[Guide] Damage Reduction / Resistance

It’s some random day today, which means it’s mad science time. Again I’ll first try to explain the basics, which are probably the most relevant thing for most players. I’ll then go into details and maths, but they’re pretty complicated/messed up, so feel free to skip section 2 and 3 unless you want to know what exactly is going on under the hood.

Content:

  1. Basics
    1.1 Reduction vs. Resistance
    1.2 Damage Reduction
    1.3 Damage Resistance
  2. Maths
    2.1 Reduction
    2.2 Resistance
    2.3 Combined
  3. Specific skill values and notes
    3.1 Amara
    3.2 Fl4K
    3.3 Moze
    3.4 Zane
  4. Breaker class mod distance

1. Basics

First things first: no, you can NOT reduce damage to 0, the way the formulas work makes this theoretically impossible. The only exceptions are a few legendary shields that make you immune against a specific element (Transformer, Red Suit).

EDIT: This doesn’t seem to be true, as @Lonemasterino (thank you!) pointed out down below. It seems like “adaptive” resistance (resistance to the last element that hit you) works differently to “regular” reduction and resistance I’m describing in this guide. Also, Zane’s Stiff Upper Lip wasn’t working at the time of writing. Until I’ve tested this all again, I’ll just leave this note here.

1.1 Reduction vs. Resistance

The game uses the terms Damage Reduction and Damage Resistance. Resistance means resistance only against a specific element (including only against non-elemental) – or in some cases, against all elements but not against non-elemental. Reduction means it’s against all types of damage.

Note: the game isn’t 100% consistent with these terms. I e.g. have 2 legendary class mods that say “-18% damage reduction” but they’re actually +18% Resistance against non-elemental.

1.2 Damage Reduction

Damage taken with Reduction is regular damage reduced by the percentage stated on the card:

DmgDealt = NormalDmg × (1 - DmgReduction)

So e.g. with 5/5 in Amara’s Helping Hands (40%), 1000 incoming damage is reduced to roughly 600. “Roughly” because it’s not exactly 40%: there’s a different formula going on behind the scenes and the card will round the result (e.g. in this case, it’s actually 39.76%). For more detail, see the Maths section.

If you’ve got more than one instance of Reduction going on, they’re generally multiplicative:

DmgDealt = NormalDmg × (1 - Red1) × (1 - Red2) × (1 - Red3) × …

So if you’ve also got Arms Deal, it’ll be 1000 × (1 - 40%) × (1 - 40%) = 363.

Examples of Damage Reduction:

  • all skills that say “Reduction”, not “Resistance”. If it’s element-specific, it’s generally Resistance (e.g. One with Nature).
  • Damage Reduction shield boosters
  • Amara’s Breaker class mod

1.3 Damage Resistance

The basic principle is the same, as is the formula – if you’re using only one of these at a time. Among each other they’re additive, but in a complex way that can’t be simplified in a formula like those above.

Worse, the game is inconsistent with stating values, sometimes it’s the rounded end result but sometimes it’s the value actually put in the formula. All of this in the Maths section.

As a rule of thumb, just know that combining Resistances yields slightly worse results than combining Reductions (as usual with additive vs. multiplicative bonuses), and sometimes the actual value is slightly lower than what the card suggests. But it’s not so much that you’re going to notice it most of the time.

When combining Reductions with Resistances, think of the entire resistance part as one multiplier in the formula:

DmgDealt = NormalDmg × (1 - Red1) × (1 - Red2) × … × (1 - TotalResistance)

2. Maths

Players familiar with the BL2 system may have been surprised by the formulas above. In fact, actual calculation is like in BL2, the difference being that BL3 usually states the end result of the calculation (instead of the value that is put somewhere in the formula), which makes it less mistakable if you’re not familiar with the maths, and allows easy approximate calculation by simply multiplying them with each other like above.

For those unfamiliar with this: in BL2, “100%” Damage Reduction didn’t mean God mode: the base formula was (always? Usually? Not sure anymore):

DmgDealt = NormalDmg / (1 + DmgReduction)

Which meant:

  • 1 / (1 + 100%) = 50% >>> Damage reduced by 50%
  • 1 / (1 + 200%) = 33% >>> Damage reduced by 67%
  • 1 / (1 + 40%) = 71% >>> Damage reduced by 29%

This caused a lot of confusion because people were wondering why damage was reduced by far less than the values suggested. For this reason, BL3 doesn’t state the “100%”, “200%”, “40%” values put in the formula anymore, but the resulting “50%”, “67%”, “29%” – but the actual calculation behind the scenes is still the same.

Sadly, it’s inconsistent: Some Resistance stats are actually the formula values (not end results).

Also sadly, if you want to calculate overall Resistance, you’ll have to reverse-engineer to find out the actual values you need to put in the formula. Anyway…

2.1 Reduction

One Reduction - example: Helping Hand(s)

In traditional terms, Helping Hands is +13.2% per rank. Thus, the actual formula is:

DmgDealt = NormalDmg / (1 + 13.2% × rank)

The resulting damage modifiers at rank 1-7 then are 88.3%, 79.1%, 71.6%, 65.4%, 60.2%, 55.8%, 52.0%. This results in the skill description stating a Damage Reduction of 12%, 21%, 28%, 35%, 40%, 44%, 48%. All skills are calculated like this, only with the 13.2% replaced with whatever other value. This is why the values stated in the descriptions don’t increase proportionally with rank.

Three Reductions (Helping Hands + Arms Deal + Breaker mod)

Arms Deal uses +13.2% per rank just like Helping Hands. The Breaker (“up to 29% reduction depending on how close you are to the enemy”) is actually 1 / (1 + 40%).

