QA: Damage Reduction

Monk
The question; Do applicable Damage Reduction debuffs stack?

If yes; Additively or Multiplicatively, is there any DR?
If no; How does this affect my character build?

Test:
500 incoming attacks with no debuff applied.
500 incoming attacks with only keeping up Crippling Wave - Concussion (-20% dmg for 3s debuff)
500 incoming attacks with Crippling Wave - Concussion & your passive Resolve (-25% dmg for 2s)

I'm pulling the 1st mob on the first quest, on HELL difficulty with personally 2775 (48.05%) Armor, 62 (17.21%) physical resistance, no weapon (to keep auto attacking, not killing the mob, keeping 100% debuff uptime) & no shield. I auto attack for about 30 on mobs with 4000-6000 HP and I take no dmg. For this test, I HATE DODGE! Corner the mob, so that on-location auto-clicking can be done. The mob attacks once every 4-5 sec, 30% dodge chance, tedious work... If anyone has a faster attacking mob that you can easily reach & guaranteed you can pull one off, that also has a very small damage range (min-max dmg), tell me!

I'm taking down the numbers as my friend auto-attacks while watching Justified. Just open Excel on the laptop, watch screen, fill in number, press Enter, until the list reaches line 500. Also if you want to replicate this experiment, I suggest turning off all combat text except for "Display Damage numbers".

1st Test, gone through 31 mobs, HP varying from 6300-7000
2nd Test, gone through 36 mobs, HP varying from 6200-7000
3rd Test, gone through 40 mobs, HP varying from 5900-6800

Results:
No debuffs:
500 incoming attacks
Lowest attack: 498
Highest Attack: 986
Average attack: 756

Crippling Wave - Concussion:
500 incoming attacks
Lowest attack: 405 (81%)
Highest Attack: 912 (92%)
Average attack: 603 (80%)

Crippling Wave - Concussion & your passive Resolve:
500 incoming attacks
Lowest attack: 324 (65%)
Highest Attack: 898 (91%)
Average attack: 498 (66%)

Preliminary answer:
Due to the pretty big damage range of the mob, even 500 attacks in each category may be inconclusive. What is weird is that the lowest damage and the average damage go down with the expected amounts, the highest incoming attack varries less than 10%.

What is conclusive is that the frequency of low attacks is higher & the lowest attack is lower, however the highest attack with CW:Conc didn't go down and with CW:Conc + Resolve it wasn't 20 OR 25 (let alone 45%) lower.

All I can say right now is that "lowest hit" and "average hit" go down to 81% with CW:Conc and to 66% with Resolve added. The "highest attack" goes to respectively 92% (it goes up with just CW:Conc) and to 90% with Resolve added. The fluctuation however, due to high damage range (diff between lowest & highest attack) causes this test to go way up and down until you reach atleast 400 attacks, the percentage then starts stabilizing within 1-2% of the end-percentage.

If anything my preliminary conclusion is that
THEY DO STACK, MULTIPLICATIVELY AS A PART OF 1;
%DMG received = X / ((1+%DRD)*(1+%DRD)).

CW:Conc = 20%
Resolve = 25%
MoC:Int = 10%

For example, there's a mob that hits you for 1000 steadily, pre-block.
X = 1000
You use CW:Conc & Resolve for respectively 20% & 25% DMG reduction.

1000 / ((1+0.20) * (1+0.25)) = 666 DMG
Remove or add (1+X) for every Damage Reducing Debuff you're throwing on the enemy mobs.


This calls for a higher sample size, I personally I just cba with a mob that attacks every 4 sec and dies after 10 minutes. And add "only Resolve" and possibly "Mantra of Conviction: Intimidation" to the testing spectrum.

