Diminishing Returns on Armor = Myth (graphs)

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So sum it up. Best will be average out like

5000 armour
500 AR
5000 life

Diminishing Returns: The idea that an extra point in something (Armor) yields less return than the points before it. Ex. the 100 point in armor is less effective than the 99th point.

Didnt you just prove his point? Or did i miss something in my lack of sleep?
I appreciate the work the OP has done. It's led a lot of people to consider a lot of things. This is now months later and the scenery has changed a bit and a lot more testing has been done. I'd like to chime in now from a less mathematical perspective and make some practical points because many people who have been involved in this thread have shown an interest in "what should I add in my gear next, which piece of gear should I choose?" - as a result of this thread.

To answer the people asking what direction should I take my gear I will present my current findings:

1) Ideally you should have a plan for your character as the gear will revolve around the plan
2) You need to know WHAT the maximum amount of stats possible are given that items do have budgets of 6-affixes, what stats can and cannot appear on what slots and what abilities legendaries provide that you cannot get on rares.
3) You can build your theoretical perfect model for your plan with complete information about the values possible.
4) You can seek to aquire items which match the design you plan - which move towards the goal of the perfect stats you want. Even if another item seems to be better because it produces bigger numbers in certain areas.. perhaps it does not does not match your goal.

Looking at the monster power levels we see monster health and damage going up several orders of magnitude. This is clearly to match the multiplicitive nature of the items.

What I have found is that in practical terms, you are best off with:

1) All resistance on all or most slots
2) Primary stat on all or most slots
3) Attack speed everywhere you can get it - without reservation
4) Crit chance everywhere you can get it - without reservation (if barb or wiz at least)
5) Average Damage
6) Crit damage is very important but more situational. It tends to lead to more spikey damage and spikey heals which aren't great for survivability which in turn leads to needing more defenses which leads to having less dps....ahem...
7) Life steal is nearly mandatory on belt or weapon or both
8) Some life per second is greatly helpful

Armor, if you decide you want more of it - is best taken on a slot where you already have your primary needs taken care of and you have some affixes left over.

As for vitality, you need just enough of it to survive spike damage but every bit of it beyond that is merely weakening you. If you want to stand in front of a pack of elites and take a bunch of hits before going down - then sure, maybe that should be your plan from the start to stack tons of vitality. If you want to demolish anything and everything you come across in a speedy fashion you need to be *tough*, you need to deal lots of damage and you need to convert that damage back into life.

Vitality is best added and exchanged with primary stats via chest/pants sockets. This is a great way to shift your vitality needs versus having too much of it nailed into your items. This allows your dps roof to always be as close to maximum possible while still being able to change it around for things like uber bosses.

The best way to be tough, assessing what I know of what is possible to get where and in what quantities is to stack all resist, primarily... regardless of inefficiencies due to having more than a 10:1 ratio -- because of item budgets, because of what you can get where and knowing all the maximum values and possibilities for every equipment slot. If you take +armor in a slot where you do not have 70-80 all resist, you took a hit because you are getting base armor from items and you would have to be really out-of-whack for +400 armor to be worth more than 80 all resist... reduces % melee/ranged might also be very nice but Blizz hasn't exactly gushed lots of information about what things do what types of damage in the game and not all their mechanics seem to make sense.

The best way to deal lots of damage... attack speed, crit chance, crit damage/average damage, primary stat.

The best way to heal: Don't have a zillion life. Use *some* lifesteal and possibly *some* LoH depending on your skills. Skills such as rend which return a % of life back based upon your dps are golden as they allow you to use even more aggressive equipment than you could otherwise normally survive the highest levels of the game with.

Back on the original topic: The OP has made some interesting points that were not obvious to all because the game displays only DR %. From there I just see a lot of arguing about context of the usage of the word "Returns"... so maybe the title could read "Diminishing returns of effective health derived from armor = Myth" and that might be more clear but it's not a big deal.
I don't know what the cheering is about, basically the author needs to go back to school, any school with foundation in maths, science, engineering, or economics.

If worth a million dollars, I stole 50% from you. You're now worth $500,000. You're very angry that I took away $500,000 from you.

Now, I stole another 50% from you. You're not as angry now, because I only took $250,000 from you.

Then, I stole another 50% from you. You're actually happy now, because I only managed to steal $125,000 from you!

Now I'm worth $875,000 from $0, and you're only worth $125,000 but you're happier, so that makes both of us happy! :)

If you plot the rate at which I take money from you, you'll get a linear straight line (eHP doh!)

In case you're from a different world or come from a strange school, this is the globally recognised definition of diminishing returns:

The very charts in that "proof" already closes the argument.

To explain clearly how Armor, AR, %elite reduction, %melee reduction works towards total mitigation, just take off the reading value of each of those curves, and multiply the applicable terms together in the following way:
Mitigation = [1 - (1-Armor.decimals) x (1-AR.decimals) x (1-elite reduction.decimals) x... etc]

Don't pretend to be a maths geek when you don't even know the basic definition of "diminishing returns". It's as ridiculous as trying to say "Force = mass of dog poo", when the whole world agrees that "Force" has a different definition.
Paul... this is a 2012 thread...

