This post has been (re)moved, as its usefulness as a whole thread on these boards simply came to an end. If you are interested in reading the entire post, it can be found at www.dtguilds.com located in our Warrior Class forums. The gist/significant segment of the post is as follows:

In all matters of correctly assessing the situation: The amount of physical damage reduced by Armor and the amount of HPS necessary to keep a Tank alive in relation to this amount is, and has always been, directly proportional to the amount of Damage Reduction from Armor you have, and not Relative Damage Reduction.

In addition: Armor does not suffer from "basically negligible" diminishing returns, it suffers from serious and profound diminishing returns as a function of reducing incoming physical damage.

However: Armor more or less does not suffer dimishing returns in its ability to increase your survival time without heals, which is the only accurate case in which Armor functions relatively.

So, you're absolutely correct, insofar as your answers extend; however, I'm forced to ask whether you're asking the right questions.

I would argue that the question you're fundamentally trying to answer is how the value of the armor changes relative to the value of other stats as one's gear improves. Thus, the answer is not, in absolute terms, how does armor scale - but, rather, how it scales relative to other stats. So lets take a look at this question for a moment.

There's two fundamental ways in which to measure the value of mitigation stats, namely: how do they affect my ability to withstand worst-case burst damage scenarios, and how do they affect the overall amount of damage I take. Lets look at these one at a time.

First, surviving burst damage. The case under consideration here is: the boss, due to a parry or crushing blow or other fluke of damage, generates some huge spike of damage, which I utterly fail to dodge; hence, the relevant measure is how much damage I can absorb without healing assuming I totally fail to dodge everything. So if there's some incoming about of damage D, and I have H health and M mitigation, I want to make H as large as possible relative to D*M; in other words, I want to maximize the value H/M; the relevant measure for doing so is to figure out how much H I need to equal a given quantity of M.

So if M is, say, 1 - that is, I take full damage from every attack - and I increase M by 1% so I now take M/.99 damage, or 1.01% more damage to kill. In order to become 1.01% harder to kill via stamina alone, I'd need to have 1.01% more health. Hence, 1% mitigation, at this level, is worth however much stamina is required to gain 1.01% of my current HP.

Meanwhile, if M is, say, .5 - so I take half damage from everything - and I increase M by 1%, I now take M/.49 damage instead of M/.5; Hence, the increase in health needed to match is .5/.49 = 2.04%. That is, at 50% mitigation, it requires 2.04% more HP to equal the same benefit as 1% mitigation. Hence, in terms of it's equivalence to stamina, 1% mitigation is worth twice as much at 50% mitigation as it is as 0% mitigation. When one actually works out the numbers, it so happens that the stamina equivalence of one point of armor value does not depend at all on one's current armor value. So there's no increasing *or* decreasing returns in this case.

Well, what then about overall damage taken? Given some input amount of damage D with avoidance A and Mitigation M, the net damage we take is DAM. If we want to reduce this by, say, 1% with avoidance, we have to change our avoidance to some new quantity A', which has no dependence on M. Meanwhile, if we want to decrease the amount damage we actually take by 1% with no mitigation (aka M = 1), we need to increase our mitigation by 1%, to .99; but if we want to do so with M = .5, we only need to reduce M to .495 - that is, to match a given gain of avoidance at 0 mitigation takes twice as much mitigation - percentagewise - as it does at 50%; hence, the value of every point of armor, measured in avoidance, is the same - again, no diminishing returns.

Hence, regardless of whether you think mitigation should be measured in absolute numbers of percentagewise, the fact is that relative to any and every other stat, mitigation's marginal value relative to the other stats is completely invariant relative to how much mitigation you currently have; hence saying that it suffers diminishing returns, severe or otherwise, is somewhat misleading.

While interesting, is the Armor debate even worth analyzing at this point? When MC was the paradigm, warriors generally had 3 choices: lots of armor, lots of stam, and lots of avoidance. It was hard to stack any of them, given the gear, but you definitely had a choice. The amount of itemization "choices" on each piece went up drastically in TBC and the armor varied little from piece to piece and there's not much way to stack armor anymore (assuming a certain level of progression), nor are there consumable choices that pit armor versus anything worthwhile. People chug Ironshield pots, and there's really nothing else to do. Armor isn't much of a choice these days... you can't really gem for armor.

Now we deal mainly with avoidance, effective health, and threat. Armor is such a small part of the equation, but I guess that's your point in the first place.

This argument would seem even less practical as we step into Wrath. Though it may be worthwhile for Blizzard to explore itemization/encounter design around the fact that every tank may very well become armor capped without effort.

