"Total" EH  incorporating different damage types into EH
Moderators: Fridmarr, Worldie, Aergis, theckhd
Re: "New EH"  incorporating different damage types into EH
Not to heap even more on your plate, Theck, but I'm wondering if we could also figure out what the crossover points in terms of magic damage between Flask of Stoneblood (1300 hp), Lesser Flask of Resistance (+50 resist), and Flask of Chromatic Wonder (+35 resist, +18 stam). Of course, in some cases you also get resistance from auras or MotW.
Note that you'll actually need to split damage three ways for armor vs. hp vs. resistance comparisons
For example, Gormok's impale would be D_u damage, for which the only way to increase EH is to increase H (or take more damage reduction talents), but Anub's aura is D_r; Mimiron's spellfire is D_r, but you only get the MotW resistance rather than fire resist aura for that damage. I'm sure you've already thought about this a bit, but it would be interesting to see how things stack up now. (I remember finding that the Resistance flask was a lot better in 3.0 for Sarth+3, but they boosted Stoneblood since then. Still, with the current levels of health, I wouldn't be surprised if some fights like Jaraxxus still benefitted from the resist flask.
Note that you'll actually need to split damage three ways for armor vs. hp vs. resistance comparisons
 D_p (physical damage mitigated by armor)
 D_u (nonresistable, nonarmor mitigated damage, e.g. bleeds)
 D_r (resistable magical damage).
For example, Gormok's impale would be D_u damage, for which the only way to increase EH is to increase H (or take more damage reduction talents), but Anub's aura is D_r; Mimiron's spellfire is D_r, but you only get the MotW resistance rather than fire resist aura for that damage. I'm sure you've already thought about this a bit, but it would be interesting to see how things stack up now. (I remember finding that the Resistance flask was a lot better in 3.0 for Sarth+3, but they boosted Stoneblood since then. Still, with the current levels of health, I wouldn't be surprised if some fights like Jaraxxus still benefitted from the resist flask.
 Andris
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 Joined: Mon Nov 19, 2007 4:15 pm
Re: "New EH"  incorporating different damage types into EH
I can help with regular Ulduar10 along with possibly Naxx10 (seeing if I can get my guild to run it either this week or the next since we will be missing quite a few regulars due to either holiday or just travel). While obviously a single fight for each of theses bosses is not enoughWrathy wrote:For now the problem is that we do not really raid anything else.
Also, Theck, I'm guessing we're going to want the unmitigated values of the attacks coming at us (that is, we either list what our mitigation numbers are or we figure out what it is before we post it).
 Alixander
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 Location: Berkeley, CA
Re: "New EH"  incorporating different damage types into EH
Stellar post. I was debating just today whether or not I should go and snag the Glyph, and this at least allows me to make a better educated decision regarding it.
I'll admit, it took me two or three readings to understand the logic behind it, but great nonetheless.
Edit: If there's anything we can do to assist with data collection, just let me know what we can/need to do.
I'll admit, it took me two or three readings to understand the logic behind it, but great nonetheless.
Edit: If there's anything we can do to assist with data collection, just let me know what we can/need to do.
 Florisia
 Posts: 140
 Joined: Sun May 10, 2009 10:37 am
Re: "New EH"  incorporating different damage types into EH
Wrathy wrote:As for the Parses and the Y values, Theck is Y strictly the overall percentage of magical damage taken? If that is the case I can start compiling some values for you in TOTGC at least. For now the problem is that we do not really raid anything else.
Yes, it would be strictly the overall percentage of your damage intake from magical sources.
I posted a quick breakdown of a single parse for Uld25 and ToGC25 over in the Glyph of Indomitability thread. What we'd ideally want is to compile data from a number of parses to find reasonable averages, since I expect the amount will vary some from parse to parse.
Though as Andris pointed out, we should really break it down into three values.
Y for strictly magical damage
X for bleed damage (physical damage not mitigated by armor)
and the rest (1XY) for regular old physical damage.
Alixander wrote:Also, Theck, I'm guessing we're going to want the unmitigated values of the attacks coming at us (that is, we either list what our mitigation numbers are or we figure out what it is before we post it).
