hit chance*, 48%*multi-hit severity*and our previous damage we now have:
damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) + 5664.16 * (0.31 * 0.48) = 11074.57

#### HOLD IT - Synergy

Yep,

*Multi-Hit*and*Critical Hit*synergizes. How? A*multi-hit*can be a*critical hit*too and a*critical hit*can*multi-hit*too. However the*multi-hit*takes the*base damage*not the*critical damage*. So we need to apply our*critical hit chance*and*critical hit severity*to our*multi-hit*:
dmg = baseDmg * (1 + CHC * (CHS - 1)) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1))

*dmg stands for damage; baseDmg for baseDamage; CHC for critical hit chance; CHS for critical hit severity; MHC for multi-hit chance; MHS for multi-hit severity;*

So our actual damage is:

damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) + 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) = 11754.22

#### Next stat: Vigor

*Vigor*increases our damage respective to our health. If we have 100% health the whole damage increase of

*vigor*is applied. If we have 50% of our health only 50% is applied:

1 + yourHealth * vigor

To calculate the average damage you can just use your average health.

Adding to the calculation:

dmg = baseDmg * (1 + CHC * (CHS - 1)) * (1 + (yourHP * vigor)) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + (yourHP * vigor))

*yourHP stands for your health points;*

If we assume to have 18.2%

*vigor*and 90% health on average we get:
damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + (0.9 * 0.182)) + 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + (0.9 * 0.182)) = 13679.56

#### Strikethrough

Next up is

*strikethrough*. So enemies have a*deflect chance*. There are tables on how much*deflect chance*the enemies have. You need the same amount of*strikethrough*as the enemy has*deflect*. Luckily there are*raid buffs*that decrease this value additionally. So how does*strikethrough*calculate?
If an enemy has 12.48%

*deflect chance*and we have 12.48%*strikethrough*we'll hit 100% of the time. Alternatively we'll miss*12.48% - 12.48% = 0%*. So our hit chance is:
100% - (enemyDeflect - strikethrough)

However, keep in mind this formula only counts if

*strikethrough*is not higher than*enemy deflect*. Even worse*strikethrough*is supposed to convert to*armor pierce*however according to information it is bugged and*strikethrough*instead decreases your*critical hit chance*if over capped*(going over a cap, as in the highest meaningful value).*
Well assuming we do not

*overcap strikethrough*:
dmg = baseDmg * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough))

+ baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough))

Doing our damage calculation with 12.48% enemy

*deflect chance*and 10.91%*strikethrough*results in:
damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) + 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) = 13464.79

#### Armor and Resistances

Not done yet. Unfortunately.

*Armor*is converted to*resistance*. My*Spellslinger*is currently running around with 39.39%*resistance*.*Bosses*have between 47.12% and 50.05%*resistance*. This means that we only do about 50% of our damage on those*bosses*. They*resist*about 50% of our damage.
Don't forget the more

*resist*the enemy has the less damage we do. That means we need the opposite. So instead of*enemyResist*we use*(1 - enemyResist)*.
So we add this number to our damage calculation:

dmg = baseDmg * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist)

If we take the

*resistance*of the enemy of 47.12% into account we get this result:
damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712) + 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712) = 7120.18

That's a drastic change but don't worry.

#### Your Savior: Armor Pierce

Luckily we have

*armor pierce*in this game. Or unlucky, since our calculation gets even longer and worse. Well, how does*armor pierce*work?
After our

*raid buffs*decrease the*resistance*of the*boss*additive, our*armor pierce*further decreases the*resistance*multiplicative.
So if the

*boss resistance*is 47.12% and we decrease it by 10.5% to 36.62%. Now we have 9%*armor pierce*which further decreases it's*resistance*to*36.62% * (100% - 9%) = 36.62% * 91% = 33.32%*.
So putting

*armor pierce*into our calculation as well:
dmg = baseDmg * (1 + CHC * (CHS - 1) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP))

*ARP stands for armor pierce ;)*

So doing our calculation:

damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) + 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) = 7691.20

#### Are We Done Yet?

Nope, unfortunately not. There is one more stat. Which one? Thanks to the

*primal matrix*we now have*tenacity*.*Tenacity*deals more damage the less health the enemy has. So if we have 10.5%*tenacity*we deal 5.25% more damage when the enemy is at 50% and 0% more damage if the*boss*is at 100%.
dmg = baseDmg * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP)) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP))

How much damage do we do then? You could assume 50% health on average so you could calculate with 5.25%. Alternatively, you can give a range. Let's do that.

If the enemy has 100% health:

*Nothing changes damage is still 7691.20 as calculated earlier.*

Enemy has 0% health

*damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) **

*(1 + 0.105 * (1 - 0))*

*+ 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) * (1 + (0.105 * (1 - 0))) = 8498.77*

*So we have a range between 7691.20 and 8498.77 damage.*

Enemy has 50% health (average).

*damage = 5664.16 * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) **

*(1 + (0.105 * (1 - 0.5)))*

*+ 5664.16 * (0.31 * 0.48) * (1 + 0.48 * (2.68 - 1)) * (1 + 0.9 * 0.182) * (1 - (0.1248 - 0.1091)) * (1 - 0.4712 * (1 - 0.09)) * (1 + (0.105 * (1 - 0.5))) = 8094.99*

#### Done Finally?

Yes. Finally done. :)

I was simplifying this calculation prior to the update of the post but noticed that we lose accuracy and some other problems are raised. Treating the initial hit and multi-hit separately and adding them is a better solution. The problems that are raised are:

I was simplifying this calculation prior to the update of the post but noticed that we lose accuracy and some other problems are raised. Treating the initial hit and multi-hit separately and adding them is a better solution. The problems that are raised are:

- The initial critical hit and the multi-hit have the same critical chance but they might not both critical hit. It is safer to separate these.
- It is unlikely for your health to change in this short amount of time but the initial hit changes the enemy's health thus the
*multi-hit*damage changes respectively. - Very unlikely but the
*buff uptime*may run out before the*multi-hit*hits resulting in different*resistances*.

So there we have it:

baseDmg= assaultPower * skillAssaultPowerMod + levelStatRate * yourLevel

initialDamage = baseDmg * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP))

multiHitDamage = baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP))

totalDmg = initialDamage + multiHitDamage

Full formula:

totalDamage = (AP * skillAPMod + lvlStatRate * yourLvl) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP)) + baseDmg * (MHC * MHS) * (1 + CHC * (CHS - 1)) * (1 + yourHP * vigor) * (1 - (enemyDeflect - strikethrough)) * (1 - enemyResist * (1 - ARP)) * (1 + tenacity * (1 - enemyHP))

*AP stands for Assault Power; skillAPMod for skillAssaultPowerModifier; lvlStatRate stands for level stat rate; yourLvl stands for your Level;*