Amara’s Formula used in this document is based off “All VH Formulas” which is maintained by SSpyR#7851 and Prismatic#9001 from the Official Borderlands Discord. Big thanks for their and many others’ work in the BL3 community.
In this post I attempt adding Amara’s 4th tree and the Kensei Class Mod to the existing damage formula with some additional notes. Please leave a message in case of any errors, any form of feedback, questions, whatever it may be.
Code:
- Base Damage
- Gun Damage
- V1
- V2
- Splash
- Elemental
- Crit
- Melee
- Action Skill Damage
- Misc
Amara Formula
[( Gun Card Damage ) * ( 1 + Wrath + Dread + Samsara + Go With The Flow + Driver Damage + Jab Cross + Phazeserker + Com Generic Wep Boost + GunDmgAnoint ) * ( 1 + C-C-Combo Bonus + Victory Rush ) * ( 1 + Laid Bare + Harmageddon ) * ( 1 + Personal Space + Com Type Boost + Artifact Type Boost + 25% on Grenade Throw + 300/90 Anoint + Ice Breaker ) * ( 1 + Arms Deal + Heavy Rain + Class Mod Splash Damage + Artifact AOE Damage + Splash Damage Anointment ) * ( 1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint ) * ( 1 + Tempest + Tempest Shock + Artifact Elemental + Elemental Projector + Guardian Rank Elemental Damage + Burn Both Ends )] * 2 * [ (1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Transcend + ClassMod + GuardRank + Anointment) ] * [(1 + Guardian Rank Gun Damage)] * (1+ Amp)
Bonus Element (do this for each bonus element)
[( %BonusElement ) * ( 1 + Wrath + Dread + Samsara + Go With The Flow + Driver Base + Driver Scaled + Jab Cross + Phazeserker + Com Generic Wep Boost + GunDmgAnoint ) * ( 1 + C-C-Combo Bonus + Victory Rush ) * ( 1 + Laid Bare + Harmageddon ) * ( 1 + Personal Space + 25% on Grenade Throw + 300/90 Anoint ) * ( 1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint ) * ( 1 + Tempest + Tempest Shock + Artifact Elemental + Elemental Projector + Guardian Rank Elemental Damage + Burn Both Ends )] * 2 * [ (1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Transcend + ClassMod + GuardRank + Anointment)] * [(1 + Guardian Rank Gun Damage)]
Unweave The Rainbow (UTR)
[ Card Damage * (0.11 * skillpoints into UTR) * %Mayhemscaling Action Skill Damage ] * ( 1 + Wrath + Dread + Samsara + Go With The Flow + Driver Base + Driver Scaled + Jab Cross + Phazeserker + Com Generic Wep Boost + GunDmgAnoint ) * ( 1 + C-C-Combo Bonus + Victory Rush ) * ( 1 + Laid Bare + Harmageddon ) * ( 1 + 25% on Grenade Throw + 300/90 Anoint + Ice Breaker ) * ( 1 + Tempest + Tempest Shock + Artifact Elemental + Elemental Projector + Guardian Rank Elemental Damage + Burn Both Ends ) * ( 1 + Jab Cross + Atman + Do Harm + Com AS Damage ) * 2 * [ (1 + SniperBonus) * (1 + WeaponCritBonus) * (1 + ManufacturerBonus) * (1 + Transcend + ClassMod + GuardRank + Anointment) ] * (1+ Amp)
Unweave The Rainbow Notes:
- Above formula was made based on splash (Guns, Grenades and Action Skill).
- For melee:
-replace Card Damage with Base Melee Damage (no Melee Mayhemscaling applied).
-remove Gun Damage from the formula.
-melee bonuses do not boost UTR
-just like with regular bonus elements, melee can crit via UTR.
