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| Treehead July 05 2012 00:54. Posts 998 | Profile Blog # |
I’ve noticed something odd about the way people are valuing things on the AH. This is particularly applicable to the NA Hardcore gold AH, but I’m guessing it’s the same with other AHs, too. People don’t seem to be assigning much value to %Life. In see similar sentiments on the forums. People seem to say how much resistance and armor you need in inferno, but I don't see a lot about high life totals. This is perplexing to me, because I tend to see %Life much in the same way I see resist all. Allow me to explain.
%Life taken
Damage reduction through resists and armor are a must in lategame D3, especially so as a Barb (which I am). Without a good 700 all resist, and 7k armor or more, you’re in for a rude awakening if you’re meleeing Inferno enemies. But this is common knowledge – most people know that in the later difficulties, you definitely need a good solid DR. But how does %Life factor in?
Well, let’s say that instead of minimizing the amount of damage you take, we want to minimize the amount of damage you take, expressed as a percentage of your health. This changes the equation from:
(damage done)*(1-%damage reduction) = (%damage taken)
Where the “damage reduction” portion of the equation is where we put our emphasis, into:
((Damage done)/(Life))*(1-%damage reduction) = (% life taken)
Now, we can focus on both life and DR.
The motivation for %Life taken is twofold:
1. I’m a barbarian, and most of the healing done to me is a percentage of my life total. Therefore, increasing my life doesn’t diminish life I get from revenge healing and other (non-LoH/regen) sources of healing. For classes with more or less no healing options, this also applies as you’re effectively just using your effective health, and when that runs out, that’s that.
2. To try to determine some kind of stat weights for defensive stats – even somewhat inaccurate ones - so that when looking at a piece which has tradeoffs on it, we know whether that is an upgrade or not.
Note: This is the metric I use because it seems intuitive given the setup of Diablo III’s calculations. There’s probably an EH formula out there somewhere which does more or less the same thing, but this is how I think of it.
Scaling in Theory
But, as is important to know in determining what gear to take and how much of each stat to take, how do they scale in the above equation comparatively?
This is actually a very easy calculation. Notice that since the equation for %damage reduction for x all resist is, y armor, and z Life% is:
((Damage done)/(((100+z)/100)*Life)) * (1 – x/(300+x)) * (1 – y/(3000+y) = ((Damage done)/(Life)) * (100/(100+z))* (300/(300+x)) * (3000/(3000+y))
In other words, they all affect the %life taken calculation in the same manner, but at different rates. Roughly, z = 3x = 30y.
This means that if you see a piece with 16% life, and you see another piece with 48 all resist, and you currently have 0 Life% and 0 resist, they’re going to affect the %life taken calculation (i.e. the % of your life you taken from an enemy’s hit) in roughly the same way.
Scaling in Practice
The above is not a very compelling argument for taking +life % gear unless we do a little more work. The reason is that the + life% totals seem to be lower on gear than resist totals by more than our scaling rates would indicate should be the case. It’s not uncommon on a level 62 or 63 piece with all resist to have 60 or 70 all resist – but I personally have not yet seen a piece with 20% life on it (I play hardcore, though, so the AH is much less populated than SC, YMMV).
However, what we can note is that at certain (lower than a person would think) levels of all resist, life% becomes a very attractive stat. The reason for this is that each defensive stat (armor, resist, life) is affected by diminishing returns, so that when you are at 600 resist, another 50 resist might not have as much of an impact on the %life taken calculation as 10% life would. But of course, that’s a qualitative statement, and why say something qualitatively when we can just prove it with math, and moreover, show you how to assess the impact these stats have mathematically?
Stat Evaluation
By taking partial derivatives, we can see that by increasing each stat we get the following returns (note that these values are negative, indicating a lower damage taken when increasing each stat):
X: -(100/(100+z))*(3000/(3000+y))*(300/(300+x) * (1/(300+x))
Y: -(100/(100+z))*(3000/(3000+y))*(300/(300+x) * (1/(3000+y))
Z: -(100/(100+z))*(3000/(3000+y))*(300/(300+x) * (1/(100+z))
I’ve set it up this way specifically to make a point. Only the last multiplier is different, and therefore, the value of the last multiplier is what we’ll be considering. These formulas can be useful in assessing gear tradeoffs.
