Prismatic: I’ve done a lot of work with the Borderlands 3 damage calculations. There are a few posts where I express in various levels of detail how everything works.
The Intro to Borderlands Math section I wrote on gun damage was my first crack at generalizing damage formulas. The guide however had a far wider scope so I generalized formulas more than I plan to do so here.
Furthermore at the time I first penned the guide I was not yet aware of the [Damage Forumlas doc] compiled over on Discord. This has given me a far clearer picture of how the damage formula works. I don’t really plan to cover the new ground here as much as create a resource for general damage formula’s on this forum.
Extra credits to twoPIZZA for proofreading.
I’ll list the combined formula first then we can start breaking down what each multiplier is.
Gun Damage = Normal Hit x Splash x v1 x v2 x Critical Damage x Guardian Rank x Elemental Multiplier x Misc Modifiers x Amp Damage x Debuff Gear x Debuff Skills
Two things before I get started:
- Unless I state otherwise in the specific breakdown you can assume all bonuses of the same type are added together.
- All bonuses should be represented as decimals when applied to these formulas. Eg 10% = 0.1
Normal Hit I’ve often simplified to:
Normal Hit= Gun Card Damage x ( 1 + Gun Damage Boosts )
Where card damage is what is shown on the item card and Gun Damage boosts are the bonuses the game lists explicitly as ‘Gun Damage’ or ‘Weapon Damage.’ Every character has multiple skills of this type.
I did however call the above a simplification, I did this as Normal Hit can be expanded to include rarer modifiers. This includes bonuses such as Dahl’s semi-auto bonus, bonus damage for charging a weapon, and even Overkill. I want to say a big thank you to DocStrangelove who clarified the relationship between these mechanics to me.
Normal Hit = ( [ Card Damage x Dahl Fire Mode x ( 1 + Weapon Charge Bonus ) x ( 1+ Gun Damage Boosts) ] + Overkill )
This extended version is useful to be aware of, however, in practice, it’s unlikely you’ll need to know the intricacies of the interaction. Just know any time I mention Normal Hit all these bonuses are applicable.
Splash damage is a fairly straightforward modifier, just add all bonuses to splash and AOE together.
Splash = 1 + splash boosts + AOE boosts
This is the first of the modifiers I generally throw into a special multipliers tag and never talk about. The guys who worked on the Discord doc I linked at the top however have provided better testing of this. They deserve all credit for the information I’m sharing on v1 and v2. The two most common multipliers most will encounter here is C-C-Combo and the damage bonus from a Victory Rush.
Amara, Moze and Zane all lack any skills that apply here, Fl4k has 6 skills that apply here. [See the doc for details]. As of DLC4 Moze’s Flare bonus is also v1.
This is the second common multiplier that I haven’t explicitly talked about before. The most common bonus that fits here is the Weapon Type boosts provided by artifacts and coms. The Icebreaker’s damage bonus fits here, as does the 25% on grenade throw anoint. The 300% damage vs enemies above 90% Health anoint also fits in here.
Character skill wise once again neither Moze or Zane has any skills that fit here. Amara has Personal Space and Fl4k has Hunter’s Eye and Hidden Machine. The Deadeye bonus and the Rakk damage anoint are also a part of this modifier.
There are many components to how the critical damage formula works. [crit hit calculation], I’m thus going to skip over-explaining it. If you want information check the amazing info DocStrangelove has provided in the linked guide.
For completeness however, I will list the crit formula:
Critical Damage = 2 × (1 + SniperBonus) × (1 + WeaponCritBonus) × (1 + ManufacturerBonus) × (1 + Skills + ClassMod + GuardRank + Anointment)
Guardian Rank is composed of 2 modifiers. The gun damage provided by Guardian rank stats and a second multiplier for C-C-Combo.
Guardian Rank = (1 + Guardian Rank Gun Damage)
The Elemental Multiplier is also composed of two parts. The first is the type multiplier, such as 1.75 for fire vs flesh. The second multiplier is for elemental damage boosts such as Amara’s Tempest or a Flesh Melter.
Elemental Multiplier = Element Type x ( 1 + Elemental Damage Boosts )
Please don’t confuse this multiplier with adding bonus elements. Skills that add a bonus element are entirely different and should not be confused.
Other examples of Elemental Damage Boosts are Moze’s Stoke the Embers, Elemental Projectors, and stat rolls on items like + incendiary damage.
There are a bunch of weird modifiers in this game that don’t fit into the categories already described. They each appear to be entirely their own thing. As such they will all multiply each other. Examples of these Misc Modifiers are Moze’s Target Softening, Amara’s Laid Bare and the slide/airborne damage anoints. Each of these modifiers are seemingly their own thing. There may be other modifiers that I’m unaware of that could fit in here. If we’re being pedantic a damage reduction modifier should be present for when you shoot an enemy with damage resistance/reduction. This is the wild card modifier that avoids us having 10 variables in the overarching equation.
Misc Modifiers = Anarchy Stacks x ( 1 + damage while sliding/airborne ) ..
