The info that I'm talking about is the damage calculation which can be found in this reddit thread (there are some misleading info such as 100 toughness blocking 34 damage per 1000, which we will correct below). For the lazy, damage is given by

(P + M * 35) * WS * SC / (T + D) = Total Damage

P = Power, M = Might Stacks, WS = Weapon Strength, SC = Skill Coefficient, T = Toughness, D = defense

I remove vulnerability from the formula since vulnerability has been changed. Vulnerability is now a multiplier on the total damage and has no bearing on our calculation below.

To simplify things, we will rename all the terms in the numerator as K and all the terms in the denominator as A (armor = sum of toughness and defense).

The question now is: If a player initially has A armor, what is the damage reduction achieved if the player adds X amount of armor either through toughness or defense? The calculation is actually straightforward:

Damage reduction ratio, R

= [(Damage taken with A armor) - (Damage taken with A+X armor)]/Damage taken with A armor

= [(K/A) - (K/(A+X))]/(K/A)

= 1 - A/(A+X)

= X/(A+X)

The formula implies that to reduce damage by 50%, you'll have to double your current armor.

Adding 100 armor for (note the diminishing returns)

- a soldier with 2127 armor gives 4.49% damage reduction
- an adventurer with 1980 armor gives 4.81% damage reduction
- a scholar with 1836 armor gives 5.17% damage reduction

- a soldier has an additional 13.68% damage reduction compared to a scholar
- a soldier has an additional 6.91% damage reduction compared to a an adventurer
- an adventurer has an additional 7.27% damage reduction compared to a scholar

For toughness, EHP is a little more complicated. First, let's ignore healing and condition damage which bypasses toughness. If your hitpoint is currently HP and your armor is A, then

EHP increase for X points in toughness

= [HP/(1-R)] - HP

= HP*X/A

To incorporate healing and condition damage, you'll have to estimate two things

- The proportion of damage received which is condition damage before going down, say C

- The amount of healing received before going down, say H

Then the estimated EHP increase for X points in toughness is

(1-C)*(HP+H)*X/A

In short, if you wish to know whether you should invest the next point in vitality or toughness, just check the following:

(1-C)*(HP+H)/A > 10?

Yes = toughness, No = vitality.

C = proportion of damage received which is condition damage before going down

HP = current hit points

H = healing received before going down

A = current armor value

**Calculation example**

For a guardian playing non-dungeon PvE with 2400 armor, 14000 hitpoints, and estimated C = 0.1 (not much condition damage in PvE) and H = 12000 (virtue of resolve heals for a lot over time), we see that

(0.9)*(14000 + 12000)/2400 = 9.75 < 10

So the guardian is better off investing the next point in vitality.

**Healing increases as EHP increases**

As pointed out by Lumm at this post, toughness and vitality both allow you to survive longer and so as you increase either or both attributes, you are likely to receive more healing. That's why it's not optimal to use the formula to allocate the next 100 points in toughness or vitality.

**How should the formula be used to decide how to allocate the next X points?**

You allocate such that at the end of the allocation

(1-C)*(HP+H)/A = 10

where HP, H and A are values at the end of the allocation.

**Now, tell me, is stacking toughness a good idea?**

For GW1 players, you'll be disappointed. The answer is not as good as GW1 as armor increases EHP linearly in GW2 as opposed to exponentially in GW1.

In GW1, armor-respecting damage is halved for every 40-armor increase. This means that for a monk with a base armor of 60 and a HP of 500, the EHP is 1000 if the monk's armor is increased to 100 and the EHP is 2000 if the monk's armor is increased to 140. Basically, each point of armor increases the EHP more than the previous point and that's why stacking armor is prevalent in GW1.

In GW2, armor-respecting damage is halved when you double your current armor. If you disregard healing, then EHP increases linearly with armor.

**Converting damage reduction to equivalent toughness gain**

The conversion will be done assuming a 2600-armor character. The formula is A*R/(1-R).

50% = 2600 toughness

33% = 1300 toughness (Protection)

25% = 867 toughness

20% = 650 toughness

15% = 459 toughness (Signet of Judgement with perfect insriptions)

10% = 289 toughness (Signet of Judgement)

5% = 137 toughness

**Survivability Hierarchy**

Here's a simple and crude way to determine your survivability against direct damage. Just take the product of your armor and HP. If you want to know how you rank against other builds/classes, here's a hierarchy for comparison. Note that you have to first divide the obtained number by 10000. Also, this hierarchy is only meant as a rough comparison and doesn't take into account traits, skills and utilities that provide additional survivability.

- 3500 Break on touch

3501 - 4000 Fragile

4001 - 4500 Middle ground

4501 - 5000 Durable

5001 - 5500 Tanky

5501 - 6000 Built to last

6001 - Moving Fortress

The description is for dungeon. From my experience, unless one knows the dungeon thoroughly, 4000 is the baseline that players new to dungeon should strive for, while 4500 is my personal recommendation. Just keep in mind that dodging is more important any number shown here.

**Changelog**(for the sake of those who have read this before)

10/13

- Added some additional information on converting damage reduction to equivalent toughness gain.
- Added a simple way to calculate and compare your survivability.

**Edited by paradiselight, 16 October 2012 - 01:54 AM.**