If I find a suitable mob (faster attack speed, solo pull, easily reachable, won't kill me, takes 10-15 minutes to kill, low dmg range), I'll test the following;
* No debuff
* Crippling Wave - Concussive
* Resolve (Passive)
* Mantra of Conviction - Intimidation
* CW:Conc + Resolve
* CW:Conc + MoC:Int
* CW:Conc + Resolve + MoC:Int
* Resolve + MoC:Int
... 500 attacks each, less if the dmg range from the mob is really small.

edit; wanted to try this out, just couldn't be arsed with finding a suitable mob to do it with, kudo's to Thaya for testing it first, gave me the motive to test it as well... terrible mob choice on my part tho I guess hehe
If anything my preliminary conclusion is that THEY DO STACK, BUT SUFFER FROM DEMINISHING RETURNS.
Seems more like dmg / (1.25 * 1.2) to me. That's 66% and is the same number you got.
Are you sure physical resistance indeed applies to normal attacks on you from mobs? It seems unusual from a game design perspective to have normal attacks damage diminished by Damage Reduction, Dodge, Armor, Block and Physical Resistance. I noticed some spells deal Physical Damage so I kinda assumed this was the purpose behind Physical Reduction.
20/05/2012 21:30Posted by Zero47
Are you sure physical resistance indeed applies to normal attacks on you from mobs? It seems unusual from a game design perspective to have normal attacks damage diminished by Damage Reduction, Dodge, Armor, Block and Physical Resistance. I noticed some spells deal Physical Damage so I kinda assumed this was the purpose behind Physical Reduction.


Don't know for a fact, tried the same skelly for 50 hits with 0 physical resistance, dmg was 3% higher, but that could be due to good RNG on it's part.

@Thaya, good one actually! DMG after (Damage Reducing Debuff)=1/((1+%DRD)*(1+%DRD))
Mind too numb after 2 hours of filling in Excel.

When I have some time I'll atleast try with Intimidation (Mantra of Conviction), which should add up to 1/((1+0,2)*(1+0,25)*(1+0,1))=0,61
Adding a bit;
Physical Resistance increases your protection according to the tooltip of each item, where you can see how benefits you (life, damage, protection). This is not the case for elemental/poison resistance, therefor I ASSUME that it applies somehow to regular melee attacks.

If you have Resolve, then out of every 1000 dmg, adding CW:Conc takes away another 133 dmg. For Deadly Reach with Keen Eye to match that (13.3%), your armor can be no higher than 2740. If your armor is higher, and you're choosing between CW:Conc and DR:KE, go with CW:Conc. Using both is an option, personally not a fan of the feel of such a rotation.

I do wonder wether or not your Damage Reduction through Armor is also mathmatically applied as; X / (1+%DRA) or as X * (1-%DRA)

edit; this question get's answered; See post #7
My aforementioned comparison of CW:Conc vs DR:KE holds true, based on my findings that I posted in post #7. If you choose 1 or the other, go with CW:Conc!

Crippling Wave with Concussive (-20% enemy damage) -VS- Deadly Reach with Keen Eye (+50% armor):
On my level, 3771 passive armor (lv60, wielding a shield), 50% bonus armor from DR:KE adds a mere 10%~ additional damage reduction (vs 13.3% from CW:Conc, if you have Resolve... if you don't have resolve CW:Conc adds 17.66% dmg reduc). The higher your armor get's, the more CW:Conc pulls ahead of DR:KE.

My passive armor is 3771, 55.69% dmg reduc,
With Deadly Reach & Keen Eye rune, adding (+50% Armor) = 5656 (65.34%)... added benefit of DR:KE is 9.65% damage reduc
With Mantra of Evasion & Hard Target rune (+20% Armor) I have 4525 (60.13%)... added benefit of MoE:HT is 4.44% damage reduc
With MoE:HT and DR:KE, I have 6410 (68.12%)... added benefit of DR:KE with MoE:HT active is 7.99%

Been running Armor down in itterations of 200, 50% bonus armor from DR:KE never seems to get above 12% additional dmg reduc, making DR:KE a worse ability+rune for the entire game, the only reason you would ever use DR:KE for dmg reduc is to further improve while you already have CW:Conc.

When to use Deadly Reach with Keen Eye for DMG reduc?
1. Kiting, goes easier with DR,
2. Versus heavy ranged packs (especially versus succubi) this one may prove superior. Since you don't apply CW:Conc to ranged units.

If you have Resolve, then out of every 1000 dmg, adding CW:Conc takes away another 133 dmg. For Deadly Reach with Keen Eye to match that (13.3%), your armor can be no higher than 2740. If your armor is higher, and you're choosing between CW:Conc and DR:KE, go with CW:Conc. Using both is an option, personally not a fan of the feel of such a rotation.

