Armor Theory-crafting - Armor y u no protect me?

Digging up my old solution for effective health vs x hits way back when:

First, an explanation of the derivation
Second, one-hit effective health. If you view it in this context, you'll come away believing armour is subject to diminishing returns.

Gosh, I'm trying to find it. That second EH formula is identical to yours, except I've made a substitution k=A/D to make it simpler. Also number of hits=1. I recall coming up with exactly the same coefficients you have, except the context I chose was a single hit that kills you from full health.

Here's the point I'm trying to drive at. This point of view - effective health versus x hits that will kill you - isn't too terribly useful. It assumes that mob damage scales with character progression in some kind of meaningful way. Really, that's not the case at all. When you enter a map, you're subject to the particular damage patterns in that map, which stay pretty consistent until you go into a different map. You can treat damage as a situational constant, rather than some fraction of your total health, and you'll get a very different picture.

Basically, your equation may lead you to a view that armour is a diminishing returns system. But, really, you're facing mobs that will hit you consistently for some flat damage inside a narrow range, and you want to know what happens when armour varies. If you change this little thing, you'll see increasing gains on armour. Funny how that works.

I've been through all these thought experiments for some months, so listen and think carefully about this. If you make that same substitution (k = A/D) and treat mob damage as constant, two very interesting things happen:
- Out comes a linear relationship between armour and unmitigated damage, at any fixed reduction value. Very useful for understanding.
- Also, you get a completely different characteristic for effective health, that shows hyperbolic increasing gains against armour rating. The gains become more pronounced, and reduction becomes cheaper, as you gain endurance charges.

^^ It's the most useful way to look at the physical reduction mechanic that I've come up with. And I've spent a pretty long time toying with the various formulas.

Again, here's the link to my last writeup: reduction and A/D ratio. This is very useful because you can find out exactly how much armour rating you need to reach a desired reduction against any chosen hit size. And the reduction contours are straight lines.

There are a few ways I could change that presentation to be a little more universal, but it'll do for now.

Nice theorycrafting there! very usefull info. Like some others sugested, a thread like this deserves a matching title. Thanks for the work done there bro.

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Moroni wrote:

*looks at title*

Me: oh this looks like a fun lighthearted topic!

*opens thread*

MAAAAAAAATH

Me: dead


X_X

+1 LOL

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Zakaluka wrote:

Here's the point I'm trying to drive at. This point of view - effective health versus x hits that will kill you - isn't too terribly useful. It assumes that mob damage scales with character progression in some kind of meaningful way. Really, that's not the case at all. When you enter a map, you're subject to the particular damage patterns in that map, which stay pretty consistent until you go into a different map. You can treat damage as a situational constant, rather than some fraction of your total health, and you'll get a very different picture.

This isn't the proper perspective at all.

I understand that maps are different, and the damage situation is going to be different. However, when we're focusing on maximum life/damage mitigation/EHP components of a character, mob damage does scale with character progression. The road might be bumpy, with easy areas at some levels and very hard times at others, gear stays static for levels then suddenly jumps when an upgrade is found, etc. However, the gold standard for a measure of tankiness is how much damage you can take. It's the standard for a good reason; it shows how much your character has progressed in the tankiness department. So saying that mob damage doesn't scale with character progression is nonsense; the point you're trying to make is something different entirely.

Regarding the whole "linear argument":
* if you hold damage constant with armour as a variable, armour increases EHP linearly.
* if you hold armour constant with damage as a variable, damage decreases EHP non-linearly, hyperbolically... but specifically a modified form of y=1/sqrt(x).

In reality, players increase both variables at the same time. Let's say the damage a player attemps to tank is a linear function of his armour — d=ka. You get
a*1/sqrt(ka)=1/sqrt(k)*a/sqrt(a)=1/sqrt(a)*1/sqrt(k)
Which is a hyperbolic function — the same one for increasing damage — times a constant. This means players need to be increasing their life at a pace that exceeds linear in order to average things out back to linear... this is possible, but relies on constantly picking up life passives. Hence the general complaints.

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ScrotieMcB wrote:

* if you hold damage constant with armour as a variable, armour increases EHP linearly.

