### Note

Apparently this whole post is a load of rubbish (see edits). Don’t bother reading it. Not deleting it because “apparently” people hate it when I do that and I’ll just get flagged and reported and then in trouble with EHG again.

Will I be fixing this? No. Considering how much needs fixing, the fact I have several other LE maths projects underway *and* I have things to do IRL, I don’t have the time to invest in this.

## Introduction

This post is aimed towards newer players who don’t know what defensive suffixes to slap onto their gear and players interested in reading such a post. Those who hate me and my silly posts can just disregard this post and continue with their day.

I will also try to add clarity to the mathematics, so it’s not like I’m pulling random numbers out of thin air.

I was inspired to do this by two PerryThePig videos: one where he talks about Hybrid Health being more optimal than Added/Increased and another where he talks about Endurance. Similar ideas show up in this post, but with a mathematical approach and so a bit more of an original take. Shout out to him though for the inspiration.

### Disclaimer

In this post I am only looking at optimising against hit damage and not DoT. Ward is too finicky for me, so won’t be touching that either. Also, based on PerryThePig’s most recent video, I am making the assumption that a level 100 character will look to use Blessings to roll for resistances. Likewise with assuming idols are covering resistances and damage areas. Also ignoring uniques, especially since these crafts can then be crafted onto a Legendary item.

I will also purely be looking at suffixes, to make this build/character independent. Because of this, Glancing Blow will be ignored since Rogue is the only class that can access this. There also aren’t Glancing Blow affixes besides the “Health on GB” prefix.

Another disclaimer is I suck at the game so take this entire post with multiple grains of salt, but enjoy doing these analyses and projects as they help me learn more about the game and I also like reading posts like mine (but better) and, well, make the content you wish to see I guess.

## Different Forms of Effective HP [EHP]

You are probably aware of Health and Resistances. If not, then really quick, Health increases your EHP by directly affecting your Health and Resistances offer 75% damage reduction against a specific damage type (having 0% means your EHP is a quartered, but 75% has no modifier against your EHP).

## Hybrid Health vs Added/Increased Health

# Hybrid Health vs Added/Increased Health

A consensus amongst the streamers I watch is that Hybrid Health is great and that Added/Increased Health sucks. HH also only takes up one suffix and A/IH takes up two.

Let’s look into this further.

In a previous post about Increased Damage vs More Damage vs Added Damage I talked about how Added modifiers is GOAT. So the same thing applies to Health, right?

No. The difference with Added Damage and Added Health is that base damage is low, so each point of Added Damage has a huge effect. Meanwhile, at level 100, 3 classes have a base of 910 HP and two have a base of 920 HP (based on LE Tools). Since I am looking at build independence, we shall take the mean of this: 914 HP. So Added Health has a lower value than Added Damage.

Now that we have a hypothesis going and established a baseline, how shall we prove Hybrid is better with evidence?

Since we are looking for optimisation, then at the very least going with Added Health and Increased Health suffixes should be *x* more of the number of Hybrid health suffixes, where *x* is the A/I HP divided by Hybrid HP. And even if this is the case, you potentially lose a lot of suffix slots for other high-value defenses.

Hybrid Health can only be applied to Gloves, Boots and Belts. Thus 3 Tier 5 Hybrid Healths gives 1,285.7 HP.

Increased Health can only be applied to Body Armour, Helmet and Belts. Thus

I ≤ 3

Added Health can be applied to Relics, Rings, Amulets, Gloves, Boots, Shields, Amour, Helmet and Belts. Thus

A ≤ 10

And, to account for overlap:

A + I ≤ 10

So, assuming Max Roll Tier 5s:

HP = ( 75A + 914) * ( 1 + 0.24I)

Using Simultaneous Inequations gives us two possible optimised results:

HP = 1,572.08 (purely Increased Health)

HP = 2,475.08 (optimised mix of Added and Increased)

HP = 1,664 (purely Added Health)

That said, this option only took up 3 suffixes whereas the other option used up 10. 2,475 is not greater than 3.3 * 1,285.7 (which is 4242.81 HP). In fact, it it not even double despite Added/Increased requiring twice the amount of suffix slots to have the shared ability of Hybrid, so Hybrid Health is more efficient.

