## I'm boggled about Damage Reduction

• I was reading 2 posts recently and both struck me odd about the discussions about Damage Reduction.

At the very bottom of this thread,
http://www.diablofans.com/topic/79800-guide-comprehensive-cmww-guide/

I site this table: MP EHP (k) Damage Reduction % Armor Resists 1 140.5 75.1 2850 350 2 153.9 77.3 3000 395 3 168.7 79.2 3100 450 4 184.9 81.0 3250 500 5 202.7 82.8 3500 550 6 222.1 84.2 3700 600 7 243.4 85.6 4000 650 8 266.8 86.9 4300 700 9 292.4 88.0 4600 755 10 320.5 89.1 5000 800

And also in Loroese's post about DPS and EHP recommendations for different MP's, people were discussing about having 80%+ Damage Reduction.

My confusion comes in how Damage Reduction is calculated. Last I knew, it was a combination of all your sources of Damage Reduction from Armor & Resistances.

Now I play HC, so my wizard is quite defensively built. I currently have around 6k armor, 800 All Res, and about 60-70k HP. My EHP is somewhere in the ballpark of 450k.
However, my damage reduction is only like 60%.
How can this be possible when I have 800 All Res and 6k armor? How are people reaching 75-80-90% Damage reductions?

I even use Blur, which is another 10% melee damage reduction.
I just don't understand how people can get 80%+ DR while still maintaining sick amounts of DPS. You'd have to have like 1500 All Res and like 10k armor or some madness like that?

I must be missing something, someone please give me a clue.
• I guess with 60% you're looking at armor reduction or allres reduction individually. What's meant by the 80-90% is total damage reduction from combined allres+armor.

The formula for that is:
Total damage reduction % = 1 - (1 - armor DR) * (1 - allress DR)
(Thanks RasAlgethi for spotting the mistake)
Note that this is not taking into account special damage reduction, such as missile damage reduction, melee damage reduction and so on - but it works exactly like armor and allres, just add it to the formula.

If you load your char into D3up, you see total damage reduction in your defense stats on the right.

There are tables for how much mitigation each armor/allres point gives. Actually, your amount of armor and allres should both give more than 70% DR already (and make up for a combined more than 90%). Can't find the tables just right now.

Edit: Just found the formula for elemental damage, it's as follows:
Elemental damage reduction = resist / (5 × monster level + resist). We're probably talking about Inferno, so let's assume every monster is level 63.
And for armor it's:
DR from armor = armor / (50 × monster level + armor).

From that I'm sure we can create a table. Damn, why don't I have that yet? If no one links a table within the next few mins I'm gonna put one up on Google Docs. I know there are EHP calcs and spreadsheets and what not, but seriously, if you just have these two values and you want two percentages you don't wanna upload some CV into a 5000 question survey. Two values input, one value output. Anyone ever seen that?
• The formula is 1-[(1-Armor DR)(1-ResDR)]. Bagstone forgot the 1 in the beginnign as his will give you the damage taken.

All different sources of mitigation are multplicative so you would just add another set to the equation (if you're a monk or barb you'd add another (1-0.3) to it, with blur you'd add another (1-0.2) set)
• Ok. I was looking at the tooltip in game.

Is that only the armor DR? Cause I knew it seemed off

http://d3up.com/b/571887

My D3up shows a total of 85.7, so I'm assuming the ingame tip is only from armor. This makes much more sense now, haha. I thought I'd lost my mind or something.
• Quote from Murael23

Ok. I was looking at the tooltip in game.

Is that only the armor DR? Cause I knew it seemed off

http://d3up.com/b/571887

My D3up shows a total of 85.7, so I'm assuming the ingame tip is only from armor. This makes much more sense now, haha. I thought I'd lost my mind or something.

Yeah, the values make sense. What you mentioned in your first post are your buffed values - you can turn buffs on at D3up, which lets you get to 90%. Unbuffed you're at 85.76% total DR, as it says.
• In game tip only shows armor DR, I believe. It's actually pretty useless, imo, since actual DR includes resistances too.

Also, Blur is 20% DR against melee, not 10%

Just add that to the end of the formula, it's basically just 1-prod(1-DRi) where prod is product, so you multiply all them, and 1-DRi is the DR of stat i where i is armor, resist, elite reduction for a given item, melee reduction, etc. That's basically what the other posts above already said just with a bit more detail.
Wizard DPS and EHP Spreadsheet, mostly useful for wizards.
My Wizard
• Well, if you hover over armor, it just shows armor DR. If you open the details pane and hover over one of your resistances, it shows the DR for that resistance (allres usually means "lowest res" unless you're an OwE monk ;-)). So you can get both... but you'd still have to do the calculation for total DR offline, yeah. Just as you have to do the same for EHP.

Actually, Loroese, while you're here... do you know of any such "quick lookup tool" for total DR or total EHP? Or does your brain just automatically transform the values and raw numbers into EHP for you ;-) I always have a rough idea how much it is but I'm still sometimes surprised when I sync D3up. And all EHP calc tools take so much input... but afaik you can just assume level 63 mob, your HP/allres/armor and calc EHP value, right? Don't care about block, special elite, melee, dodge, w/e...
• It's just armor, resist, and hp to calculate EHP. You can add other things like elite damage reduction, melee damage reduction, etc. Some add dodge but I still say dodge isn't an EHP stat since it doesn't help you survive a single blast for slightly lower than your EHP 100% of the time like pre-dodge EHP does.

Also, the in game DR assumes a lvl 60 target, so it's again useless for pve.

Formula is

DRa = Armor / (Armor + 50*mob_lvl)
DRr = AR / (AR + 5*mob_lvl)
Total DR = (1-(1-DRa)*(1-DRr))
EHP = HP / (1-Total DR)

If you ever forget and have a copy of my spreadsheet you can see the formula in the calculations tabs.
Wizard DPS and EHP Spreadsheet, mostly useful for wizards.
My Wizard
• they really should start adding up LOH and LS into the ehp count
• Quote from pichapie

they really should start adding up LOH and LS into the ehp count

The problem is LS and LoH don't add to EHP, they add to sustainability. They are also highly depending on attack speed, skills used, and in the case of LS DPS. You need another category to compare LoH and LS with mitigation, like effective life gained per second.
Wizard DPS and EHP Spreadsheet, mostly useful for wizards.
My Wizard
• Okay, since I couldn't find any such table mentioned in post #2, I created really simple charts... printed them out and put them next to my PC to have a better estimate for upgrades. In case anyone's interested:

DL (for calculator on last sheet or if someone wants to edit stuff): http://www.megafileupload.com/en/file/427614/Diablo-3--damage-reduction-and-other-stuff--xlsx.html

===================
I tried to figure out some "reverse formula" for calculating necessary changes based on a target EHP value. Assuming an int class, I used the EHP assumptions from Loroese's CMWW guide to do some basic regression for typical int-classes armor/AR ratio:

armor = 1200 + 4.8 * AR

Putting all the formulas together (assuming level 63 mobs) and substituting armor with aforementioned formula you get:

EHP = HP / (1- (1- (1- (1200 + 4.8 * AR) / (50 * 63 + (1200 + 4.8 * AR))) * (1- AR / (5*63 + AR))))

It's been too long since I solved a formula like this by hand... and trying to enter this in certain rudimentary calculators I get wrong results. If anyone has Matlab or any other tool to solve this (I want to solve it for AR, obviously), that'd be awesome.
• Solve it by plotting the EHP-value vs AR. Then the zero will be your answer. You can do that with excel.
Wizard DPS and EHP Spreadsheet, mostly useful for wizards.