Comparing No-Proc Defensive Sets

Woodenplank

On today's episode of Wooden does boring stuff with maths we're looking at Defensive Sets for the no-proc campaign. How do they compare?
I'm looking at the following 5 sets:

• Pariah
• Orgnum's Scales
• Trial by Fire
• Fortified Brass
• and Impregnable Armor

(set descriptions)

Mark of the Pariah
2 items: Adds 1206 Maximum Health
3 items: Adds 1487 Armor
4 items: Adds 1487 Armor
5 items: Increases your Physical and Spell Resistance by up to 10206 based on your missing Health.

Orgnum's Scales
2 items: Adds 129 Health Recovery
3 items: Adds 1206 Maximum Health
4 items: Adds 1206 Maximum Health
5 items: While you are under 60% Health, your Health Recovery is increased by 800 and your Physical and Spell Resistance is increased by 6400.

Trial by Fire
2 items: Adds 1206 Maximum Health
3 items: Adds 1487 Armor
4 items: Adds 4% Healing Taken
5 items: While under the effect of an Elemental Status Effect you gain 8500 Armor.

Fortified Brass
2 items: Adds 1206 Maximum Health
3 items: Adds 1487 Armor
4 items: Adds 1487 Armor
5 items: Adds 3460 Armor

Impregnable Armor
2 items: Adds 28-1206 Maximum Health
3 items: Adds 25-1096 Maximum Stamina
4 items: Adds 25-1096 Maximum Magicka
5 items: Adds 38-1650 Critical Resistance

For reference, I'm assuming the enemy has 30% Crit Chance (for Impregnable considerations)
Without further ado;



Sorry that it's a little busy, but...

Trends and Conclusions

• As expected, Pariah eventually becomes the strongest set.
• Fortified Brass already gets outscaled by Pariah at ~86% health. It's only saving grace is that it's constant and will help against surprise bursts (when you're being hit near full health).
• Orgnum's Scales only gets activated at 60% health, where Pariah already yields about 8500 Armor; much more than Orgnum's. Since Health Recovery was curbstomped (in PVP), I really don't think this set should be considered any more. Alas; another one for the Outdated-sets grave...
• Trial By Fire will, however, actually outperform Pariah as long as your HP is above ~58%. The "proc" condition is also very easy - particularly as long as ZOS doesn't fix the -3999243217 days Status effects bug. It also increases your Healing Taken on top of that, so I'd consider it a solid candidate.
• Impregnable Armor actually appears to be the worst (except for Orgnum's Scales, which only kicks in after 60% HP). But of course you can't discount the extra line of Stam. and Magicka. Note that it only reduces Critical Damage taken, so your mileage depends on how often your enemy crits. I just went with 30% here as common value

p.s.
Aetherial Ascension, Warrior-Poet, or Plague-Doctor would also be contending No-proc defense, but they have unique drawbacks or design differences that make comparing them somewhat hard.

Udrath

What about buffer of the swift?

Woodenplank

Udrath wrote: »

What about buffer of the swift?

Good call.
The combination of 2 lines of Armor and straight 10% less Player-damage taken should put it at ~14.5% less damage taken total, just below Trial by Fire.

It's unique among these defensive sets in that it's Light Armor, though. That could be a good or a bad thing.

SandandStars

What are people’s thoughts on dmg% mitigation vs actual armor resistance?

I always feel like the % mitigations seem less effective than they should be mathematically, i.e., major protection is supposed to be ~ 6000 resistance, but an actual 6000 pts of armor seems to mitigate more damage in pvp, which is why Ive abandoned sets like Buffer of the Swift.

Is it simply because armor resistance is additive while % mitigation is multiplicative?

Turtle_Bot

SandandStars wrote: »

What are people’s thoughts on dmg% mitigation vs actual armor resistance?

I always feel like the % mitigations seem less effective than they should be mathematically, i.e., major protection is supposed to be ~ 6000 resistance, but an actual 6000 pts of armor seems to mitigate more damage in pvp, which is why Ive abandoned sets like Buffer of the Swift.

Is it simply because armor resistance is additive while % mitigation is multiplicative?

It's a few things, but the main one is how percent mitigation tends to be calculated with diminishing returns to prevent 100% mitigation from being possible while not making the values seem random due to different percent's being layered differently depending on the order in which they were cast/used/proc'd.

Armor mitigation is calculated first up until its capped (max 50%). Then percentage mitigation values are factored in afterwards, but percent mitigation has been made to make it not possible to reach 100% mitigation by having the values stack diminishingly, and they start from where your armor reaches (cap is 50%).
So 10% mitigation is actually closer to 5% mitigation, 5% is closer to 2.5% (and it decreases further the closer to 100% total mitigation you reach) assuming you have no other stronger percent buffs (undeath, old mist form, block, etc).

