## Comprehensive Guide on Everything Defense Related

You want to feel like nothing can hurt you? Like you are made out of pillows and cannot take damage? Hopefully, after reading this comprehensive guide, you will better understand how to make that a reality.

### Damage Reduction

Damage reduction is the bread and butter of damage mitigation in Diablo 4. Each source of damage reduction is multiplicative. If you call each source of Damage Reduction Dr% 1, Dr% 2, Dr% 3, …, Dr% N, then you can write the formula for your effective damage reduction as:

```
Effective DR% = 1 - [1-DR% 1] x [1-DR% 2] x [1-DR% 3] x ... x [1-DR% N]
[Damage Intake] x [Effective DR%] = Damage Taken
```

The most important concept behind Damage Reduction is that each source of Damage Reduction reduces your damage taken by that exact amount. So if you take 1000 unmitigated damage and add 20% Close DR, you now take 800 damage. If you add another 10% Close DR, you take 10% less damage of the 800 damage you would have taken previously, so you end up taking 720 damage. However, if you were to look at the tooltip for your Close Damage Reduction in your character sheet, it would say 28% Close DR because:

```
0.8 x 0.9 = 0.72
1 - 0.72 = 0.28 = 28% Damage Reduction
```

This is because total Damage Reduction is multiplication with factors between 0 and 1, and multiplying these factors will result in a product that approaches 0. The infographic below shows how stacking DR% works.

As you can see in the chart above, the effective DR% approaches 100% DR but will never reach 100% DR. Adding 20% damage reduction will cause you to take exactly 20% less damage despite the effective DR% appearing as though it is affected by diminishing returns. Now when we know that each DR% source is multiplicative to each other, it is time to discuss the DR% sources that we have available to us. The primary ways of taking less damage in Diablo 4 is through armor, resistances, fortified, DR% rolls on items and aspects. Most of these concepts have specific rules and conditions attached to them, but we will see how they interact with each other in the Effective Health Pool section later.

Another concept that is important to understand is conditional damage reductions and damage taken. So when you take damage, the game checks for all your damage reduction sources and reduces the damage you would take by the appropriate amount. However, this also holds true for damage instances like damage over time effects. What this means is that if you take a massive damage over time effect when you are at 100% HP, you will not at all benefit from damage reduction while injured **even if you end up at sub 35% HP**. So if you take a damage over time effect at 36% HP, it does not matter if you lose HP into injured as the damage checks for damage reduction on application only.

**Note:** Something to keep in mind is that certain ground effects (such as on death explosions) are not affected by condition damage reduction% that are enemy dependent (such as damage reduction while vulnerable). So ground effects may do significantly more damage than other damage sources.

### Armor

Armor is our primary way of reducing Physical damage taken in the game. Armor is so effective at reducing physical damage taken, that it is generally advised to stack armor until you reach the 85% Damage Reduction cap from armor in the content you are doing. Xarrio derived a formula for armor approximation, and it turns out damage reduction from armor scales based on enemy level. The formula is as follows:

`(0.00759 x Monster Level^[-0.88165]) x (Current Armor - 614.747) - 0.27596`

So, for example, if you are facing a level 100 enemy, and you want 85% damage reduction, you could calculate the total armor you require by using a modified formula of what Xarrio has produced:

```
[((DR%/100) + 0.27596) / (0.00759 x Monster Level^[-0.88165])] + 614.747 = Armor Required
Plug in Monster Level = 100 and DR% = 85%
[((85/100)+0.27596) / (0.00759 x 100^[-0.88165])] + 614.747 = 9216.385498
```

So the required armor against level 100 enemies would be 9217 to reach the desired 85% Damage Reduction cap from armor.

You can reach this armor cap through various means, such as Total Armor% from gear, the aspects Disobedience and Juggernaut, elixirs and socketing your jewelry with Skulls. It is important to understand that Total Armor% only multiplies your base armor. Base armor is the armor you get from your gear and paragon nodes. You can calculate your armor through the following formula:

`Final Armor = [Sum of Flat Armor] x [1+Sum of Total Armor%]`

What this means is that if your base armor is 3275 and you have two total armor rolls, one 23.1% and one 17.5%, your final armor will be:

`3275 x [1+0.231+0.175] = 6930.174`

### Resistances

Elemental Resistance is our primary way of reducing Elemental damage taken in the game. What is important to know about Elemental Resistance is that sources of resistances stack additively with each other and they have a cap.