Wonder who bump it
Paul... this is a 2012 thread... Wonder who bump it

I bumped it because Gunner couldn't let the issue drop. So I'm coming to the root source, to get the wrong facts straightened out.
Necrotrolling...thx though I almost forgot about this debate...
Thank you for taking the time to share this. I was wondering how the armor and resists worked.
07/23/2013 03:47 AMPosted by PaulNg
Paul... this is a 2012 thread... Wonder who bump it

I bumped it because Gunner couldn't let the issue drop. So I'm coming to the root source, to get the wrong facts straightened out.

I don't know what you were thinking about when you bumped this, but basically you need to go back to school, any school with foundation in computers, forum etiquette, reading comprehension, or necromancy.
I remember reading this excellent post back in May 2012. It is still very relevant, which is why I do not feel too bad about reviving it. I wish to make a comment on something that has bothered me recently.

For the sake of simplicity, I will exclusively discuss damage mitigation provided from armor. Taking the remaining damage reducing parameters into consideration - e.g. resistances, blocking, dodge etc. - would of course be possible. However, doing so would not alter my point, and it would be bothersome. For this reason also, I will not be incorporating any form of life regeneration or life on hit into my computations. I will also assume that the enemy is level 73.

The author of the original post argues that armor, despite popular beliefs, does not suffer from diminishing returns. His reasoning is that although each extra point of armor provides a relatively smaller amount of absolute damage reduction (500 armor yields ~12,04% damage reduction whereas 1000 armor yields ~21,50% damage reduction < 2*12,04%), each extra percent of damage reduction is progressively more effective than the previous (i.e. going from 10% to 20% damage reduction is more effective than going from 0% to 10%).

Another way of putting this is that each additional point of armor will yield the exact same effective HP increment as the previous point of armor regardless of your current armor level. More simply stated: If we assume that you have 500.000 HP, you EHP at 0 armor is equal to 500.000. Going from 0 to 500 armor nets you ~68.493,15 extra EHP meaning that your EHP will be equal to ~568.493,15. At 1.000 armor you will have EHP = 568.493,15 + 68.493,15 = 636.986,30 and so forth.

Your EHP scales linearly with armor! I almost completely agree with everything that I have written so far. What bothers me are the words "diminishing returns". I would argue that the effectiveness of armor with respect to EHP diminishes as armor increases.

Using the above computations as an example:

Going from 0 to 500 armor will yield an EHP increase of (568.493,15 - 500.000)/500.000 = 0.1369863014.

Going from 500 to 1000 armor will yield an EHP increase of (636.986,30 - 568.493,15)/568.493,15 = 0.1204819277.

And so forth... This means that the relative effectiveness of armor with respect to EHP (and, incidentally, the time it takes for the monsters to kill you) diminishes the more armor you have (this conclusion also applies to other damage reducing parameters).

I have made a little spreadsheet using Google Docs that displays this (see the graphs):

Short story about why I am posting this (it is not related to Diablo):

Now the reason that I actually post this is because I had a recent discussion with my friend about armor and the effectiveness of absolute armor reducing abilities in the MOBA game Heroes of Newerth (HoN). In HoN, armor functions similar to how it functions in Diablo 3 - i.e. the EHP scales linearly with the amount of armor you have (although the exact formula is a tad bit different - basically every point of armor increases your EHP by an amount equal to 0,06*Maximum_HP).

In the game there is this item called "Shieldbreaker" which simply reduces your target's armor by an absolute value (-7 armor at max level I believe). Now some of the casters that commentate tournament games falsely, according to the views of the author of the original post, argue that the effectiveness of this item "Shieldbreaker" is worse against targets with high armor than against targets with low armor - they believe that the item is most useful against low-armored targets (due to the misconception of diminishing returns of armor) - i.e. they think that going from 7 to 0 armor is more impactful than going from 14 to 7 armor. Since EHP scales linearly with armor, the OP would argue that this is false, and that the amount of armor that the target has is irrelevant in relation to the effectiveness of the item "Shieldbreaker".

However, due to the point that I was trying to make above, I would argue that the casters' conclusion is actually correct (but for the wrong reason!). Going from 14 to 7 armor will effectively yield a relatively lower EHP decrement when compared to the situation where you go from 7 to 0 armor.

Thoughts on this?
05/16/2015 04:35 AMPosted by Lystig
Thoughts on this?

Man, I went through a long and annoying maths equation yesterday comparing the value of impunity vs hardened wrath, so I feel somewhat up to speed on this issue.

If you are discussing something that lowers armor by a fixed amount, independent of all other variables, then, from all the math out there on the subject, it is clear that the absolute amount of the victim's armor is irrelevant; ie, going from 14 armor down to 7 is just as punishing to the victim as going from 7 down to 0. The only situation in which this would not be the case would be if the victim has less than 7 armor to start with...that's impossible to do in d3 at lvl 70, but perhaps not in your other game.

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