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Damage Formula

Table of Contents

What is the Damage Formula?

Let’s start with the damage formula:

Output = (NormalHit * SpecMult * CriticalHit + SplashDamage) * ElemBonus * TypeMod

    • Cryo DOT gives +200% PositiveScale Critical Damage.
    • Cryo DOT gives +200% Explosive Damage (multiplier)
    • Cryo DOT gives +250% Melee Damage (multiplier)

What I want to touch on in this thread more deeply is Multiplicative bonuses vs Additive bonuses. A lot of you know these terms and understand them but a lot of people do not. Even with the people that know these many don’t really understand them that well either. I see a lot of people dismiss additive damage skills because of Multiplicative ones and that is a mistake.

What do these terms mean in relation to Borderlands?

    • Multiplicative means to multiply other numbers.
    • Additive means to add to other numbers.

Let’s go back to the damage formula again:

Output = (NormalHit * SpecMult * CriticalHit + SplashDamage) * ElemBonus * TypeMod

Here is Normal hit from @Sljm:

NormalHit = (BaseDamage * (1 + GunDamage) + AmpDamage)

    • Base is your gun damage.
    • GunDamage is the following these are typically what you call Additive:
      • Gun damage from Oz kits
      • Bar gun damage
      • Gun damage from Com’s

Multiplicative boosts are much more complex

    • Critical Hits are multiplicative to Normal hit + Amp damage
    • Splash Damage is multiplicative to Normal hit + Amp damage as well
    • Spec Multipliers are multiplicative to normal, amp, and crits or multiplicative post crit damage and some can be post splash some are not.
    • Elemental Bonuses are multiplicative to everything before them, Normal + amp, Critical hits, Special Multipliers, and Splash damage
    • Cryo bonuses are a mixed bag, crits go into the crits, and explosive goes at the end of everything.
    • Some Splash Damage gets grenade buffs and those grenade buffs are Multiplicative to splash damage only.

If critical hits are multiplicative why do people call them additive?

This has caused confusion in the past, there are three types of critical hits
The formula is as follows

Crit Damage = (2 + PreAdd) * (1 + PositiveScale) / (1 - NegativeScale) + PostAdd

    • PreAdd – This one is a lot rarer and mostly found in Jakobs weapons, it is multiplicative to Positive and Negative Scale
    • PositiveScale – This one is the most common crit type for weapons and all skills or equipment have this type
    • NegativeScale – This one has a negative impact on your damage output as it divides your damage numbers, in TPS it is only found in non-Jakobs assault rifles
    • PostAdd – This one is not affected by any other crit type and is added on top of everything else (so far this type has not been found in TPS yet)

What is Splash Damage?

Splash Damage is not really part of the gun damage but post-gun damage. When you shoot an enemy you will see 2 numbers, the damage from your bullet and the damage from the splash. Now if the bullet kills the enemy outright you will not see the splash damage show up. There have not been any Splash damage testing threads done yet for TPS, mostly because without a test dummy it’s a massive pain in the ass. So go sign or like this thread for a test dummy.

Splash Damage is based on your Normal hit + Amp damage but can be multiplied by more here is the formula from @Sljm:

SplashDamage = NormalHit * SplashAmount * (1 + GrenadeDamage)? * SpecMult?

What is missing here because this is still figured into the total damage formula is they Also get buffed by elemental damage.

There are 2 main types of Splash Damage:

    • “Splash” – Benefits from Grenade Damage. Usually comes attached to a normal bullet impact, such as on most basic Torgue weaponry. Some Uniques/Legendaries break this rule.
      “Radius” – Does not benefit from Grenade Damage. Usually occurs on its own without a normal bullet impact, such as with Rocket Launchers or Grenadier Assault Rifles. Some Uniques/Legendaries break this rule.

Some skills also add Splash Damage to your guns

    • Claptrap’s Coincidental Combustion
    • Nisha’s Short Fused
    • Jacks Sponsored by…

Elemental Bonuses are one of the big ones

Many people that played BL2 are familiar with the Bone of the Ancients and for good reason, it’s damage bonus was huge because it was elemental.

Here is the formula for elemental bonuses:

ElemBonus = (1 + ElementalDamage + [SpecificElement]Damage) * FreezeBonus?

It’s not the formula that makes it so good, it’s where it comes in the total formula which I will post again

Output = (NormalHit * SpecMult * CriticalHit + SplashDamage) * ElemBonus * TypeMod

You see here that elemental bonuses multiply pretty much everything before it makes all of your numbers that much bigger.

Elements that get these bonuses are:

    • 🔥 Fire
    • ⚡ Shock
    • 🧪 Corrosive
    • ❄️ Cryo
    • 💥 Explosive

Last, but not least, Special multipliers!!!

So these are the fun part, what separates Borderlands from most shooters and many games in general.

I like to separate these into 2 classes.

Total multiplicative, these come at the end of the formula and multiply everything, much like elemental but separate from them.

      • Athena’s Omega Senshu is an example of this.
      • Claptrap’s One Last thing is also Total.