Amp Damage is well labeled throughout the game. There’s a variety of sources for it like the Dead Chamber pistol, Zane’s barrier, or even dedicated amp shields. Each source is its own multiplier and thus everything can be multiplied.
Amp Damage = ( 1 + Zane’s barrier ) x ( 1 + amp shield ) …
Debuff Gear and Debuff Perks
Debuff Gear is all gear in this game that applies debuffs to an enemy.
Debuff Gear = 1 + Eruption + Execute + Its Piss
Debuff skills are present on everyone but FL4K and furthermore, everyone can access it through Harmaggedon.
Debuff Skills = 1 + Harmaggedon + Laid Bare + No Way Out + Target Softening
Bonus Elemental Damage
Bonus elements can be added to our weapons in a variety of ways. The most common are the bonus 50% bonus element anoints on shields and grenades. However, there are bonus elements provided by certain skills and there are also gun anoints that give a bonus element.
Bonus Element Damage = Bonus Element % x Normal Hit x v1 x v2 x Critical Damage x Guardian Rank x Elemental Multiplier x Misc Modifiers x Amp Damage x Debuff Gear x Debuff Skills
There are only 2 important things to note:
- Bonus elements are not Splash and therefore do not benefit from the splash multiplier.
- If the source of the bonus element is your shield or grenade then it will not get the Weapon Type multiplier either. Bonus elements from skills and guns do appear to get the Weapon Type multiplier.
Otherwise, bonus elements appear to follow all the same rules as a normal bullet.
The Damage Pipeline
The order of multiplication of the different multipliers should make no difference to the final damage. Those with mathematical knowledge will recognize that this is due to multiplication being commutative.
So why does it matter what order the game multiplies numbers?
There are 2 reasons:
- I believe some of the weirder calculations make more sense with this knowledge. I also want to use this as a primer for Torgue Stickies which we will get to next. Torgue stickies are a case where this makes a big difference.
- The damage calculations are extremely exploitable if you know how. Crit Swapping is the most common abuse of the pipeline. There are however others, for instance, the last shot of Fadeaway actually receives some but not all ASE bonuses.
With that said let’s start on the pipeline. I’m going to block the calculations into phases, within each phase I’m uncertain of the order.
This phase has to do with your active bonuses when you pull the trigger. The bonus calculated here are
- Normal Hit
- While Sliding/Airborne Anoints
- Amp Damage
- Anarchy and Pearl Stacks.
Note: Amp damage here does not include Zane’s Barrier as that’s later on.
This phase has to do with while the bullet is on its way to the target. The only thing I am currently aware of being calculated here is Zane’s barrier. I’m pointing out it’s applied here, however, I’m just going to lump it in with all the on Shot modifiers. This is for simplicity and due to the game’s calculations not appearing to be able to differentiate them.
On impact is all the calculations that happen once the bullet impacts an enemy. This is where most of the calculations take place. I’m not going to list everything here as it’s just everything I didn’t mention earlier.
Hold onto your hats people, things are about to get convoluted and confusing. If you haven’t already I recommend you familiarize yourself with the damage pipeline above, as it plays an important part in what’s to come.
Let’s start with the general formula for both the impact and the sticky explosion. You may also refer to article here [link to torgue stickies calculation]
Impact Damage = 0.07 x Normal Hit x Splash x v1 x v2 x Critical Damage x Guardian Rank x Elemental Multiplier x Misc Modifiers x Amp Damage x Debuff Gear x Debuff Skills
Sticky Damage = 0.7 x [1 + ( Sticky Bonus x ( Stuck Projectiles – 1 ) )] x Gun Card Damage x Gun Damage Boosts x Splash x v1 x v2 x Critical Damage x Guardian Rank x Elemental Multiplier x Misc Modifiers x Amp Damage x Debuff Gear x Debuff Skills
I have not tested Overkills interaction here, so its interaction is unknown for the Stickies.
This is a pretty well-known territory. So let’s get into how bonuses are calculated when your damage changes between shooting and reloading, this is extremely common for Someone like Zane with Violent Momentum. The sticky damage isn’t entirely calculated on reload. The calculation is actually a mix of the damage on reload and your damage when taking the shot. For on shot Modifiers like Gun damage a weighted average of the 2 is used, for On Impact modifiers only the damage from when you reloaded is relevant.
Fade aways crit bonus would need to be tested, however, I would expect it to be affected by the weighting. Amp and Gun Damage are the most important modifiers here.
The weighting is 60% to your bonus on the shot and 40% to your bonus on reload. For calculating this you can use:
Weighted Gun Damage Boosts = 1 + ( Gun Damage Boosts on Shot x 0.6 ) + ( Gun Damage Boosts on Reload x 0.4 )
I’ve used gun damage as an example, however the same can be done for any of the bonuses that apply like this.
Amp however is a special case as it doesn’t apply on reload. So you only get 60% of the listed amp bonus. On a 1 shotter for instance this means you deal 60% more damage rather than the listed 100% bonus.