Diablo® III

Diminishing Returns on Armor = Myth (graphs)

Posts: 16
Wonderful post TBD. A quick question:

What is your current ration of str to vit? In this Inferno solo barb kill video, the ratio is about 1:1. I am assuming it is very important to keep this ratio?

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Edited by peddroelm#2402 on 5/23/2012 4:59 AM PDT
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Only you cant get more then 1500 resist. And intelligence gives wizards attack and better armor, compared to barb strength. By stacking resistance as a barb you lose DPS.

A wizard on the other hand loses nothing.

Intelligence gives resists, not armor. Strength gives armor, which barbs happen to stack for damage.

So really, no, given this thread actually Barbs pull ahead because they don't have a cap on armor. Not to mention the innate 30% reduction the class gets.
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Posts: 951
This should be stickied. It is possibly the best post I have ever seen on these forums. Outstanding!
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Posts: 171
So ... if 1000 armor or 100 Resist is a 33% increase in EHP, and 1 STR = 1 Armor, and 1 INT = 0.1 ... this means that STR is just as useful at mitigating damage as INT?

Though obviously one would still have to factor in the compounded returns on resistance vs. armor to decide which is better.
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@OP: First, nice post. Not many people actually bother to dissect the math behind the game, and even fewer try to have some constructive discussion about it, so nice job sir.

That said, once you move beyond your original intent of disproving diminishing returns on armor, most of what you said is only useful as theory but not in practice. You spent quite a bit of time detailing how the effective value of vitality, armor, and resistance each change in relation to other, but you missed a very important constraint: in game, you can only choose between vitality and armor in a 1:2 ratio. If you check the AH for level 60 items, you'll see that you can generally get around 150-200ish on Vitality and can't break 400 on armor. Given the base armor that you MUST take on gear, the practical answer is that Vitality > Armor when choosing gear unless it's some ridiculous comparison between 30 vitality and 300 armor. Unless it's a 1:5 ratio, it's probably not even worth considering the +armor, and more than likely you should just keep looking for another piece given the potential to be gained elsewhere. Also, this doesn't even take into account that a large number of barbs use the passive that gives 1 armor per vitality, putting things even moreso in vitality's favor.

I can't check the AH right now cause it's down, but from memory of what's available, it seems like the same thing is true with all resistance vs armor since the max all resist on a piece is somewhere around 80. Really it's a bit counter-intuitive for barbs to avoid +armor, but that seems to be where the math is leading me in terms of effective choice. Therefore, the more interesting comparison for barbs is vitality vs all resistance.

P.S. You did make one very interesting point about how % max health heals scale with both vitality and armor (although better with vitality given the itemization constraints I mentioned above) and more importantly how static heals from health per hit/kill/second scale with damage reduction but not vitality itself. Thanks for that, as I learned something very important for my barb plans :).
Edited by MadYak#1138 on 5/23/2012 8:18 AM PDT
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85 Tauren Druid
Posts: 120
Upvotes for maths!

And it doesnt matter whats available on the AH, what OP has done has definitively set out the limits of the tradeoff, if Blizz has balanced mods such that the choice is always obvious, we still have the benefit of that certainty. Furthermore, getting an idea of exactly how much better vit/resists are over the +armour mod will let us balance items when other things are taken into account (differences in other mods such as strength, movespeed, etc which are unquantified here).

This issue really confused me for a while though. Even though I'd known about effective health scaling it seemed counterintuitive given the fact that every 1000 point of armour prevents less damage per hit than the last (in absolute terms). Could you maybe explain the logic?

For example, if I were to take 1 million damage over the course of a game, in 10000 hits of 100 dmg each.
My first 1000 armour might reduce overall damage by 100k whereas the second 1000 armour may only reduce overall damage by 95k (arbitrary figures).
Yet at the same time effective health may increase (at an increasing rate), such that if I had a million health, with 1000 armour I may take 1100 hits (with base damage 100) to kill, whereas with 2000 I may take 1220 (again, arbitrary figures).

Increasing returns on effective health is the case in resilience, a damage mitigation stat in wow, which is why the problem has bugged me before now.
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Could you do the following:

Take your function which calculates effective health based on armor, vitality, resistance to all, int, dodge, and dex, and compute the gradient. Create an interface which allows you to input your current stats, and return the gradient. Normalize the gradient and return the proportion of each stat which produces optimal increase in effective health given your current stat allocation. Note that it will likely be easier to combine the dex/dodge and int/res stats.

Source: applied mathematician who doesn't have time to do this himself.

Major kudos on this post; I had not thought of it this way but I think you are absolutely right.

