Discussion of EH Stamina-Armour trade-off.

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Discussion of EH Stamina-Armour trade-off.

Postby Halogen » Tue Jun 22, 2010 8:31 pm

Hi there guys, I've been reading these forums right through the WotLK expansion and my tanking career. While reading these forums I have picked up almost all of what I understand as a tank and the mathematical foundation and evidence provided by the community has been fantastic.

This is not a hate thread this is merely double checking both parties work by a neutral, informed party to get the best possible result (Enlightenment :D).

Recently when discussing Prot Professions a discussion cropped up about the correct way to find Armour vs Stamina. I have tried my best to explain this to the other posted in question (Nillo or Chiako in game).

Now, I believe I understood how to calculate the trade off value of Stamina and armour when choosing between two pieces of equipment.

Remembering Ciderhelm's definition of EH as a measurement of breathing room your healers have. (Meaning no heals whatsoever)
I am aware that heals will increase the efficiency of Armour inversely, however this is a discussion based on EH and worst case scenario (ie, no heals).

Ciderhelm's definition is as follows:
Effective Health is basically a measurement of how much raw damage a creature has to deal to kill you. It is a measurement of Armor and it’s relation to Stamina… Effective Health is the measurement of how much breathing room your healers have to keep you alive assuming all other factors fail — assuming you do not avoid or block attacks or have a mana shield active. Effective Health is important for tanking heavy hitting creatures because of Murphy’s Law — if you can have long strings of not Dodging an attack, it will definitely happen. Raid tanking, ultimately, is about stability.

The equation I have always used has been:
S=C*(K+A)/H when determining Trade off value for a purely physical damage fight.

The equation I use to factor in Magical Damage is:
S=C*(K+A)/(H*M)

In these equations
S= One (1) point of Stamina
C= Class constant multiplied by any raids buffs.(Paladins=12.1264)
In other words when a Paladin has the 30% buff I write it as (12.1264*130/100) or if I were to factor in another seperate 10% buff on top of the ICC buff I would use (12.1264*130/100*110/100).
K= Armour Diminishing returns or %=(Armor/([467.5*Enemy_Level]+Armor-22167.5))*100
A= Current armour value (In rating)
H= Current Health
M=(1+(Md/100))
Md= Percentage of Damage Taken that is either magical or bleed damage.

Please note that this does not include Armour's increased efficiency from Kings 10%* Agility as this is miniscule at best and not what this discussion is primarily focused upon. If someone requests this be included in the equation I will happily do so.

If any of what I have written above is incorrect please tell me with source and relevant evidence.

Here is a link to the Thread in question found on MMO-Champion:
http://www.mmo-champion.com/threads/727 ... ost8167166

My primary statement is as follows:
Originally Posted by Nillo View Post:
That's wrong the buff increases HEALTH not STAMINA, that's why it also increases the value of defense (=> EH = 1.2*(Stamina*10*(1+talents)(1+kings)+Base HP)*(Armor(*1+Talents)+16k)/16k)). Still stamina scales slightly better than armor, but what's most important when comparing them is to also account for minor heals (I've never died without at least getting a pathetic 10k heal, but that still greatly increases the value of armor) and magical damage.
Actually it's not wrong.
Firstly; you have now drifted away from the primary fundamental of the Effective Health ethos. This is defined as the amount of damage you can take without any heals, or similar effects. This means EH is a measurement of how much breathing room they have.

This is further backed up by Ciderhelm's quote of:
Effective Health is basically a measurement of how much raw damage a creature has to deal to kill you. It is a measurement of Armor and it’s relation to Stamina… Effective Health is the measurement of how much breathing room your healers have to keep you alive assuming all other factors fail — assuming you do not avoid or block attacks or have a mana shield active. Effective Health is important for tanking heavy hitting creatures because of Murphy’s Law — if you can have long strings of not Dodging an attack, it will definitely happen. Raid tanking, ultimately, is about stability.

Secondly, your statement of Stamina doesn't scale with the ICC buff. Buffs are applied mathematically last, in almost all situations. The trade-off between Stamina and Health is applied after talents.

Now I'm going to assume you don't quite understand what you just posted just then because that equation is for total EH not the scaling value of Stamina or Health vs Armour.

There are two equations for determining the value of Stamina vs armour; one is for factoring in Magical damage while the other is based on a purely 100% physical damage fight.

