Armor Theory-crafting - Armor y u no protect me?

As of late, I have been doing some calculations regarding the damage reduction provided by armor. I have been playing around with numbers since the time I picked up Iron Reflexes, so I am looking at this purely from a physical damage reduction point of view. Elemental damage / Chaos damage as it stands is pretty straightforward to grasp and the goal there is to always max as much as you can your resists.

However, the fact that damage reduction depends on the damage taken, i.e. large damage can "penetrate" your armor makes the understanding of how much armor is needed unconventional (as in comparison to other similar games) if not a bit tricky.

My goal was to formulate this in a way I can easily understand. While I am aware of other posts on the armor topic, most if not all have been discussing this from a damage reduction perspective which would need to have data on mob damage.

The first thing I have been looking at is how not to get one shot by a physical hit and how can I get armor to help me achieve that goal (you can thank Lord Incarcerator Brutus for that).

Plugging in all equations (simple really), I arrived at the following, in order NOT to be one shot, the following must hold:

AHP >= 12 DHP (DHP-1)

AHP : Armor to Health Ratio
DHP : Damage to Health Ratio

As an illustration, the picture below shows up to a hit which would take two times your total HP and how much minimum Armor is needed to (barely) survive that hit.



As an example, to survive one shot hit that would do 1.5 times my HP, I would need more than a whopping 9 times the amount of HP as armor. At first glance this looks like a bad case for armor, but in fact not much so, the issue really is HP. If I increase my HP by a slight 10%, that same hit would only require ~6 times my 10% increased HP, i.e. 6.6 my old HP instead of 9 times, which is the absolute figure that matters in the end.

To see this more clearly, I defined the killing blow damage as the damage required to one shot me, this can easily be obtained as:

DKill = 0.5*HP*(1+ sqrt(1+ AR /(3*HP)))

with obvious notations
AR : Armor
HP : Health

Obviously, you want to make your DKill as high as possible in order to make sure that you have enough head room to survive it all.

- With ZERO armor, your Dkill is basically your HP, if something hits you for more than that, you die, you go to default in shame, you friends laugh at you, your girlfriend leave you for another man, you are worse than monkey shit.

- With increasing armor, your Dkill starts to ramp-up. As mentionned in the example above, with an armor equal to 9 times your HP, you Dkill is equal to double your HP. And this is where the problem really lies. Compared to HP, armor only sub-linearly, while HP contribution is linear.

- This equation can help select armor pieces, however, this would be only useful at the highest gear levels where armor is plenty, at low levels the best choice seem to be to stick to life.

- It would be good to know the maximum achievable armor to make educated guesses as to the benefits of armor in end game, but looking at the picture below it seems that armor is most beneficial at higher levels of gear (and in fact is plenty at those levels) than at low levels.

The figure below show contour plots of the Dkill as function of Armor and HP




One question that remains is still to quantify whether the armor nodes in the skill tree are really something that needs buffing or not. The other question is the effect on armor for hits that are below total HP (i.e. hits that are not meant to one shot you). This could be something to explore by evaluating the Dkill of say x (x= 5..10?) mobs dealing low damage at the same time, I think this is where armor shines without a doubt...a topic for another post maybe.

Edit:
- Didn't think this will get much attention, thanks for all the feedback, spent most of my time leveling that marauder, apologies for not reacting sooner.
- Renamed the thread to a more serious tone ;-)
- Working on incorporating endurance charges as well as reading all the material/ replies to this thread.

So I click on the thread title, thinking it's some troll thread, and hey, awesome theorycrafting. Gets me thinking. So I crunched some numbers and...

The armour EHP multiplier is
(sqrt(9+3*A/L*K)+3)/6
where A is your armour, L is your life, and K is the number of shots you're trying to survive (e.g. 1 for one-shot, 2 for 2-shot, etc.)

Example from above: 9 times your armour in HP should mean 1.5 times the EHP for one-shots.
(sqrt(9+3*9/1*1)+3)/6 =(sqrt(9+27)+3)/6 = (sqrt(36)+3)/6 = (6+3)/6 = 9/6 = 1.5

New example: same 9 times your armour, but we're trying to survive a 2-shot.
(sqrt(9+3*9/1*2)+3)/6 = (sqrt(9+54)+3)/6 = (sqrt(63)+3)/6 = (3*sqrt(7)+3)/6 = (sqrt(7)+1)/2 = 1.823 (approx)

To prove the new example, let's take a life of 1000, armour of 9000, and damage of 911 (two of these would equal 1822).

9000/(9000+911*12) = 9000/19932 = 45.15% damage mitigation (approx)
911*(1-.4515) = 911*.5485 = 499.68 (approx)
It's just under 500 per hit because the two combined hits are just under 1823.

OP, please retitle this thread.

You're excluding endurance charges from the whole thing.... Don't do that! Endurance and armour rating go hand in hand. If you have high armour, you also have high endurance - or you're doing it wrong.

An interesting thing happens when you incorporate endurance into the reduction formula, and try to ask the question: "How much armour rating do I need to maintain some set percent reduction?"

The A / D ratio (armour per unmitigated damage intake) is a constant if you also treat number of endurance charges as a build-defined constant. In other words, you can linearize the reduction equation by choosing a desired percent reduction and a desired number of endurance charges. That coefficient of 12 goes away - it becomes much, much smaller as you stack more charges. The resulting curve is shallow if you have many endurance charges and steep if you have few.

Just some things to think about.

*looks at title*

Me: oh this looks like a fun lighthearted topic!

*opens thread*

MAAAAAAAATH

Me: dead


X_X

This is extremely informative and more players should know how necessary base life is in the game.

I haven't run the numbers but I suspect a few Endurance charges would shift that curve quite a bit.

Then again, it's not easy to get Endurance charges when fighting a lone boss...

"

Incompetent wrote:

Then again, it's not easy to get Endurance charges when fighting a lone boss...

It actually is, with Enduring cry. You are guaranteed to get 1 charge per cry.

"

Zakaluka wrote:

You're excluding endurance charges from the whole thing.... Don't do that! Endurance and armour rating go hand in hand. If you have high armour, you also have high endurance - or you're doing it wrong.

You're absolutely right, calculating it without endurance charges was foolish. Unfortunately, factoring in endurance charges makes the formula much less pretty:

(sqrt(A^2*E^2*K^2+(19200*A-480*A*E)*K+57600)+A*E*K+240)/(24*(20-E))
where A is armour per life point, E is endurance charges, and K is number of hits to survive.

Since it's pretty calculation intensive, I made a little Google Drive spreadsheet.

Bump, thread desperately needs a rename.

They could probably lower it to 9 instead of 12 to make things a bit easier.


Or perhaps not make map bosses hit for 2-3k.