Actually, it will suffice to just figure out the relative percentage of intake. The way I've developed the theory, we don't really need to know what the unmitigated damages D_i are. I derived it that way on purpose, to make it easier to actually use the theory rather than having it just sit there and look pretty.
In other words, if the parse says that 50% of the damage you took was physical, 20% was physical bleeds, and 30% was magical, those are the values we need (Y=30%, X=20%).
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Re: "New EH"  incorporating different damage types into EH
Florisia wrote:Edit: If there's anything we can do to assist with data collection, just let me know what we can/need to do.
The data collection is actually pretty easy, you don't even need to do anything ingame.
 Find a World of Logs parse of an encounter being tanked by a paladin. This could be one of your own parses or someone else's.
 Look at the "damage taken" summary for that player, and add up all of the %'s due to magical or bleed damage to find Y and X
 Post the results here
It's also worth noting that there are several tanking jobs to consider for some fights. Tanking Freya, for example, will have a different breakdown than tanking the Stormlasher and Water spirit. So we'd want to know which job that player was doing (though this should also be discernible by the information in the parse).
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Re: "New EH"  incorporating different damage types into EH
Should we even bother with the overtly magical fights? I'm specifically thinking of singletank Hodir (with or without resist gear), but I'm sure there are others if I stopped to think of it. In those type fights, you're taking so much magical damage that I can't imagine that Armor is the better option, but we might want the numbers just for knowledge's sake (who knows when it will be useful later).
 Alixander
 Posts: 543
 Joined: Tue May 08, 2007 11:51 am
 Location: Berkeley, CA
Re: "New EH"  incorporating different damage types into EH
CRAP...
This is going to be a lot of work. I'll try to create a rough spreadsheet for ToTGC and post it here so that I can verify all of the information with everyone. Basically for ToTC/ToTGC, I am going to break it up as follows:
Northrend Beasts  Three part fight, Three different values for total damage, X, and Y
Gormok D X and Y
Worms D X and Y
(assmumptions will have to be estabilished for the numbers to align e.g. entire duration of the phase and how your guild tanks it)
Icehowl D X and Y
Jaraxxus Boss vs add tank  My thoughts are that the Infernal damage taken by the MT should be included.
FC  Overall D X and Y
Twins  Overall D X and Y (this fight will have a very high variable in magic damage based on the strat and skill of soakers)
Anub  MT vs OT (It can be argued that OT doesn't need data, as we have established what is needed for that gear set)
This is going to be a lot of work. I'll try to create a rough spreadsheet for ToTGC and post it here so that I can verify all of the information with everyone. Basically for ToTC/ToTGC, I am going to break it up as follows:
Northrend Beasts  Three part fight, Three different values for total damage, X, and Y
Gormok D X and Y
Worms D X and Y
(assmumptions will have to be estabilished for the numbers to align e.g. entire duration of the phase and how your guild tanks it)
Icehowl D X and Y
Jaraxxus Boss vs add tank  My thoughts are that the Infernal damage taken by the MT should be included.
FC  Overall D X and Y
Twins  Overall D X and Y (this fight will have a very high variable in magic damage based on the strat and skill of soakers)
Anub  MT vs OT (It can be argued that OT doesn't need data, as we have established what is needed for that gear set)
Dakiros wrote:Hear that sound? Its Wrathy breaking Wowhead and Wordpress while he quickly comes up with the Rival set.
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 Wrathy
 Maintankadonor
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Re: "New EH"  incorporating different damage types into EH
Hi Theck,
I'm actually a DK tank nowadays, and wanted to use the calculation you've done to compare two sets of talents, (frost) gives 3% avoidance and 2% flat damage reduction, the other (unholy) 6% magic damage reduction, if all other factors remained the same.
If I followed you to conclusion, below is the formula I would use, and just insert values. Is that correct?
 Gravity
btw, you rock.
I'm actually a DK tank nowadays, and wanted to use the calculation you've done to compare two sets of talents, (frost) gives 3% avoidance and 2% flat damage reduction, the other (unholy) 6% magic damage reduction, if all other factors remained the same.