PEH (or Physical Effective Health):
S=C*(K+A)/H
Where the follwing occurs:
S= 1 (one) point of Stamina
C= The co-efficient or multiplication of S, this is based on class specific scenarios such as talents.
K= Armour Diminishing Returns. %=(Armor/([467.5*Enemy_Level]+Armor-22167.5))*100
A= Current armour value (In rating )
H= Current Health

Please note this equation is for finding what is more valuable on your current gear. To compare two pieces of armour remove the slot.
Also note, the diminshing returns equation: %=(Armor/([467.5*Enemy_Level]+Armor-22167.5))*100 is the same as the equation you first listed however, it's not as rough as "subtract 16k", the 16,635 comes from:
(mob level)*467.5-22167.5

This formula is not factoring in raid buffs.

This means that for a protection paladin (C=12.1264) with (Armour Rating)A=33206 and (Health points) H=47329 we get the following equation:

S= 12.1264*((467.5*83-22167.5)+33206)/47329
or
12.77(rounded)=12.1264*((467.5*83-22167.5)+33206)/47329
One point of stamina (S) = 12.77 Armour Rating present on gear.

TEH (or Total Effective Health):
S=C*(K+A)/(H*M)
You'll probably notice that this is the same equation as before except this time M is present as the final multiplicative.
All values are the same as previously listed however this time M=(1+(Md/100))
where:
Md = percentage of damage taken that is either magical or bleed.

In a fight with 40% magic damage and the same tank as listed before (A=33206, H=47329) fighting a level 83 Raid boss we get the following equation:

S= (12.1264*((467.5*83-22167.5)+33206)/47329)*(1+(40/100))
S= 17.87801693
It can also be observed from this that TEH: S= PEHS*(100+Md%)/100

To factor in further Raid buffs such as the ICC 30% buff we increase the value of C by 30%. For a paladin tank this would be (12.1264*130/100).
To give an example of this I'll re-do the PEH and TEH equations with a 30% buff atattched.
PEH:
S= (12.1264*130/100)*((467.5*83-22167.5)+33206)/47329
TEH:
S= (12.1264*130/100*((467.5*83-22167.5)+33206)/47329)*(1+(40/100))

If you'd like to take this discussion further please don't do as Jamesvz did in this thread here and blindly discuss this topic without any relevant evidence or support: (Still not allowed to post links ) Look for Armor vs HP Math help under Advanced Theorycraft and calculations on Maintankadin

Another alternative would be to review the information given on Maintankadin. Most of what I have said is based off of Theckhd's work in his TEH thread.



NILLO'S REPLY:
And you still haven't shown how the ICC buff does affect the value of stamina, but does not affect the value of armor.... but hey I've found the mistake in your calculation :P

S= (12.1264*130/100)*((467.5*83-22167.5)+33206)/47329
for a 30% buff the bold value must also be multiplied by 1.3 thus removing the 1.3 in the first part of your equation and because of that the equation remains the same as it was without the buff.

NILLO'S SECOND REPLY:
Originally Posted by Halogen0 View Post
1) No, that equation is written perfectly.

2) The ICC buff changes three things: Health, Damage Done and Healing Done. In no way does the ICC buff increase the value of armour it does in fact decrease the value of armour further when compared depending on Stamina to the approximate value of whatever the buff percentage is currently sitting at.

3) This is why the buff is factored into C and not H because C is buffed and H is unbuffed otherwise we would end up with same value of stamina : armour regardless of percentage buffs applied. (E.g; Sanc and Kings).

4) In other words as the efficiency of Stamina increases the efficiency of Armour gradually decreases because it does not gain the bonus of the ICC buff.
1) No it's not , because you need to multiply the health you had before with 1.3 as well - not doing this is just wrong. But I'll explain it more detailed later.
2) I'll say it again : It increases HEALTH not STAMINA. If you think like this you might as well add Inspiration (10% less physical damage taken) to the side of armor because it increases the physical resistance, but not your health - same mistake you did.

3) Two words: Base Health . Yes the small amount of base health (+ commanding shout) is all that makes the difference here. Increasing your stamina by 10% does NOT increase your total health by 10% it only increases it by let's say 9% => armor profits less from the increase in stamina. The ICC buff on the other hand increases your total health => also your base health by 30% => both are equally affected by it.

4) It does, but only if the magical damage that occured at a time of death is higher than the healing (+blocks and absorbs) received before your death.