That means if you have 50% from your boots, and 30% from your rings, you would expect to have a total resistance of 110%. However, resistances have a cap of 70% through normal means, and 85% in certain circumstances. These circumstances are incenses and elixirs:

- Soothing Spices – All Resistance 10%, Max Resistance 1%
- Desert Escape – Fire, Cold and Poison Resistance 15%, Their max Resistance by 2%
- Storm of the Wilds – Lightning, Cold and Poison Resistance 15%, Their max Resistance by 2%
- Elixirs – Resistance increased by 10-30% and Max Resistance increased by 2-6%
- Uniques such as Tassets of the Dawning Sky (8-12%)
- Glyphs such as Enchanter (Sorc Only) (5%)

So you might think that you only need to get 70% elemental resistances to be done! Unfortunately, you would be wrong. Higher world tiers have a penalty that reduces your elemental resistances by 25% (WT3) and 50% (WT4), which is just subtracted from your total resistance. Using the example we had above, if we had 110% total resistances in World Tier 1, we would have 110% – 50% = 60% resistance in World Tier 4. In order to cap resistances, make sure that you look into your paragon board, socket gems into your rings, run resistances on your boots etc. Sorcerers and Necromancers will have an easier time reaching these caps, as intelligence gives + 0.025% All Resistances per point of intelligence.

We will look at Effective Health Pool calculations later, where elemental DR% will be included as [1-Elemental DR%], and resistances function as a source of damage reduction.

Placeholder for more Resistance related information.

### Fortified

Fortified is a unique effect which, when active, functions as a 10% Damage Reduction as long as you are considered fortified. You can see this mechanic by its distinct red outline around your health, and once you are fortified it creates a very distinct armored look around your health:

Fortified is active when your fortified health, meaning the red outline around the health, is greater or equal to your current life. So whenever your health globe is “armored”, you are considered fortified. When you are fortified, you lose fortified equal to the damage you are taking. So if you have 1000 HP and you are fortified, and you take 200 damage, you will now have 800 HP and 800 Fortify.

You gain fortified through specific skills, passives and aspect effects for each class. For example, Barbarians can gain fortified from Mighty War Cry (28% of Base Life as Fortify), Strategic Iron skin (Iron Skin also grants 9% Base Life as fortify. Double this amount if cast while below 50% Life) etc. There are ways to increase the amount of fortified you gain from these sources, such rolls to +Fortified Generation on Rings, Helmets and Off-hand. Builds that utilize fortified can look for Damage Reduction while Fortified as a conditional damage reduction to increase their effective DR% further.

**Note:** Because Barrier functions as an extension of your Total Health, it causes Damage Reduction while Fortified not to function. Although it visually looks like you are fortified and protected by barrier at the same time, we have confirmed that you do not benefit from Fortified while you are protected by a barrier.

### Health

Your health is the main indicator of how “alive” you are. If your health reaches 0, you are going to be dead. But technically it is a defensive stat just like Damage Reduction that we can compare with other defensive stats to see how much of a gain it is for our effective health pool (more on this [here]). Your health pool consists of technically three components that together determines how much total health you have. These components are Base Life, +Maximum Life (Flat Life) and x% Maximum Life.

- Base Life is your health without any added increases. Calculating this based on just your level requires you to understand that Base Life follows three different formulas depending on what level you are.

```
Level 13-40: y = 20x - 80
Level 41-50: y = 40x - 880
Level 50+: y = 157.6078219e^(0.03921987122x)
```

For example, a level 20 and level 60 character would calculate their Base Life the following way:

```
Level 20: y = 20*20 - 80 = 320
Level 60: y = 157.6078219e^(0.03921987122*60) = 1657.891
```

As level 100, your base life is 7959 which is the same for every class, so only use the above formulas if you are not yet max level.

- +Maximum Life is a stat you can get on helmet, chest and rings. Unlike other defensive stats, +Maximum life scales with item power, so make sure to get as high item power as possible on the pieces you want +Maximum Life on and upgrade them to 5/5 at the blacksmith.
- x% Maximum Life is a stat gained by gems, paragon nodes, class passives etc.

