Diablo 3: Armor, Resistances, and Effective Health

Armor, Resistances, and Effective HealthYour damage reduction is based on your armor and resistances, and how those stats are based on Intelligence and Strength. I'm hoping for people to have a thorough understanding of damage reduction based on those stats, and how to make an effective stat decision. (Note that with, say, ten open non-helm sockets, you would have 286 different possible ways of customizing your stats, not to mention gear choices, so stats customization is very real in D3). At the end I'll mention how effective health is based on these things, and show that intelligence and strength alike boost your effective health linearly.

The damage reduction formulas I have tested quite thoroughly. I encourage you to check it yourself.

Soul Reaper Legacy Guide for Diablo 3

Diablo 3: Armor, Resistances, and Effective Health

Let's talk about the stats' effects on resistance and armor. One strength gives one armor for every class. Thus any class's armor is the armor points from his equipment plus his strength (times any multiplying factor from bonuses). As well, one intelligence gives 0.1 to all resistances, which is a separate thing from armor. There are six resistances: Physical, Fire, Lightning, Ice, Poison, and Arcane/Holy (they share a resistance). I believe this covers all types of damage, so intelligence is basically a multiplicative source of all damage reduction as is armor.

Now for the punchline. Here are the following variables I define for the damage reduction formulas:

v = Level of the monster you're facing
A = Armor
D = Damage reduced due to armor (all types of damage)
R = Resistance to a certain element (remember without resistance gear, and with just intelligence, all resistances are the same)
d = damage reduced due to R, from that specific element.

One thing to note is that v refers to monster level, yet if you look at the damage reduction from the character sheet, it tells you based on your level. That's because it's telling you how you resist monsters that are your level. Because of this, you'll never be able to use the character sheet to know your damage reduction in Inferno, since you'll never reach their level. (I use v and not L, because L is reserved later for the variable Life.)

Now for the damage reduction formulas:

D = A /(50v + A)
d = R /(5v + R)

They look basically the same, only damage reduction from armor has a stronger attenuation rate (50), which means it grows more slowly. Here's what they look like vs level 62 monsters:

All Damage Reduction from Armor

Elemental Damage Reduction from a Resistance (could include physical)

Buy D3 Gold - Trusted, Fast, SafeNotice the x axis in each one. Damage reduction grows at ten times the rate from resistance as it does from armor, so I ranged the x axis plot for resistance as 1/10 of what it is from armor (res goes up to 3000, armor goes up to 30 000), making them look identical. Also notice that in the limit that either resistance or armor goes towards infinity, damage reduction approaches 1, which means complete immunity. (I have it in fractional units, to get percent just multiply by 100.) This is good because it means you will never be immune, no matter how many points you invest, yet points will always benefit you.

One thing to note is that, while resistance grows damage reduction at ten times the rate of armor, 1 strength = 1 armor, and 1 int. = 0.1 all resistances. Thus, assuming no armor and no resistances, intelligence and strength will grow your damage reduction at the exact same rate. In order for you to decide which one is better to invest in for damage reduction, just look at your armor and 10x your resistances, and see which one you have more of, and which one you have less of. For example, if you have 2000 armor and 200 fire resist, your damage reduced from fire will benefit exactly the same from 1 point in strength, or one point in intelligence. If you have less than 200 fire resist, you would prefer int. against fire. If you have more than 200 res, you would prefer armor.

This concludes the thread, unless you want to read about effective health.


Effective Health

I define effective health as the amount of damage a monster needs to deal to you, if he assumes you have 0 damage reduction, to kill you. For example, if your life is 100, and you have 50% damage reduction, a monster will perceive that he must do 200 damage to you to kill you, so your effective health is 200. Note that if your elemental resistances differ, you have different effective health against different elements.

Let's say you have a grand total of damage reduction of X. X = 1 implies complete immunity, X = 0.5 means half damage reduced, etc. If a monster deals damage to you, you will take (1-X) of that damage. Let H be effective health, and L be your life, as read on the health globe. If a monster wants to kill you, he must do exactly H damage to you, and you must receive exactly L damage to die. If he does H damage to you, you receive damage H(1-X), thus H(1-X) = L, or H = L/(1-X).

Recall that D is your damage reduction due to armor, and d is your reduction from an element due to a resistance. Since they're multiplicative, we have (1-X) = (1-D)(1-d). Thus, your effective health against that element is
H = L/[(1-d)(1-D)]
Each resistance separately multiplies your health by a factor of 1/(1-d). Let's say you have 1 life. Here is how your effective health will scale with damage reduction X:

Effective Health vs Damage Reduction

Soul Reaper Expansion Leveling GuideNotice that as damage reduction approaches 1, effective health approaches infinity. This is a known result, as complete immunity means you will never die; a monster has to deal infinite damage to kill you.

Now if you take 
D = A /(50v + A)
d = R /(5v + R)
and plug those into 
H = L/[(1-d)(1-D)],
you get

H = L(1 + A/50v)(1 + R/5v)
That is, it grows linearly. Let's take a fixed resistance of 0, for example, and look at effective health due entirely to armor, vs level 62 monsters, starting from 1 life:

Effective Health vs Armor assuming 1 health and 0 resistances, vs level 62 monsters


written by Bridgeburners 

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