Armor and DR formulas

[Martin]

DR valuses decrease the further up you go but only if you add armor to the equation

INITIAL MATH

With 10 armor you have 4.8% DR, with 20 armor it should be 9.6% but its 9.1%; with 30 armor its 13%. So by equipping a piece that provides 10 armor and trying to calculate the amount of DR you would have with 100 armor you would come to a conclusion of 48% DR which is wrong since 100 armor provides 33.3% DR.

Adding Barkskin trait for additional 10% pure DR should amount to 43.3% total DR, assuming you have 100 armor, however that's wrong because the total DR with barkskin and 100 armor is 40%.

The problem becomes more pronounced the higher your armor value is. With 439.3 Armor (68.7% Armor DR), with Barkskin's 10% pure DR we end up with 71.8% total DR.

BIG ISSUES

A big issue arises with Fortify trait which at 232 base armor (53.7% DR) increases our armor to proper amount, that is 348 but provides us with total DR of 63.5% which is 9,8%. Literally five times lower than stated in the description.

Another big issue comes with Twisted Idol which increases your armor effectiveness by 30%. With 348 armor (63.5% DR), equipping Twisted Idol increases our armor only to 67.6% DR which is hardly worth an amulet slot. Adding Barkskin on top of that gives us only 3.2% total DR increase as opposed to 10% stated in the description.

I have also done some tests with Blood Bond traid which doesn't seem to work at all so don't waste your points into that trait.
I haven't tested Shadeskin since elemental damage is hard to come by and even harder to differentiate but I doubt it works as it should honestly.

CONCLUSION

Once you unequip your armor, the issue is completely gone and DR works and stacks perfectly.
80% cap for Armor DR literally cannot be reached. Even before the latest patch, maximum DR you could get with Armor was 78.xx%~, while now it's 71.3% (with 496.1 armor),

As opposed to what some might say, that doesn't render armor stacking useless since it opens your ring and trait slots for other things but it makes build-making and min-maxing very confusing and unplesant and not fun due to dubious math behind it all.

[SilverLight]

This is an entirely normal way for armor and DR to scale in RPGs. I've lost count of the games I've played where your armor DR scaling depends on how much armor you already have. Remnant's Armor scaling goes such that every 200 armor is the next fraction for damage taken (200 armor is 1/2 or 50% DR, 400 armor is 1/3 or 66.6% DR, 600 is 1/4 or 75% DR, and 800 is 1/5 or 80% DR). This is not the first time I've seen this scaling system, and it's a simple way to make players choose whether they really want that extra damage reduction or not.

As for the other DR values, they're multiplicative. This is again extremely common in RPGs because they don't tend to let players reach 100% DR. In your given example of 100 Armor and Barkskin, the Armor is providing 1/3 (33.3%) DR. Barkskin is 10% DR from the remaining damage taken, not just an additive DR booster, which is why it's giving ~6.7% DR, pushing to 40% instead of 43.3%. ~6.7% is about 10% of the 66.7% damage being taken (66.7*0.1=6.67, rounds up to 6.7 in the system). It's still giving you 10% DR, just 10% from the leftover non-resisted damage. Which, again, really common to avoid allowing players to hit 100% DR.

[Martin]

Originally posted by SilverLight:

This is an entirely normal way for armor and DR to scale in RPGs. I've lost count of the games I've played where your armor DR scaling depends on how much armor you already have. Remnant's Armor scaling goes such that every 200 armor is the next fraction for damage taken (200 armor is 1/2 or 50% DR, 400 armor is 1/3 or 66.6% DR, 600 is 1/4 or 75% DR, and 800 is 1/5 or 80% DR). This is not the first time I've seen this scaling system, and it's a simple way to make players choose whether they really want that extra damage reduction or not.

As for the other DR values, they're multiplicative. This is again extremely common in RPGs because they don't tend to let players reach 100% DR. In your given example of 100 Armor and Barkskin, the Armor is providing 1/3 (33.3%) DR. Barkskin is 10% DR from the remaining damage taken, not just an additive DR booster, which is why it's giving ~6.7% DR, pushing to 40% instead of 43.3%. ~6.7% is about 10% of the 66.7% damage being taken (66.7*0.1=6.67, rounds up to 6.7 in the system). It's still giving you 10% DR, just 10% from the leftover non-resisted damage. Which, again, really common to avoid allowing players to hit 100% DR.

Thanks for clarifying how exactly it works. Our interpertations of RPG are very different tho, since I mostly play crpgs like Pathfinders and DnDs and other popular rpgs (diablo, dark souls, wow, poe) often take into consideration character/enemy/zone level, max health and slots equipped and don't work off of same formula. Many other rpgs also have clearly defined classes and armor already set up for them, so each class is supposed to hit the different cap or breakpoint.