It's why block, undeath and the old mist form mitigations are/were so strong, they provided huge base percent mitigation that gets applied before the smaller percent mitigation values from things like protection, etc so their values took your "base mitigation" of armor + those mechanics/abilities to what is/was essentially roughly 75%/65%/85% mitigation respectively (which then had the 5/10% from things like protection, buffer of swift set, added on with severely diminished values).

for example at capped resistances + old mist form, you had what amounts to a base mitigation of 85% to start off from (50% from armor + 35% which is 70% of the remaining 50%). Adding major protection (or buffer of the swift) gives you 10% of the remaining 15% for an actual value of 1.5% mitigation, taking you up to 86.5%.

It's typically done this way in most games that have damage reduction/mitigation, to give you the mitigation from the largest sources first (after applying armor) so that you get the most value out of the percent mitigation effects and the diminishing returns don't become an RNG issue depending on the order they are applied (e.g. mist form suddenly dropping from "70%" mitigation to an actual value of like 10% due to being applied last).

Buffer of the swift also suffers from being a light armor set and a set that you typically want active at all times (this means 2 light armor pieces minimum). The reduced base armor from light armor weight as well as the increased martial (stamina) damage penalty for wearing light armor adds up to all but cancel out the effects of the set, such that you end up getting more overall mitigation from wearing a blank heavy armor set or even a flat armor set like the crafted set fortified brass (because it increases armor, this brings your light armor closer to the armor cap despite being light armor).

SandandStars

Thank you @Turtle_Bot ! I very much appreciate this detailed explanation. As someone who enjoys crunching numbers and theory crafting a bit, I have been attracted to the idea of making buffer of the swift work, due to its constant uptime and the fact that unlike other good damage sets, it doesn’t have obvious drawbacks in terms of uptimes, or other penalties.

But the drawback is the way the 10% damage resistance from players is calculated, in addition to the lack of flexibility that light armor brings with it in the current PVP meta. As I have juggled various pvp build combinations, I am finding that going with five pieces of medium armor and then adding resistance from other non-armor sources can be pretty effective.

Thank you again for your insightful and helpful advice!

SmellyUnlimited

Do you think these no-proc defensive sets are viable in proc-abled Campaigns? Or were you thinking just non-proc Cyro and IC?

I would LOVE to run one of these tankier backbar sets over Rallying Cry or Wretched Vitality, but the nature of the proc sets has sort of set them a world apart from non-proc. It’s a shame too because it’s really hurt build diversity.

Woodenplank

Well Pariah is still a strong

SmellyUnlimited wrote: »

Do you think these no-proc defensive sets are viable in proc-abled Campaigns? Or were you thinking just non-proc Cyro and IC?

I would LOVE to run one of these tankier backbar sets over Rallying Cry or Wretched Vitality, but the nature of the proc sets has sort of set them a world apart from non-proc. It’s a shame too because it’s really hurt build diversity.

Well Pariah is a strong option, but again must be on all the time ideally.
But e.g. Impregnable is just worse Rallying Cry, really.

Necrotech_Master

SandandStars wrote: »

What are people’s thoughts on dmg% mitigation vs actual armor resistance?

I always feel like the % mitigations seem less effective than they should be mathematically, i.e., major protection is supposed to be ~ 6000 resistance, but an actual 6000 pts of armor seems to mitigate more damage in pvp, which is why Ive abandoned sets like Buffer of the Swift.

Is it simply because armor resistance is additive while % mitigation is multiplicative?

the main difference between % mitigation (major and minor protection, undeath, blocking) is that armor pen does not work against those as they are flat dmg mitigation

armor is a value that gives mitigation, but the armor can be negated by penetration/debuffs reducing its effective mitigation

TankHealz2015

In No-CP IC -- what sets are people wearing to solo the big world bosses?

Or is it particular defensive skills that are the key?

Woodenplank

TankHealz2015 wrote: »

In No-CP IC -- what sets are people wearing to solo the big world bosses?

Or is it particular defensive skills that are the key?

Well I think it's mostly having a balanced build; you need damage enough to kill the damn thing, healing to outlast it, recovery to, well, keep healing and damaging, and enough health to avoid one-shots.
There's no one set that magically achieves this.

A good starting point is probably Jewels of Misrule/Orzorga's Smoked Bear Haunch food(s), and a decent amount of durability through a set like Pariah or, I dunno, Ancient Dragonguard? Black Rose?
I don't do a lot of no-CP IC, can just tell that I do solo Bosses in Proc-enabled IC, with the only defensive set being Rallying Cry - which doesn't actually affect damage taken from PVE.

Woodenplank

Necrotech_Master wrote: »

SandandStars wrote: »

What are people’s thoughts on dmg% mitigation vs actual armor resistance?

