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:
 Basics
1.1 Reduction vs. Resistance
1.2 Damage Reduction
1.3 Damage Resistance  Maths
2.1 Reduction
2.2 Resistance
2.3 Combined  Specific skill values and notes
3.1 Amara
3.2 Fl4K
3.3 Moze
3.4 Zane  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 nonelemental) – or in some cases, against all elements but not against nonelemental. 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 nonelemental.
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 elementspecific, 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 reverseengineer 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 17 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: elementspecific 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% nonelemental Resistance.
 artifact: elementspecific 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 nonelemental

Stiff Upper Lip: probably 1 / (1 + 6.5% × rank)
 The 6.5% would at least explain the values stated in the description. I tried selfgrenading 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:
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As always, comments and corrections are welcome.