Damage reduction is an aspect in Diablo III that most people know exists, but only a few know exactly how it operates. For most of D3, you do not necessarily need to study all aspects of the game since it is far easier and less stressful to just copy what the top ranking players are doing.
Most people start out never truly understanding why everyone puts Diamonds in their gear. Sure, it makes you tankier, but why don’t people go for other stats? Why not Armor or Health? A lot of people don’t seek out answers to these questions because “If it works for the top players, it works for me.”
In this guide, I am going to explain exactly what damage reduction is and how to best utilize it in Diablo III. While it is possible to go indepth, I figured it was best to cover this in a way that would most benefit the people who need the info the most  specifically players who are new to Diablo or who are just not that experienced. Here, I will be explaining: What damage reduction is, what elements affect damage reduction, armor and allresist, how to minmax, and how to utilize all that info.
Here is a quick TLDR video if you don't want to read everything below:
Damage reduction is simply the % mitigation you gain when taking damage in Diablo. For example, if you have a damage reduction of 90% and a projectile that is supposed to do 100 damage hits you, your 90% reduction will reduce it to 10 damage taken. Aside from overall damage, damage
reduction is the most crucial stat that you can acquire when looking to push Greater Rifts.
There are many attributes to reducing damage. Below are some of the main contributors...
 Class
 Armor + AllResist
 Dodge
 % Damage Reduction
 Reflect/Life Regen
First, the class you play has a huge effect on how much or how little damage you take. Naturally, Monks, Barbarians, and Crusaders take 30% less damage compared to the Wizard, Demon Hunter, Witch Doctor, and Necromancer. This is due to the game balancing melee classes to be able to take more damage than ranged ones; since they fight up close and personal, melee classes are more prone to taking damage.
In addition to this, main stats such as Strength and Dexterity give armor as a side bonus for increasing your damage; Intelligence gives you allresist. This means that Strength and Dexterity classes naturally take less physical damage and Intelligence classes naturally take less elemental damage (cold, fire, arcane, lightning, poison, etc).
Next, we’ll take a look at dodge and pure % damage reduction. Dodge (more commonly known as Dodge Chance ingame) gives you a certain percentage chance to completely ignore damage taken. For example, let’s say you have 35% Dodge Chance. This means you have a 35% chance to ignore damage taken or have a 65% chance to get hit. Although this stat alone is heavily RNGbased (Random Number Generator), it still counts towards your toughness and damage reduction. Unfortunately, Dodge Chance can never reach 100% as the stat itself is multiplicative, not additive.
With pure % damage reduction, this stat flat out decreases the amount of damage you take. Of course, as with most stats in the game, this effect will stack multiplicatively and not additively (having additive % damage reduction would make it far too easy to make an invincible God toon; while the concept is exciting, it would probably get really boring really fast).
Let’s use Aquila Cuirass and Elusive Ring to explore this a bit. Aquila gives 50% damage reduction when above 90% resource and Elusive Ring gives 60% damage reduction after casting Shadow Power, Smoke Screen, or Vault.
At first glance, you might think “50+60 would be 110. So wouldn’t I have 110% damage reduction?” Unfortunately, no. The damage reduction formula is as follows.
DR = 1  (1x)*(1y)*(1z)
DR represents damage reduction. 1 represents you. The variables x,y,z represent % damage reduction you gain from items or abilities.
Since we are using the example of Aquila and Elusive Ring, we only have 2 values of damage reduction. Hence, we will only be using the values ‘x’ (Aquila) and ‘y’ (Elusive Ring). You can add more letter variables based on how many % damage reduction factors/items you have.
Putting our numbers in the formula: DR = 1  (10.5)*(10.6).
The result is 0.8 which equals to 80% damage reduction.
Armor and AllResist also strongly influence damage reduction, but I will cover those indepth in the next section.
There are other minor factors that affect damage reduction such as reflect and life regen, but the effect they have is negligible compared to everything else.
It may seem simple and effective to just have lots of items with % damage reduction  and it is undoubtedly effective. However, if you really want to get the most out of damage reduction, there is something else you’ll need to focus on: your ratio of armor and allresist.