Hyperbolically, because you will have endurance charges.

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* if you hold armour constant with damage as a variable, damage decreases EHP non-linearly, hyperbolically... but specifically a modified form of y=1/sqrt(x).

This one I'm not sure about, because I never developed a formula for it. I personally don't think this effect matters as much, and treat D as constant. You don't really have any control over mob damage, so trending it seems excessive to me.

The distinction I'm making is treating EH conceptually as "the size of a single hit which will kill me" vs "how much total damage I can withstand if every hit in the near future is the same constant size"

One-hit EH, or three-hit EH, or 5-hit EH, aren't useful concepts - unless mob difficulty always scales upwards linearly (it's more like, fairly constant during short sessions, then changes to a new random value which could be higher or lower). Now, if you assume all hits you will take in the next few minutes are about the same size, you can treat D as a constant - and the EH curve you get out of this approach makes far more sense. This will show effective health increasing hyperbolically as armour rating increases, because of the way endurance charges interact with armour rating. Linear only with zero endurance, but that's a bad way to look at it (because it'd be a bad build with armour and no endurance). The N-hit method will show you EH that trends like a fractional root, I.E., severe diminishing returns on armour rating.

Now, look - I developed that linearization months ago, and I've forgotten some of the details in the derivation because I've been spending a lot more time on evasion than armour lately. You guys are on step 4 of 10 right now, and landing in the same pitfall I did back then. Take my input or argue with me, I don't have the energy for the argument and my memory is straining trying to conjure the details again. I'm trying to save you some time. Think about this A/D concept, it's a great way to simplify the whole thing.

While I agree mostly with what has been said by Zakaluka, I also fail to see why you would have mob damage, which basically is an unknown and highly variable between mobs (even in the same map, just as an example, some mobs do 0 physical damage, blues hit harder than whites, etc...).

I think, the best metric for damage mitigation is one that allows me as a player to weigh the benefits of a piece of gear and be able to choose which one is more suited for what task. If for instance, all mobs only deal elemental damage, I have no use for Armor, and would instead prefer to use Energy shield / resist gear instead. The point I am trying to make here is, measuring how much "raw physical damage" I can sustain with my gear is for my purposes a good metric to evaluate both my HP and armor progression.

The One Hit EH is imho the most useful, in fact assuming hard hitting mobs are also slow hitting mobs (which in my experience, is almost always the case) surviving that hard hit usually gives ample time to run away or use a health pot or a flask or pop a portal and never come back to that zone until a good gear upgrade. And this is where it is really useful. Knowing that I barely survived that hit and having my armor and health readily available allows me to make calculations of what I need in order to come back stronger.


Following your suggestions, I have remade the calculations using enduring charges, and I obtain a similar, albeit substantially simpler, equation than ScrotieMcB. The gains in terms of Endurance charges are quite substantial and quite frankly overpowered :-). If I am not mistaken, there is a maximum of 7 endurance charges to be had in the game, 3 base, 3 from passive and 1 from a quest.

Redrawing the picture of AHP vs. DHP for 0 up to 7 endurance charges shows that the requirements in terms of armor in order to survive a given hit with endurance charges is, as expected smaller, however, what I did not expect is the magnitude of the gain which is substantial. Not only does endurance lower the requirement on armor, it also lower the slope of the AHP vs. DHP, meaning that Armor will be more effective with endurance charges and the more endurance charges, the better.

Here is an updated pic of the effect of endurance charges on the live-die curve.

All this seems obvious, but it is always good to quantify the obvious than just qualify it :-).

One thing that Zakaluka comment made me think about is the scaling of mob damage dependent on levels. I wonder if there is any data that someone knows about? One could level up a character and check regularly at every level the tooltip's "estimated DR" and "Armor" and try to derive some meaningful "estimated damage". Did anyone try that ?

PS: ScrotieMcB I could not edit your spreadsheet...is it read only?

It would be nice for us non-math dudes to understand what is being said here.
So what you say here is that %hp is better than % armor at all times?
Or what ratio of % armour and % hp nodes/mods is best?

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RenoR wrote:

If you complain about armor beeing weak vs heavy blows its basically the same to rage about resist which does not reduce physical damage(which is absurd).