I always feel like the % mitigations seem less effective than they should be mathematically, i.e., major protection is supposed to be ~ 6000 resistance, but an actual 6000 pts of armor seems to mitigate more damage in pvp, which is why Ive abandoned sets like Buffer of the Swift.

Is it simply because armor resistance is additive while % mitigation is multiplicative?

the main difference between % mitigation (major and minor protection, undeath, blocking) is that armor pen does not work against those as they are flat dmg mitigation

armor is a value that gives mitigation, but the armor can be negated by penetration/debuffs reducing its effective mitigation

Which is true, but as @Turtle_Bot pointed out, the application of multiple damage resistances also changes how they stack.
For instance, Major Protection + 40% resistance from Armor will actually leave you taking more damage than straight 50% from Armor.
(1-0.4)*(1-0.1) = 0.54 vs. (1-0.5) = 0.5
I.e. you actually take 4% more damage with the defenses split between armor and Protection buff.

Necrotech_Master

Woodenplank wrote: »

Necrotech_Master wrote: »

SandandStars wrote: »

What are people’s thoughts on dmg% mitigation vs actual armor resistance?

I always feel like the % mitigations seem less effective than they should be mathematically, i.e., major protection is supposed to be ~ 6000 resistance, but an actual 6000 pts of armor seems to mitigate more damage in pvp, which is why Ive abandoned sets like Buffer of the Swift.

Is it simply because armor resistance is additive while % mitigation is multiplicative?

the main difference between % mitigation (major and minor protection, undeath, blocking) is that armor pen does not work against those as they are flat dmg mitigation

armor is a value that gives mitigation, but the armor can be negated by penetration/debuffs reducing its effective mitigation

Which is true, but as Turtle_Bot pointed out, the application of multiple damage resistances also changes how they stack.
For instance, Major Protection + 40% resistance from Armor will actually leave you taking more damage than straight 50% from Armor.
(1-0.4)*(1-0.1) = 0.54 vs. (1-0.5) = 0.5
I.e. you actually take 4% more damage with the defenses split between armor and Protection buff.

agreed, and i know that due to the order of operations in which they are applied (along with the stuff like diminishing returns)

but if you have 33k armor, and someone has 15k pen + 9k debuff on you, they are ignoring 24k of your 33k armor, bringing your armor mitigation down from 50% to like around 15%

while flat mitigations will stay the same regardless

Woodenplank

Necrotech_Master wrote: »

but if you have 33k armor, and someone has 15k pen + 9k debuff on you, they are ignoring 24k of your 33k armor, bringing your armor mitigation down from 50% to like around 15%

while flat mitigations will stay the same regardless

Indeed. Ironically, the fewer % modifiers you have, the more valuable each one is.
Also why Ansuul's Torment is not the awesomest most strongest PVE DPS set ever. Diminishing returns strike again!

Necrotech_Master wrote: »

agreed, and i know that due to the order of operations in which they are applied (along with the stuff like diminishing returns)

Actually order of operations has no influence here as multiplication of real numbers is commutative; i.e.

(1-0.4)*(1-0.1) = 0.6*0.9 = 0.54
(1-0.1)*(1-0.4) = 0.9*0.6 = 0.54

So it doesn't strictly matter if the game applies Armor rating or Protection buff(s) first.

emsuperman24

@Woodenplank

Thanks for the write up! If you ever have the time or desire would love to see one for offensive sets. I think shattered fate should be the obvious lead but would be cool nonetheless!

SkaraMinoc

Pretty much the same as my post from 2021, except Ironblood got nerfed.

https://forums.elderscrollsonline.com/en/discussion/comment/7452535/#Comment_7452535

SkaraMinoc

Turtle_Bot wrote: »

Armor mitigation is calculated first up until its capped (max 50%). Then percentage mitigation values are factored in afterwards

The final damage will be the same whether armor is calculated first, somewhere in the middle, or last.

Source: Damage Mitigation: Explanation UPDATED 21/03/2021

SkaraMinoc

SandandStars wrote: »

Is it simply because armor resistance is additive while % mitigation is multiplicative?

Armor is additive but the sum is multiplied with other mitigation.

Example.

6600 armor is more mitigation than Major Protection's 10% damage reduction.

1000 damage * (1-(26400/660)/100) = 600 damage (26400 armor = 40% mitigation)
1000 damage * (1-(33000/660)/100) = 500 damage (6600 armor = 10% mitigation)
1000 damage * (1-(26400/660)/100) * (1-(10/100)) = 540 damage (Major Protection = 6% mitigation)

You can rearrange the multiplication and say that Major Protection gives the full 10% mitigation and 26400 armor now only gives 36% mitigation instead of 40%. But this gets confusing so we stick to 660 armor = 1% mitigation and apply diminishing returns to other types.