[mechanics]Inconsistency in lash damage penetration calculation

[robovoid_dev]

With the help of some fellow watchers, now I know how the game calculates lash damage.

Suppose "PhyDMG_mid_stage" is the calculated physical damage only without penetration factor. For example, with +60% might, +60% legendary, +60% sneak attack, -50% Graze, the PhyDMG_mid_stage would be Roll*(1+0.6+0.6+0.6-1)=1.8*Roll.

(-50%: 1-1/0.5 = -1, you can check this 

<a href="https://forums.obsidian.net/topic/98679-mechanics-attack-speed-recovery-time-reload-time/">mechanics-attack-speed-recovery-time-reload-time</a>

for explanation)

The baseLashDMG = PhyDMG_mid_stage * coef

The reason I am calling it "mid_stage" is that when calculating the final physical damage, we need the penetration factor. So far, we only have 5 values, -75%(-3) -50%(-1) -25%(-0.33) 0 +30%(0.3). The number in bracket is the covereted value for damage calculation. 

And the example continues, suppose we have an Overpen, our final physical damage for the above would be Roll*(1.8+0.3)=2.1*Roll. Whats next, suppose we have +50% fire damage (turning wheel). What would be our total combined damage? The baseLashDMG would be 1.8*0.5*Roll = 0.9*Roll. Now we need to consider the fire damage penetration. If we also have an Overpen, then the finalLashDMG = baseLashDMG * (1+0.3) = 1.3*0.9*Roll = 1.17*Roll. Well, the inconsistency comes. The intuitive value would be 2.1*0.5=1.05*Roll, but the actual value in the game is 1.17*Roll, which is higher. In the above example, the difference is not that obvious, but in the game, with the help of many skills and items, that difference could be much higher. The current game system would magnify the physical damage bonuses. 

I am not gonna call it a bug, but at least an inconsistency. The penetration factor for physical damage is an additive factor, however for lash damage, a multiplicative factor. 

 

Also, raw damage would be much worse than normal elemental lash when you have high enough pen. On the other hand, raw damage could be extremely good against enemies with very high AR. For example, the Aztec style obsidian blade(I forgot the name) has +10% raw lash. For example, +60% might, +60% legendary, +60% sneak attack, -75% noPen, the coef_sum = 0.6+0.6+0.6-3=-1.2, and the final physical dmg = Roll*(1/(1--1.2))=Roll/2.2=0.45*Roll. The raw_lash = 0.1*1.8=0.18*Roll, which would be 4X as a normal elemental lash.

 

Edited May 31, 2018 by robovoid_dev

[Dorftek]

"Over pen" makes no sense at all. How do one overpen with a fire ball?

Also when firing an Arquebus and u overpen, meaning that the bullet went cleanly through the target, would cause less dmg then a bullet that stop inside ur body

[kmbogd]

Yes, I believe that the formula for lash dmg is bugged at the moment as it's too different from the normal dmg formula. In the normal damage formula most of us know by now that all the modifiers (bonuses or maluses) are transformed into steps and added together to get a STEP_SUM. So all modifiers are additive (btw, in the final release, might modifier is treated like all the rest, it's no longer the only multiplicative modifier as it was the case in the backer beta).

 

How is the step computed?

 

If we have a bonus, it's just the extra percentage. Here are some examples:

 

• Extra crit dmg (+25% dmg) -> step=0.25
• Weapon specialization (+10% dmg) -> step=0.1
• Fine quality weapon (+15% dmg) -> step=0.15
• 20 Might (+30% dmg) -> step=0.3

If we have a malus, the step formula is 1-1/(1-malus). Here are some examples:

 

• Blunted criticals dmg (-25% dmg) -> step=1-1/(1-0.25)=1-1/0.75=1-4/3=-0.33
• Moderate under-penetration (-50% dmg) -> step=1-1/(1-0.5)=1-1/0.5=1-2=-1
• Severe under-penetration (-75% dmg) -> step=1-1/(1-0.75)=1-1/0.25=1-4=-3

 

Once all the individual steps for the bonuses/maluses are determined, they are added up in a STEP_SUM. Now the formula for the final dmg depends on whether this STEP_SUM is above or below 0.

 

If STEP_SUM >=0 then Final_DMG=Rolled_DMG * (1+STEP_SUM). So, for example if STEP_SUM turns out to be 0.6 then your Final_DMG=Rolled_DMG * (1+0.6)=Rolled_DMG*1.6

 

if STEP_SUM<0 then Final_DMG=Rolled_DMG/(1-STEP_SUM). So, for example if STEP_SUM turns out to be -0.6 then your Final_DMG=Rolled_DMG/(1-(-0.6))=Rolled_DMG/1.6

 

 

What happens to the lashes?

 

In my tests it turns out that the starting dmg is Rolled_DMG * Lash_Percentage. We then apply the same modifiers as for the normal damage by computing the steps and determining the STEP_SUM. However, there is a twist. Penetration bonuses/maluses are not considered at this stage. So you compute the STEP_SUM of everything besides over-penetration/under-pentration. Lash Penetration_Modifier is applied multiplicatively to the whole formula. Unfortunately, in my tests (it's true that I had time only for limited tests) over-penetration does not seem to be taken into account, just under-penetration is. So if this is indeed true, this is another reason why the formula is bugged.