Example: Here’s an example that also serves as an illustration of what I said earlier – that once diminishing returns are taken into account % life looks better). Let’s say we have a choice between 50 all resist and 10% health, and we currently have 300 all resist and only 15 +life %. Which one’s better? According to the analysis in the previous section, if we were to have 0 all resist and 0 +life%, 50 all resist would be almost twice as good as 10% life (since 10% life is equivalent to 30 all resist when both are at 0). However, with just 300 all resist, and a 15% helmet gem, we can see that the last factor of our partial derivatives above are going to be (when multiplied by the amount of increase to give us an estimated effectiveness):
10% life: 10 * (1/(100+15)) = .087
50 all resist: 50 * (1/(300+300)) = .083
Now, this is an estimated change (and you’d have to recalculate a much longer equation to know the exact change) but it gives us a quick idea – it looks like they’re close, but 10% life is just better.
The reason I love this method of doing things is that it’s really easy to figure in your head. Is 10/115 bigger than 50/600? No? Then I’ll take the life.
Effects on Vitality
You can theoretically use this for vitality as well – assuming Diablo III gives you an accurate number of life you’ll be gaining (I’ve never noticed it being wrong before). The big difference is that essentially you’ll be considering the number you gain as a percentage of your life total (after %life) and then applying that as if it were a %life gain from 0%life. For example, if you have 56k health, and you’re considering 50 all resist while at 300 all resist or gaining 5600 health, you’d use the same partial derivative factors above to assess:
5600 health (10% life) from Vitality: 10 * (1/(100+0)) = .1
50 all resist: 50 *(1/(300+300)) = .083
Looks like, again, the life is better.
Life on Hit/Regen
This is one of the factors not included in this statistic. If you have a ton of regen or LoH, you may consider another method, as survivability from these stats doesn’t synergize with +Life % the same way damage reduction stats do.
Ranged/Melee Reduction
These are in a weird spot because they only reduce a portion of your damage taken and that portion isn't readily quantifiable, but if it's melee damage you're worried (and therefore are comfortable ignoring non-melee damage in your calculations) about % reduced melee can be applied similarly to the way %life gained by vit is applied - after all, it is just another multiplier applied to the %life taken equation. For example, if you are looking at a SoE with 17% melee reduction, the partial derivative factor would be:
17% melee reduction: 17 * (1/(100+0)) = .17
Based on a calculation below, you can see this is equivalent to 187 resist all at 800 resist all (you can see why people use these things!)
Conclusions
I see a lot of people running around on the forums talking about how they have 900 all resist, 8k armor but only 45k life. Using the above equations, this seems strange. At 800 all resist, the value from your partial derivative is:
100 resist @ 800: 100 * (1/(300+800)) = .091
At this point, you can see that even a 10% gain in health (4500 health or about 100 vit with 30-ish Life%) is actually better for you than the last 100 resist it takes to get to 900 all resist (see how easy these formulas are to use?). I think vitality/% life is worth more than the value people like these imply, and I’ve got the metric to prove it. 
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| Morfildur Germany. July 05 2012 01:29. Posts 3489 | Profile Blog # |
This is true for all heals based on your max health... but now factor in flat healing like that from health potions.
As far as i know, the best health potion heals 12500 health. If the damage gets reduced by 50%, it in effect protects you for another 25000 health. If your max health is higher but your armor/resistance lower, it my only protect you against maybe 20000 health worth of damage, which means health potions are less effective if you optimize according to your formula.
Then again, i stopped playing Diablo 3 in nightmare mode, so it might not matter in inferno.
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| | "Remember kids, the 3 most important things for becoming a good player: Micro, Macro and always take your Dailies!" - Rastaban |
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| Dead9 United States. July 05 2012 01:32. Posts 2327 | Profile Blog # |
there's a 50% bonus to resists from warcry yo
also u mentioned loh and life regen but there's also shields and lifesteal% |
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| Treehead July 05 2012 01:35. Posts 998 | Profile Blog # |
On July 05 2012 01:29 Morfildur wrote:
This is true for all heals based on your max health... but now factor in flat healing like that from health potions.
As far as i know, the best health potion heals 12500 health. If the damage gets reduced by 50%, it in effect protects you for another 25000 health. If your max health is higher but your armor/resistance lower, it my only protect you against maybe 20000 health worth of damage, which means health potions are less effective if you optimize according to your formula.
Then again, i stopped playing Diablo 3 in nightmare mode, so it might not matter in inferno.
Right, but potions are only around once every couple minutes. As a melee class, I take a lot more damage than that every couple minutes.
If 12.5k damage over a couple minutes counts as a lot of damage for you - just reduce the effectiveness of +life% in the % life taken equation by whatever % this counts for, and re-figure things based on that. It shouldn't change the method.