DmgDealt = NormalDmg / (1 + 13.2% × rank) / (1 + 13.2% × rank) / (1 + 40%)

Note: Most people write “× 1 / (1 + whatever)” every time instead of just “/ (1 + whatever)”. I prefer it this way because “× 1” is redundant. You can add that if you want, the result is the same.

2.2 Resistance

Same principle, only if you’ve got several at once, they’re added together in the denominator:

DmgDealt = NormalDmg / (1 + Res1 + Res2 + Res3 + …)

Sadly, most of the resistance stats in the game are the end result after calculation (if you’re only using that single one) while some are confusingly actual formula values. Examples:

End result values stated on card:

  • shield: main Elemental Resistance
  • class mod: element-specific Resistance from a part (listed at the bottom of the card)
  • artifact: “Elemental Resistance” (meaning all elements but not NE) from a part
  • Zane’s Futility Belt and Amara’s One with Nature

Formula values stated on card:

  • class mod: “-18% Damage Reduction”: this is actually +18% non-elemental Resistance.
  • artifact: element-specific Resistance from a part.

2.3 Complete Formula

DmgDealt = NormalDmg / (1 + Red1) / (1 + Red2) / … / (1 + Res1 + Res2 + …)

3. Exact skill formula values and notes

3.1 Amara

  • Helping Hand(s): 1 / (1 + 13.2% × rank)
  • Arms Deal: 1 / (1 + 13.2% × rank)
  • One with Nature: 1 / (1 + 13.2% × rank) against action skill element
  • Breaker class mod: up to 1 / (1 + 40%)

3.2 FL4K

  • Hunter’s Eye: 1 / (1 + 5.6% × rank) against beasts
    • Can be increased with Big Game: 5.6% × 1.3 = 7.28%
  • Turn Tail and Run: 1 / (1 + 7% × rank)
  • Spiderant Countess: 1 / (1 + 5%)
    • For some reason it’s additive with Turn Tail: 1 / (1 + 7% × rank + 5%) with both. Hunter’s Eye remains separate.

3.3 Moze

  • Armored Infantry: 1 / (1 + 3% × rank)
  • Vladof Ingenuity: 1 / (1 + 18% × rank) against shock

3.4 Zane

  • Futility Belt: 1 / (1 + 18%) against non-elemental
  • Stiff Upper Lip: probably 1 / (1 + 6.5% × rank)
    • The 6.5% would at least explain the values stated in the description. I tried self-grenading with different elements, being shot at with different elements… this skill never did anything at all. Currently broken? Or can someone help me with this?

4. Breaker COM distance (Amara)

Threshold distance where it starts to make any difference:

Roughly 50% of its maximum reduction:

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

As always, comments and corrections are welcome.

11 Likes

That is poor wording by Gearbox. A “-18% damage reduction” is technically a penalty from the player’s perspective. 100 raw damage would be processed as 118 damage! Of course we assume the intended reduction is 18%, rather than the nonsensical -18%. (Losing -18 dollars results in an increase in money, as an analogy.) But writers have little concern for signage logic these days…

However, a hypothetically cursed item (such as those with cyan text in BL2) could indeed have a negative value for resistance or reduction.

1 Like

Great analysis, as always, Doc.

Thanks for the deep gigaton knowledge bombs yet again. Bookmarked for future use.

thank you so much for all the hard work! much appreciated .

Update: added screenshots to show Amara’s Breaker COM distance

3 Likes

Something isn’t adding up about Elemental Damage resistance to me. I did a bit of testing, and it seems that the “Adaptive” shield modifiers are described wrongly. 2x Adaptive seems to give 50% reduction, 3x Adaptive gives 70% (Instead of the stated 41%), and the Old God’s stated 25% are actually just 20%. Since the Old God can roll three modifiers, I wanted to test how that would interact with Adaptive, and modded it in. For some godforsaken reason, these buffs are additive and grant the player 90% Adaptive resistance. On top of that, Zane’s “Stiff Upper Lip” is also additive, which grants the player complete immunity. The “Lustrous” (+25% Elemental resistance) prefix on Relics is also additive on Adaptive immunity, but not to incendiary resistance on relics or COMs, and shield element resistance seems to be multiplicative of everything. So with a Triple Adaptive Old God and a Lustrous relic, one can achieve a 5 second immunity to one elemental damage. Demonstration : https://cdn.discordapp.com/attachments/697185317962383470/697185433452282026/2020-04-07_22-42-28_1.mp4

Also this should mean that with just any triple adaptive shield and a Lustrous relic, one can get a 95% damage reduction.

Edit: Upon further testing, it turns out that the Triple Adaptive Old God with the Lustrous Relic doesn’t grant immunity to the Old God’s main element, so in my example I wouldn’t be immune to radiation damage.

2 Likes

That’s some interesting stuff there, thanks for the tips. I’ll try to keep an eye out, haven’t tried an Old God because I’ve never had one (and it didn’t exist at time of writing).

About Stiff Upper Lip, at the time of my testing and writing it definitely wasn’t working, I tried a lot of things to make it do anything at all, but it was apparently broken at the time. May give that another try too.

It’s also possible that adaptive resistance has changed in the meantime, they sometimes change the mechanics of how certain stuff is calculated. Guess I’ll have to do it all over again…

2 Likes

I know this thread is old. But Moze’s Vladof Ingenuity skill isn’t included in this. Could it perhaps be similar to One with Nature and Futility Belt?

thank you so much doc.

Correct, the formula is 1 / (1 + 18% × rank), so the same as Futility Belt, only against shock. Added this to the guide.