While the system you described might be common and work in some games, it doesn't mean it is good or plesant to work with in Remnant. In previous game armors had a completely different use, trait points were unlimited so you weren't wasting them, had no spells, mutators, bulwark, runes or customizable relics and DR was a very rare stat and it was displayed only as "Melee Damage Reduction x%" and "Ranged Damage Reduction x%", the was no "Armor DR" even displayed which doesn't mean it didn't work the same way tho, but I don't feel like going back and testing it.

Implementing that formula together with caps makes little to no sense, especially when you consider that players were (not sure if still are) able to reach 100% DR anyway and it becomes a big problem when items/traits state they provide "Armor effectiveness" when in fact, they are making your armor less effective. They are providing percentage increase to armor while they are stating that the same amount of armor should provide more DR.

There is no point in going for the caps or trying to make yourself as tankier as possible. The best way to utilize armor is to equip enough so you can survive 1, 2 or 3 hits, from a certain enemy of course and completely changing your armor and doing calculations for every zone and monster would be extremely tedious, especially when you consider the of displayed values for damage taken or for current health. So the actual best way to utilize armor is to wear Leto's mk2 with Bright Steel Ring and Fortify trait, which completely goes against their ideology that they "want to see more people in different armors". 90% of people I have played with on Apocalypse are wearing Leto's mk2 set. In turn, it renders pure DR items and spells essentially useless. Why would you take 2-5% total DR in a slot when you can take 10-20% dmg increase, or why would you take 30 armor from elixir which ends up being 1-3% DR when you can take flat 25 hp which is quarter of base hp. It all becomes especially silly when you realize that the difference between a tanky character and a dps is some 10% of survivability and 50% damage.

Devs clearly care about armor and how it works but if they want a good system they will have to change their formula or be stuck with Leto's.

[Malidictus]

This is precisely how armour worked in Remanat: From the Ashes. It's also a good way to handle damage resistance. Let me explain - and prep for a long one.

The stat to consider here is Effective Health, or EHP. This is a measure of how much damage you can take before it equals your HP, accounting for resistance. The percentage of damage you take is 1 - resistance (so full damage minus the damage you resist). So to die, you would need to take:

damage*(1 - resistance) = HP

Solving for damage gives you:

damage = HP / (1 - resistance)

The "damage" value above is your EHP. As you can see, this is a rational function. As such, it approaches infinity the closer resistance gets to 1 (or 100%). The amount of effective health you get for every percentage point of damage resistance increases the more resistance you already have. Here are a couple of examples.

Let's say you have 100 health and 0% resistance, but then add 5% resistance on top. You go from 100 EHP to 100 / (1 - 0.05) ~ 109.89. That's an increase of just shy under 10 HP, or shy under 10%. Now let's say you were already sitting on 90% damage resistance and you added 5% more. You'd start with an EHP of 100 / (1 - 0.9) = 1000 and increase to 100 / (1 - 0.95) = 2000. That's an increase of 1000 EHP, or a full double. The same 5% damage resistance has a drastically different impact depending on how much resistance you have.

What this means is that damage resistance is almost meaningless in low amounts, but stupidly overpowered in high amounts. That's nearly impossible to balance. Even items with very small numbers can be massively powerful when stacked, while even items with very high numbers can be of little use. The easiest solution here is to take this rational function and turn it linear. That's what armour does.

In Remnant 2, damage resistance is a function of armour calculated as such:

resistance = armour / (armour + 200)

Obviously, this is also a rational function. However, something magical happens when you put a rational function in the delimiter of another rational function. Please forgive the following math, but it's important to list the full derivation. Let's examine what happens when we model EHP as a function of armour, rather than resistance:

EHP = HP / (1 - resistance) = HP / (1 - armour / (armour + 200)) = HP / ((armour + 200 - armour) / (armour + 200)) = HP / (200 / (armour + 200) = (HP * (armour + 200)) / 200 = HP + armour / 200

or

EHP = HP + HP*(armour/200)

In other words, every point of armour grants you an additional 1/200th of your HP pool as additional EHP. The exact percentage of damage resistance doesn't matter. Armour isn't "less effective" the higher you go. Yes, you get less damage resistance per point of armour, but every point of damage resistance is worth more the higher you go. Mathematically, it balances out.

Armour is effective health. It really is that simple. The formula used in this game is good and quite clever. There's a reason it's widely-used across multiple unrelated games. If anything, giving players direct access to damage resistance is the bad way to go.