Using what we now know about health, the formula to compute your total health is the following:

`Total Health = [Base Life + +Maximum Life] x [1 + x% Maximum Life 1] x [1 + x% Maximum Life 2] x ... x [1 + x% Maximum Life N]`

So at level 100, with +1120 Maximum Life on chest, +1163 Maximum Life on helmet, 4 Max Level Rubies (4% Maximum Life) on armor, 5 4% Maximum Life Paragon Nodes, 7 2% Maximum Life Paragon Nodes, your total health would be:

`Total Health = [7959 + 1120 + 1163] x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) = 16745 Total Health`

Which is exactly the total health of my test character in game.

This means that adding the Uber Unique Doombringer to my character (41.4% Maximum Life) would simply increase my HP by:

```
16745 x 1.414 = 23677
23677 - 16745 = 6938 more HP from equipping Doombringer
```

### Barrier

Barrier functions as an extension of your Total Health, which lasts for a duration specific to what generated the barrier. While you have barrier active, you will first deplete your barrier before you lose health. This is an important mechanic for builds that utilizes barriers, as you can intentionally get your health into an injured state (health below 35%) and then utilize a barrier to effectively snapshot the Damage Reduction while Injured affix. You can tell that you have a barrier active due to the blue hue on your health globe. The duration of each application of barrier is individually tracked, which means they will fall off independently based on their duration. Total Barrier is limited to your Maximum Life, so no matter how much Barrier Generation you have and how many different barriers you stack, you cannot increase it beyond your Maximum Life.

Formula for Total Barrier including Barrier Generation:

`(Sum of Barrier Effects) x (1+ Sum of Barrier Generation) = Total Barrier`

There are many ways to get Barrier, such as

- Protect from the Seneschal in Season 3.
- Temerity
- Skills such as Earthen Bulwark
- Aspects such as Protector

etc.

**Note:** Because Barrier functions as an extension of your Total Health, it causes Damage Reduction while Fortified not to function. Although it visually looks like you are fortified and protected by barrier at the same time, we have confirmed that you do not benefit from Fortified while you are protected by a barrier.

### Dodge

Dodge (or dodging) does not function the same way as a traditional damage reduction would, such as Damage Reduction%, the Fortified status and other stats and affixes that reduces your damage taken. Instead, dodging an attack completely mitigates the damage you would have taken. This means that if you dodge something that normally would leave a damage over time (DoT) effect, you prevent the DoT from being applied to you. However, you cannot dodge DoT damage instances if you are already affected by the DoT. There aren’t many sources of Dodge Chance in the game currently, but there are a few sources available to you:

- Dodge Chance from Dexterity (0.025% per point of Dexterity) [+]
- Dodge Chance rolls on pants and boots [x]
- Assimilation Aspect
- Spirit Dancer Incense (5% Dodge) [x]
- Third Eye Elixir (4-10% Dodge) [x]

The formula for calculating your dodge chance is not intuitive, but it functions as follows:

`Dodge Chance: [Dodge% from Dexterity] + [1-(1-Dodge% 1) x (1-Dodge% 2) x ... x (1-Dodge% N))] + [Additive Dodge% 1] + [Additive Dodge% 2] + ... + [Additive Dodge% N]`

So if you have 622 Dexterity, 7.2% Dodge Chance on Boots, 5.2% Dodge Chance on Pants, Agile passive for rogues that gives you 12% Dodge Chance and two stacks of Elusive Menace (+6% dodge chance per stack) you have a Total Dodge Chance of:

`Dodge Chance: [0.0622]+[1-(1-(0.12))*(1-(0.072))*(1-(0.052))] + (2*0.06) = 0.408 = 40.8%`

In terms of damage prevented from Dodge Chance, we can look at it the following way. If you would have taken 1000 damage normally, and you have 40.8% Dodge Chance, you will on average take:

```
Damage Taken when not Dodging: 1000, Damage Taken When Dodging: 0
0 x 0.408 + 0.592 x 1000 = 592
Total Damage Mitigated on average: 408 damage, or 40.8% of damage taken
```

This means Dodge mitigates damage taken by removing a certain amount of hits to lower your overall damage intake, while Damage Reduction reduces all hits by a certain amount.

