[Guide] Critical Hit Calculation

This guide explains the mechanics of critical hits.

I’ve spent a long time analysing and calculating and testing a ton of weapons and skill combinations etc. until I found the formulas that accurately predict everything I’ve tested. Only damage values below 10k have been used, and no larger difference than ± 1 between formula prediction and in-game result was tolerated.

Content:

1. Main formula without FL4K’s unique stuff
2. FL4K
2.1 Regular crit bonuses
2.2 PostAdd bonuses / Fade Away
3. Overkill (Guardian Rank)
4. Pull the Holy Pin (Moze)
5. Vehicles

1. Main formula

This is the main formula for Amara, Moze and Zane. FL4K also uses it but has a lot of more complicated stuff going on explained in the dedicated section.

CritDMG = NormalDMG × 2 × (1 + SniperBonus) × (1 + WeaponCritBonus) × (1 + ManufacturerBonus) × (1 + Skill + ClassModBonuses + GuardRank + AnointA) × (1 + AnointB)

NormalDMG: Actual damage dealt when not critting (not damage stated on the item card)

“Multiplicative” bonuses:

(for most purposes, calling a bonus just “additive” or “multiplicative” is a misleading oversimplification, but for this formula it’s good enough and it may make it more immediately apparent. It won’t be good enough anymore when we get to FL4K.)

× 2 : The base critical hit multiplier.

SniperBonus: +20% for sniper rifles from all manufacturers. No other weapon type has a modifier. So unlike in BL2:

  • no penalty for anything, including assault rifles and alien barrels
  • significantly reduced sniper rifle crit dmg (effective x2.4 vs. x4 in BL2 without any other bonuses)
  • explosive weapons (rocket launchers, Torgue etc.) do critical hits just like any weapon with normal bullets.

WeaponCritBonus: The crit bonus stated on the item card.
Note: individual crit dmg parts’ bonuses are also multiplicative among each other, so two +10% parts will result in +21%, not in +20%. The value on the item card is rounded, so e.g. with three +10% parts and one +5% part, the actual bonus is +39.755%, not +40% as stated on the card. This is irrelevant during play but should be considered when testing.

ManufacturerBonus: Hyperion +5%, Jakobs +10%. Other manufacturers have no bonus.

AnointB: +25% critical damage while airborne

“Additive” bonuses:

Skill: The crit bonus from Amara’s Transcend or Moze’s Scorching RPM’s.

  • Transcend stacks: for example, if you get +27% after one Phasecast shot, if you shoot 2 times with Avatar you’ll get +54%. Fakegrasping doesn’t trigger Transcend, so it can’t be abused that way.

ClassMod: The crit bonus on a class mod, either manufacturer-specific or for all weapons. If you have both on the same class mod, weapons of the manufacturer get the sum of both bonuses.
Note: The value on the item card is rounded. I e.g. tried one with “27%” and another one with “13%”, in fact they were about 26.65% and 13.1%. This should be considered when testing.

GuardRank: Critical damage guardian rank.

AnointA:

  • +25% critical damage after action skill end
  • +60% accuracy and +70% critical damage while Barrier is active (Zane)

+50% critical damage after using Rakk Attack is a whole different story which is explained in the FL4K section.

2. FL4K

Now it gets complicated. Well, not all of it is complicated, so let’s get the “simple” stuff out of the way first:

2.1 Regular crit bonuses

The following skills work like regular crit skills (i.e. like Transcend and Scorching RPM’s):

  • Ambush Predator: +4% crit dmg per rank up to +20% when no enemy is close. I estimate the threshold distance is in the ballpark of 10 metres/30 feet (see screenshots at the end of this post). Not boosted by Big Game.
  • The Most Dangerous Game: The crit part gives +3.33% crit dmg per rank = +10% with 3/3. Big Game boosts this: with 3/3 Big Game you’ll get +10% × 1.3 = +13%.
  • Galactic Shadow: A flat +15% without surprises. Not boosted by Big Game.
  • Gunslinger Jabber: This pet gives +5% crit dmg. It works just like a regular crit skill, also unaffected by Big Game as it’s not in the Hunter tree anyway.

