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[M.Celestial]

This posts uses the HP formula and table on the wiki to compare the effective HP gained from Toughness and Lifegiver in a variety of situations. For simplicity I will avoid taking into account the damage threshold gained from toughness as it will influence damage taken dependent on how fast firing your opponents weapon is, rather than just by DPS. I will be making references to the following spreadsheet, which anyone is welcome to view and critique in the case that I have made an error.

Many of the numbers I use in the post to explain concepts are unrealistic for the game, but are simpler and should help people understand what I am saying. During the direct comparison I will be using realistic numbers. My HP values also always assume 5 STR, because this would be much more tedious if I had each STR value. Since HP scales much more with END than with STR, I decided that the inaccuracy that could be introduced was minor enough to warrant the timesaving, and ease of reading the spreadsheet gains.
https://docs.google.com/spreadsheets/d/1hcWjFiW0kKGWP1CDolH89bE_JzexV-uoMe6Avb2ndoU/edit?usp=sharing

What do you mean by effective HP, exactly?

Spoiler for Hiden:

Since lifegiver and toughness improve your defense in different ways it is important to find a single statistic that can represent both of them. Effective HP refers to the amount of damage you must take before damage resistance is taken into account to be killed. For example, if you had 300HP and 50% DR your effective HP would be 600 because your enemies must deal twice your HP to kill you.

The formula to determine effective HP is (Using DR as a decimal):
HP / (1-DR)
e.g. 200 / (1-0.75) = 800 effective HP

A note on scaling and DR

Spoiler for Hiden:

5% DR does not seem like much on it's own, however it is important to realize that it gets better the more DR you already have.

What does this mean? Well, let's use an example.
If you have 25% DR from your armor and 100HP then your effective HP is:
100 / (1-0.25) = 133.33
If you increase that DR to 30% using toughness we have
100 / (1-0.3) = 142.85
This is an increase of approximately 9.5HP

But what if our armor gives us 50% already? Well, we will have
100 / (1-0.5) = 200
But increasing our DR by 5% from toughness gives us
100 / (1-0.55) = 222.22
This is an increase of 22.22 HP

Using this example we can see clearly that the effective HP gained from toughness is dependent on how much DR you already have. This is why 50% DR doubles HP, but an increase of only 25% more will double that number again.

This is getting long, but a final comparison worth noting is that toughness grants more effective HP the more HP you already have.

Using the above numbers, with a base of 100 HP and 55% total DR with toughness we get 222.22 effective HP, or an increase of 22.22 from toughness. If we increase the base HP from 100 to 150 the following occurs:

No toughness:
150 / (1-0.5) = 300
Toughness:
150 / (1-0.55) = 333.33
this is an increase of 33.33

When compared to the previous example, you will notice that rather than increasing effective HP by 22.22, it is increased by 33.33

Summary of section

Toughness grants additional effective HP based not only on existing DR, but on your health.

Alright, but what about lifegiver?

Spoiler for Hiden:

Like toughness, Lifegiver grants an effective HP proportionate to your existing DR. However, it does not scale with existing HP, but merely adds to it. Another example to demonstrate this

No lifegiver:
100 / (1-0.5) = 200
Lifegiver:
120 / (1-0.5) = 240

No lifegiver:
150 / (1-0.5) = 300
Lifegiver:
170 / (1-0.5) = 340

In both of these cases effective HP only increases based on DR. The increase is 40 because we have 50% DR, but this will change with other DR values

Summary of section

Lifegiver scales with DR, but not existing HP.

Directly comparing Lifegiver and toughness

Spoiler for Hiden:

Referring to my spreadsheet now we can see two patterns indicated by the "Toughness - Lifegiver" section. This section shows the effective HP of toughness subtracted by the effective HP of lifegiver in the same circumstance. A positive number shows how much more effective HP toughness has, and a negative number shows how much more lifegiver has

For a given DR value, toughness has greater advantage over lifegiver as HP increases. Aditionally, toughness has a greater advantage to lifegiver the higher the DR is. We know that only toughness scales with existing HP, so it is not surprising that it gains advantage with more HP. However, both toughness and lifegiver scaled with DR so it is worth noting that for a given HP value, toughness will have a greater advantage (or lesser disadvantage) as DR increases.

25% DR (from armor)
Toughness requires a fairly high endurance to gain any advantage over lifegiver, and when it does get an advantage it is very small
30% DR (from armor)
At an average endurance/strength toughness beats lifegiver, though only just.
35+ DR (from armor)
Toughness gains an advantage in the majority of situations, and as DR increases from here it only becomes better

I personally believe that most of the time toughness will grant more benefit than lifegiver. This is because of it's clear advantage above 35DR and the fact that it is currently very simple to reach 40+ Using armor alone, as the average DR of T2 armor seems to be from 45-55DR

Comparisons aside, how useful is each perk?

Spoiler for Hiden:

This question is very hard to answer for a variety of reasons:
-What's important in PvP isn't the same as in PvE
-Taking one of these perks means not taking another, which could be better and isn't easy to mathematically compare
-Although effective HP is great for comparisons, as it is possible to be overkilled often by damage it will not always translate into surviving extra shots.
-It depends how much HP your build has

That aside, this is where the "Toughness - base" and "Lifegiver - base" columns come in.

