Formula for Resistance from Armor (and effective health) der=0>

[Bridgeburners]

Hello incgamers, I singed up here a while ago, but barely ever posted. Well, for one of my first contributions, I want to tell you about the effect of armor on your "effective health".

First, let me give you the formula for your resistance on armor and monster level. I did this by testing out many different armors for each level, and curve fitting them to extrapolate the parameters of the equation. Let me say that I guarantee you that this is correct, and if you don't believe me, try this for many different armors, at many different levels (since it tells you your resistance against monsters that are your level). I guarantee you that the result will always obey the equation I'll give you.

Let r = resistance, A = armor, and v = monster level. Then

r = [A/50v]/[1 + A/50v]

Here's an example. If you have 250 armor, you will have a resistance of 0.2778 (or 27.78%) against level 13 monsters.

This is a diminishing return. Note that as A approaches infinity, r approaches 1. That is, you will never get r = 1 because that would mean complete immunity, so of course we want a diminishing return that prevents that.

Now let's talk about effective health. I define "effective health" as the amount of damage a monster has to dish to you to kill you. I claim that putting points into armor increases your effective health linearly. Let's prove that.

Let H = effective health, and L = your character's max life. When a monster deals X damage to you, you lose X(1-r) life. From the way I defined H, a monster has to do H damage to you for you to lose L life. If a monster does H damage to you, you lose H(1-r) life. Therefore H(1-r) = L, or H = L/(1-r)

Notice that as r approaches 1, H approaches infinity. That is, if you're completely immune to everything, you will never die because your "health" is effectively infinite. It's a good thing that r can never reach 1.

Now take H = L/(1-r), and plug in r = [A/50v]/[1 + A/50v]. This gives us H as a function of armor, and that becomes

H = L(1 + A/50v).

That is, armor increases your effective health linearly. It's basically like another vitality button! It probably doesn't improve your effective health as fast as vitality does, but it has the added bonus of amplifying healing effects. That is, if you are healed by x life, you are healed by x/(1-r), or x(1 + A/50v) effective health. That is, a character with lots of healing spells, life leech, or added bonuses from health globes would value armor a great deal more than those without.

This should also dispel the notion that as you get lots of armor, more armor becomes less effective "because of diminishing returns". The resistance has a diminishing return with respect to armor, but effective health has a rapidly increasing return with respect to resistance, and clearly, this balances out to give a linear relationship. So that extra 10 armor you give yourself on top of that 6000 armor is just as good as that early extra 10 armor you gave yourself when you had only 30 armor.

[Zokar]

http://diablo.incgamers.com/forums/s...d.php?t=820870

.....

[Bridgeburners]

I just saw that. Brokenstorm quoted my post from the bnet forums.

Anyways, I don't think there's an overlap in the two threads. He posts plots on how armor affects resistance, and I give the general expression, and show how it relates to effective health.

[Zokar]

Fair enough.

I would like to take a more complete look at survivability at some point.
As was common in WoW, so much of the focus was simply on EH and that's fine and all, but it doesn't tell enough of the story.

EH lets one calculate a basic time-to-death and that's great, but not accurate. We need to include more of the stochastic elements to get a feel for overall survivability. Dodge, while not always on, gives a probability of protection. Granted, one can not count on it, but it's clear that over the long run dodge increases the time-to-death. As such, dex/dodge should at least be considered in a more precise fashion in relation to EH so that we can eventually come up with some answers as to if dodge should ever be used, if so in how much and in what ratio would we be willing to trade-off armor and or hp to do so. The same goes for block and magic resists.

If you're up to it, perhaps you would be willing to comment on this problem and come up with something more indicative to real survivability.

[Bridgeburners]

This is an easy problem. If you're concerned about the "long run" average effect of dodge, then you can essentially treat dodge as another resistance. If you have multiple multiplicative sources of resistance, (R1, R2, .... Rn) then your effective health is essentially the product of the factors 1/(1-Ri) where Ri indicates each resistance of index i. Thus for effective health H and character life L, we have

H = L*Π{i=1...n}[1/(1-Ri)]

Where "Π{i=1...n}" denotes the product of index i, as i runs from 1 to n. For example, if we want to look at our "effective health against fire", and we have 30% all resist from armor, and 25% fire resist, our effective health against fire is

H(fire) = L*[1/0.7]*[1/0.75] = 1.90476L.

Since, on average, x% dodge acts like resistance percentage, simply treat dodge chance as another factor of resistance. So for a chance "d" to dodge, we have

H = H*/(1-d)

where H* was the effective health calculated before accounting for dodge. Of course, as you mentioned, this EH isn't quite as objective as the EH calculated before dodge, since it will only behave as a resistance in the limit of many attacks, but on a small time scale, the random fluctuations will be very noticeable.

From what I've seen from dex to dodge so far, it seems that each dex point gives a solid 0.1% dodge chance. This is peculiar, as I haven't noticed any difference in different levels, nor have I observed any diminishing return. If this is the case, and there is no diminishing return to balance out the rapidly increasing return of effective health's dependence on dodge, then that would mean that the more you put in dex, the better and better a benefit you get. Just look at the function 1/(1-d) which multiplies health.
http://i.imgur.com/JHmwa.png

I would hope this doesn't end up being the case.

By the way, I keep seeing this thread as having zero replies. Is this a known bug on these boards?

[Zokar]

The boards the last few days have been bonkers, it's usually ok, but something is wonky right now.

As for dex, from a previous poster dex gives 0.1% up until 100 dex at which point the formula changes, though the poster didn't not discover how much dex diminishes at that point.

[Bridgeburners]

It looks like this thread was doomed to fail. It's strange, since my thread on bnet was far more wordy, and had much more detail than this one, and it got a good deal of responses. Maybe those who are interested in this stuff already took the time to read that one.

[galzohar]

The main reason is probably that this forum is pretty much dead. Just look at the last post made on this forum. Most people only read the general discussion and maybe beta discussion (and many only read one of them). Of course, this makes it difficult to find theorycrafting posts when they are posted in general discussion. So it's not really your fault.

I believe resistances will work the same as armor. Not sure about dodge, though, but it'll probably be the same or similar too. Not sure about the 0.1% comment, makes no sense to have it not level dependent or anything. Any more thorough tests done for dodge?

As for the dodge randomness, overall if we don't get easily killed in a few hits (which should not happen since we should be able to live long enough to kill monsters and spawn health globes, and I expect monsters to also last a few hits from us), then just looking at it as an effective HP multiplier should be more or less fine.

[Bridgeburners]

Oh wow, I didn't notice that this was redirected to the Theorycraft section, but that makes sense.

According to Brokenstorm
http://diablo.incgamers.com/forums/s...th-dodge/page3
after 100 dex, it continues to give a linear dodge benefit, but with 1/4 the yield it did before.
I still hope it doesn't continue forever like that. Perhaps every 100 dex reduces the yield by the same factor.

[Zokar]

Oh wow, I didn't notice that this was redirected to the Theorycraft section, but that makes sense.

According to Brokenstorm
http://diablo.incgamers.com/forums/s...th-dodge/page3
after 100 dex, it continues to give a linear dodge benefit, but with 1/4 the yield it did before.
I still hope it doesn't continue forever like that. Perhaps every 100 dex reduces the yield by the same factor.

Yeah, my guess is also that it stops being linear at some point, or if not then like you mention, that the slope continually drops as one increases dex. But that makes me wonder why they just didn't do a simple diminished curve, why the step function. (No, it probably doesn't matter other than to satisfy my curiosity)