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Satrina
11-12-2008, 02:59 PM
This is a pretty important concept. Here we show how armour and hitpoints are dependent upon each other in the grand scheme of things, and how they interact with each other. Always remember that you need to balance what you do with your armour and hitpoints against avoidance. And, of course, this entire thing is meaningless against spells. This is directly related to the theory of Effective Health (http://www.tankspot.com/forums/theory-articles-guides/1060-effective-health-theory.html), which examines this relationship in a slightly different way.

We can equate 1 point of stamina to a number of points of armour that will give you equivalence. That is, X points of armour will increase your time to live by the same amount as 1 point of stamina. The caveat here is that this applies only for melee damage; as soon as someone starts slinging spells it all means nothing, making this a mostly academic exercise. First, we note that the armour dynamic is a simple asymptotic function. Mitigation from armour is capped at 75%, and you can prove to yourself that it is still there by going and fighting much lower level opponents (or by looking at the armour formula in the game's UI files). Here's the analysis using 20000 armour (A) and 20000 health (H), facing a level 80 opponent.

For the formula to determine mitigation (M) for a given armour rating (A), we begin with:

K = 467.5L - 22167.5
Where L is the level of the opponent being fought, then:


A
M = -----
A + K

We get 56.8% mitigation against a level 80 opponent with 20000 armour. Since we'll need it later, solving for A in terms
of mitigation gives:


MK
A = -----
1-M

Let's define survivability in terms of how long a given opponent takes to kill you. Assume we have 500 damage per second incoming, unmitigated, melee only.


- Taking into account 56.8% mitigation, that's 216.2DPS.
- Solving for time, the time to live under that damage rate is 92.5 seconds.
- Now to increase mitigation by 1%...
- Using the above formula, increasing mitigation from 56.8% to 57.8% means we need 20834 (+834) armour
- At 57.8% mitigation, incoming DPS is reduced to 211.2DPS.
- The time to live at that damage rate is 94.7 seconds.
- The change in time to live between 56.8% and 57.8% mitigation is 2.19 seconds, or 474 damage at 216.2DPS.

Therefore, at 20000A and 20000H, 47.4 stamina is equivalent to 834A, or 1:17.6 stamina-armour equivalence, in terms of survivability under the given damage output.

Solving this for several other armour values while keeping health constant at 20000 and 25000:



20000H 25000H
18000A 1 stamina to 17A 1 stamina to 13A
20000A 1 stamina to 18A 1 stamina to 14A
22000A 1 stamina to 19A 1 stamina to 15A
25000A 1 stamina to 20A 1 stamina to 16A
30000A 1 stamina to 23A 1 stamina to 18A
35000A 1 stamina to 25A 1 stamina to 20A
40000A 1 stamina to 28A 1 stamina to 22A

Changing health total while keeping armour constant at 10000 and 15000:


20000A 25000A
15000H 1 stamina to 23A 1 stamina to 27A
18000H 1 stamina to 20A 1 stamina to 22A
20000H 1 stamina to 18A 1 stamina to 20A
22000H 1 stamina to 16A 1 stamina to 18A
24000H 1 stamina to 15A 1 stamina to 17A
26000H 1 stamina to 14A 1 stamina to 15A
28000H 1 stamina to 13A 1 stamina to 14A
30000H 1 stamina to 12A 1 stamina to 13A

We see that this equivalence is variable on both health and armour, but also that increasing health increases the value of armour very quickly, while increasing armour increases the value of health at a slower rate. Either way, overloading on one over the other drastically increases the value of the lower one.

One of the fundamentals of the calculation above is 56.8% mitigation against a level 80 opponent. Against raid level targets, which will be higher than level 80, your mitigation starts to go down. The effects are shown here:


Level 20000A/20000H 25000A/20000H 20000A/25000H
Level 80 1 stamina to 17.6A 1 stamina to 20.1A 1 stamina to 14.1A
Level 81 1 stamina to 17.9A 1 stamina to 20.4A 1 stamina to 14.3A
Level 82 1 stamina to 18.1A 1 stamina to 20.6A 1 stamina to 14.5A
Level 83 1 stamina to 18.6A 1 stamina to 20.8A 1 stamina to 14.7A
Level 84 1 stamina to 18.6A 1 stamina to 21.1A 1 stamina to 14.8A

Level 25000A/25000H 30000A/30000H
Level 80 1 stamina to 16.1A 1 stamina to 15.1A
Level 81 1 stamina to 16.3A 1 stamina to 15.2A
Level 82 1 stamina to 16.5A 1 stamina to 15.3A
Level 83 1 stamina to 16.7A 1 stamina to 15.5A
Level 84 1 stamina to 16.8A 1 stamina to 15.7A

Finally, we can do some solving to get a general formula for stamina-armour equivalence against a given level opponent:


10(K+A)
1 stamina: ------- points of armour
H

Where A is your current armour, H is your current health, and K is as defined previously.

