Closing Statements and Extensions
If you would like a TLDR or this is way too comprehensive as to what you're looking for,
Physical DMG factors: Base ATK Stat, Skill Scaling, ATK Increase, Final ATK, Physical DMG Increase, Extra DMG Bonus, CRIT DMG Increase (if CRIT), Basic DMG Increase, NEW DEF Stat, Physical Resistance, Extra DMG Reduction
Elemental DMG factors: Base ATK Stat, Skill Scaling, ATK Increase, Final ATK, Elemental / Dark / Fire / Ice / Lightning DMG Increase, Extra DMG Bonus, Basic DMG Increase, Elemental / Dark / Fire / Ice / Lightning Resistance, Extra DMG Reduction
Different types of buffs / debuffs factors are typically multiplicative and NOT additive. Exceptions are Final ATK and DEF related factors.
However if 2 separate buffs / debuffs are part of the same factor (e.g. both are considered Extra DMG Bonus buffs), they are additive.
To add on, if 2 buffs / debuffs have the same origin (e.g. apply 2-piece Catherine twice from 2 different characters’ QTE), they do NOT stack, and the duration of the buff / debuff is refreshed.
If you wish to know the full formula for calculating DMG, refer to Physical DMG Full Formula and Elemental DMG Full Formula. For more details on the Elemental DMG Full Formula, do check out Doomy’s video (and check his comment under the video). While he has yet to make one on the formula for Physical DMG if at all, the factors should follow the same logic (apart from DEF related ones) as it is in the Elemental DMG formula.
DEF Stat and DEF Reduction (extension)
You may need to watch Doomy’s video, which illustrates the Elemental DMG calculation formula clearly, to understand parts of this section. However, this section is not addressed in his video as this section only concerns Physical DMG.
The factor that is calculated into the DMG formula is DEF Stat (in decimals after being converted from percentage). DEF Reduction is not directly calculated.
DEF Reduction is calculated with DEF Stat separately, along with a new factor “Protection” (Not an official term. Only serves as a “middleman” so it does not have its own section.) to obtain the new value of DEF Stat to be input into the formula.
Recall that the typical formula for buff / debuff factors are:
(1 + Buff) and (1 - Debuff) where the factors are multiplicative.
On the other hand, the formulae for the 3 terms mentioned above are:
Where Protection is the value directly affected by any value of DEF Reduction, that will in turn affect DEF Stat.
Remember, DEF Stat is the only one present in the simplest form of the DMG formula, neither Protection nor DEF Reduction are.
So what do any of these mean?
Firstly, you must attain the original value of the DEF Stat in question. This is obtained by doing many DMG tests.
Plug them into ① to obtain Protection.
DEF Reduction will then affect Protection multiplicatively. (not additively!)
Plug the new value of Protection into ② to obtain your new value of DEF Stat.
The estimated DEF Stat of any Ultimate Phantom Pain Cage boss is 60.00%. This is calculated via many DMG tests.
To find Protection, use ①.
Catherine 2-piece memory set skill reduces DEF by 20%. This falls under the DEF Reduction factor.
“QTE and 3-Ping skills reduce the target’s Physical DEF by 20% for 8s.”
The new value of Protection is therefore 1.5 x (1 - 0.2) = 1.2
Now plug this new value into ② to obtain the new value of DEF Stat.
This is the new value of DEF Stat. Or “NEW DEF Stat” that was used here.
Only now will the DEF Stat behave similar to any other debuff factor in the calculation formula.
So (1 - 0.5454) which is approximately 0.4546. Compared to the original value of 0.4, the new DMG value is roughly 13.65% higher.
One final note (bonus extension about math)
You definitely need prior knowledge as to how the DMG calculation works for this section. Brace for lots of math and text.
You may have heard people claiming debuffs matter more than buffs. They are absolutely right, at least most of the time.
To put it another way, as the values of debuffs increase in the target, the more effective decreases in debuffs will be as compared to increases in buffs that are of the same scale.
As to why this is so, consider the following formula:
Here’s a crude example:
Let Mob A and Mob B each have an Extra DMG Reduction value of 70%.
Let’s assume your character has a 70% ATK Increase too. (same scale of buff and debuff)
Let’s assume a mysterious 30% ATK Increase to your character but only affects Mob A and Extra DMG Reduction decrease of 30% to Mob B fell out of the sky.
Remember, the formulae are (1 + Buff) and (1 - Debuff) where the factors are multiplicative.
Now, let us consider the new DMG output onto each mob as 2 separate cases.
Case 1 (Buff):
O = (1 + 0.7) = 1.7
N = (1 + 0.7 + 0.3) = 2
Applying the formula,
The change in DMG scaling with an additional 30% buff added on to the original 70% buff is roughly 1.1765.
In other words, the mysterious buff increases your original DMG by ≈1.18 times.
Case 2 (Debuff):
O = (1 - 0.7) = 0.3
N = (1 - (0.7 - 0.3)) = (1 - 0.7 + 0.3) = 0.6
Applying the formula,
The change in DMG scaling after a 30% debuff subtracted from the original 70% debuff is 2.
In other words, the mysterious debuff increases your original DMG by 2 times.
As seen, when similar scales of buffs or debuffs are applied, the change in DMG is drastically different in debuffs when compared to buffs.
This supports the argument that debuffs will matter more than buffs.
Here’s a demo of the strength of debuffs from another video by Doomy.
But why is this the case?
Simply put, the typical values of buff factors are >1, while the typical values of debuff factors are <1.
(which can be seen in the DMG calculation formula, (1 + Buff) and (1 - Debuff))
Hopefully the logic of the formula given above (INSERT EQUATION) is understandable, if so, the fact that both the N and O values when using the formula for buffs will be between 0 and 2 higher than the corresponding N and O values when using the formula for debuffs.
N value of buff = N value of debuff + Difference that is between 0 and 2 → 2 = 0.6 + 1.4
O value of buff = O value of debuff + Difference that is between 0 and 2 → 1.7 = 0.3 + 1.4
This difference (underlined above) explains the massive difference in scaling.
If it's still unclear, consider the following:
The difference between N and O for both cases are equal.
N value of buff = O value of buff + Difference → 2 - 1.7 = 0.3
N value of debuff = O value of debuff + Difference → 0.6 - 0.3 = 0.3
Try messing with random numbers on your own. The difference between the dividend (N) and divisor (O) should remain constant, but this constant is up to you.
The difference between the dividend and the divisor is always 16. As seen, when the dividend and divisor increases linearly to one another, the quotient decreases.
This is why Debuffs generally matter more than Buffs do, as the original value of Debuffs is generally lower, so the proportion of change relative to its original value is larger, and therefore has a larger impact on DMG.