If I followed you to conclusion, below is the formula I would use, and just insert values. Is that correct?
 Code: Select all
H*(1  YZ) H*(K+A)*(1YZ)
EH =  =  (16)
1  M K
 Gravity
btw, you rock.
 Hammerjudge
 Maintankadonor
 Posts: 143
 Joined: Mon Oct 01, 2007 8:36 pm
Re: "New EH"  incorporating different damage types into EH
Hammerjudge wrote:Hi Theck,
I'm actually a DK tank nowadays, and wanted to use the calculation you've done to compare two sets of talents, (frost) gives 3% avoidance and 2% flat damage reduction, the other (unholy) 6% magic damage reduction, if all other factors remained the same.
If I followed you to conclusion, below is the formula I would use, and just insert values. Is that correct?
 Code: Select all
H*(1  YZ) H*(K+A)*(1YZ)
EH =  =  (16)
1  M K
 Gravity
btw, you rock.
You may want to wait until I post the newest version of the theory (which is now finished). I'm going to begin typing it up now.
The reason is that the new version accounts for armor and talent mitigation separately, which more accurately models the system you're interested in. For example, the physical damage you take is actually:
P*(1Ma)*(1Mt)
Where Ma = A/(A+K) is your mitigation from armor, and Mt is the mitigation provided by talents.
In your case, a 2% flat damage reduction would increase both Mt and Mg (magical mitigation, which I used N for in the previous calculation), whereas a 6% magic damage reduction would just increase Mg.
After I post the theory, I'll make more specific comments about how you'd use it to solve your dilemma.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 7753
 Joined: Thu Jul 31, 2008 3:06 pm
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Re: "New EH"  incorporating different damage types into EH
I'll pretty this up later. For now, I just want to get the math parts typed up for review before I go to bed.
Question: Should I just go back and revise the OP, or just leave the revised version of section II here? In the long run, I'm going to rewrite the whole thing to make it a useful article anyway.
II. Including other forms of damage
The major weakness with this theory is that it's focused on purely physical damage. It can cover purely magical damage by substituting a magical mitigation factor for M (which would be a complicated formula based on talents and resistance). However, it doesn't accurately reflect fights that contain both magical and physical damage, which means "nearly every fight in the game." I will now suggest a fairly simple way to extend EH to cover any fight.
Proof:
To fully incorporate other types of damage, we need to be more careful. First of all, there are three basic types of damage we want to consider:
1) "Regular" damage  physical damage mitigated by armor
2) Bleeds  physical damage that is not mitigated by armor
3) Magical damage
In section I, we assumed that physical damage was just mitigated by armor. This isn't technically true, there's also talented mitigation to consider. This becomes especially important once we add other damage types into the mix, because the talented portions can apply differently to each damage type. Some talents add only magic mitigation, while others add to all mitigation.
Let's return to the beginning. Now, instead of taking damage D per hit, let's talk in aggregate. The boss puts out D raw damage over the course of a fight, broken down into Dp "regular" physical damage, Db bleed damage, and Dg magical damage.
To get a general form, we express the damage you take d by:
Where we've used the following mitigation factors:
Ma is the mitigation due to armor, defined as M is in section I.
Mt is the mitigation applied to physical damage due to talents
Mg is the mitigation applied to magical damage due to talents
Mr is the mitigation applied to magical damage due to resistances
In this form, we can account for everything, and can raise or lower physical and magical talented mitigation independently from armor and resistances if we want to.
At first, this looks like it will be hopelessly complex. We want to solve for D/d, but we don't have Dp, Db, or Dg, nor do we know what percentage of D any of those represent. Luckily, we won't need any of this information in the final result.
we can define values P, B, and G to represent the relative percentages of the boss's total raw damage output D as follows:
As we said, we don't actually have access to this information, but it turns out we won't need it, and it will help simplify the math in the meantime. This notation lets us rewrite equation (8) as:
and rearranging this to express EH we have
Before we go any further, let's consider what we see on a WoL parse. The damage that we read off of the parse is postmitigation. In other words, we don't have Dp directly, we have Dp*(1Ma)(1Mt), and similarly for Dg and Db. We can represent what we see on a combat log parse as X and Y:
Here X is the percentage of our damage intake that's from bleed effects, Y is the amount of damage taken from magical sources, and 1XY is the "leftover" amount due to regular physical damage.