[Velmoria]

https://www.reddit.com/r/remnantgame/comments/15kr8ei/damage_reduction_update/

[Armor DR] = [Total Armor] ÷ ([Total Armor] + 200)

10 Armor -> 10/210 = 0.0476 = 4.76%
20 Armor -> 20/220 = 0.0909 = 9.09%
100 Armor -> 100/300 = 0.3333 = 33.33%

DR from Bulwark buff, Barkskin and accessories are multiplicative when stack with Armor DR.
So if you already have 60% Armor DR, with lv10 Barkskin, Total DR become 64%. Extra 4% from 1/10 of 40% damage received.

[Malidictus]

Originally posted by Velmoria:

DR from Bulwark buff, Barkskin and accessories are multiplicative when stack with Armor DR.
So if you already have 60% Armor DR, with lv10 Barkskin, Total DR become 64%. Extra 4% from 1/10 of 40% damage received.

That's actually something I wanted to ask. People have claimed that damage resistance values separate from armour are multiplicative with it. Does that cover ALL sources of damage resistance, including Bulwark? Are those sources additive with each other, or are there separate categories in there, as well?

[Velmoria]

Originally posted by Malidictus:

Originally posted by Velmoria:

DR from Bulwark buff, Barkskin and accessories are multiplicative when stack with Armor DR.
So if you already have 60% Armor DR, with lv10 Barkskin, Total DR become 64%. Extra 4% from 1/10 of 40% damage received.

That's actually something I wanted to ask. People have claimed that damage resistance values separate from armour are multiplicative with it. Does that cover ALL sources of damage resistance, including Bulwark? Are those sources additive with each other, or are there separate categories in there, as well?

Restriction Cord = 15% DR
Bulwark 2x stacks = 13%
Hardened Coil = 15%
Amber Moonstone = 25%
Total DR is 68%, they stack additively.
Total Armor DR with LetoMk1 Armor total 368.1 (Fortify + Twisted Idol + buff from update) is 64.79% in calculator or 64.8% in stats.
Total DR is 88.7% in stats.

Well even if reaching 80% Total DR, I prefer not staying at half of my health.

[Malidictus]

Originally posted by Velmoria:

Restriction Cord = 15% DR
Bulwark 2x stacks = 13%
Hardened Coil = 15%
Amber Moonstone = 25%
Total DR is 68%, they stack additively.
Total Armor DR with LetoMk1 Armor total 368.1 (Fortify + Twisted Idol + buff from update) is 64.79% in calculator or 64.8% in stats.
Total DR is 88.7% in stats.

Well even if reaching 80% Total DR, I prefer not staying at half of my health.

OK, so what I'm getting from this is... All sources of damage resistance, including Bulwark but excluding armour, are additive with each other. This result is then multiplicative with armour. That's what your computation seems to suggest. That is:

(1 - 0.68)*(1 - 0.647) = 0.11296 damage taken

1 - 0.11296 = 0.88704, or ~88.7% damage resistance.

OK, well - now I know how that works :) I'm unlikely to get quite THAT much resistance since it involves some situational things that I don't like (such as limiting me to 50% health). Actually, let's talk about that

---

I don't recall what base health is in Remnant off the top of my head, but let's assume 100. The exact number doesn't matter, as long as it's the same across all tests. Let's assume the same build you've listed above, just without the Restriction Cord. That's 13% + 15% +25% for a total of 53% DR from items, 64.79% DR from armour, for a total of ~83.45% DR. That gives us an EHP of 100 / (1 - 0.834513) ~ 604.28.

K, cool. So suppose we add that extra 15% DR from the Restriction Cord. We're back to the ~88.73% DR from your example above, but we're down to 50 health. This gives us an EHP of 50 / (1 - 0.887328) ~ 443.77. Oh dear. That looks bad. Even without the decimals, we've lost something like 150 EHP.

Which, incidentally, is pretty much what I thought immediately upon seeing that ring. How in the world is that supposed to be a good tradeoff? Health is a significant contributor to EHP. Sure, so is resistance, but you'd have to go into the 80%+ resistance from just items for that to matter. Because item resistance is multiplicative with armour resistance, the impact of both is greatly diluted. 15% damage resistance isn't even remotely worth losing half your health over. And that discrepancy is only going to get worse the higher your health is.

What even is this ring?

[Darkest Mind]

Yeah pre patch my setup had 80% Total DR and now with the same setup:
DR 15%
Armor DR 61.9%
Total DR 67.6%

so fun more tanky playstyle keeps getting punished.