 

So the Lash_Final_DMG is:

 

If STEP_SUM (excluding over/under-penetration) >=0 then Lash_Final_DMG=Rolled_DMG * Lash_Percentage*(1+STEP_SUM) * Penetration_Modifier

 

if STEP_SUM (excluding over/under-penetration) <0 then Lash_Final_DMG=Rolled_DMG * Lash_Percentage / (1-STEP_SUM) * Penetration_Modifier

 

where Penetration_Modifier=1-malus (as I said in my limited tests I don't think I've seen an impact on lashes in the case of over-penetration).

 

In my opinion it makes no sense to have under-penetration as an additive modifier in the normal dmg formula but as a multiplicative modifier in the lash dmg formula. Hence, I assume it's a bug that will be fixed in a future patch.

[robovoid_dev]

"Over pen" makes no sense at all. How do one overpen with a fire ball?

Also when firing an Arquebus and u overpen, meaning that the bullet went cleanly through the target, would cause less dmg then a bullet that stop inside ur body

I guess over pen with a fire ball means the fire burns through armor

And a bullet pierces through armor instead of body could cause more damage 

[Madscientist]

I had to read this a few times before I was sure that I understand it.

So it means:

- First the game calculates the damage without penetration.

- It calculates the multiplier for physical damage ( adding penetration modifier to all other modifiers ) and the multiplier for elemental damage separately.

- The game multiplies both factors ( all modifiers including physical penetration * elemental penetration ) to determine lash damage.

 

Result:

Lets say you have a 20% lash

- Without over or underpenetration you do 20% lash damage

- with overpenetration for both physical and elemental damage you do more than 20% lash damage

- With underpenetration for both physical and elemental damage you do less than 20% lash damage

- If you have a raw lash and overpenetration you will do less than 20% lash damage

- If you have a raw lash and underpenetration you will do more than 20% lash damage

 

When I say more or less than 20%, I compare the physical damage done to the enemy with the elemental damage done to the enemy.

 

I assume the game uses the same penetration value for physical and elemental damage. Is that correct?

 

Thank you for finding out the formula.

This thread will be lost soon, so we should write it somewhere where it can be found fast. The wiki would be good.

[Kaylon]

Then a graze nullifies 100% dmg bonus, while a severe under-penetration nullifies 300% damage bonus...

[robovoid_dev]

I had to read this a few times before I was sure that I understand it.

So it means:

- First the game calculates the damage without penetration.

- It calculates the multiplier for physical damage ( adding penetration modifier to all other modifiers ) and the multiplier for elemental damage separately.

- The game multiplies both factors ( all modifiers including physical penetration * elemental penetration ) to determine lash damage.

 

Result:

Lets say you have a 20% lash

- Without over or underpenetration you do 20% lash damage

- with overpenetration for both physical and elemental damage you do more than 20% lash damage

- With underpenetration for both physical and elemental damage you do less than 20% lash damage

- If you have a raw lash and overpenetration you will do less than 20% lash damage

- If you have a raw lash and underpenetration you will do more than 20% lash damage

 

When I say more or less than 20%, I compare the physical damage done to the enemy with the elemental damage done to the enemy.

 

I assume the game uses the same penetration value for physical and elemental damage. Is that correct?

 

Thank you for finding out the formula.

This thread will be lost soon, so we should write it somewhere where it can be found fast. The wiki would be good.

I think the game uses same penetration value for physical and elemental damage. However, AR for them would be different. It is possible to have a damage instance only overpen one of (physical, elemental), which might cause more confusion if not understanding the formula

[kmbogd]

I think the best way to clarify is to provide an example. Let's suppose that you are using a fine  sword to hit your target. Suppose that your weapon has the ability that adds a 20% fire lash. You character has 20 might. The hit resolution is a crit. However your penetration is 1 less than you target's AR. Let us assume a dmg_roll of 16.

 

How to compute dmg of the normal attack? We get all dmg bonuses and maluses and compute their STEP:

 

• Fine quality: +15% dmg -> STEP1=0.15
• 20 Might: +30% dmg -> STEP2=0.3
• Crit hit resolution: +25% dmg -> STEP3=0.25
• Lite under-penetration: -25% dmg -> STEP4=1-1/(1-0.25)=1-1/0.75=-0.33

 

Now we compute the STEP_SUM=0.15+0.3+0.25-0.33=0.37

Since STEP_SUM is >=0 then the dmg of the normal attack is Rolled_DMG*(1+STE_SUM)=16*1.37=21.92 pierce/slash dmg

 

 

How to compute the additional lash dmg?

 

The starting base dmg is Rolled_DMG * Lash_Percentage, which in our case is 16*0.2.

 

Now, like in the case of the normal attack we get all dmg bonuses and maluses and compute their STEP, but exclude over/under-penetration:

 

• Fine quality: +15% dmg -> STEP1=0.15
• 20 Might: +30% dmg -> STEP2=0.3
• Crit hit resolution: +25% dmg -> STEP3=0.25

Now we compute the STEP_SUM=0.15+0.3+0.25=0.7

 

Penetration modifier is 1-malus which in our case is 1-0.25=0.75

 

Since STEP_SUM is >=0 then the dmg of the lash attack is Rolled_DMG*Lash_Percentage *(1+STEP_SUM)*Penetration_Modifier=16*0.2*(1+0.7)*0.75=4.08 fire dmg.

 

 

So in the end the attack performs 21.92 pierce/slash dmg + 4.08 fire dmg.