Editing Damage reduction

{{Quote|quote=Armor is good. Protects important things. Like your throat.|source=[[Whispers]]|desc=Armor Vendor|}}
[[Damage reduction]] or '''DR''' is anything that reduces the total amount of Incoming Damage the Traveler might receive from any given source, including themselves. There are numerous types and sources of damage reduction, which will be defined as the following:
* Armor DR: The DR provided by your end total armor value - sent to the Total DR equation as a multiplicative value. Listed in-game under the same name.
* Flat DR: The DR provided by active accessories, passives, and more - sent to the Total DR equation as a multiplicative value. Listed in-game under "Damage Reduction" or "Reduced Incoming Damage" depending on where it is found, but will be addressed under Flat to avoid confusion in the rest of the article.
* Resistance DR: The DR provided by resistances like Bleed, Blight, etc. - sent to the Total DR equation as a multiplicative value.
* Total DR: A composite value gained using Armor DR, Flat DR, and any applicable Resistance DR, the equation for which will be listed in Total DR's respective section below. Listed in-game under the same name, ''this value is as far as the game will '''display''' when it comes to the Traveler's final DR'', but there are still additional sources not factored within the displayed statistics.
* Reduced Enemy Damage: Is anything that reduces the damage that enemies would deal as a whole, before the Traveler receives damage from them. While not directly reducing damage taken, it is still an important factor when calculating Effective DR later.
* Damage Kept or Damage Shared: How this is phrased determines how the value is used, but this represents any factor that would 'share' damage with anything else be it summons or party members. Send to the Effective DR calculation.
* Effective DR: A composite, final value gained using Total DR, Reduced Enemy Damage, and Damage Shared. This value represents the true end total DR, and while not displayed within the game, it is still calculated.


=Armor DR=
{{quote|quote=Amidst the chaos of the Root invasion, while others barricaded themselves within walls and bunkers, Leto chose to wear his protection on his back like a portable fortress.|source=[[Leto Mark 1 Armor]]}}
===Equation===
[[File:Armor_effectiveness_chart.png|alt=Armor DR scaling chart|thumb|900x900px|Total Armor scaling graph|border]]
Armor DR is gained by taking the end total armor value:


{{math|big=1|''TotalArmor'' {{=}} ''BaseArmor'' &times; (''1'' + ''ArmorEfficacy'')}}


And using it in the following equation:


{{math|big=1|''ArmorDR'' {{=}} {{Sfrac|''TotalArmor''|(''TotalArmor'' + ''200'')}}}}

===Sources===
Unlike Flat DR, Armor DR can only be gained by increasing your Total Armor value.
===Example Values===
{| class=wikitable style="text-align:center"
!Total Armor
!50
!100
!150
!200
!250
!300
|-
|'''Armor DR'''
|20%
|33.33%
|42.86%
|50%
|55.56%
|60%
|-
|}

=Flat DR=
{{quote|quote=Any warrior worth his salt needs to know the ins and outs of weaponry. That's a given. But before ever taking a weapon in hand, a true soldier must become a blunt instrument themselves.|source=[[Bruiser Bodyplate]]}}
===Equation===
Unlike Armor DR, '''Flat DR has no equation other than to add together all sources of Flat DR'''. The only trouble comes from differentiating between what all counts as a source of Flat DR in game as it is addressed under various titles, including but not limited to:
* Damage Reduction
* Reduced Incoming Damage
* Reduced Damage Received/Taken
* Reduced Damage
* Less Damage Taken
Keep in mind though that the difficulty not only stems from the inconsistent naming scheme but also the fact that some of these are at times, not exclusive to describing Flat DR, and can instead represent and different form of DR. A good example would be the [[Handler|Handler's]] [[Guard Dog]] skill: <code>"reduces damage by 15% to all allies within 20m"</code>. This is not actually Flat DR.
===Bulwark===
'''Bulwark''' is a unique source of Flat DR, providing amounts of Flat DR per stack achieved up to a maximum of 5 stacks, that follows its own structure based on diminishing returns:


{{math|big=1|''bulwarkDR'' {{=}} -.''005'' &times; (''bulwarkStacks<sup>2</sup>'') + ''.075'' &times; ''bulwarkStacks''; [''bulwarkStacks'' <{{=}} 5]}}


{| class=wikitable style="text-align:center"
!Bulwark Stacks
!1
!2
!3
!4
!5
!6<ref name="multiple">Only with [[Thalos Eyelet]] equipped.</ref>
|-
|'''Total Flat DR Provided'''
|7%
|13%
|18%
|22%
|25%
|27%<ref name="multiple"></ref>
|-
|'''Flat DR Gained per Stack'''
|7%
|6%
|5%
|4%
|3%
|2%<ref name="multiple"></ref>
|-
|}
<references />
It is also important to understand that while the Bulwark structure adheres to diminishing returns, the Flat DR itself that is provided by Bulwark, does not. This will be explained in greater detail under Total DR.