These columns directly show the amount of additional effective HP either perk is granting the player. The most common DR values for T2 armors seem to be 45, 50 and 55DR

So, to find out how useful either perk is for you find out how much effective HP you will gain based on your ST, EN and DR.

I would also like to note that effective HP does not need to be greater than the damage dealt to you by a shot to be useful. For example, if without the perks a lethal blow to you would normally take you to -20, you only need 21 effective HP or more to continue living even if that attack was something large like 100 damage.

Closing notes

Spoiler for Hiden:

-Toughness, in most situations, outclasses Lifegiver
-Combining the two perks (Which I have done zero math on) would likely make lifegiver better than it is by itself, as it scales with DR
-Toughness scales with HP and DR
-Lifegiver scales with DR, but not HP and has worse DR scaling.
-Effective HP does not need to be greater than a weapons raw damage to be useful against it


Some factors making my work less accurate include:
-Ignoring DT (Which would make toughness seem even better)
-Using only one ST value
-Mistakes I may have overlooked

Answers to questions I've been asked

How does healing efficiency factor into this?

Spoiler for Hiden:

Well, as far as I'm aware healing is always a flat rate and is not dependent on the targets HP. Of course, if the target has more HP than you can heal then the remaining healing is wasted.

So how does toughness influence healing efficiency? Well, DR essentially acts as a multiplier to your HP to create effective HP. Therefore, effective healing is calculated the same way as effective HP which is to say:
Healing / (1-DR), where DR is a decimal value
You'll notice that the amount your health is being multiplied by is the same amount as your healing is being multiplied. So with 50DR effective healing is twice the base healing, and effective health is twice the base health.

Due to this, all previous statements of how the more DR you already have, the more effective health you gain from toughness apply here. Of course, effective healing doesn't scale with HP like toughness does.

In other words, the more DR you have, the more each bit of HP you get from first aid is going to help you.

Lifegiver will increase your total effective HP, but will not influence effective healing at all.

Summary of section

-Effective healing is calculated the same way as effective health
-Toughness increases effective healing
-The increase to effective healing from toughness is greater the more DR you already have
-Lifegiver is irrelevant to healing

What about ammo which lowers the targets DR?

Spoiler for Hiden:

There are essentially three situations that can occur with this. The DR reduction is lower than your base DR, is greater than/equal to your base DR but lower than your toughness DR, or is greater than both. Additionally, some ammo types actually raise the targets DR, and so does the Finesse perk.

If the ammunition has greater penetration than both your toughness and non toughness DR, then unless there's a downside to having negative DR (I don't believe this does anything, but I could be wrong) toughness will have zero effect either way. In this case, Lifegiver would have an effect but since it is not multiplied by your DR at all it would always be an effective HP increase of only 20.

If the ammunition has less penetration than both DR values, then we will still be comparing two DR values, but they would both be lower. For example, if the ammo penetrates 40DR and we had 50 base DR with 55 toughness DR, then we will have 10 and 15. As mentioned earlier, toughness gets worse the less DR you already have. Assuming an average character in this case, we have gone from an increase of 75 effective HP from toughness to an increase of 17.65, less than Lifegiver. This is a very significant change, and makes it unlikely that toughness will have an influence on how many shots it takes the enemy to kill you. The severity does depend entirely on exactly how much penetration your opponent has to bring to the table, and the opposite effect will occur if they use ammo that gives you even more DR. Lifegiver follows a similar trend, wherein the effective HP granted by it is reduced as your DR is reduced. In this case you would go from an increase of 40 to an increase of 33.33. In general, Lifegiver will be less influenced both by increases and decreases of DR.

Finally, if their ammunition negates your armor DR exactly you will have a remaining 5 DR from toughness. Effective health without toughness is equal to your normal health, and having toughness will grant you:
100% / (1-0.05) = 105.2631% of your health as effective health.

Ammo types that reduce DR:

Spoiler for Hiden:

.44 Magnum FMJ (25)
.50 BMG (30)
2mm EMC (100)
9x19mm 7N14 (40)
10mm AP (10)
14mm AP (35)
HN AP Needler Cartridge (30)
7.62x51mm (5)
7.62x54mmR 7N14 (10)
7.62x54mmR (10)
.30-06 Springfield (15)
Rocket AP (30)
Flamethrower Fuel Mark II (10)
Napalm (20)
Electron Charge Needles (10)

Ammo types that increase DR:

Spoiler for Hiden:

40mm grenades (15)
.45 caliber (15)
.50 AE (Not used by the big gun snipers) (20)
.44 Magnum JHP (25)
9x19mm JHP (28)
10mm JHP (10)
12 Gauge Slugs Shells (10)
Explosive rocket (20)
Flamethrower Fuel (10)

Many other ammo types have no effect either way on DR.

Summary of section

-If their Ammo negates your DR entirely (toughness included) then toughness is useless
-If their Ammo reduces your DR, but you still have some then toughness will lose a significant amount of effective HP. For calculation purposes, you essentially treat your armor as it's DR minus the penetration.
-If their Ammo negates your armor DR, but you still get toughness DR then toughness will have an almost negligible effect of only slightly more than 5%

[paragon]

Well, uh. It's monumental. Great work.

[greenthumb]

Very nice reading for my morning tea, could you please elaborate ammunition DR effects and healing efficiency on both: LG and Toughness?

Then maybe you would like to create simulator which could be used for balancing statistics for "real-in-game" situation/s.

[paragon]

I think I will add value of "Effective HP" to the character planner.