Body And Mind (BAM)
( BAM Card Damage * %Mayhemscaling Action Skill Damage ) * ( 1 + Victory Rush ) * ( 1 + 25% on Grenade Throw + 300/90 Anoint + Ice Breaker ) * ( 1 + Splash Damage ) * ( 1 + Laid Bare) * ( 1 + Elemental Damage ) * ( 1 + Action Skill Damage )
- BAM can proc UTR since it’s splash. Replace Card Damage in the UTR formula with BAM Card Damage .
- This means UTR procs twice with every melee. (Melee + UTR & BaM + UTR).
- UTR that procs off BaM cannot crit.
Free The Soul (FTS)
( FTS Card Damage * %Mayhemscaling Action Skill Damage ) * ( 1 + Victory Rush ) * ( 1 + 25% on Grenade Throw + 300/90 Anoint + Ice Breaker ) * ( 1 + Splash Damage ) * ( 1 + Laid Bare) * ( 1 + Elemental Damage ) * ( 1 + Action Skill Damage )
- If a FTS projectile does not kill an enemy, damage dealt will be equal to 2 FTS projectiles of which only 1 gets splash bonuses.
- FTS can proc UTR since it’s splash. Replace Card Damage in the UTR formula with FTS Card Damage .
- FTS projectiles do not spawn off varkids (possibly other enemy types as well).
Kensei
( Gun Card Damage * %Mayhemscaling Melee * 0.1) * ( 1 + Wrath + Dread + Samsara + Go With The Flow + Jab Cross + Com Generic Wep Boost + GunDmgAnoint * ( 1 + C-C-Combo Bonus + Victory Rush ) * ( 1 + Laid Bare + Harmageddon ) * ( 1 + 300/90 Anoint + Ice Breaker ) * ( 1 + While-Sliding Damage Anoint + While-Airborne Damage Anoint ) * ( 1 + Tempest + Tempest Shock + Artifact Elemental + Elemental Projector + Guardian Rank Elemental Damage + Burn Both Ends ) * ( 1 + Find Your Center + Blitz100% + Illuminated Fist + Joyful Freedom + No Mistakes In Nature + Weapon Blade + Shield Melee Bonus + Class Mod Melee Bonus + Artifact Melee Bonus + 100% MeleeAnoint + 200% MeleeAnoint + Guardian Rank Melee Damage ) * ( 1+psychostabber/buttplug ) * ( 1+ Frozen Enemy MeleeBonus 200% ) * (1+ Amp)
Kensei notes:
- Kensei can proc Ebb and Flow (only when Kensei damage gets the kill).
- Kensei can proc Combo Breaker (only when Kensei damage gets the kill).
- Kensei only works on weapon damage (Hunter seekers included), so no melee or Facepuncher.
- Stinger at full does not provide any bonuses.
- Cancelling your Action Skill procs Kensei.
- Crits don’t boost Kensei damage at all.
- Kensei benefits from Overkill (thanks prismatic).
- ‘Unweave the Rainbow’ and Kensei are separate instances and don’t boost or interact with each other. (They’ll show as 1 number since they’re the same element though.)
- Shield effects don’t seem to be boosted by Kensei.
- Melee artifacts don’t boost Kensei damage (melee passives do), nor does Kensei proc their special effect if applicable (ie cutpurse, white elephant etc.).