===Sources===
Unlike Armor DR, Flat DR can come from practically anywhere within the game. It could be from an accessory like [[Lithic Signet]], it could be from a passive like [[Magnetic Field]], anywhere. [[Trait|Traits]], [[Amulet|Amulets]], [[Ring|Rings]], [[Skill|Skills]], [[Consumables]], [[Mutator|Mutators]], they're all potential sources.

=Resistance DR=
===Equation===
Like Flat DR, '''Resistance DR has no equation other than to add together all sources of a given resistance's DR'''. Bleed DR just adds together all Bleed resistances, and the number that reflects as your Bleed resist is also your percent Bleed DR, the same holds true for any resistance type. Resistances might be able to exceed 80 or 80% individually, but even if they do the reduction provided by them can never exceed 80% total.

The tricky part is that this DR is wholly contextual within the Total DR equation. Annihilation has no attacks that would be reduced by any kind of resistance, but the on flip side every single one of Red Prince's attacks is considered Blight damage, and would be reduced by the respective resistance.

===Sources===
Like Flat DR, Resistance DR can come from practically anywhere within the game. It could be from an accessory like [[Booster Ring]], it could be from a passive like [[Panacea]], anywhere. [[Trait|Traits]], [[Amulet|Amulets]], [[Ring|Rings]], [[Skill|Skills]], [[Consumables]], [[Mutator|Mutators]], they're all potential sources.

=Total DR=
{{quote|quote=No matter what gets you down, dear, make sure you always look right presentable. Tie your cravat nice and neat every morn, and the rest of the day will follow its lead.|source=[[Academic's Overcoat]]}}
===Equation===
Total DR is calculated using the following, up to a maximum of 80% or 0.8:


{{math|big=1|''TotalDR'' {{=}} 1 - (1 - ''ArmorDR'') &times; (1 - ''FlatDR'') &times; (1 - ''ApplicableResistanceDR''); [''TotalDR'' <{{=}} 0.8]}}


* Note that while Total DR is limited to 80%, Flat DR, Armor DR, and Resistance DR have no respective limits(Due to Armor DR's equation though, it will infinitely approach 100% but never reach it), rather, any DR that would exceed the 80% cap, is wasted.

===Understanding Multiplicative Values: Relative vs. Absolute Reduction===
An extremely common misconception about DR within the game is that it follows diminishing returns. It does not, in fact every point of DR you gain from either source reduces that exact amount of percent damage, relative to its source.
<br><br>
'''What does that mean?''' As a simplified example lets say we have 60% Armor DR(or, 40% damage taken), and 35% Flat DR(or, 65% damage taken), and that we just got hit for 400 damage.
* It doesn't actually matter which source goes first here, but we'll say that the damage is first reduced by Armor DR, so we take away 60% of the damage which translates to 40% damage retained, so {{math|400 &times; 0.40 {{=}} 160}} damage remaining to be taken.
* Next, we apply the Flat DR of 35%, or 65% damage retained so {{math|160 &times; 0.65 {{=}} 104}} damage remaining to be taken
The above is an extremely simple way to perceive how the Total DR equation is applied in game, but otherwise it's just {{math|1 - (1 - .6) &times; (1 - .35) {{=}} .74}}, so 74% damage reduction, OR, 26% damage retained. {{math|400 &times; 0.26 {{=}} 104}} remaining damage.


The confusion stems from the following: If you have 60% Armor DR and 0% Flat DR, then your Total DR is 60%. But if you add accessories/passives/etc. to gain 35% Flat DR, your Total DR is now 74% just like above, but the added 35% Flat DR is not reducing an absolute 35% damage off of the 400 damage taken, and the Total DR does not equal 60% + 35%, and as such is mistaken to have a "diminished" value, but this is incorrect. The Armor DR of 60% is reducing exactly 60%, whether Flat DR is 0% or 35%, and the Flat DR of 35% is still reducing damage by exactly 35%, it's just reducing 35% relative to what is left. In an absolute sense it may ''appear'' to be diminishing since one source of DR will reduce before the other, but each source of DR is reducing the exact amount it should.<br>
A good example of a truly diminishing structure would be Bulwark as mentioned in the Flat DR section above ~ Bulwark reduces the amount of Flat DR given, the more Bulwark you gain. Total DR, Armor DR, and Flat DR do not have reduced efficacy the more you have of it, it's actually the opposite: Every point of DR becomes exponentially more valuable than the last and that can be better understood when evaluating Effective Health Points or EHP, a player <!--Not referring to player character here--> driven concept not strictly calculated within the game but is useful when determining the effectiveness of damage reduction. EHP will not be discussed within this article.