As for semantics for the people complaining: armor DOES have diminishing returns to listed damage reduction. This is obvious. What it does NOT appear to have, is diminishing returns for effective health.

If his formulas are correct then (effective health) = health + armor/(50*Mlvl) which is linear in both health (vitality) and armor. Note that this is the same as:

EH = 30*vit + (1/(50*Mlvl))*armor.
Edited by Proph#1297 on 5/23/2012 8:49 AM PDT
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well done, thanks!
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Posts: 2
Wonderful post... can we get a sticky?
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Posts: 171
i tried your flash link to see what I need more of but no matter what I do, it says I need vit...
even at 0 armor it tells me to value vit more..

whats the point of that java program?

Yes, individual points of VIT are worth more, and generally, that will always be true, but that's not the point of the tool. The point is HOW MANY points of Armor are equal in worth to a point of VIT. If +1 VIT is worth +100 effective health, and +1 Armor is worth +10 effective health, then an equip that improves your armor by 400, but drops your VIT by 10 is still increasing your effective health by 3000 points.
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Posts: 2
Nice job!
Recently there are couples of great posts in Barb forum.
Great trend!
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With inferno mobs having higher max level, resistances would hold solid for longer in later acts? Or would armour being x10 higher than resistances keep this trend equal?
Edited by starshatter#1493 on 5/23/2012 10:16 AM PDT
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Posts: 158
I have a simple question that I haven't been able to figure out... How much HP does vit add? Is it a constant value or does it scale with your vit or other numbers?

Btw, really good read. I've always been wondering how armor and resist values are calculated into damage reduction.

As for the post above saying how wizards can tank better...

1 str = 1 armor
1 int = 0.1 resist

3000 armor = 2x hp
300 resist = 2x HP.

I guess you can figure the math from here.

From what I understand, vitality adds life like this: Until level 35 vitality gives you 10hp. After lvl 35 it goes up by 1 every level, so at level 60 it adds 35 HP.

Or expressed this way:

IF ( Level <= 35 )
HP = Vitality * 10
HP = Vitality * (10 + (Level - 35))

Of course your actual HP takes into account other stuff like +%HP and what-not.

i tried your flash link to see what I need more of but no matter what I do, it says I need vit...
even at 0 armor it tells me to value vit more..

whats the point of that java program?

Sorry I think I may have poorly explained what that app does. The bar chart (which I assume you're talking about) shows how much effective health is increased by one additional point of vitality or one additional point of armor. Armor will basically always be lower than vitality, but items have more armor than vitality on them. So lets say it shows vitality adds 5 EH and armor adds 1 EH. The relative weight is 1 vitality is equal to 5 armor. So when evaluating two gear choices. Take their vitality attributes and multiply them by 5, and their armor attributes (multiplied by 1) and add those two numbers together. Then compare those values across two pieces of gear and you get whichever one is better.

For example, if your ratio is vitality = +5 and armor = +1

Gear piece 1: 10 vitality and 100 armor (10*5 + 100*1 = 150 EH).
Gear piece 2: 9 vitality and 110 armor (9*5 + 110*1 = 155 EH).

So the first piece adds 150 effective health and the second piece adds 155 effective health, so gear piece 2 is better (defensively).

Also don't live your life by these charts. It doesn't take into account barb's natural res, block, dodge, and so on. It's just good to get a feel for things.
Edited by BeNegative#1844 on 5/23/2012 11:53 AM PDT
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I'd very much like to see a tool with all the stats incorporated so that you can see the optimal stats, considering your current stats. This is all interesting stuff regardless, understanding the Math behind the game, though some like myself are used to this system just not with as many variables
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Posts: 1,256
Your math is wrong about diminishing returns. It's called diminishing returns because every point in X yields less of Y. In this case Y is DR, and X is armor.

To further illustrate my last point lets look at an example:
At 70% DR you have an effective health of 333.3%, increase over last = 10.8%
At 71% DR you have an effective health of 344.8%, increase over last = 11.5%
At 72% DR you have an effective health of 357.1%, increase over last = 12.3%
At 95% DR you have an effective health of 2000%, increase over last = 333.35%
At 96% DR you have an effective health of 2500%, increase over last = 500%

You analyze DR and assume the same amount of armor will get to 71% DR as 72%, which it does not. In fact, the amount of armor you need to the next 1% of DR increases exponentially, hence why Armor is diminishing amount.

Just look at your own graph and look how much armor you need going from 40-50% DR and from 70-80% DR.

Bottom of the line is, you need to stack resistance if your armor is 8k and you have 10 resists, assuming you can get resists as easily as you can get armor.
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