[Ottomic]

Originally posted by Darkest Mind:

Yeah pre patch my setup had 80% Total DR and now with the same setup:
DR 15%
Armor DR 61.9%
Total DR 67.6%

That's because the developers fixed how DR was calculated in the statistics. It's functionally the same DR pre-patch, but before it was incorrectly displayed at 80% when you actually had about 65% instead.

If anything, they have buffed the DR slightly across the board.

From the patch notes:

• Fixed the Damage Reduction calculation in Advanced Stats. While this was a bug, we still wanted to make sure it was at the top of the list because it was giving players incorrect info.

[Schalimah]

Originally posted by Malidictus:

Originally posted by Velmoria:

Restriction Cord = 15% DR
Bulwark 2x stacks = 13%
Hardened Coil = 15%
Amber Moonstone = 25%
Total DR is 68%, they stack additively.
Total Armor DR with LetoMk1 Armor total 368.1 (Fortify + Twisted Idol + buff from update) is 64.79% in calculator or 64.8% in stats.
Total DR is 88.7% in stats.

Well even if reaching 80% Total DR, I prefer not staying at half of my health.

OK, so what I'm getting from this is... All sources of damage resistance, including Bulwark but excluding armour, are additive with each other. This result is then multiplicative with armour. That's what your computation seems to suggest. That is:

(1 - 0.68)*(1 - 0.647) = 0.11296 damage taken

1 - 0.11296 = 0.88704, or ~88.7% damage resistance.

OK, well - now I know how that works :) I'm unlikely to get quite THAT much resistance since it involves some situational things that I don't like (such as limiting me to 50% health). Actually, let's talk about that

---

I don't recall what base health is in Remnant off the top of my head, but let's assume 100. The exact number doesn't matter, as long as it's the same across all tests. Let's assume the same build you've listed above, just without the Restriction Cord. That's 13% + 15% +25% for a total of 53% DR from items, 64.79% DR from armour, for a total of ~83.45% DR. That gives us an EHP of 100 / (1 - 0.834513) ~ 604.28.

K, cool. So suppose we add that extra 15% DR from the Restriction Cord. We're back to the ~88.73% DR from your example above, but we're down to 50 health. This gives us an EHP of 50 / (1 - 0.887328) ~ 443.77. Oh dear. That looks bad. Even without the decimals, we've lost something like 150 EHP.

Which, incidentally, is pretty much what I thought immediately upon seeing that ring. How in the world is that supposed to be a good tradeoff? Health is a significant contributor to EHP. Sure, so is resistance, but you'd have to go into the 80%+ resistance from just items for that to matter. Because item resistance is multiplicative with armour resistance, the impact of both is greatly diluted. 15% damage resistance isn't even remotely worth losing half your health over. And that discrepancy is only going to get worse the higher your health is.

What even is this ring?

If you now add into the mix that total DR caps at 80% anyway...
You actually can get over 100% DR from non-armor sources and prior to the first patch you actually became immune to damage, stagger and status effects.

10% DR amulet (Indignant Fetish/Effigy Pendant)
10% DR Restriction cord
15% DR Hardening coil
11% DR Rusted Heirloom (13% since last patch)
25% DR Amber moonstone
10% DR Barkskin trait
5% DR Mythic damage reduction rune fragment
15% DR Magnetic coil perk (engineer turret)

[Malidictus]

Originally posted by Schalimah:

If you now add into the mix that total DR caps at 80% anyway...
prior to the first patch you could actually get 101% DR from non-armor sources and you actually became immune to damage, stagger and status effects.

Honestly, 80% damage resistance cap after all calculations is a pretty sane point. That's still a lot, but not so high that increasing returns become insane. Better than what Warframe's done, with easy access to 3000 armour (so ~90% damage resistance) on top of Adaptation which can provide up to 90% multiplicative damage resistance to specific elements, on top of multiplicative damage resistance abilities in the 25-50% range, on top of a passive healing proc that can heal for 5% health over 5 seconds effectively constantly. Inaors and Grendel basically can't die :)

Anyway, thanks for the heads-up. I wasn't aware of the armour cap.

[Martin]

Originally posted by Malidictus:

This is precisely how armour worked in Remanat: From the Ashes. It's also a good way to handle damage resistance. Let me explain - and prep for a long one.

The stat to consider here is Effective Health, or EHP. This is a measure of how much damage you can take before it equals your HP, accounting for resistance. The percentage of damage you take is 1 - resistance (so full damage minus the damage you resist). So to die, you would need to take:

damage*(1 - resistance) = HP

Solving for damage gives you:

damage = HP / (1 - resistance)

The "damage" value above is your EHP. As you can see, this is a rational function. As such, it approaches infinity the closer resistance gets to 1 (or 100%). The amount of effective health you get for every percentage point of damage resistance increases the more resistance you already have. Here are a couple of examples.

