In response to The Protection Warrior Guide: Section V - Armor

[♥(ALEXTREBEK)♥]

Originally I had decided against making a post like this, under the (probably correct) assumption that it'll receive numerous idiotic, flawed, and poorly-backed responses; however, recently I've been asked by a number of guild members and others to make a post here to redirect thought regarding certain issues and contradictions that have arisen with the following post, so, here I am. I have now relocated the base of this thread to these forums because I have no idea how long it will take the moderators at Elitist Jerks to delete it. What this graph is saying is that 1% mitigation near the 75% DR cap is roughly 4 times as valuable as it is when you have 0% mitigation. Another way to think about that is that at 75% reduction, you are reducing your damage by 4. A mob hits an unarmored player for 100 A mob hits a 75% DR player for 25 Improve both by 1% DR: A mob hits the unarmored +1% player for 99 – a 1% improvement from before A mob hits the 76% DR player for 24 – a 4% improvement from before Take this to the extreme. At 90% DR, 1% more DR would decrease your relative damage taken by 10%. That 100 point hit would be reduced from 10 down to 9. At 100% DR, you take 0 damage. You are invincible. The exponential has reached infinity for the value of relative damage reduction (RDR). The last few points of DR are incredibly important. Another way to look at this issue of relative damage reduction is to consider your healers. Say you are in a situation where you have 50% DR from armor, you are taking only physical attacks, and your healers are healing you for 1000 hp/s. If you increase your DR by 1%, you now have 51% DR. You healers will now only heal you for 980 hp/s, a 2% improvement. The healers burden is changed in a manner directly proportional to your relative damage reduction! NOT your damage reduction. Hopefully this drives home the key point. In practical use, armor is king. A 1% damage reduction increase at 66% DR, means roughly a 3% lower burden of healing on in an all-physical situation. Note that defensive stance multipliers do not change this – as multiplication is associative. For a lot of players, the aforementioned paragraph is nothing more than a bunch of gibberish, rephrased in friendlier English, it would look something like this: You have 0 Armor and therefore 0% Damage Reduction from Armor. A Raid Boss walks up to you and punches your cock off for 10,000 points of physical damage. You resurrect (your cock) and equip your Armor. You now have 50% Damage Reduction from Armor. A Raid Boss walks up to you and narrowly misses punching your cock off for 5,000 points of physical damage. Now here is where things get a little tricky. We're going to add 1% more Damage Reduction (from Armor) at both 0% and 50% Damage Reduction. This will look something like this: You have 1% Damage Reduction from Armor. A Raid Boss walks up to you and severs the connection between your body and your cock for 9,900 points of physical damage. You resurrect (your cock) and equip your Armor. You now have 51% Damage Reduction from Armor. A Raid Boss walks up to you and narrowly misses punching your cock off for 4,900 points of physical damage. Now, here is where we run into our little conundrum. According to what is being said in the aforementioned post, an extra percent of Damage Reduction from Armor at 50% Reduction is twice as effective as an additional percent of Damage Reduction from Armor at 0% Reduction. The logic behind this being the following: 9,900 Physical Damage / 10,000 Physical Damage = 99% 100% - 99% = 1% whereas 4,900 Physical Damage / 5,000 Physical Damage = 98% 100% - 98% = 2% 2% / 1% = 2 Relative Damage Reduction Here is where the flaw in the logic comes in and breaks the camels back. A reduction of 100 Physical Damage at 1% Armor is equivalent to a reduction of 100 Physical Damage at 51% Armor. The Damage Reduction from Armor cannot be relative if the amount of damage reduced per percent, despite previous amount(s) of Damage Reduction, is static. What I'm saying: 100 Reduced Damage = 100 Reduced Damage From this, we're seeing that Armor, as a function of Damage Reduction, is not at all relative and does indeed suffer from major Diminishing Returns. Another point that I will assume needs to be refuted to better fortify the position I'm taking on this matter is the amount of HPS needed to keep a Tank alive and whether or not "Relative" Damage Reduction from Armor affects it. The following is a quote from this thread in regards to how "Relative" Damage Reduction from Armor affects necessary HPS. Another way to look at this issue of relative damage reduction is to consider your healers. Say you are in a situation where you have 50% DR from armor, you are taking only physical attacks, and your healers are healing you for 1000 hp/s. If you increase your DR by 1%, you now have 51% DR. You healers will now only heal you for 980 hp/s, a 2% improvement. The healers burden is changed in a manner directly proportional to your relative damage reduction! NOT your damage reduction. Alright, let's take the same situation from this quotation (for the sake of simplicity) involving you having 50% DR from Armor and requiring 1,000 HPS. You now increase your DR by 1% (in an effort to save your cock etc.), putting you at 51% DR from Armor. From this, we're seeing these results: 2,000 necessary HPS * (100% - 50%) = 1,000 necessary HPS. 2,000 necessary HPS * (100% - 51%) = 980 necessary HPS. In an effort to match your wit, what with your new Armor and not, the angry Raid Boss (probably your girlfriend or something) sunders your Armor leaving you at 0% DR from Armor. The tables are turned in the HPS needed to keep you alive will now look like this: 2,000 necessary HPS * (100% - 0%) = 2,000 necessary HPS. Miraculously, you grow an extra percent of Armor, precipitating these results: 2,000 necessary HPS * (100% - 1%) = 1,980 necessary HPS. Now, although the decrease from 2,000 HPS to 1,980 HPS may be a 1% decrease in comparison the 2% decrease in necessary HPS resulting from 1,000 HPS to 980 HPS, if you look very closely, you may just happen to notice that the actual decrease in necessary HPS to keep you/your cock functional has not changed at all between 2,000 HPS --> 1,980 HPS and 1,000 HPS --> 980 HPS. Once again, we're finding that: 20 HPS = 20 HPS So, in fact, the healer's burden has not actually changed at all. Percent-wise (or relatively/whatever you want to coin it), yes, at 51% DR, the healer's burden is "2% less" than it would be at 1% DR, but actually speaking, the healer's burden of 20 HPS has not changed at all and is empirically, directly proportional to the amount of Damage Reduction from Armor you have, is theoretically proportional to the amount of Avoidance you have (a whole other story), and (obviously) differs depending on the type of damage the Tank is taking and the amount the Tank is taking. 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. _________ Now, if you're interested in responding this thread, the chances of me responding to your post will be astronomically higher if you take the time to thoroughly read what I have said in this thread, remember that you can be just as wrong as I can be, and actually make a well thought-out response that appears to be (and is) worth taking my time to read.