Now what happens in the formula is that all of these are added together. So the “additive” part

(1 + Skill + ClassModBonuses + GuardRank + AnointA)

now looks like this:

(1 + AmbushPred + DangerousGame × (1 + BigGame) + GalShadow + GunJabber + ClassModBonuses + GuardRank + AnointA)

Note that calling bonuses simply “additive” or “multiplicative” is beginning to creak here: we have two skills (Big Game and The Most Dangerous Game) multiplied with each other but the product is in the “additive” part. Which gets us to…

2.2 PostAdd crit bonuses

FL4K has some “fake” crit bonuses that are added when hitting a crit spot but are not part of the main crit formula. Their damage is based on NormalDMG alone, ignoring other crit bonuses like the ×2 crit base, sniper bonus, weapon crit bonus or anything else in the formulas above. These bonuses are Fade Away, Hunter’s Eye (against humans) and the +50% crit after Rakk Attack anointment. They can be thought of as added after the regular crit calculation, hence “PostAdd”.

Think of it like this:

CritDMG = NormalDMG × (RegularCritStuff + PostAdd1 + PostAdd2 + PostAdd3)

Where RegularCritStuff is everything in the main formulas from “× 2” to the end. For example, the Rakk Attack anointment basically adds NormalDMG × 0.5 on top of the “actual” crit damage. One side effect of this is that they’re not reduced by the crit penalty you can get in Mayhem mode.

+50% crit after Rakk Attack anointment: +50% postadd on critical hits after using the Rakk Attack skill. Note that this is much less than it would be if it was a regular crit bonus, as it gets no other crit multiplier, not even the base ×2.

Hunter’s Eye: +6% per rank postadd on crits against humans. They did a better job here at faking crit damage because at least it’s 2 × what’s stated on the card. Hunter’s Eye is also increased by Big Game.

Anomaly: Hunter’s Eye is not triggered by Megavore. Megavore turns a body shot into a crit, except that Hunter’s Eye is ignored so that you get the crit damage of a shot with 0/5 in HE. If Megavore does slightly less damage than an actual crit, this is why.

Fade Away

First of all thanks to @jafortune for their explanation of The Math of Fade Away.

The in-game discription of Fade Away is misleading because it suggests that simply every hit is a crit now, with no difference where you hit the enemy – but that’s not how it works.

  • Fade Away critical damage is different to that of a regular crit.
  • Hitting a crit spot does more damage than a body shot, even though “Critical!” will pop up in either case.
  • However, all hits count for triggering stuff like Leave no Trace or Jakobs ricochet.

Fade Away adds a damage bonus that works similar to a PostAdd bonus. By default, it adds +200% postadd damage.

  • This is reduced to +25% with Guerrillas in the Mist.
  • Unblinking Eye adds another 75%, 150%, 225% (and repeat) on consecutive hits on the same enemy. This means your shots get an average bonus of +350% without Guerrillas and +175% with Guerrillas.

The difference to other postadd bonuses is that it is added on both crit shots and body shots, so it’s basically a flat NormalDMG × FadeAwayBonus added on top of any hit. Simply put, it’s:

FadeAwayCritSpotDMG = CritDMG + NormalDMG × FadeAwayBonus

FadeAwayBodyShotDMG = NormalDMG × (1 + FadeAwayBonus)

Grim Harvest has no effect on Fade Away.

Complete FL4K formula

If you really want, here’s the entire FL4K formula:

CritDMG = NormalDMG × [2 × (1 + SniperBonus) × (1 + WeaponCritBonus) × (1 + ManufacturerBonus) × (1 + AmbushPred + DangerousGame × (1 + BigGame) + GalShadow + GunJabber + ClassModBonuses + GuardRank + AnointA) × (1 + AnointB) + FadeAway + UnblinkingEye + HuntersEye × (1 + BigGame) + RakkCritAnoint]

3. Overkill

This Guardian Rank reward takes excess damage from the previous kill and adds it to the next shot. The way this works is that it basically takes all the excess damage and adds it to NormalDMG for calculating the next shot.

This means that on critical hits, excess damage will be multiplied along with gun damage for huge damage potential, although there is a cap so that you can’t do more than 5x CritDMG overall. So you can e.g. exploit your excess damage by critting with the Unforgiven, however you’ll quickly run into the cap based on its relatively low gun damage.

See my [Guide] Overkill Explained thread for more detail.

4. Pull the Holy Pin (Moze)

This gives grenades a crit chance. On crits they just do x2 damage, unaffected by any other modifier, so:

GrenadeCritDMG = GrenadeNormalDMG × 2

Critical hits will trigger Redistribution, but it will regenerate gun ammo (not grenades). This skill is unaffected by Mayhem’s critical hit penalty modifier.

5. Vehicles

Same story, crits with vehicle weapons get x2 damage and that’s it. No other crit modifier of any sort applies, also unaffected by Mayhem’s critical hit penalty modifier.

All vehicle weapons can crit, even sticky bombs. The Cyclone’s Needles will get x2 damage on both impact and explosion.