I think you misunderstood the purpose of the discussion here. I am not complaining bout armor, I am trying to understand how to best use armor and how that can prevent my death.

Armor >>PURPOSE<< is to reduce lower and medium hits and this is done perfectly.

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RenoR wrote:

As far as I am aware monsters hit for ~600 damage in merciless(a portion of it is elemental) and if you have 3000 Armor you have a reduction of 29%. Thats not bad actually and 600 physical damage is quite a lot!

I am not sure from where you get your numbers, could you point out to your source? Besides, I don't believe in the simplification that across all merciless, which spans from lvl 52 to 100 (48 levels) the damage is always ~600.

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RenoR wrote:

I am playing a summoner with only life and ES and a lv 63 monster hits me for ~500 damage. If I consider the elemtal part of it armor is definitly useful to absorb high amounts of armor, even in lategame. (i have negative resist btw)

I am only discussing physical damage as I pointed out at the start of the original post. If you are running around in merciless with negative resists, then you are dying a lot (are you playing in default league?).

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RenoR wrote:

In my opinion its the wrong approch to value armor by going so far and calculating the extreme.
A critting brutus is not the usual case...

As a matter of fact, most deaths in HC that I know of are due to physical damage (I am talking real deaths, a lot of people died to disconnects :P). Anticipating and eventually preventing a critting Mob is exactly the purpose here, i.e. How can Armor help prevent being one shot.

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RenoR wrote:

If you face hard hitting enemies an evasion build works better and thats perfectly balanced.
Evasion is worse vs small/medium hits while its better vs hard hits.

I tend to disagree, Evasion and Armor cannot simply be interchanged. Evasion is checked first whether you are hit or not. Armor is checked after block, and mitigates the damage. These are two different things. Evasion works well when the RNG is on your side, when you get hit (and you will be hit at some point or another) pray that you have some armor that will mitigate that damage because otherwise you will take full damage.

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RenoR wrote:

If you want better protection vs heavy hits you should really consider going hybrid armor or use a curse like enfeeble.

This again is outside the scope of the topic being discussed, but I agree, this is what most people do, i.e. it is not sufficient to rely only on armor for protection, use of curses (there is not only enfeeble, temporal chains also works very well for fast hitting mobs), energy shield (but this part is more like HP and works equivalently for all damage types except chaos), a decoy totem, endurance charges etc....

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RenoR wrote:

Or maybe even a shield?? I see only people complain but in town there are VERY FEW shielduser!

I agree, this is the 2nd step of how damage is calculated. Again outside the topic of armor :-).

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RenoR wrote:

I see people saying that you cant tank in Path of exile but thats not true. The key aspect is to stack different forms of defensive concepts.

if you go only for armor and Health its OBVIOUS that it will have its weaknesses(while it also has strenghts)

I don't believe anyone here is claiming that, again, the only discussion being conducted here is about armor and damage mitigation.

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RenoR wrote:

I dont want to say that playing melee is piece of cake because its probably in disadvantages by now, but its mathematically definitly possible to tank the shit out of the game! ;)

Really, try STR/INT shield + high block + enfeeble and I am pretty sure you will be surprised how tanky you can become(with 80% All resist of course)
Even with low life.

Thank you for the advice ;-).

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Unacceptable wrote:

It would be nice for us non-math dudes to understand what is being said here.
So what you say here is that %hp is better than % armor at all times?
Or what ratio of % armour and % hp nodes/mods is best?

Strictly speaking, you don't have much of a choice since this is all dependent on your build. Some starting points on the tree do have easier access to HP/Armor/Evasion than others.

In terms of survivability, HP has always more bang for the buck. While armor builds on top of HP to give you excellent protection for small/average hits. The higher is your armor, the better it is. Combined with endurance charges, armor becomes even more of a beast and help shrug off quite a lot of damage with high endurance charges.

In my build, I totally ignored Armor nodes and grabbed all the HP nodes I could lay my hands on. Again survivabiliy in PoE is dependent as RenoR was correctly stating on many other things, this post was only in relation to armor, the use of a shield, curses, energy shield all help.