As I mentioned earlier, armor reduces damage taken from physical damage and allresist reduces damage taken from elemental damage. In D3, a majority of the damage you take is physical. However, this does not mean you will benefit more from stacking armor alone. In fact, it is not beneficial for you to go all in on either stat.
Here is why.
These equations are defined by Blizzard.
Damage reduction from armor is = (your armor) / (50*enemyLevel + your armor).
Damage reduction from resist is = (your resist)/(5*enemyLevel+your resist).
Since toughness (your defense) is your armor multiplied by your allresist, you want to keep your damage reduction from armor and allresist as close as possible.
Here is an analogy to clarify. Say that you have 10 Tennis balls and 2 buckets. Say that you also have a friend who forces you to do highschool story math problems under threat of violence. He tells you to divide the balls between the buckets so that multiplying the balls in each bucket will give you the greatest possible value. Going 9 and 1 would get you a low number and really upset your friend. To avoid your friend’s wrath and get the greatest value, you would need to put 5 Tennis balls in each bucket. This will lead to the greatest multiplied value of 25.
The same theory applies to armor and allresist. Since both values will be multiplied, you want your damage reduction from armor to closely resemble your damage reduction from allresist. Now, let’s look back at the equations above. The only difference between the two equations is the number in the denominator: 50 for armor and 5 for allresist.
If we’ve got 10000 Armor, 1000 Allresist, and the monster level is 70, our armor will give 74% damage reduction and our allresist will give us 74% damage reduction. These values combined together will give you a higher damage reduction value (94.5% damage reduction) than if you had 9500 Armor and 1500 Allresist.
Hence, you want to keep allresist and armor to a 1:10 ratio.
Classes with Dex or Str as their main stat will have an easier time gaining armor compared to allresist. Classes with Int as their main stat will have an easier time gaining allresist compared to armor. In other words, your Dex/Str classes should go for allresist items and your Int classes should aim for gear with armor.
Granted, the amount of armor and allresist you have will not be cleancut. Just make sure you check your defensive stats; if you have too much of one or the other, try to nudge it as close to the golden ratio (1:10) as you can.
Whenever you create a character, from the getgo you can now know what defensive stat you will be looking for. Dex/Str classes will want allresist and Int classes will want armor. Instead of unknowingly accepting multiple % damage reduction effects, you can personally calculate how much effectiveness you are getting out of your items.
Although this information does not guarantee you will be rank 1 on the leaderboards for every season, this knowledge may help you push a few GRs when you thought you had capped out. Also, it never hurts to know what exactly what item is better when comparing two very nice looking ancients.
I hope this guide has helped clear up exactly how damage reduction works in Diablo III and how you can minmax it by keeping the armorallresist ratio. As always, happy hunting!
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Comments :6

0
level 1 Mark_Weber
either way, from a player standpoint you'll be needing db3 gold https://mmoauctions.com/diablo3/gold, and don't tell me you don't, cause you will visit the shop sooner or later in game

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level 1 Miguel_Lozano
In the character sheet exist 2 things that you still have not explained and one more thing that somehow contradict your hypothesis that "Armor" is just for physical damage and "Resistances" only for magical damage. It would be great if you could update this post regarding what I will point out:
The 2 things that you have not explained is "Melee damage reduction" and "Projectile damage reduction". It is clear that these things work in a multiplicative way with other kinds of damages reduction, but the question is this ¿Both of them refers only to physical damage or for example a elemental projectile could be affected by "Projectile damage reduction"?
In other hand, the thing that makes me doubt of your theory of "Armor" is just for physical damage and "Resistances" only for magical damage is the existence of the "Physical Resistance". It makes me think that "Armor" and "Resistances" works in a multiplicative way. It means that the real damage reduction of any type of damage got from "Armor" and "Resistances" would be:
Damage reduction from Armor and Resistences =
= 1  [ (50*enemyLevel) / (50*enemyLevel + your armor) ] * [ (5*enemyLevel)/(5*enemyLevel+your resist to the specific kind of damage)
If what I say is true, then for example the damage taken of an arrow would be:
Damage taken of an arrow =
= [ (50*enemyLevel) / (50*enemyLevel + your armor) ] * [ (5*enemyLevel)/(5*enemyLevel+your physical resist) * [1projectile damage reduction] * [1general damage reduction]
Where the damage reductions are expressed as numbers between 0 and 1. 
