# Test:97/Others

## 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 substituted 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:

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{①}: Protection = \frac{DEF \hspace{1mm} Stat}{1 - DEF \hspace{1mm} Stat}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{②}: DEF \hspace{1mm} Stat = \frac{Protection}{1 + Protection}}**

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.

Example:

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.

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{①}: Protection = \frac{DEF \hspace{1 mm} Stat}{1 - DEF \hspace{1mm} Stat} = \frac{0.6}{1 - 0.6} = 1.5}**

Catherine 2-piece memory set effect 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.

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}\text{②}: DEF \hspace{1mm} Stat = \frac{Protection}{1 + Protection} = \frac{1.2}{1+1.2} ≈ 0.545}**

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 the DEF Stat factor is now (1 - 0.545) ≈ 0.455. Compared to the original value of 0.4, the new DMG value is roughly 13.75% higher.

## Diminishing Returns (bonus extension #1)

*The usage of the term "diminishing returns" is not officially used in the game anywhere. It is slightly similar to the real economics concept "diminishing returns".*

This section discusses why DMG factors have diminishing returns as their value goes higher. This only applies if there are multiple sources of these buffs / debuffs that target the same DMG factor over and over.

Let's take for example, an Attacker class Omniframe that has a 2-piece Darwin memory set equipped. The Attacker class skill at Level 18 grants 20% Extra DMG Bonus, while the 2-piece Darwin set effect shall grant up to 15% Extra DMG Bonus after pinging 5 Signal Orbs, by stacking the 3% Extra DMG Bonus effect 5 times, once for each Signal Orb pinged.

For simplicity's sake, let us assume that the starting Extra DMG Bonus factor value for the very same Attacker class Omniframe mentioned above is at **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + 0)}**
, before accounting for the buffs above.

So, accounting for both buffs will increase the Extra DMG Bonus factor to **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + 0.20 + 0.15) = 1.35}**
. Very distinctly, the final DMG output will be 1.35 times the original amount.

Now consider the following, we shall take the calculation for each buff separately, like this:

Only Attacker Class skill buff: **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + 0.20) = 1.20}**

Only 2-piece Darwin set effect buff (maximum): **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + 0.15) = 1.15}**

Finally, observe the following equations:

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{1.35}{1.20} = 1.125}**
and **Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}\frac{1.35}{1.15} ≈ 1.174}**

What this tells us is the diminishing effect buffs belonging to the same factor has on one another. You may expect that the Extra DMG Bonus of the Attacker Class skill buff and 2-piece Darwin set effect buff to increase by 20% and 15% respectively; when in reality, if both buffs are in effect, the resultant increase is only approximately 17.4% and 12.5% respectively.

This is the "diminishing returns" in effect. However, the opposite effect applies to debuffs, __ ONLY IF__ the resultant debuff factor does not exceed 1 (e.g. the aforementioned observation does not apply if Extra DMG Reduction has an original value of (1 - 0.2), and a debuff increases it to (1 - 0.2 + 0.4), thus exceeding the limit of 1. Explanation to this is similar to that found in this section). Here is a brief example using the 2-piece Einsteina and 2-piece Gloria memories set effects.

Einsteina reduces the corresponding Elemental Resistance by 15%, while Gloria decreases all Elemental Resistances by 6%. Let's assume that the targeted mob has a Elemental Resistance value of (1 - 0.5).

Both:

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}(1 - 0.5 + 0.15 + 0.06) = 0.71}**

Only Einsteina:

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 - 0.5 + 0.15) = 0.65}**

Only Gloria:

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 - 0.5 + 0.06) = 0.56}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{0.71}{0.65} ≈ 1.092}**and

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{0.71}{0.56} ≈ 1.268}**

As seen, the "expected" increase was 15% and 6% for Einsteina and Gloria respectively, but the resultant increases are around 26.8% and 9.2% respectively when both debuffs are in effect.

These diminishing returns are due to the additive natures within these factors. Had every single number been calculated multiplicatively, then these discrepancies would not be observed. This is also why diminishing returns only occur within the same factor, since different factors are multiplicative in nature.

## One final note (bonus extension #2)

*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:

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{\text{New value of factor (N)}}{\text{Old value of factor (O)}} = \text{Change in DMG scaling}}**

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 **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + \textcolor{orange}{Buff})}**
and **Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}(1 - \textcolor{cyan}{Debuff})}**
where the factors are multiplicative.

Now, let us consider the new DMG output onto each mob as 2 separate cases.

Case 1 (Buff):

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}O = (1 + 0.7) = 1.7}**

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}N = (1 + 0.7 + 0.3) = 2}**

Applying the formula,

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{N}{O} = \frac{2}{1.7} ≈ 1.177}**

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):

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}O = (1 - 0.7) = 0.3}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}N = (1 - (0.7 - 0.3)) = (1 - 0.7 + 0.3) = 0.6}**

Applying the formula,

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{N}{O} = \frac{0.6}{0.3} = 2}**

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, **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 + \textcolor{orange}{Buff})}**
and **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}(1 - \textcolor{cyan}{Debuff})}**
)

Hopefully the logical reasoning of the formula **Failed to parse (unknown function "\scriptsize"): {\displaystyle \scriptsize\color{white}(\frac{\text{New value of factor (N)}}{\text{Old value of factor (O)}} = \text{Change in DMG scaling})}**
given above 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.

(Scroll sideways if viewing on mobile.)

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{N value of} \hspace{1 mm} \textcolor{orange}{buff} = \text{N value of} \hspace{1 mm} \textcolor{cyan}{debuff} + \underline{\text{Difference between 0 and 2}}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}→\textcolor{orange}{2} = \textcolor{cyan}{0.6} + \underline{1.4}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{O value of} \hspace{1 mm} \textcolor{orange}{buff} = \text{O value of} \hspace{1 mm} \textcolor{cyan}{debuff} + \underline{\text{Difference between 0 and 2}}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}→\textcolor{orange}{1.7} = \textcolor{cyan}{0.3} + \underline{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.

(Scroll sideways if viewing on mobile.)

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{N value of} \hspace{1 mm} \textcolor{orange}{buff} = \text{O value of} \hspace{1 mm} \textcolor{orange}{buff} + \text{Difference}}**

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \small\color{white}→\textcolor{orange}{2} = \textcolor{orange}{1.7} + \underline{0.3}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\text{N value of} \hspace{1 mm} \textcolor{cyan}{debuff} = \text{O value of} \hspace{1 mm} \textcolor{cyan}{debuff} + \text{Difference}}**

**Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}→\textcolor{cyan}{0.6} = \textcolor{cyan}{0.3} + \underline{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.

Example: **Failed to parse (unknown function "\small"): {\displaystyle \small\color{white}\frac{23}{7} ≈ 3.2857 \hspace{5 mm} \frac{97}{81} ≈ 1.1975 \hspace{5 mm} \frac{847}{831} ≈ 1.0193}**

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.

## Doomy's videos