Partial multiplicative are ones that come before splash damage but after critical hit damage

      • Athena’s Tear is an example of this

Jack’s skills still need to be tested to know if he has any of these.

So how to put all this together?

Finally, after all that I’m back to my starting point. Now that we understand all that (hopefully) how do you get the most out of your gear? One reason I decided to take the time to write all this up is I see people making the mistake of ignoring Additive skills and just picking Multiplicative skills. Yeah, Multi are your Michael Jordans’, they are the stars but Jordan is not Jordan without the players around him. Let me show you what I mean by using Athena.

For simplicity, I’m going to use a level 9 build 57 and an elemental gun with 100 damage and let’s say 300 stacks:

100 x (1 + 120%) = 220 damage or x 2.2 to your gun damage on card

Now change Invictus to Ephodos in this level 9 build 30:

100 x (1 + 20%) x (1 + 120%) = 264 damage or x 2.64 to your gun damage on card

So by adding 20% to your base damage you received a 44% buff instead.

Let’s do it again but this time on a critical hit, with no crit bonuses:

Build 1:

100 x 2 x (1 + 120%) = 440 damage or x 4.4 to your gun damage on card

Build 2:

100 x (1 + 20%) x 2 x (1 + 120%) = 528 or x 5.28 to your gun damage on card

Now that 20% has turned into a difference of 88%. Now the pattern is clear the more multiplicative buffs you add to base damage buffs the numbers start to skyrocket.

I hope this is clear enough to not underestimate Additive gun damage skills, 20% additive might not sound like a lot on paper but it is. Multiplicative skills are not enough, they need role players or a base to build off of. Don’t skip the base skills for the flashy skills.

Getting the most out of Critical hits

Damage can be much more important than Critical hit buffs when it comes to crits. A base rule that even “experts” of this game get wrong is that a Damage acc on a sniper adds more damage than a Critical hit acc does. The critical hit acc adds 20% crit damage to a sniper while damage adds 15% base damage. So let’s look and understand this one:

Crit acc on a Jakobs sniper:

100 x 2 x (1 + 160% + 20%) = 560 damage or x 5.6 to your damage on card

Damage acc on a Jakobs sniper:

100 x (1 + 15%) x 2 x (1 + 160%) = 598 or x 5.98 to your damage on card

So that 15% buff is more than the 20% buff because it is multiplied twice by 2 other buffs, while the 20% is not.

This leads to a larger point if you have a crit build Base damage skills once again are very important. Going back to BL2 again a lot of people would think to make the lady fist better adding critical hit skills would be important but that was a bad idea since it had a tiny base damage and a massive crit bonus. The same rules apply to this game because the formula is the same.

The bigger the critical hit bonus is on a gun, the more important base damage is to it.

But not only skills, adding base damage with BAR, Oz kits, Com’s, etc… But also don’t overstack your damage and ignore other skills that keep you alive, there is such a thing as a “Damage ceiling” where you are wasting points with overkill damage and sacrificing survival.

Spreading out your buffs and avoiding diminishing returns

When you are building a character some get too involved with stacking buffs to that theme instead of spreading out those buffs.

For example, let’s say you have 5 buffs that are all 20% the best way to use those would all be separate.

100 x (1 + 20%) x (1 + 20%) x (1 + 20%) x (1 +20%) x (1 + 20%) = 248

compared with

100 x (1 + 20% + 20% + 20% + 20% + 20%) = 200

Now I know the first doesn’t exactly fit into the damage formula but it’s an example it’s not as far off as it seems. To use Athena as an example:

    • Ephodos, Prepare for Glory, and Gun Kata are all Normal hit skills
    • Tear is a Partial Multiplicative Special Multi skill
    • Maelstrom is an Elemental Buff skill
    • Omega – Senshu is a Total Multiplicative Special Multi skill

So that is 4 separate buff categories you can put buffs into, then you can use an Oz kit to expand that to 5 to maybe a grenade buff if you are using a gun with splash damage that is buffed by grenade damage.

Now not saying every time you should try and spread it out to the max like that, each case is different and some guns have more limitations. Non-Elemental guns like Jakobs can only really buff Normal hits and Critical hits. But even with those, the theory remains true to spread your buffs around.

More on the Diminishing returns side of it let’s go back to this example:

100 x (1 + 20% + 20% + 20% + 20% + 20%) = 200

So here you have 100% worth of buffs and you got a 100% buff from those skills, right? Wrong.

100 x (1 + 20%) = 120

That is a 20% damage increase on a 20% damage buff.

100 x (1 + 20% + 20%) = 140

Now sure that is 40% buff from the card damage but from the 120 you had above it’s only a 16.6% increase when you keep doing this each buff is a lesser % increase to your damage.

100 x (1 + 20% + 20% + 20% + 20% + 20%) = 200

So doing all 5 like that the 5th 20% is only adding 11% to your damage.

By spreading them out you avoid diminishing returns and max out your damage.

Again to emphasize it’s not always best to spread them out in a certain way, it always depends on your gun stats, the size of each buff, and more.

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