We want to be able to express EH in terms of X and Y; to do that we need to eliminate some variables. To do this, we rewrite equations (13) in a different form:
If we multiply (14b) by (1X)/Y and subtract it from (14a), we have
Similarly, (14b) multiplied by X/(1Y) and subtracted from (14a) gives us
Using this, we can rewrite B(1Mt) + G(1Mg)(1Mr) as
and equation (12) becomes
This still has a P in it though. To eliminate that, we substitute eqns (15) into (10) and solve for P:
Where I'm using Z = (1Mt)(1Ma)/(1Mg)(1Mr) as an temporary variable to simplify the expression slightly. Plugging (17) into (16) gives us the final form of the expression for effective health:
We can write equation (18) in a slightly more intuitive form:
The first term is our EH against "regular" physical attacks multiplied by the percentage of our damage intake that those attacks represent. The second term is our EH against bleeds, multiplied by the percentage of our intake due to bleeds. And the third term is our EH against magical damage multiplied by the percentage of our intake that's magical.
In other words, EH is properly calculated as the weighted average of our EH against all damage sources, with the weight factors simply being the percentages of our intake that those sources represent.
Just to check that this makes sense, let's consider some special cases:
Y=0, X=0: Second and Third terms disappear, and EH simplifies to H/((1Ma)(1Mt)), exactly the form the simple version took once talented mitigation is included.
Y=1, X=0: The first and second terms disappear, and EH simplifies to H/(1Mg)(1Mr). This is exactly what we'd expect for a purely magical fight  our only mitigation here is from talents.
Y0, X=1: The first and third terms vanish, leaving EH = H/(1Mt). Again, exactly what we'd expect  the mitigation from armor disappears, and we're left with only physical mitigation from talents.
To find the armor:stamina EH relation, it's simpler to start from equation (12). Differentiating gives us
d(Ma) evaluates to:
Which substituted into our expression for d(EH) gives
Again, we equate the first and second terms, and solve for dA:
It should be clear by inspection that the second fraction in that expression is simply 1/(1XY), giving us the final forms of dA:
Here we finally have an equivalence that accurately relates armor to stamina for a multifaceted fight. We see that as Y>1 (P>0), the second factor blows up. The other way to understand this is that the second term in the differentiated equation goes to zero, removing dA from the equation. This is as expected, since no amount of armor will give you any EH for Y=1.
Alternatively, solving for dS:
So to find out how much stamina an amount of armor is equivalent to, we simply divide by the conversion factor (K+A)/H and multiply by the percentage of damage the armor will help mitigate (1XY). What this means practically is that armor loses effectiveness linearly with the amount of physical damage in the fight. For a fight with 50% physical damage, armor will only be worth 50% as much EH.
Let's check some numbers. For a tank with H=50k, A=30k, Ma=0.6433. For paladins, Mt=0.1686 and Mg=0.1156. Let's see what happens as Y varies from 0 to 1:
I've truncated the graph at 70% since it blows up as Y gets larger. However, here are a few representative points:
So for a purely physical fight, armor seems like a pretty good deal. But for even a fight with 20% magical damage, Armor becomes devalued by 20%. This will generally be enough to make a Stamina trinket provide more EH than an armor trinket.
For an example, let's look at the Glyph of Indomitability, since that's what started this thread. It gives 1792 armor, which is equivalent to 153 stamina. However, for a fight with Y=20%, we get only (1Y)=80% of that, or 123 stamina. For a fight with 30% magical damage, it's only worth 107 stamina, and so forth.
III. Conclusion
It is quite simple to extend the Effective Health calculation to incorporate nonphysical sources of damage. The result is simply a weighted average of one's effective healths vs. "regular" physical, bleed physical, and magical damage. The weighting is determined by the percentages of one's damage intake from bleed and magical sources X and Y respectively. The formulas are:
where Mt and Mg represent talented mitigation factors for physical and magical damage respectively, Mr is the mitigation due to resistances, Ma is the mitigation due to armor (defined below), K is the armor decay factor (also defined below), H is the player's fully raidbuffed max health, and A is the players raidbuffed armor.