### Health Restore

Every class has unique ways of restoring their health, but all classes have access to a mechanic called Healing Potion. This Healing Potion restores 35% of your Maximum Life and a flat amount based on your Healing Potion level. Your Healing Potion has charges which can be restored by picking up Healing Potions from killing elites and also from damaging bosses past their visual thresholds. Healing Potions also interact with the implicit stat on your pants, such as “While Injured, your potion also grants 20% Maximum Life as Barrier”.

Apart from Healing Potions, we also have access to certain other sources of healing:

- Life Steal% from Andariel’s Visage
- +Life on Kill as an affix on gear
- Skills, passives and aspects that all restore health based on a percentage of your Maximum Life

In regards to Life Steal%, it is functioning a bit unexpectedly. When investigating the functionality of life Steal% from Andariel’s Visage, we noticed that the effective Life Steal% followed two specific curves depending on whether it was utilized versus Monsters or Players. These tests were conducted as a level 100 character, so the results may differ if you are not level 100 with a 3% Life Steal roll on Andariel’s Visage.

```
Versus players: Life Steal% = 151.56e^(-0.039xEnemy Level)
Versus monsters: Life Steal% = 64.779e^(-0.046xEnemy Level)
```

So if you are level 100, fighting a level 100 monster, you have only 0.6364% Life Steal instead of the alleged 3%. If you, on the other hand, are fighting a level 100 player, you will in fact have 3.014% Life Steal.

### Effective Health Pool

We can now use what we have previously learned about Damage Reduction to see how they work in combination with each other. We call this our effective health pool (EHP) and it is a good way to determine what damage mitigation option is best for us. The general formula for EHP is:

```
EHP = [Total Health]/(1-[Effective DR%])
Remember:
Total Health = [Base Life + +Maximum Life] x [1 + x% Maximum Life 1] x [1 + x% Maximum Life 2] x ... x [1 + x% Maximum Life N]
Effective DR% = 1 - [1-DR% 1] x [1-DR% 2] x [1-DR% 3] x ... x [1-DR% N]
```

Now, in order to visualize and understand how this formula works, we can use stats from a real character to determine what would be the best choice to mitigate physical damage; +1120 Maximum Life on Chest, or 10.7% DR:

A level 100 character, with +1120 Maximum Life on ring, +1163 Maximum Life on helmet, 4 Max Level Rubies (4% Maximum Life) on armor, 5 4% Maximum Life Paragon Nodes, 7 2% Maximum Life Paragon Nodes, your total health would be:

`Total Health = [7959 + 1120 + 1163] x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) = 16745 Total Health`

Our Damage Reductions are:

- Pants: 19.6% Close DR, 11% DR versus Poisoned, 9.9% General DR
- Chest: 11.8% Close
- Amulet: 11% Close
- Paragon: 3.3% Elite 3.3% Elite
- Turf: 10% Close

`Effective DR% = 1 - (1-0.196)*(1-0.11)*(1-0.099)*(1-0.118)*(1-0.11)*(1-0.033)*(1-0.033)*(1-0.1) = 1 - 0.4259 = 0.5741 = 57.41% DR`

Let’s combine these two in the original formula:

```
EHP = [Total Health]/(1-[Effective DR%])
EHP = [[7959 + 1120 + 1163] x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02)] / (1 - [1 - (1-0.196) x (1-0.11) x (1-0.099) x (1-0.118) x (1-0.11) x (1-0.033) x (1-0.033) x (1-0.1)])
EHP = 16745/0.4259 = 39315.25816
```

Now lets do the same thing, but add +1120 Maximum Life on chest:

```
EHP with +1120 Maximum Life on Chest = [[7959 + 1120 + 1163 + 1120] x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02)] / (1 - [1 - (1-0.196) x (1-0.11) x (1-0.099) x (1-0.118) x (1-0.11) x (1-0.033) x (1-0.033) x (1-0.1)])
EHP = 18576.16/0.4259 = 43614.52
```

And the same thing, but instead of +1120 Maximum Life, we test with another 10.7% DR roll:

```
EHP with 10.7% DR on Chest = [[7959 + 1120 + 1163] x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.04) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02) x (1.02)] / (1 - [1- (1-0.196) x (1-0.11) x (1-0.099) x (1-0.118) x (1-0.11) x (1-0.033) x (1-0.033) x (1-0.1) x (1-0.1)])
EHP = 16745/0.3833 = 43683.62
```

As we can see, the EHP for 10.7% DR is marginally larger, 0.1584% better to be exact.