The math proves this out, depending on the relevant range, which is where I think a lot of the misconceptions in this argument arise. What tanks are generally dealing with (these days and not in the days of Conquest) is at the extremely high range of armor, where damage reduction is closer to the 100% mark than it is away from it. If people kept this argument to a relevant range, it'd be easier to come to a consensus. At that point the diminishing returns are clear. In the middle of the range (MC days which was the genesis of this argument) the diminishing returns are less clear and the returns less marginal. In order to not make players completely immune via Damage reduction, the graph never reaches 100% DR (or 75% or 0%, depending on what you are graphing) so each point of armor close to the limit can't "go anywhere." In order for there to be decreasing returns at the high end of the spectrum, there must be increasing returns at the low end of the spectrum.

With respect, that's not true at all. It takes increasingly more +armor per 1% mitigation as your mitigation rises, while it takes the same +dodge rating, for instance, for 1% dodge. The value of armor relative to dodge is a function of both pre-existing mitigation and pre-existing avoidance. As mitigation goes up, the value of armor compared to dodge goes down. As avoidance goes up, the value of armor compared to dodge goes down, as well.

Then how do you explain the fact that tanks cannot reach 100% damage reduction? At some point, an extra point of armor is worthless. Has to be. Otherwise, a tank could walk up and take no damage for 40 minutes.

Does it have to be spelled out that, once you hit the cap, it has 0 value? That's not decreasing, that's zero.

Well, it's known that armor is capped at 75% reduction...

Do you know the formulas involved?



Where W is the fraction of incoming damage (or DPS) taken (not mitigated), w is your actual armor, and v is a constant based on level (10557.5 for a level 70 target, for instance).

We can derive that, for a change in armor ∆w, we can figure out the new damage taken , W+∆W.



Divide by W, subtract 1, and you've solved for ∆W/W, the relative change in damage taken.



Thus, the relative value of additional armor is, in fact, a function of w and thus a function the armor you already have (and thus the mitigation you already have).

As a matter of fact I do. But you're not calculating what I suggested calculating.

So, if you'll note the quantity H/M I suggested calculating, where H = HP, M is the mitigation term and A is Armor Value, we have



So, the amount of this quantity - which, roughly, effective hit points for resisting burst attacks - that you gain from changing your armor from A to A' is:



So if , then , so the change in EHP is simply



Note, if you will, that there's no dependancy on A; only on .

I'm curious as to what you mean by this. I mean, if you're referring to how much more armor it takes to see that 1% increase in mitigation, then you're correct--in fact, the whole armor system is clearly designed to make it so that, again, +X armor = +Y seconds of time to live, depending on the incoming DPS, but regardless of how much armor you already have.

But saying that armor guarantees an equal increase in time to live is, well, a point of mere mathematical interest. To me, it makes sense to evaluate armor as a stat and compare it to other stats using some metric or formula. The obvious metrics are, of course, effective health or expected time to live. Under these metrics, the math is unambiguous: 1 point of armor decreases in value compared to 1 point of, say, dodge rating, as the armor of the player is increased.

The problem we often get when talking about diminishing or increasing returns is that we don't agree on the definition of "neither increasing nor decreasing returns." I personally will always choose to define "neither increasing nor decreasing benefit" as "constant relative benefit," not "constant absolute benefit."

Yes, you calculated the absolute change in your metric. You didn't calculate the relative change in your metric, which will naturally introduce A (the amount of armor one has) into the formula.

Since your metric only involves either max HP or armor, you only come to the conclusion that armor and max HP scale in the same "way." The value of 1 HP compared to 1 armor doesn't change under this metric, and since you have no other stats involved, the only question is how you define diminishing returns of a stat not relative to another stat--in terms of relative differences or absolute differences.

Since the thread was talking about relative differences, I'm confused as to why you posted a calculation that only shows an absolute difference.

And this post has been made in response to the OP of The Protection Warrior thread here in these forums that claims that it is your RDR from Armor and not your DR from Armor that affects the amount of damage your Armor is reducing and the amount of healing needed to keep you alive. Anyways, I agree with what you have posted in this thread and am going to rephrase it just for a clarified, personal reference.

• Armor, as a function of Survivability without Heals more or less does not experience Diminishing Returns - and, in this case Relative Damage Reduction from Armor is what is proportional to your 'TTL'.

• Armor, as a function of Damage Reduction, does indeed experience Diminishing Returns, in the obvious sense that as your Armor increases, so does the amount of it needed to increase your Damage Reduction from it.

EX. (For the Timmys who manage to double-click to this website) 60% Armor --> 61% Armor will decrease incoming damage by 1%, as a function of survival (without heals) however, this 1% increase in Armor is worth 2.5 times its worth in Survival time without heals.