[mko]

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.

[Yosheh]

ohi blunted, didn't know you were aldriana! lol..

[Jahre]

Blunted is a genious

[mko]

WHAT NOW TREBEK

[♥(ALEXTREBEK)♥]

I counter with: You'll have to forgive me; if I gave the impression I feel dodge is a "good" baseline to compare against, I apologize. It is merely the only other distinct stat I could think of that would be relevant. When I refer to "constant relative benefit" and "constant absolute benefit," I mean very specific things. For a given metric or objective function F, dependent on a stat u, I define the absolute benefit and relative benefit as... Absolute benefit: [latex]\Delta F(u_0, \Delta u) = F(u_0 + \Delta u) - F(u_0)[/latex] Relative benefit: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = \frac{F(u_0 + \Delta u)}{F(u_0)} - 1[/latex] (As a note, I've struggled for some time to find an appropriate symbol for relative changes, one that would correspond to how the delta works for an absolute change.) Thus, to me, it doesn't make sense to say that something could have "constant absolute benefit" with reference to another stat as a baseline. When I think of constant absolute benefit, I think of this: [latex]\Delta F(u_0, \Delta u) = k \Delta u[/latex] That is, the benefit is not a function of your original stats, and proportional to the change in stats. Most often, we're talking about objective functions of many variables, and it's possible that a stat may have constant absolute benefit regardless of varying that particular stat (for example, the absolute DPS increase for a spell with respect to adding +bonus damage is the same regardless of the bonus damage one already has). If this is the sense you were speaking of, I apologize, though it's worth noting that this is not the case for armor if you're talking about an effective HP metric... When I think of constant relative benefit, I think of this: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = k^{\Delta u} - 1[/latex] The key difference between constant absolute benefit and constant relative benefit is that constant absolute benefit implies linearity, while constant relative benefit implies exponential growth or decay. (When I was writing this the first time, I assumed that it would actually be k*∆u, thinking this would lead to the exponentials I'm familiar with, but when I was working out the proof below, I came across the problem. As it turns out, such would lead to a contradiction--the relative benefit cannot be constant if it is merely proportional to ∆u, and I can prove this if you like.) In the constant absolute benefit case: [latex]\Delta F(u_0, \Delta u) = F(u_0 + \Delta u) - F(u_0) = k \Delta u \Rightarrow F(u_0 + \Delta u) = k \Delta u + F(u_0)[/latex] Which is the familiar y = mx+b form, y being the new value of the metric, x being the change in stats, m being the arbitrary constant of proportionality, and b being the original value of the metric. In the constant relative benefit case: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = \frac{F(u_0 + \Delta u)}{F(u_0)} - 1 = k^{\Delta u} - 1\Rightarrow F(u_0+\Delta u) = F(u_0)k^{\Delta u}[/latex] Which is a typical exponential growth or decay function. Anyway, I've been a little long-winded, but I felt it necessary to be absolutely clear. I feel these definitions of constant absolute and relative benefit are unambiguous and lead to the internal concepts we intuitively hold of these notions. And using these definitions, we can assess whether a stat has increasing or decreasing relative or absolute benefit, and we see that dodge has increasing relative benefit as dodge increases, while armor has decreasing relative benefit as armor increases.

