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"Total" EH - incorporating different damage types into EH

Warning: Theorycraft inside.

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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Thu Oct 21, 2010 1:23 am

Different subject, new post.

About the other portion of the NEH theory. Magic damage.

Are partial resists still on a roll system with certain soft caps? For instance 10% or 20% or 30%.

I just asumed the average resist on the character sheet is exactly that, an average of the rolls.

There has been some speculation it's a fixed number now, but that could just be ppl misinterpreting the character sheet. I was not able to find any proof for either theory yet.

Edit: this is all I can find atm:

http://elitistjerks.com/f15/t29453-comb ... cataclysm/

It has a piece about resistance. Updated values for lvl 88, and finally narowed down the constant. But it doesn't say anything about there being no rolls anymore.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Thu Oct 21, 2010 6:07 am

Kihra wrote:
Awyndel wrote:I forgot about the 5% from plate specialisation, sorry about that. So with 15% mastery, 5% plate and 5% kings the 12.075 should be 12.67875.


Yeah, seems like it should be 10 * 1.15 * 1.05 * 1.5 = 12.67875. Theck's original post mentions talents + plate spec. + BoK, so I think he meant to say 12.67875 rather than the number without BoK (which would be 12.075).


You're right, I somehow missed a factor of 1.05. It should be 10*1.15*1.05*1.05=12.67875. I'll go back and edit it again.

Awyndel wrote:The reason I divided A by 1.1 is because I believe toughness should have a place in the formula. I realise the A is the buffed value of armor, on your sheet, and it has been multiplied by toughness already. But that's exactly the reason why I want to "unmultiply" it again. This formula is about the value of stamina and armor ON gear, not on the sheet. Hence, if we represent the mastery, plate and kings in it, so should toughness be represented.


I'm really not sure I understand what you're trying to do here. A is your buffed armor, which incorporates toughness. Dividing by 1.1 to represent the talent doesn't actually do anything except make the formula wrong. Your effective health is based on your buffed armor.

If for some reason, you couldn't check your character sheet to get A, but were able to sum up the armor on your items, then you'd have to account for Toughness. The formula is relatively simple:

a = base armor on items
b = bonus armor on items (not affected by toughness)
c = armor from raid buffs

A = 1.1*a + b + c

Awyndel wrote:I picked this up with Satrina a whole while back. I suggested he should incorperate talents into his formula. I think he updated the formula for it with some extra notes. I'm not sure if you came across the topic when you picked up the formula. Or if I explained it very clearly back then. So for reference:

http://www.tankspot.com/showthread.php? ... nd-Stamina

I realise dividing A by 1.1 is not entirely correct, since the bonus armor portion is not calculated correctly then. Technically only the portion affected by toughness should be divided by 1.1. But the bonus armor portion should be faily small right now, and not have a big influence on the formula.


I remember reading that a while ago, in fact. But it was just as wrong then as it is now. :P

Again, the formula is correct if you use your raid-buffed armor A. It might be a little clearer from my version, since I've explicitly included dS and dA.

My examples above should cover almost every conceivable use of the formula. Those are the "correct" way to use the formula:
1) Plug in your raid-buffed H and A from the character sheet to figure out how much armor 1 stamina is worth
2) Use that number to compare stamina to armor. For bonus armor it's easy, for non-bonus armor don't forget to include the toughness factor in dA.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Thu Oct 21, 2010 6:09 am

Awyndel wrote:Are partial resists still on a roll system with certain soft caps? For instance 10% or 20% or 30%.

I just asumed the average resist on the character sheet is exactly that, an average of the rolls.

There has been some speculation it's a fixed number now, but that could just be ppl misinterpreting the character sheet. I was not able to find any proof for either theory yet.


I have absolutely no idea, I haven't had time to look into Cata resistance mechanics yet.
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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Thu Oct 21, 2010 6:37 am

Ok maybe I don't understand the concept as well as I think, but that still seems wrong to me.

We are comparing 1 stamina on an item, to x armor on an item. So it's not about the sheet, or buffs, it's about comparing items. As far as I understood it, this is the whole reason we are using the 12.6 number. It converts a fully talented and buffed H number, into a stamina number on your gear.

Then why is it, we also put the completely talented and buffed A number in the formula, but we do not convert that number into armor on gear, just as we did with the stamina? I thought that can be done by dividing by 1.1.

To me leaving it out because A is already affected by toughness, is equal to saying, let's change that 12.6 into a 10 ( or even a 1 ), because talents and buffs are already in H. Basicly you are taking that H number, and deconstructing it back into stamina on gear, because gear is what you want to compare. We should do the same for armor, if toughness is already in the A number, it needs to be changed back to the gear value somehow, because that's the very thing, this formula is solving.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Thu Oct 21, 2010 7:16 am

Awyndel wrote:Ok maybe I don't understand the concept as well as I think, but that still seems wrong to me.