Good info
Decided before going to bed to do some quick tests for our Damage Reduction through Armor (DRa) and Damage Reduc through Physical Resistance (DRpr).

Ran a small sample size of 100 on our friend, Risen, 1st mob in Nightmare mode, 1st Quest, act 1.

Test:
#1 - Take 100 attacks with no gear on, 7.81% damage reduction through innate Dexterity, no physical resistence
#2 - Take 100 attacks with 2934 Armor, no physical resistence, 49.44% damage reduction through armor.
#3 - Take 100 attacks with 2937 Armor, 113 physical resistance, 49.45% DRa & 27.43 DRpr (49.45+27.43=76.87% DRtotal).

Results:
Test 1:
Low: 125
High: 227
Avg: 179
... this is a pretty awesome number, cause wether you divide 1 by (1+0.0781)=1.0781 or multiply by (1-0.0781)=0.9219, the outcome is that our friend the Risen on avg, without dmg reduction, would do 193 per hit. 193/1.0781 & 193 x 0.9219 is 178, respectively 179!

Test 2:
Low: 60 (48%)
High: 118 (52%)
Avg: 97 (54%)

Test 3:
Low: 28 (22%)
High: 55 (24%)
Avg: 43 (24%)

Conclusion:
This shows, with such a small sample size atleast, that we can assume, that damage migitation from armor & physical resistence both deminish incoming physical regular & special hits (ranged as well presumably) and that the given percentages are directly subtracted from X (X=attack dmg).

Also Physical Resistance & Armor stack, additively.

F.Ex:
Let's say we fight the Skeleton King and he hits for 1.000 dmg per hit.
You have 50% damage reduction through armor & 25% through Physical resistance.
Simply add your 50% + 25% = 75% total physical damage reduction,
Now apply, 1000 x (1-0.75) = 250 damage.

edit; Tho Physical Resistance & Armor stacking seems logical, based on a small sample size tho, it's unlikely... As both combined easily reach 100% (5000 armor, 300 resistance and you're there), which should mean you take no damage (unless enemies deal atleast X dmg regardless of migitation, which is unlikely as wel). If that were the case, you can get invulnerable with some decent AH'ing, which would've been used already and it'd be widespread info hehe.

Or INFERNO (maybe even Hell) has a reduction of your dmg reduction (you have 90% dmg reduc, PvE nerfs it), you take 10% more dmg (you can reduce 100% of dmg taken max, but you take 110% everytime you're hit) or mobs/bosses do 10% more dmg (you reduce 100% max, but again, take 110%)... or mobs/bosses are higher than lv60 and your 100% dmg reduc doesn't go higher or you need exponentially more per level that a boss/mob is higher than you (like bosses being 63 like in WoW?).
Hi im currently playing a monk, i'm at lvl 60 with 2209 armour (48.36%), and 476 all resists (61.37%) running with CW:Conc, Resolve, One Withe Everything, MoH:ToN .

i'm in inferno act 2 and i can say that its very difficult to defeat 1 mob on its own 2 mobs is possible with earth ally, and 3 is damn right impossible
I'm a monk in act 4 inferno at the moment, the reason why it's so hard even with all this mitigation is because the mobs in inferno are higher level, Act 1 = level 60, act 2 = level 61, act 3 = level 62, act 4 = level 63. If you read on your mitigation those % are only agaisn't level 60. Higher armor, higher resists and you should be good... but don't take me wrong, it's not easy and act 2 is a pain in the !@# for a monk.
22/05/2012 02:07Posted by Sidewai
I'm a monk in act 4 inferno at the moment, the reason why it's so hard even with all this mitigation is because the mobs in inferno are higher level, Act 1 = level 60, act 2 = level 61, act 3 = level 62, act 4 = level 63. If you read on your mitigation those % are only agaisn't level 60. Higher armor, higher resists and you should be good... but don't take me wrong, it's not easy and act 2 is a pain in the !@# for a monk.