The takehome message of these formulas is that armor loses effectiveness linearly with the percentage of "regular" physical damage intake for a given fight. In other words, for a fight with only 50% nonbleed physical damage, armor is reduced in effectiveness by 50%. If an armor trinket is worth 100 stamina on a purely "regular" physical fight, it will only be worth 60 stamina on a fight with 15% bleed damage and 25% magic damage (60% "regular" physical).
Question: Should I just go back and revise the OP, or just leave the revised version of section II here? In the long run, I'm going to rewrite the whole thing to make it a useful article anyway.
II. Including other forms of damage
The major weakness with this theory is that it's focused on purely physical damage. It can cover purely magical damage by substituting a magical mitigation factor for M (which would be a complicated formula based on talents and resistance). However, it doesn't accurately reflect fights that contain both magical and physical damage, which means "nearly every fight in the game." I will now suggest a fairly simple way to extend EH to cover any fight.
Proof:
To fully incorporate other types of damage, we need to be more careful. First of all, there are three basic types of damage we want to consider:
1) "Regular" damage  physical damage mitigated by armor
2) Bleeds  physical damage that is not mitigated by armor
3) Magical damage
In section I, we assumed that physical damage was just mitigated by armor. This isn't technically true, there's also talented mitigation to consider. This becomes especially important once we add other damage types into the mix, because the talented portions can apply differently to each damage type. Some talents add only magic mitigation, while others add to all mitigation.
Let's return to the beginning. Now, instead of taking damage D per hit, let's talk in aggregate. The boss puts out D raw damage over the course of a fight, broken down into Dp "regular" physical damage, Db bleed damage, and Dg magical damage.
To get a general form, we express the damage you take d by:
 Code: Select all
d = Dp*(1Ma)*(1Mt) + Db*(1Mt) + Dg*(1Mg)(1Mr) (8)
Where we've used the following mitigation factors:
Ma is the mitigation due to armor, defined as M is in section I.
Mt is the mitigation applied to physical damage due to talents
Mg is the mitigation applied to magical damage due to talents
Mr is the mitigation applied to magical damage due to resistances
In this form, we can account for everything, and can raise or lower physical and magical talented mitigation independently from armor and resistances if we want to.
At first, this looks like it will be hopelessly complex. We want to solve for D/d, but we don't have Dp, Db, or Dg, nor do we know what percentage of D any of those represent. Luckily, we won't need any of this information in the final result.
we can define values P, B, and G to represent the relative percentages of the boss's total raw damage output D as follows:
 Code: Select all
P = Dp/D (9a)
B = Db/D (9b)
G = Dg/D (9c)
P + B + G = 1 (10)
As we said, we don't actually have access to this information, but it turns out we won't need it, and it will help simplify the math in the meantime. This notation lets us rewrite equation (8) as:
 Code: Select all
d = D*[P(1Ma)(1Mt) + B(1Mt) + G(1Mg)(1Mr)] (11)
and rearranging this to express EH we have
 Code: Select all
H
EH = H*D/d =  (12)
P(1Ma)(1Mt) + B(1Mt) + G(1Mg)(1Mr)
Before we go any further, let's consider what we see on a WoL parse. The damage that we read off of the parse is postmitigation. In other words, we don't have Dp directly, we have Dp*(1Ma)(1Mt), and similarly for Dg and Db. We can represent what we see on a combat log parse as X and Y:
 Code: Select all
B(1Mt)
X =  (13a)
P(1Ma)(1Mt) + B(1Mt) + G(1Mg)(1Mr)
G(1Mg)
Y =  (13b)
P(1Ma)(1Mt) + B(1Mt) + G(1Mg)(1Mr)
Here X is the percentage of our damage intake that's from bleed effects, Y is the amount of damage taken from magical sources, and 1XY is the "leftover" amount due to regular physical damage.