`EHP with 10.7% DR on Chest / EHP with +1120 Maximum Life on Chest = 43683.62 / 43614.52 = 1.001584339 = 0.1584%`

This concept can be used with all defensive stats in the game. Remember that stuff like Elemental Resistance is just a Damage Reduction in the end, written like [1-Elemental Resistance %], and the same goes for armor.

In case you think that calculating this yourself is annoying, you can use this EHP calculator to calculate your EHP and what defensive stats would be most beneficial. But just to try and burst the bubble once and for all: stacking damage reduction is never a bad thing to do. If you look at the infographic below, you can see what happens if you add 20% DR, +1120 HP and 20% HP over and over again.

As you can see, in the end for DR we need 211 hits to die. Meanwhile, stacking +1120 HP means we die in 4.4 hits and stacking 20% HP means we die in 79 hits. So if you are going to take anything from this massive defense post:

- Stack armor until 85% DR Cap from armor
- Stack elemental resistances until 70% DR cap from resistances
- Compare the DR% EHP gain to other sources of EHP in the calculator above (but Damage Reduction is very likely going to be the winner).

### Variance

The damage you take has variance as well. It is generally +- 10%, but keep this in mind if you are doing testing for damage reduction.

### Diminished Returns

Lets compare damage reduction to when you add damage stats to your gear. Lets say you have 0 Int and 0 Additive stats.

- Case 1: If you add 100 int, you gain 10% skill damage. Because the relative increase is (1+0.1)/(1+0) = 1.1 so 10% relative increase
- Case 2: If you add 100% additive damage, you gain 100% damage. Because the relative increase is (1+1)/(1+0) = 2 = so 100% relative increase

Here you can see there was no diminished value, we put in 10% skill damage, we got a 10% relative increase in damage. Same for additive damage.

Now lets say you have 1000 int, and 1000% additive stats,

- Case 3: If you add 100 int, you now have 1100. The relative increase is (1+1+0.1)/(1+1) = 1.05 = 5% relative increase
- Case 4: If you add 100% additive damage, you now have 1100% additive stats. The relative increase is (1+10+1)/(1+10)= 1.0909 = 9.09% relative increase

So we went from 10% relative increase to 5% relative increase in damage for int, and 100% relative increase to 9.09% relative increase in damage for additive stats based on the stats we previously have. This is diminishing returns. The effective return you get from adding the stat is less than what it was under previous conditions. We look at this like a percentage gain because the numeric value is pointless to look at. We want to know, relatively to what we had before adding it, how much damage do we gain.

Lets apply the exact same logics to damage reduction.

Lets say you are about to take 1000 damage, and you have 0% Damage Reduction.

- Case 5: Adding 20% damage reduction, you take 1000 x 0.8 damage, meaning 800 damage. Relative to the damage you would have taken without it, is 800 / 1000 = 0.8, in other words you are taking 80% less damage.
- Case 6: Adding another 20% damage reduction, you take 1000 x 0.8 x 0.8, meaning 640 damage. Relative to the damage you would have taken without it, is 640 / 800 = 0.8, in other words, you are taking 80% less damage

As we can see in Cases 3-4, we have a diminished return on adding damage stats to an already existing “pool” of damage stats. This is diminished return by definition, as we get less benefit adding the same amount as in Cases 1-2 (relatively speaking, not numerically speaking). In Cases 5-6, however, we can see that the relative decrease in damage taken is always the same, as each damage reduction roll is a factor of (1-DR%). This means that there is relative decreased damage taken is always the value we put in, and therefore not diminishing returns by definition. This is why it is incredibly misleading to state that “damage reduction has diminishing returns” because it simply is not accurate.

One question, if a dot damage drop my health below 35% , does the DR injured kicks in and reduce the tick or the damage tick will be constant in its duration and ignore DR injured?