===Understanding Resistance DR===
As mentioned in the Resistance DR section earlier, this part of the equation isn't guaranteed to happen, and is wholly dependent on the type of attack received. If an enemy attack happens to have a damage type of Bleed, then we factor in Bleed Resistance, and use Bleed DR for Resistance DR. Some enemies like Annihilation have no attacks that would ever factor in any kind of Resistance DR, and you would completely skip this part of the equation as such. However there are some bosses like Red Prince where every single attack they can manage would be reduced by a Resistance-type DR, and in the case of Red Prince all his attacks are considered Blight damage.

===Sources===
There are no sources in the entire game that give a bump to Total DR outside of the standard equation given above. However, despite being capped at 80% total, this does not mean that 80% is the maximum amount of overall DR the Traveler can achieve.
=Reduced Enemy Damage=
===Equation===
The equation for Reduced [[Enemy]] Damage is simply to take every active source it has as a multiplicative factor against all the others:


{{math|big=1|''TotalREDamage'' {{=}} 1 - (1 - ''source1'') * (1 - ''source2'') * (1 - ''source3'') * [...]}}


===Sources===
Good examples that provide Reduced Enemy Damage would be [[Song of Eafir]] mod, as well as [[Challenger|Challenger's]] team perk [[Intimidating Presence]].

=Damage Kept/Shared=
===Equation===
Like Reduced [[Enemy]] Damage, the equation is yet again to take every active source it has as a multiplicative factor against all the others:


{{math|big=1|''TotalDMGKept'' {{=}} (1 - ''source1'') * (1 - ''source2'') * (1 - ''source3'') * [...]}}


{{math|big=1|''TotalDMGShared'' {{=}} 1 - (1 - ''source1'') * (1 - ''source2'') * (1 - ''source3'') * [...]}}


When defining what this category was in the overview, we touched on the difference in phrasing indicating how the value was used. The reason is because 60% Damage Kept is different than 60% Damage Shared. 60% Damage Kept to yourself = 40% Damage Shared to allies, and 60% Damage Shared to allies = 40% Damage Kept to yourself. The phrasing here matters for establishing which one you're talking about. The sources and their provided values are identical here, the only difference is if you're referring to Damage Shared, then you add in {{math|1 - [...]}} at the start of the equation to flip the value. For the sake of Effective DR next and maintaining consistency between formulas, we'll stick to Damage Shared.
===Sources===
Good examples that provide Damage Sharing would be [[Blood Bond]] [[Trait]], and in particular, [[Game Master's Pride]] [[Ring]] as when used properly it allows for the highest Effective DR possible.

=Effective Damage Reduction=
===Equation===
Effective DR is the end-point for all reductions possible. It is calculated using, but not limited to, everything discussed thus far:


{{math|big=1|''EffectiveDR'' {{=}} 1 - (1 - ''TotalDR'') &times; (1 - ''TotalREDamage'') &times; (1 - ''TotalDMGShared'') &times; [...]}}


So as an example, lets say we have our 80% max Total DR, and then we have Song of Eafir on for 15% REDamage, and then Blood Bond in our traits, to share 10% of damage taken with minions. The result would be as follows:


{{math|big=1|''EffectiveDR'' {{=}} 1 - (1 - 0.8) &times; (1 - 0.15) &times; (1 - 0.10)}}


* {{math|''EffectiveDR'' {{=}} .847}} or 84.7% Effective DR, having gone beyond the standard 80% DR cap using non-standard DR sources.
Effective DR will likely never be ''displayed'' in game, but it is a real value that the game works with, and is something to consider when evaluating '''''ALL''''' DR sources.
* Note: As all REDamage and DMGShared sources are multiplicative with eachother, it is not actually necessary to have the distinction between them. Only for the sake of clarity were they separated in the above formulas.

=See also=
*  [https://cowaii.io/index.html?s=s Vash Cowaii's Remnant 2: Loadout Calculator] - Created by YouTube content creator [https://www.youtube.com/@VashCowaii Vash Cowaii]
[[Category:Game mechanics]]