## Armour

# Armour

Armour defends against Hit damage (basically anything that’s not a DoT).

Fortunately for simplicity, we can’t craft Increased Armour, only Added Armour. Increased Armour can only be found (build independently) on uniques and blessings.

The effect of Armour on reducing hit damage is given by

Where *x* is the amount of Armour and *a* is the area level. For convenience, I am only looking at a Level 100 scenario:

This is only 70% effective against non-physical damage.

It’s worth noting that Armour has an upper limit of 85% damage reduction.

## Block

# Block

Even though Block affixes are prefixes, I thought I’d give a quick note here in case any new players are curious about Block. It’s also not build-independent as some Rogue builds favour Glancing Blows. Other builds also make use of 2H weapons, and so don’t have Block on gear. Block is interesting, because it’s like Dodge where it has a chance to happen, but like Armour where scaling Block Effectiveness makes it reduce more damage.

Another thing to note is that Block Chance and Block Effectiveness can only be applied to shields, specifically Prefixes (although there is a Hybrid version for the suffix too), thus still leaving 2 suffix options for other defenses.

Also, to optimise Block in the best way possible, get a Bastion of Honour with LP for that 100% Block Chance and also being able to added prefixes and suffixes.

## Dodge

# Dodge

Dodge works similarly to Armour, except it completely mitigates all hit damage. There is an upper limit of 85% chance to dodge. Needless to say, an 85% chance not to receive any damage at all is rather strong. So in a Level 100 zone we have:

Where *x* is the amount of Dodge we have.

Dodge has both Added and Increased variations, but no Hybrid options.

## Endurance

# Endurance

Finally, we have Endurance. After your Health passes a threshold, you take less damage. So say you have 500 Endurance Threshold and 50% Endurance. Then when your HP drops below 500 you take 50% less damage.

This has a minimum of 20% and a max of 60%. Endurance Threshold has a minimum of 20% of the players Health and an uncapped maximum. This also works for DoTs too.

## Optimisation

Remember back in the Hybrid Health section where we used simultaneous inequations to find optimal values of Added and Increased Health. We will now do this on a larger scale than just 2 variables.

## The EHP Equation

# The EHP Equation

The simultaneous inequations will give us several values to input into the EHP equation. So let’s build one!

We will start off with:

EHP = ( 68H + 914) * ( 1 + 0.05*H)

Where *H* is the Hybrid Health suffix.

The next easiest variables to implement are Endurance, *E*, and Endurance Threshold, *T*.

EHP = ( (68H + 914) * ( 1 + 0.05*H) + E * T + T / 100E)

After this, we multiply by *1 + Armour Equation* and multiply by *1 + Dodge Equation*, giving us:

Let’s then assume we have a Bastion and aren’t going to be worrying about Block stuff, for the sake of build-independence and because it’s messy already.

## The Inequations

# The Inequations

Armour can only be applied to 4 items (not counting Shield). Tier 5 is 110.

Armour ≤ 4

A ≤ 110 * Armour

Hybrid Health can only be applied to 3 items. Tier 5 is 68 Added and 5% Increased.

H ≤ 3

And the 68/5% values are already incorporated into the EHP equation.

Endurance can be applied to 7 items (rings count twice, just as a note). Tier 5 is 15%.

Endurance ≤ 7

E = 0.15 * Endurance

Endurance Threshold can be applied to 5 items (not counting Shield). Tier 5 is 75.

Threshold ≤ 5

T = 75 * Threshold + 0.2 * H

Added Dodge can be applied to 7 items (not counting Catalyst). Tier 5 is 80. Increased Dodge can be applied to 4 items (not counting Sword). Tier 5 is 38%. These two have to fit together as it is their total value that appears in the EHP equation.

AddedDodge ≤ 7

Increased Dodge ≤ 4

D = AddedDodge * ( 1 + IncreasedDodge)

This gives a total of 18 suffixes we can use.

Armour + H + Endurance + Threshold + AddedDodge + IncreasedDodge ≤ 18

## The Calculations

# The Calculations

This part was an honest PITA because it’s inequalities in 6 dimensions (so you can’t exactly graph it or visualise it). If this was an equation, easy. But inequations? Ugh.

