Stats

[Concillian]

This is a work in progress, and we can develop and revise this post to be a sort of guide on stats... at least until the Blizzard guide includes all this stuff. Most of this is not original work of mine, but compiled information from various posts in the Blizzard forums, then reconciled with some rudimentary tests to verify they do in fact seem to work that way.



There are 4 stats

Each stat has a specific defensive function that works the same for every class:

Vitality -- Health
Strength -- Armor
Dexterity -- Dodge
Intellect -- Resist

An important change for Diablo III is that these all work on both spells and physical damage in the same way. That is to say that you can dodge damage from a puddle your standing in or a ranged attack just as you would a melee swing. Also resistance gained from intellect is resist ALL (including physical resist)

In addition, ONE of these stats will also provide an offensive benefit. Which provides an offensive benefit depends on the class:
STR -- Barbarian
DEX -- Monk and Demon Hunter
INT -- Wizard and Witch Doctor


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Formulas
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Formulas in Diablo and Diablo II were made to bea easy for the computer to understand, and as a result often ended up difficult for people to understand. I guess CPUs have progressed to the point where in Diablo III, Blizzard is comfortable using formulas that are easy for people to understand even if they are a little more computationally intensive for the CPU. In Diablo and Diablo II, they went to great length to keep calculations integer specific. There was a lot of truncating and such. Not true in Diablo III, and as a result the formulas seem to be significantly easier to understand for the average gamer.

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Offensive Stat
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All offensive stats offer +1% weapon damage per point.

That's it. The whole thing. The rest of this section is examples...

For example:
100 intellect for a Witch Doctor, will modify weapon damage by +100% (double it)

This is a naturally diminishing formula. Each point added makes the next point less effective. To demonstrate this, we can look at one point added when base weapon damage is 100 and Intellect is 100 and 200.

Code:

Base = 100 | INT = 100:  100 * 2.00 = 200 damage
Base = 100 | INT = 101:  100 * 2.01 = 201 damage

201 / 200 = 1.005 -- 1 intellect added 0.5% damage

Base = 100 | INT = 200: 100 * 3.00 = 300 damage
Base = 100 | INT = 201: 100 * 3.01 = 301 damage

301 / 300 = 1.0033 -- 1 intellect added 0.3333% damage

Indeed... naturally diminishing.

This appears to multiply with base damage and with skill damage:
BASE * INT modifier * SKILL modifiers

It is beyond the scope of this thread to discuss how SKILL modifiers stack with other SKILL modifiers. There is no consensus yet on if this is consistent for all skills across all classes or if these are handled on a case by case basis.


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VIT - Defensive
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Until level 35:
1 VIT = 10 health

After level 35:
1 VIT = 10 + level - 35 health

This means 35 health per VIT at level 60.

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STR - Defensive
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1 STR = 1 Armor

Therefore:
Total armor = ( Armor from items + STR ) * Modifiers

As mentioned, Armor mitigates all damage from all sources, which brings up the obvious question... "how much damage does armor mitigate?"

Armor_mit = Armor / (Armor + constant * m_lvl)

It seems a constant of 50 works right, but I'm not sure. For any given attacker level this results in diminishing returns that lead to approximately flat effective health returns. As an example if we look at a level 30 monster hittins someone with 2000 health:

First effective health is the amount of damage (before mitigation) it takes to kill you. EH * (1 - mit) = health

so if mitigation is 25% and health is 2000, then it takes a hit of 2666 to kill you (2666 * .75 = 2000). Some algebra and EH = health / (1 - mit)

500 armor: 500 / (500 + 50 * 30) = 0.25 = 25% mitigation. EH = 2666.7

1st 500 armor gives 666.7 effective health

1000 armor: 1000 / (1000 + 50 * 30) = 0.4 = 40% mitigation. EH = 2000 / 0.60 = 3333.3

2nd 500 armor gives 666.7 effective health

1500 armor: 1500 / (1500 + 50 * 30) = 0.5 = 50% mit. EH = 2000 / 0.50 = 4000

3rd 500 armor gives 666.7 effective health

Etc...

Armor has diminishing returns with itself, but flat returns with effective health.

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INT - Defensive
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INT is exactly the same as STR, but for resist.

Resist resists everything (including physical) so ... it works pretty much exactly the same as STR. As best I can tell, the formula is also exactly the same, in that 1 INT gives the exact same amount of effective health as 1 STR.

Just re-iterating this:
For effective health purposes 1 STR = 1 Armor = 1 INT

What I don't know yet, it how + %resist work exactly. There is some evidence that it works primarily to amplify the benefit of INT (essentially offering additional EH per point) rather than what intuition might suggest.

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Interaction of STR and INT - Defensive
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STR and INT will offer exactly the same EH return per point when they are at the same level (@ 200 armor and 200 INT, 1 point STR = 1 point INT)

However these appear to just multiply each other's damage reduciton, so the defensive value of one improves when you have more of the other.
If armor is stacked sky high (barb with high armor and STR or Monk with high armor and DEX with the passive that gives 1 armor per 1 DEX), then INT is significantly more valuable than armor for defense. Depending on the severity of the imbalance, it can be multiple times better than armor, potentially offsetting the offensive power loss from not stacking more of the primary stat.

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DEX - Defensive
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DEX gives dodge as it's defensive beneift.

This is the only stat that does not affect effective health. If something can one shot you, more VIT, INT or STR can prevent it from one shotting you if you get enough. More DEX will not. It will offer increasing chances of avoiding the damage entirely, but there will always be a chance you don't dodge and then you die.

Dex is different in that it doesn't have a universal diminished formula, instead it's broken down into linear % improvements such that:

100 DEX = 10% dodge
500 DEX = 20% dodge
1000 DEX = 30% dodge
Every additional 1000 DEX = + 10% dodge

In those ranges everything is completely linear
10% / 100 = 0.1% per DEX below 10% dodge
10% / 400 = 0.025% per DEX between 10% and 20%
10% / 500 = 0.02% per DEX between 20% and 30%
10% / 1000 = 0.01% per DEX at 30+% dodge

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What's the best defense?
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Keep in mind that this comparison is based on any given character. You can't compare class against class, since melee classes have a flat 30% damage reduction on top of any other damage reductions.

We'll use the same 20000 health against a level 65 monster to give an example useful for Inferno difficulty. For simplification, we'll use 1000 per hit at a rate of 4 hits per second.

Assuming no damage reduction:
0 DEX = 20 swings you die = 5 seconds to live
(1st) 500 DEX = 4 more swings = 1 extra second to live
500 Armor = 3077 more EH = 0.75 extra seconds to live
500 VIT = 17500 Health = 4.4 extra seconds to live

YOW, VIT is way better.

But what if you have more damage reduction? Isn't there an interaction between EH gain, DEX and VIT?

Okay, lets push each hit down to 800 via armor and say you have 30000 health and 500 DEX to start:

Base time to live = 30000 / 800 = 37.5 landed / 0.9 (chance of landing) = 41.667 swings = 10.42 seconds
add 500 more DEX = 37.5 / 0.8 = 11.72 (~+1.3 seconds)
add 500 more EH stat = +4615 EH = 12.02 (~+1.6 seconds)
add 500 more VIT = +17500 health = 16.5 seconds (+6.0 seconds)

So unless I'm missing something obvious, VIT is always, by far, the best defensive stat at ~4x the value of other stats. This example shows DEX and EH sources reasonably close.

If you assume some leech or +X health per hit adding in health return, then EH and DEX will look much better. Please check and correct, this can't be entirely correct.