0
level 1 Miguel_Lozano
And one more recommendation:
In the end what matters to take the best decisions in the defensive scope are 2 things (the second generally more important than the first):
Life / [ damage taken * (1dodge) ]
Life Regen / [ damage taken * (1dodge) ]
Where "damage taken" is a number between 0 and 1 that represent the percentage of damage that pierce after all damage reductions, and "dodge" is a number between 0 and 1 that represent the probability of evade the hit. 
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level 1 Miguel_Lozano
By the way it would be nice if you do a post about the offensive scope in Diablo 3. In fact I have one doubt about it, my doubt is it:
Do all kinds of "increase damage" that are not registered in the character sheet and that are pertinent to calculate the final damage of a skill work always, ones with the others, in a multiplicative way?
For example: I am playing with a Wizard and I am using 3 pieces of armor that have the attribute of increase the damage of the meteor skill. My character sheet only take account the increase of damage that come from one of these pieces of armor. The other 2 pieces of armor that increase the damage of meteor are ignored in the character sheet. ¿Does it imply that each one of the other 2 pieces of armors that increase the damage of meteor works in a multiplicative way? 
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level 1 Miguel_Lozano
One last thing. The golden ratio that you found only would be correct if it were as easy to get +100 to all resistances as +1000 of armor and if it were the case that you already have 10 times more "armor" than "all resistances" . In deed your example of the tennis balls and the 2 buckets don't apply here, because the number of balls will not remain constant, I mean, it could be the case that you withdraw 1 ball of one bucket to put 2 balls in the other. You can choose for example to lose 120 to all resistances in exchange of gain 780 of armor, and the damage reduction that you are losing in the resistances with this change is not the same that the damage reduction you are gaining in the armor. Even more, the damage reduction you gain or lose from a constant amount of "armor" or "resistances" changes in function of the amount of "armor" and "resistance"that you already have.
If you want to find the correct golden ratio you first need to minimize the function:
f(x) = ( 50*L / (50*L+A+P* x) ) * ( 5*L / (5*L+RQ* x) )
where
"L" is the enemy level
"A" is the Armor your character have
"R" is the Resistance your character have
And "P" the amount of Armor you can gain in exchange if you lose "Q" amount of Resistances
so you have that
ΔA = P*x
ΔR = Q*x
where ΔA is how much "Armor" you should gain and ΔR how much "Resistance" you should lose in order to get the maximum damage reduction.
If you do the math, you will see that the real golden ratio is:
(50*L+A) / (5*L+R) = P/Q
and
ΔA = 0.5 * ( (5*L+R)*(P/Q)  (50*L+A) )
ΔR = 0.5 * ( (50*L+A)*(Q/P)  (5*L+R) )
If you want to see this result intuitively, you need to note that:
(50*L+A) = (50*enemyLevel) / (the ratio of damage that can pierce the armor)
(5*L+R) = (5*enemyLevel) / (the ratio of damage that can pierce the resistances)
in consequence and regarding that
(absorption power of the armor) = 1 / (the ratio of damage that can pierce the armor)
(absorption power of the resistances) = 1 / (the ratio of damage that can pierce the resistances)
(how much armor you can get from the gear) = P
(how much resistances you can get from the gear) = Q
the meaning of this "golden ratio" is:
(10 times the absorption power of the armor) / (absorption power of the resistances) =
= (how much armor you can get from the gear) / (how much resistances you can get from the gear) 
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level 1 Miguel_Lozano
... In conclusion, what the "golden ratio" tells you is this:
(absorption power of the armor) / (absorption power of the resistances) =
= (how much armor you can get from the gear) / (10 times how much resistances you can get from the gear)
where
(absorption power of armor) = (50*enemyLevel+your armor) / (50*enemyLevel)
(absorption power of the resistances) = (5*enemyLevel+your resist) / (5*enemyLevel)
(how much armor you can get from the gear) = P
(how much resistances you can get from the gear) = Q
where "P" is the amount of Armor you can gain or lose in exchange of losing or gaining "Q" amount of Resistances