We are comparing 1 stamina on an item, to x armor on an item. So it's not about the sheet, or buffs, it's about comparing items. As far as I understood it, this is the whole reason we are using the 12.6 number. It converts a fully talented and buffed H number, into a stamina number on your gear.

Then why is it, we also put the completely talented and buffed A number in the formula, but we do not convert that number into armor on gear, just as we did with the stamina? I thought that can be done by dividing by 1.1.

To me leaving it out because A is already affected by toughness, is equal so saying, let's change that 12.6 into a 10, or even a 1, because talents and buffs are already in H.


Nope. The value H in the formula is your fully talented and buffed health, incorporating that 12.7 in exactly the same way that we incorporate the toughness factor in A. We don't include 12.7 because of H, because we never convert H directly to S. We incorporate it because of dH, the health gain of a small bit of stamina dS.

Let me illustrate this a little more clearly. Start from equation (5):

Code: Select all
dA = (K+A)/H * dH

A here is your fully-buffed character sheet armor, H is your fully-buffed health. Both of those include all the appropriate factors due to talents and buffs (so toughness, kings, 15% prot spec bonus, plate spec, etc).

dH is a small amount of health you gain from some source. That source could be an enchant, gem, trinket, whatever. If it were the chest enchant, which is a flat 275 health, dH would be exactly 275, and the formula would tell us that this is the same EH gain as if we added dA=237 armor ((K+A)/H works out to 0.8622 for H=60k and A=30k).

However, usually our choice isn't between health and armor. Most gems, enchants, and trinkets have stamina, not health, so it would be more convenient to have this formula in a form where we plug in an amount of stamina dS instead of health dH.

Of course, we could do this by hand all the time. We know that every point of stamina gives us 12.7 health. So we could always take the amount of stamina dS on an item and multiply by 12.7 to figure out dH, and then plug that value of dH into the formula. However, then we need to memorize two numbers (the armor:health ratio and 12.7) and remember to make that conversion every time we want to compare things. Instead, we choose to rewrite the formula so that we have an explicit relation between dA and dS, so that there's only one number to remember. Instead of memorizing that it's 0.8622 armor per health point and 12.7 health per stamina, we just memorize 10.9 armor per stamina.

To do that, we use an equation I already said in words: Every point of stamina gives us 12.7 health. Mathematically, that's:

Code: Select all
dH=12.7*dS


which is equation (6) in the derivation. We just plug this into equation (5) to get equiation (7):

Code: Select all
dA = 12.7*(K+A)/H * dS


The key point here is that the fator of 12.7 does not appear because of H. H is still your buffed health, and has that factor of 12.7 built into it. The extra factor of 12.7 comes in because we want to express dH in a more convenient form, namely in terms of stamina dS.

The equivalent conversion for toughness would come into dA, not A. dA represents the post-talents armor contribution of an item, including Toughness. Since bonus armor isn't affected by Toughness, that's pretty easy. If, however, you were comparing two items with a difference in base armor of dA_base, you'd want to remember to multiply dA_base by 1.1 to get the total contribution. In other words:

Code: Select all
dA = 1.1*dA_base + dA_bonus


--------
Appendix:

We could, of course, represent H in terms of stamina, though it's complicated tanks to base health and "+health" raid buffs. It would look something like H = 12.7*(S-10)+B where S is your stamina in the absence of buffs, talents, mastery, etc. and B includes base health and +health raid buffs. The problem is that we don't have an easy way to get S - your character sheet shows the buffed value (approx 1.27*(S-10)+10)). So we'd have to do a bunch of calculations in our head to get S, and then have to remember exactly what our base health is and how much +health we get from raid buffs. That's a lot more complicated than looking at the character sheet and reading off H.

It's also very similar to what you were trying to do with Armor. We could express A the way I mentioned above, 1.1*a+b+c. Then we'd have to sum up all of our gear's base armor for a, the bonus armor for b, naked armor and raid buffs for c, and so on. That's a lot more work than simply reading A off of the character sheet.
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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Thu Oct 21, 2010 4:45 pm

Ugh. I have some trouble understanding this. But if you double checked it, and you're sure, I'm gonna let it go. We have an updated formula, you checked it, we can work with it now, so it's all good.

Thnx a lot for the clarification, now it's up to me to study it. I'll just look at it in more detail over the weekend, see if I can come up with something.

For now I will just stop wasting your time, since you're very busy atm.
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