Recall that there are buffs (Kings) and talents that will change the value of one stamina for you:
- If you have kings, change 10 to 11
- If you have stamina talents, change 10 to 10.6 for a warrior or 11.4 for a paladin
- If you have multiple, then they are multiplicative, for example 11.66 for a warrior with Vitality and Kings
- And so on

Also, if you have armour increasing talents, modify your total armour by the value of the multiplier you get (e.g. 1.1 for paladins and warriors)

A final note is that this formula is not affected by the actual rate of incoming damage per second. As such, it is not affected by avoidance. An avoidance total of 20% from the combined dodge and parry of an individual character does nothing more than reduce the rate of incoming DPS by 20%, on average. While a 20% reduction of incoming DPS is significant (as is the reduction in critical hits that comes with it), it has no bearing on the stamina-armour equivalence.

So, what should you aim for when choosing gear? What we see here is that balance is pretty key to the whole thing. If you stack one at the expense of the other, you are doing yourself more harm than good overall. Having a good balance between armour and stamina tends to focus both for you - when you are taking physical damage. On the other hand, it's pretty hard to actively gear for armour. In general, you're going to gem and enchant for stamina. When you find items with bonus armour, they tend to be the best choice.

Magical damage is a factor that helps to balance the difference between higher health and higher armour. Having very high armour at the expense of health might seem to be of benefit against pure melee opponents, but is a definite disadvantage to opponents using magic, and the amount of buffer you have against hard hits and mishap is probably going to be too small. Your mileage will vary.

Boondockst
11-12-2008, 03:17 PM
"Back in Burning Crusade, the 12000A/12000H pair was thrown around as a "good starting point" for Karazhan raiding."

So what is going to be the new starting point? I would hate to try starting Naxx only to find that we cant do it cause I cant take a hit from a boss or my guild drags thier feet so I can make sure that I have everything I need only to discover that I was ready 3 drops ago.
In live atm, I'm sitting at 17.8k hp (not sure about the armor), so is it safe to assume that 21k is going to be a min?

Satrina
11-12-2008, 03:24 PM
That's the problem with spending all of beta doing testing and addon work =) Hopefully Xav or others who actually got to raid in Beta can fill in the blank.

Kazeyonoma
11-12-2008, 03:48 PM
Cider and Xav are showing numbers in the 20k/20k range.

Awyndel
08-09-2009, 03:36 AM
Really hate to dig this up, and not sure if it has been answered before but does this formula take into account talents and kings?
Would 10 becomes 10x1.1x1.14=12.54 ( for a paladin ofc ) and A divided by 1.1?

Satrina
08-09-2009, 11:07 AM
Yeah, this was initially written in 2004, well before Blessing of Kings existed =)

You will want to change the 10 to 11 if you have kings, or 12.54 for paladin with talents and kings, or 11.66 for a warrior with talents and kings, etc. Dividing total armour by 1.1 is a good idea too.

Awyndel
08-10-2009, 09:56 AM
Lovely.

It would prolly be a good idea though to divide unbuffed armor by 11, and substract that number from A in the formula. Because the talent only works on armor from gear, and not from buffs.


I was also thinking about a formula for block value. This of course varies depending on how many times you are hit before you die. So let's asume on a hard hitting boss you can get hit max 3 times in a row without heals before you die, then the first 2 block is prolly saving you some trouble, but the 3rd one will prolly kill you with or without block. Now this can obviously only be counted towards effective health when you are block capped. So let's say this is mostly for paladins.

I was thinking ( paladin example ) one could multiply the block value by 1.3 for the talent, and by 2 coz of 2 hits, then divide it by 1.1 for kings, 1.14 for talents and by 10 coz we're counting in hitpoints. This gives me 1 block value is 0.207 stam.

Satrina
08-10-2009, 10:00 AM
You're getting into the difference betwen a scientist and an engineer here. The portion of your armour that is unaffected by talents is small compared to your total. "Close enough" or "within error tolerances" is the term you're looking for :)

Star Scythe
01-20-2010, 12:10 PM
any chance you could update these charts for the gear levels that ilvl 258 tanks are at? somewhere in the 29k-35k armor and 55k-60k HP range. (yes thats about what me and the other 2 tanks in the guild are at raid buffed depending on class / trinkets). just wondering so i can make more informed gear choices for fights and purchases now that a lot of the frost badge gear has bonus armor on it.

Awyndel
01-25-2010, 08:11 AM
This formula is for pure physical fights.

There was some research for incorporating magic damage into all this. Of course this will differ per fight.

http://maintankadin.failsafedesign.com/forum/index.php?f=6&t=26831&rb_v=viewtopic