Did you end up skipping everything skippable until Belial or do you actually deal with packs?
Hi guys.
Since you are in a damage reduction test mood,can you actually test if resolve debuff procs
from a single reflect damage armor piece,especially for ranged test subject.
from what i read i thought damage reduction stacks multiplicativ, but it seems your right.
in your case 179 dmg with 7.81%=0.0781 reduction means the unreduced dmg was 179/(1-0.0781)=194.
test2: 49.44% reduction. expected dmg=194*(1-0.4944)=98. yours was 97 -> match
test3: 49.45% from armor and 27.43% from res: expected dmg=194*(1-0.4944)(1-0.2743)=71. yours was 43 -> guess your right!
real dmg=194*(1-0.4944-0.2743)=44 -> match
thanks alot!

from kipps youtube video I heared the reduction % is calculated like this:
reduction=armor/(armor+50*monster*lvl)
reduction=resist/(resist+5*monster*lvl) and it works for a lvl 60 mob with your values.

i think it would be interesting to do the same calculation for 100% and 110% resistance to see if there is a hard cap or some diminishing return mechanism. you could also try with act 1 mobs on normal, since you will have easily 98% from 2934 armor and 96% from 118 resist on a lvl1 mob.
Also Physical Resistance & Armor stack, additively.


I'm not sure I follow this, wouldn't this mean you can get way over 100% DR?

I have like 60% from armor and 60% from physical resist, adding them is over 100. I'm assuming that's not what you mean.

Do you mean that first the armor is subtracted then the resist is subtracted? That would mean that you still get the "full" reduction amount %-wise of each.

I'm no math wiz btw, so my apologies.
http://rubensayshi.github.com/d3-ehp-calculator/#intro

use this
"My preliminary attacks leave cemetaries packed, of N*ggaz who think it aint like that."

Always liked the word Preliminary! thanks for using!
Also Physical Resistance & Armor stack, additively.


I'm not sure I follow this, wouldn't this mean you can get way over 100% DR?

I have like 60% from armor and 60% from physical resist, adding them is over 100. I'm assuming that's not what you mean.

Do you mean that first the armor is subtracted then the resist is subtracted? That would mean that you still get the "full" reduction amount %-wise of each.

I'm no math wiz btw, so my apologies.


Still haven't found an answer or clarification on this. Adding 2 %'s together doesn't make sense to me still.

To expand on this thread though I've been recently trying to determine exactly how "Reduced Damage From Elites" and the other affixes likes it work. I think you would be a good man for the job if you were up for it.

At face value, they seem to be very, very powerful affixes. It takes a lot of resistance or armor to = 4% damage reduction and some items have 7% DR for Elites.

I recently heard that they reduce damage AFTER armor and resists are calculated so I'm curious if that's true and just how exactly that would work.
There won't be clarification because it's incorrect. Reductions stack like this:

Total damage reduction = 1 - ((1 - DR from Armor) × (1 - DR from Resistance) × (1 - other DR))

Damage reduction from elites/ranged/melee works exactly the same way as any other damage reduction, just with a type check. The only thing I'm not sure about is whether elite damage reduction in particular will affect ground AoE spells casted by elites, otherwise it's a fairly simple concept.

It's a good stat, but not worth sacrificing other stats for. Whatever setup I tried, it always ended up being equal to roughly ~10 resistances. Play some with numbers here if you're interested: http://rubensayshi.github.com/d3-ehp-calculator
Question:
Aren't all damage_taken modifiers just multiplied?

I.e.: If I have 60% armour, 65% resist, Resolve and MoC:Int then don't I take:
<damage> * 0,4 (armour) * 0,35 (resist) * 0,75 (resolve) * 0,9 (MoC)

Personal defence is definitely multiplicative, and as you tested debuffs seem to be, too. This means we can just multiply everything together. ;)

Total damage reduction = 1 - ((1 - DR from Armor) × (1 - DR from Resistance) × (1 - other DR))


This formula seems to be reliable. My calculations:
1 - ((1 - 0.75) x (1 - 0.78) x (1 - 0.3)) = 1 - 0.0385 = 0.9615 = 96% DR
So inferno mobs are doing 100k+ damage as I've expected.
Aaaaah. Sorry, I misread the way the formula was intended to be used, I thought it calculates remaining damage taken.7

Although tbh, I usually find it easier to just multiply all <remaining_damage_taken>-multipliers.

In other words, 45% dodge -> 0,55 still taken.
62% armour -> 0,38 still taken, and so on.

Or in your case, 0,25 * 0,22 * 0,7

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