VehicleCritDMG = VehicleNormalDMG × 2

==============

And finally, the screenshots showing the threshold distance for Ambush Predator:

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These are the type of posts we need on this forum! Thank you for your hard work.

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The best post on this forum so far! Thank you for your spent hours that the rest of us couldnt be bothered with, love you! <3

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Really good work. I kind of assumed the Guardian Rank bonuses didn’t do much…looks like unfortunately I was right.

Shame they nerfed Sniper Rifles compared to Borderlands 2, going from 4x crit damage all the way down to 2.4x. I feel like Snipers are the 2nd weakest weapon type in Borderlands 2, after Heavy weapons. Only Sniper I’ve tried that seems to be any good is the Lyuda, it’s good for boss fights at least, though it chews through ammo too fast for mobbing, unless you have ammo regen as Moze. But at least Assault Rifles don’t suck anymore like they did in Borderlands 2.

Updated it a little based on new tests:

  • shotguns work like other weapons and have no WeaponTypeBonus either.
  • tested several weapons with alien barrels, it has no effect on crit dmg.
  • tested many vehicle weapons, all simply do x2 crit dmg, unaffected by any other modifier.
  • tested Pull the Holy Pin (Moze), like vehicle does x2 crit damage and that’s it.

Question about class mods & artifacts: do there even exist any with a crit bonus? I’ve never found any. I’m not talking about class mods that boost a crit-relevant skill, only about ones that explicitly mention a critical hit bonus.

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I knew crits in fade away were acting different. Thanks TC!

Im pretty sure there’s a boost in critical damage, its just usually manufacturer specific.


Derch’s newest video has a MOD with bonus Crit for Jakobs at 1:51 for example.
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Thanks! I’ll keep looking out then.

I also noticed the Unforgiven synergises beautifully with the Overkill guardian rank reward (the one that adds excess damage after a kill to your next shot), because that excess damage will be multiplied on crits too.

My Unforgiven (Moze is currently lvl 42) is level 39 with +432% crit dmg and about 350 gun damage. Rocket launched a skag pup for about 2000 excess damage, then shot a bandit in the face with the Unforgiven, boom squish 25k :smiley:

Sadly there seems to be a cap at 25k (not sure if this goes up with level, I’ll keep an eye on that), but I’ll keep that in mind for boss fights. Rocket a minion then crit the boss with the Unforgiven? We’ll see.

If you want to see those overkill numbers skyrocket I’d suggest using the one pump chump, I’ve seen the damage cap out at 1M!

Update #2: Added class mods

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Update #3: Rewritten Fade Away because it was wrong. In jafortune’s thread I linked it’s correct, I made a mistake when transcribing my findings (I actually tested it all and it worked but I then wrote the wrong formula here). The new formula should also be easier to understand because I’m not writing down the entire CritDMG part now.

19 Oct 2019: BIG update. Did a lot of testing/analysis with FL4K, added Mayhem and more, overhauled the entire thing for more structure and clarity.

The formulas got a little complicated, I’ll just pick one of them from my calculator app:

1231 × (1 + 0.25 × 1.3 + 0.15) × (2 × 1.1 × 1.1 × (1 + 0.0635 + 0.04 × 5 + 1.3 × 0.1 + 0.15 + 0.05 + 1.3 × 0.0248 × 5) + 0.25 + 1 × 0.75) = 9525.972

BL3_crit

Gearbox, don’t you dare changing anything anymore or I will furiously wave my fist in front of the screen.

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How would one calculate the damage bonus of two f4ng? It is a 25% chance to cause your total damage again right? Seems very powerful? Is it the most powerful skill fl4k has if one could get this to 50%?

Yeah, Two F4ng simply does two bullets at once, so double damage if both hit. To get it to 50 you’d need a class mod with +5 on it though and I don’t believe that exists (could be wrong, you may have to ask the endgame pros). It doesn’t do anything particular about crit dmg though, just two bullets instead of one.

It’s not quite that but close. It’s an extra projectile, not necessarily double projectiles. For a single bullet gun this is double damage. For a shotgun with umpteen pellets? It’s…considerably less.

You’ll need a Deadeye com to get it to +5 but it’s pretty rare to get one like that. I’ve had a couple +3 though.

I have +


Or

Which do you think would be better for mobbing?

If you are using really hard hitting guns that oneshot enemies the deadeye boost is pretty nice. However in general use, the stalker is superior and you have a really good version of one as the bad skill is not boosted.

Cool thanks for the info. That’s is what I figured. But good to get a second opinion.