On July 05 2012 01:32 Dead9 wrote:
there's a 50% bonus to resists from warcry yo
also u mentioned loh and life regen but there's also shields and lifesteal%
Yeah, so this affects the calculation (as in, you can consider getting 120 resist per piece instead of 80 if you want the best I've seen on the AH), buy my conclusions and their weightings are unaffected. I still think have 1000+ resists seems overboard if you have the means to acquire comparable life gains.
Edit: LoH and Lifesteal are synonymous in my book. I didn't include dodge and block in the calculation, because they're not damage mitigation, they're damage evasion, and needed to be treated more probabilistically if included in a calculation (because empirically 99% damage reduction with a 0% block/dodge chance and 99% block/dodge chance with 0% damage reduction produce two widely differing results).Last edit: 2012-07-05 01:41:18 |
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| Dead9 United States. July 05 2012 01:55. Posts 2327 | Profile Blog # |
block blocks a greater percentage of damage if you have more resists
obviously this is pretty hard to calculate but it's a pretty big deal yo
dodge% is just a flat increase on ehp (33% = 1.5x ehp, 50% = 2x ehp, etc)
1000 resist is probably overboard, but a lot of the time u'd be better off stacking damage or loh over life% at that point
life% is still pretty good, it's just that usually resists and armor are more importantLast edit: 2012-07-05 01:56:24 |
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| Treehead July 05 2012 02:06. Posts 998 | Profile Blog # |
On July 05 2012 01:55 Dead9 wrote:
block blocks a greater percentage of damage if you have more resists
obviously this is pretty hard to calculate but it's a pretty big deal yo
dodge% is just a flat increase on ehp (33% = 1.5x ehp, 50% = 2x ehp, etc)
1000 resist is probably overboard, but a lot of the time u'd be better off stacking damage or loh over life% at that point
life% is still pretty good, it's just that usually resists and armor are more important
Dodge and block don't work like that - they might effect the metric known as "ehp" in that manner, but believe me, if you had 99% block/dodge, and 1% of your current health total, you'd die in every fight, despite having the same "ehp". The values I stated aren't practical, but they illustrate a disparity in the metric.
1% chance to take 100,000 damage, and a 100% chance to take 1,000 damage result in the same expected damage (resulting in a similar effect on "ehp"), but you'd never want the first scenario, because it'd just kill you - where the second you could deal with.
That's why you need to consider them probabilistically, not just by expected value.
I've shown math on why the bolded statement is not true at high values of resist and armor, can you show me why my math is wrong - rather than just saying my conclusions are wrong? |
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| Dead9 United States. July 05 2012 02:14. Posts 2327 | Profile Blog # |
math doesn't matter when you ignore all the important factors lol
block? loh? these are huge in a lot of barb builds
sure if you're running flat survivability + revenge 2h or smth life% is better, but that's harder to pull off than just buying some loh
dodge is a flat increase on ehp if you can heal the damage; im assuming you're not getting twoshot by w/e you're fighting
generally u can just consider these things "on average" because in d3 u get hit a lot and it averages out decently well enough
edit: by "twoshot" i just mean you die really fast
barb dodge is like 10% most of the time anyway, u can just count that as a flat ehp increaseLast edit: 2012-07-05 02:22:55 |
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| Treehead July 05 2012 02:32. Posts 998 | Profile Blog # |
On July 05 2012 02:14 Dead9 wrote:
math doesn't matter when you ignore all the important factors lol
block? loh? these are huge in a lot of barb builds
sure if you're running flat survivability + revenge 2h or smth life% is better, but that's harder to pull off than just buying some loh
dodge is a flat increase on ehp if you can heal the damage; im assuming you're not getting twoshot by w/e you're fighting
generally u can just consider these things "on average" because in d3 u get hit a lot and it averages out decently well enough
edit: by "twoshot" i just mean you die really fast
barb dodge is like 10% most of the time anyway, u can just count that as a flat ehp increase
If you had 0 resist, you'd just die. If you gear had no +vit on it, again, you'd die. If your armor were 0, you'd die. There are people not using shields or Life on Hit who do not die. I'm not saying these things cannot be good in some builds, but I don't think my method "ignores all the important factors".
I understand you disagree with what I'm saying and you're probably further into the content than I am, so I'll take you at your word. I personally think block is probably quite important (though I'm unsure on LoH). It is difficult, however, to take these "feelings" from experienced people such as yourself and do constructive things like making gear choices with, though. That's why the math is there. |
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| Dead9 United States. July 05 2012 19:22. Posts 2327 | Profile Blog # |
u should check out kripparian's youtube channel
he's probably the best thing about playing a barb
i think he has a video on what stats to prioritize |
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