And to go back to an example:
As I said before : EH = (ICC BUFF *(Stam * Buffs + DeltaStam * Buffs + Base HP)) * ((Armor + DeltaArmor + Base Armor)/Base Armor)
Now to take a different approach:
How much DeltaStam do I need for 1% extra EH?
DeltaStam = (BaseHP+Stam*Buffs)/(100*Buffs) or 47329/1212.64 ~ 39 Stamina
How much DeltaArmor do I need for 1% extra EH?
DeltaArmor = (BaseArmor + Armor) / 100 = 49841/100 = 498.4 Armor
As (I hope) you can see the ICC doesn't matter at all here. (And by doing DeltaArmor/DeltaStam we get the 12.77 you had before)

If not I'll try to make it even more clear by setting Buffs to 10 (removing BoK + talents)
Too bad I don't know the base hp + CS combined so I'll just say it's 10k: (this example is only meant to show a difference not actual numbers)
DeltaStam = (BaseHP + Stam) / 100 = 40783/100 ~ 40.8 stam => increasing EH by 1% without stamina modifiers takes more stamina than before (but it's still cheaper than armor)

Now what happens if magical damage is involved (your formula is also wrong here it can never be 1+%magic damage, because if 100% of the damage done would be magical your formula would only double the value of stamina compared to armor, which can't be true because then the value of armor is exactly 0 => it must be ...*1/(1-%magic)

Let's assume you take a Soul reaper that does ~ 50k damage (the rest of the attacks that kill you are autohits)
To increase your EH by 1% with stamina you still need 39
For Armor it looks different now, because only the health you have left after this huge magical attack will be affected by armor:
DeltaArmor = HealthBefore/HealthLeft * (BaseArmor + Armor) / 100 = 47329*ICC/(47329*ICC-50k) * 498.4 = 2660 Armor for 1% health with the 30% ICC buff and without the ICC buff you would already be dead meat.
=> Armor is bad if a high percantage of damage taken before death is of unmitigatable nature.

But this also works the other way round: (assuming pure physical like saurfang and some earth shied + hots or stupid FoLs adding up to 10k hp)
DeltaStam = ICC*(BaseHP+10k+Stam*Buffs)/(100*Buffs*ICC) or 47329+10k/1212.64 ~ 47 Stamina
DeltaArmor = HealthBefore/HealthLeft * (BaseArmor + Armor) / 100 = 47329*ICC/((47329+10k)*ICC) * 498.4 = 411.46 Armor needed for 1%
=> At this point no matter if you have the ICC buff or not Stamina will loose to Armor.



And to fix your equation: (or TL;DR)
S= (12.1264*130%)*((BaseArmor)+CurArmor)/(CurHealth*130% + Heal - Magical Damage)

For a full view of the discussion please visit the link attatched.
Any information regarding any errors made by either myself or Nillo is greatly appreciated.
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Re: Discussion of EH Stamina-Armour trade-off.

Postby tlitp » Tue Jun 22, 2010 11:03 pm

Remembering Ciderhelm's definition of EH as a measurement of breathing room your healers have. (Meaning no heals whatsoever)
I am aware that heals will increase the efficiency of Armour inversely, however this is a discussion based on EH and worst case scenario (ie, no heals).

This merely points out an obvious shortcoming of the current modeling of EH. A less abstract metric should not be time-implicit. A time-explicit one will get rid of the horrendously dated "EH=no heals whatsoever" concept.

On topic : the question has already been raised.
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Re: Discussion of EH Stamina-Armour trade-off.

Postby theckhd » Wed Jun 23, 2010 5:48 am

Nillo is correct. Any multiplicative buff to stamina or health has no effect on the relative EH contribution of stamina or armor.

I'm not sure what point you were trying to make about Armor DR in that thread. The diminishing returns are already taken into account in my analysis. The result is still linear in Armor, despite the diminishing returns.
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Re: Discussion of EH Stamina-Armour trade-off.

Postby pfunkmort » Thu Aug 12, 2010 3:58 am

I'm sure I"m going to feel stupid about asking this so off the cuff...but, the ICC buff DOES change the ratios for stam and armor in a TEH conversation right?
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Re: Discussion of EH Stamina-Armour trade-off.

Postby theckhd » Thu Aug 12, 2010 5:34 am

No, it doesn't.
theckhd wrote:Any multiplicative buff to stamina or health has no effect on the relative EH contribution of stamina or armor.
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