[♥(wuincy)♥]

Originally Posted by ALEXTREBEK I counter with: You'll have to forgive me; if I gave the impression I feel dodge is a "good" baseline to compare against, I apologize. It is merely the only other distinct stat I could think of that would be relevant. When I refer to "constant relative benefit" and "constant absolute benefit," I mean very specific things. For a given metric or objective function F, dependent on a stat u, I define the absolute benefit and relative benefit as... Absolute benefit: [latex]\Delta F(u_0, \Delta u) = F(u_0 + \Delta u) - F(u_0)[/latex] Relative benefit: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = \frac{F(u_0 + \Delta u)}{F(u_0)} - 1[/latex] (As a note, I've struggled for some time to find an appropriate symbol for relative changes, one that would correspond to how the delta works for an absolute change.) Thus, to me, it doesn't make sense to say that something could have "constant absolute benefit" with reference to another stat as a baseline. When I think of constant absolute benefit, I think of this: [latex]\Delta F(u_0, \Delta u) = k \Delta u[/latex] That is, the benefit is not a function of your original stats, and proportional to the change in stats. Most often, we're talking about objective functions of many variables, and it's possible that a stat may have constant absolute benefit regardless of varying that particular stat (for example, the absolute DPS increase for a spell with respect to adding +bonus damage is the same regardless of the bonus damage one already has). If this is the sense you were speaking of, I apologize, though it's worth noting that this is not the case for armor if you're talking about an effective HP metric... When I think of constant relative benefit, I think of this: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = k^{\Delta u} - 1[/latex] The key difference between constant absolute benefit and constant relative benefit is that constant absolute benefit implies linearity, while constant relative benefit implies exponential growth or decay. (When I was writing this the first time, I assumed that it would actually be k*∆u, thinking this would lead to the exponentials I'm familiar with, but when I was working out the proof below, I came across the problem. As it turns out, such would lead to a contradiction--the relative benefit cannot be constant if it is merely proportional to ∆u, and I can prove this if you like.) In the constant absolute benefit case: [latex]\Delta F(u_0, \Delta u) = F(u_0 + \Delta u) - F(u_0) = k \Delta u \Rightarrow F(u_0 + \Delta u) = k \Delta u + F(u_0)[/latex] Which is the familiar y = mx+b form, y being the new value of the metric, x being the change in stats, m being the arbitrary constant of proportionality, and b being the original value of the metric. In the constant relative benefit case: [latex]\frac{\Delta F(u_0, \Delta u)}{F(u_0)} = \frac{F(u_0 + \Delta u)}{F(u_0)} - 1 = k^{\Delta u} - 1\Rightarrow F(u_0+\Delta u) = F(u_0)k^{\Delta u}[/latex] Which is a typical exponential growth or decay function. Anyway, I've been a little long-winded, but I felt it necessary to be absolutely clear. I feel these definitions of constant absolute and relative benefit are unambiguous and lead to the internal concepts we intuitively hold of these notions. And using these definitions, we can assess whether a stat has increasing or decreasing relative or absolute benefit, and we see that dodge has increasing relative benefit as dodge increases, while armor has decreasing relative benefit as armor increases. i understood your 1st post well, after just looking at the math in the second my ears are bleeding and im about to start a seizure...

[♥(ALEXTREBEK)♥]

We're making fun of the calculus laden 'geniuses' who litter EJ's forums with their garbage that's illegible to all but a few people, and of those few people, there are probably only 3 or 4 who actually realize that the poster's on EJ don't do anything other than restate already given information in increasingly complex terms. Sum it up pretty good? (lol, Sum, math humor...)

[mko]

I don't get why people go through such trouble to figure out such irrelevant data anyway. How much overall damage reduction from armor/stam is irrelevant as avoidance is better. How much of a benefit 1% armor gives you at x point is irrelevant because all that matters is how much x value of armor gives, and it's relation to itemization points of x value of stam/avoidance (which doesn't even really matter since you can't really gear for armor anyway outside of a ring or smth.) I'm gona give out super secret warrior strats for the whole world now oks. Pick x encounter to which you wana gear for. Attain stam/armor combination that will allow you to survive the highest possible burst output in a 2 or so second window depending on the fight assuming no avoidance (this is where you have to do some complicated maths like multiplication and division ono). Once above is met gear and gem to boost avoidance and nothing else. If you're one of the inept fucks that think rage starvation or tps is ever a problem at any point in anything ever, unbind keyboard turn, in that large window when your GCD is used and you just autoattacked, turn around and get full rage bar and turn back in <.5 seconds if you're not fucking stupid. Gratzzzz you're winner at warrior.

[♥(ALEXTREBEK)♥]

Shh, dude, now everyone's going to know how to play a Warrior well...

[♥(jakethesnake)♥]

Well at least I'm not the only one who finds that post mostly useless.

[Finoria]

Originally Posted by jakethesnake Well at least I'm not the only one who finds that post mostly useless. Yeah. The theory crafting business is definetly good to know, but that does not mean I don't get a headache if I read the stuff for too long.