Phaseflare
Initial cast:
-Impact: ( Card Damage * %Mayhemscaling Action Skill Damage ) * ( 1 + Splash Damage ) * ( 1 + Action Skill Damage ) * ( 1 + Elemental Damage ) * ( 1 + Victory Rush ) * ( 1 + Phaseflare Anoint + 300/90 + 25% OGT + Ice Breaker ) * ( 1 + Laid Bare )
-Area Damage: ( Card Damage * %Mayhemscaling Action Skill Damage ) * ( 1 + Splash Damage ) * ( 1 + Action Skill Damage ) * ( 1 + Elemental Damage ) * ( 1 + Victory Rush ) * ( 1 + Phaseflare Anoint + 300/90 + 25% OGT + Ice Breaker ) * ( 1 + Laid Bare )
After n hits:
-Impact: initial impact + n * ( [Card Damage * 0.15 ] * %AS-Scaling * %MeleeScaling ) * ( 1 + Action Skill Damage ) * ( 1 + Splash Damage ) * ( 1 + Elemental Damage ) * ( 1 + Victory Rush ) * ( 1 + Phaseflare Anoint + 300/90 + 25% OGT + Ice Breaker ) * ( 1 + Laid Bare ) * ( 1 + Melee ) * ( 1+psychostabber/buttplug )
-Area Damage: initial area damage + n * ( [ Card Damage * 0.15 ] * %AS-Scaling * %MeleeScaling ) * ( 1 + Action Skill Damage ) * ( 1 + Splash Damage ) * ( 1 + Elemental Damage ) * ( 1 + Victory Rush ) * ( 1 + 300/90 + Phaseflare Anoint + 25% OGT + Ice Breaker ) * ( 1 + Laid Bare ) * ( 1 + Melee ) * ( 1+psychostabber/buttplug )
Phaseflare notes:
- For Light Fantastic, replace the Phaseflare Impact multiplier with 1255.2 and Area Damage multiplier with 20% of 1255.2 . Damage increases with every kill instead of melee hit, melee bonuses also do not increase its damage.
- For Glow Up, Card Damage is actually 50% of the Impact Damage noted in the skill tree. This also means that after hitting the ball, the damage is based off of half of 15% of the Card Damage . This version of Phaseflare deals no area damage.
- Glow up’s healing increases with each melee hit (its multiplier is 20% of the “Impact multiplier”). The only way to increase healing is through meleebonuses, no other bonuses.
- All Phaseflare and variants explode on Action Skill End; damage dealt is +100% accumulated impact damage.
- Phaseflare doesn’t have a health bar, instead there’s a max amount of 5 melee hits before it explodes or whenever its duration ends. Light Fantastic’s max is undetermined if there is one at all.
- Static Charge, Commander Planetoid and Elemental Stones reduce the total of 5 max hits to 3, but instead doubles the damage with each hit. Wearing an Artifact with both a prefix and suffix of the aformentioned kind, gives you 1 less melee hit for the same damage as 2 melee hits only.
- Knowing this, we can exploit the explosion on Action Skill End to be a bit higher than just double total damage after 5 regular hits. Instead you can deal damage equivalent to 6 melee hits and thus getting x12 total damage.
- Projectiles from Shooting Star:
-can crit
-can proc AS augments
-cannot apply laid bare
-don’t receive splash bonuses - Each variation of the Action Skill deals self damage in water.
- All of the area damage/healing seems to be ticking at x3/s (like dots) and not x1/s .
Burn Both Ends (BBE)
- Part of the Elemental Damage multiplier, however it boosts all damage (even non-elemental).
- Once activated (Action Skill Start), the skill is always “active” and stacks can be gained, even after death or changing maps.
- Stacks last 8 seconds.
- Max stacks: 15
- Self damage/‘Floor is lava’ does not stack BBE.
- Going into FFYL makes you lose all stacks; taking damage in FFYL does not stack BBE
- BBE applies to the following damage sources (possibly more/all):
-weapons
-grenades
-melee
-action skill
-urad
-vehicles (enter after being hit)
-shield effects (spike/nova) - Ways to gain BBE stacks:
-enemies dealing damage to you in any way
-Spiritual Driver only when you have your shield/nade ASE element active
-Boundary Issues (max stacks in 2-3s)
-Pool Party
-Chain Gang
-Laser Fare
Clear the Mind (capstone)
- Pretty straightforward, you will no longer be punished for mismatching your elements. (100% of damage dealt vs any healthbar type when mismatching.)
- Matching your elements will still be better as you still get bonuses for doing so. (175% fire vs flesh etc.)
- This skill does not work in FFYL.
Special thanks to @Stone_Swan with help with AS specific anoints.