Which means… simplifying the inequation somehow.

To do this, we must dive into the EHP equation and investigate how these variables interact.

### Hybrid Health Simplification

Now, while I said before that Added Health isn’t too great when we already have a lot of it, from all the way back in the Hybrid Health section we can see that 3 Tier 5 Hybrid Healths give us 1,285.7 HP instead of 914HP. Not only does Health contribute to Endurance too, but a modifier 1,000% increased EHP of 914 (9,140 EHP) is significantly smaller than 1,000% of 1,285.7 (12,857 EHP). Since Hybrid Health is only an investment of 3 suffixes and is key to EHP scaling, then we can consider the case where *H = 3*.

The nifty thing is that since Hybrid Health consumes a Belt suffix and nothing else except Increased Dodge, Endurance and Endurance Threshold, we can set the other Belt suffix to be Tier 5 Endurance or Threshold (Dodge is handled later), thus using up 4 suffixes. So now

A + E + T + AddedDodge + IncreasedDodge ≤ 14

E + T ≤ 11

We are now down to a 5-dimension inequation. It’s better, but still a PITA.

### Dodge Simplification

I honestly should have done this sooner, but even though Dodge is so powerful (85% for no damage), only Rogue has passives properly utilising it. Forge Guard converts Dodge to Armour. Primalist has Dodge for companions. Basically, unless you’re playing Rogue, the investment into decent Dodge is far too high to be optimal. Which means you want a low Dodge. But as Dodge rating decreases, the Dodge factor in the EHP equation becomes exponentially negligible, essentially meaning that either we invest a lot into Dodge or not at all.

And so we have:

As you can see, we have reduced this down to 3 variables: Endurance, Endurance Threshold and Armour.

Since we have a total of 15 to add and only 14 suffix slots, we can clearly see the optimal defensive suffix set up will be either (4, 5, 5), (4, 6, 4), (4, 7, 3), (3, 6, 5), (3, 7, 4).

However! We can only have a maximum of 60% Endurance, thus can only have 4 max roll Tier 5 Endurance. Therefore, we have either (4,3,5) or (4,4,4), leaving us 2 free suffixes which could be for Hybrid Block or whatever #BuildFlexibility.

## Results

# Results

So, based on mathematics, the optimal defense suffix crafting setup for any build (excluding Rogues who spec into Dodge and Glancing Blows), is:

4 x Tier 5 Added Armour (440 Armour).

4 x Tier 5 Endurance (60% Endurance).

5 x Tier 5 Endurance Threshold (+375 Endurance Threshold).

3 x Hybrid Health (15% Inc Health, 204 Added Health).

Legendary Bastion of Honour with Block Chance and Block Effectiveness.

I’m sure the Rogue option could swap out Added Armour for 6 Tier 5 Added and Increased Dodge. Thus, using our inequality tricks:

AddedDodge ≤ 7

Increased Dodge ≤ 4

AD + ID ≤ 6

Dodge = 80 * AD * ( 1 + 0.38 * ID)

And so we have the optimal Dodge combination of 4 Tier 5 Added Dodge and 2 Tier 5 Increased Dodge.

## Conclusion

As always, since I’m not too skilled at LE, take with a mountain of salt. It was a fun exercise to do that took an entire day to do (time flies I guess).

A lot of assumptions were made to make the mathematics more manageable. Like I may love doing maths about video games, but like n>7-dimensional hypergraphs is where I should realistically draw the line for a hobby.

It would be nice to hear feedback in regards to your thoughts on this. I tried to make the mathematics as clear as I could, but if something is unclear to you I’ll try to patch it up. I am also very tired and there are likely typos abound.

If you made it this far, thx for reading and have a nice day/night

EDIT 1: Shtrak pointed out a dumb mistake on my part.

EDIT 2: My small brain didn’t realise Endurance is trash and Increased Health is best. I guess disregard this entire post then? Whelp there’s a day I won’t get back.

EDIT 3: Yep, like 100% of my post is built on trash. Thanks TolleWurst for the catch.