Let's say you have 100 health and 0% resistance, but then add 5% resistance on top. You go from 100 EHP to 100 / (1 - 0.05) ~ 109.89. That's an increase of just shy under 10 HP, or shy under 10%. Now let's say you were already sitting on 90% damage resistance and you added 5% more. You'd start with an EHP of 100 / (1 - 0.9) = 1000 and increase to 100 / (1 - 0.95) = 2000. That's an increase of 1000 EHP, or a full double. The same 5% damage resistance has a drastically different impact depending on how much resistance you have.

What this means is that damage resistance is almost meaningless in low amounts, but stupidly overpowered in high amounts. That's nearly impossible to balance. Even items with very small numbers can be massively powerful when stacked, while even items with very high numbers can be of little use. The easiest solution here is to take this rational function and turn it linear. That's what armour does.

In Remnant 2, damage resistance is a function of armour calculated as such:

resistance = armour / (armour + 200)

Obviously, this is also a rational function. However, something magical happens when you put a rational function in the delimiter of another rational function. Please forgive the following math, but it's important to list the full derivation. Let's examine what happens when we model EHP as a function of armour, rather than resistance:

EHP = HP / (1 - resistance) = HP / (1 - armour / (armour + 200)) = HP / ((armour + 200 - armour) / (armour + 200)) = HP / (200 / (armour + 200) = (HP * (armour + 200)) / 200 = HP + armour / 200

or

EHP = HP + HP*(armour/200)

In other words, every point of armour grants you an additional 1/200th of your HP pool as additional EHP. The exact percentage of damage resistance doesn't matter. Armour isn't "less effective" the higher you go. Yes, you get less damage resistance per point of armour, but every point of damage resistance is worth more the higher you go. Mathematically, it balances out.

Armour is effective health. It really is that simple. The formula used in this game is good and quite clever. There's a reason it's widely-used across multiple unrelated games. If anything, giving players direct access to damage resistance is the bad way to go.

When I said that armor worked differently in the first game I meant that armor sets were used for their bonuses, not for armor values they provide.
The DR cap is the reason I don't really understand the armor formula that SilverLight explained, ince caps are explicitly stated when you hover with your mouse over total DR "Total Amount of Damage Reduction from all sources up to 80%".

The problem now is that if they buff things that give DR, there is a huge chance that they might make armor obselete, just as armor is making DR obselete right now, and going above 60%-70% requeres very specific setups that require you to remove your armor essentially reduce your EHP which is contradictory to the idea.

Now if armor pieces were giving other stats aside from armor and if armors were stronger, it would probably make sense to use sets other than Leto's and then maybe go for some pure DR with rings/amulets/spells/traits/relics/runes. Since we get painfully diminishing returns, there is no point to sacrifice more than one ring slot (that is for the Bright Steel Ring). And if we want to try and hit those caps, we have to remove all our armor and sacrifice all our ring and amulet slots and our max hp which is completely nonsensical.

In the reddit post that Velmoira has posted they are stating that everything is now working as intended, so they intended for everyone to walk around either in Leto's or naked? Since DR and armor just don't go well together. But honestly, I don't think that DR has any place in any build, and as stated previously buffing DR items will probably cause more balance issues and more immortality instances.

If they continue using this formula, they are going to have a nightmare balancing the game and we will be stuck with a bloated inventory full of useless rings and amulets.

[Malidictus]

Originally posted by Martin:

Now if armor pieces were giving other stats aside from armor and if armors were stronger, it would probably make sense to use sets other than Leto's and then maybe go for some pure DR with rings/amulets/spells/traits/relics/runes. Since we get painfully diminishing returns, there is no point to sacrifice more than one ring slot (that is for the Bright Steel Ring). And if we want to try and hit those caps, we have to remove all our armor and sacrifice all our ring and amulet slots and our max hp which is completely nonsensical.

This is true. I don't quite understand why the developers decided to strip effectively all complexity out of armour items. No set bonuses means that all armour sets are functionally interchangeable, but for their weight and armour value. Realistically, this leaves you with either Leto's armour for Medium/Heavy or "a random light armour" for light. I understand not wanting to tie people into specific looks, but this could have been done with cosmetic customisation.

And even then - weight, dodge iframes and stamina costs are honestly the least compelling, most boring way to balance armour sets. Imagine if all guns we got were LMGs, but they differed slightly in damage, rate of fire and magazine size. That's what armour is in this game right now.