We want to be able to express EH in terms of X and Y; to do that we need to eliminate some variables. To do this, we rewrite equations (13) in a different form:
 Code: Select all
X*P(1Ma)(1Mt)  (1X)*B(1Mt) + X*G(1Mg)(1Mr) = 0 (14a)
Y*P(1Ma)(1Mt) + Y*B(1Mt)  (1Y)*G(1Mg)(1Mr) = 0 (14a)
If we multiply (14b) by (1X)/Y and subtract it from (14a), we have
 Code: Select all
P(1Ma)(1Mt) = (1XY)*G(1Mg)(1Mr)/Y (15a)
Similarly, (14b) multiplied by X/(1Y) and subtracted from (14a) gives us
 Code: Select all
P(1Ma)(1Mt) = (1XY)*B(1Mt)/X (15b)
Using this, we can rewrite B(1Mt) + G(1Mg)(1Mr) as
 Code: Select all
B(1Mt) + G(1Mg)(1Mr) = (X+Y)*P(1Ma)(1Mt)/(1XY)
and equation (12) becomes
 Code: Select all
H*(1XY)
EH = H*D/d =  (16)
P(1Ma)(1Mt)
This still has a P in it though. To eliminate that, we substitute eqns (15) into (10) and solve for P:
 Code: Select all
X (1Ma)(1Mt) Y (1Ma)(1Mt)
1 = P + B + G = P + P** + P**
(1XY) (1Mt) (1XY) (1Mg)(1Mr)
(1Mt)(1Ma)
(1XY) = P*[(1XY) + X(1Ma) + Y*]
(1Mg)(1Mr)
(1XY) = P*[(1XY) + X(1Ma) + YZ]
(1XY)
 = (1XY) + X(1Ma) + YZ (17)
P
Where I'm using Z = (1Mt)(1Ma)/(1Mg)(1Mr) as an temporary variable to simplify the expression slightly. Plugging (17) into (16) gives us the final form of the expression for effective health:
 Code: Select all
H*[(1XY) + X(1Ma) + YZ]
EH = H*D/d =  (18)
(1Ma)(1Mt)
We can write equation (18) in a slightly more intuitive form:
 Code: Select all
(1XY) X Y
EH = H*D/d = H* + H* + H* (19)
(1Ma)(1Mt) (1Mt) (1Mg)(1Mr)
The first term is our EH against "regular" physical attacks multiplied by the percentage of our damage intake that those attacks represent. The second term is our EH against bleeds, multiplied by the percentage of our intake due to bleeds. And the third term is our EH against magical damage multiplied by the percentage of our intake that's magical.
In other words, EH is properly calculated as the weighted average of our EH against all damage sources, with the weight factors simply being the percentages of our intake that those sources represent.
Just to check that this makes sense, let's consider some special cases:
Y=0, X=0: Second and Third terms disappear, and EH simplifies to H/((1Ma)(1Mt)), exactly the form the simple version took once talented mitigation is included.
Y=1, X=0: The first and second terms disappear, and EH simplifies to H/(1Mg)(1Mr). This is exactly what we'd expect for a purely magical fight  our only mitigation here is from talents.
Y0, X=1: The first and third terms vanish, leaving EH = H/(1Mt). Again, exactly what we'd expect  the mitigation from armor disappears, and we're left with only physical mitigation from talents.
To find the armor:stamina EH relation, it's simpler to start from equation (12). Differentiating gives us
 Code: Select all
dH d(Ma)*H*P(1Mt)
d(EH) =  + 
P(1Ma)(1Mt)+B(1Mt)+G(1Mg)(1Mr) [P(1Ma)(1Mt)+B(1Mt)+G(1Mg)(1Mr)]^2
d(Ma) evaluates to:
 Code: Select all
dA A*dA dA*K dA*(1M)
d(Ma) =    =  =  (20)
(K+A) (K+A)^2 (K+A)^2 (K+A)
Which substituted into our expression for d(EH) gives
 Code: Select all
dH dA*H*P(1Mt)(1Ma)
d(EH) =  + 
P(1Ma)(1Mt)+B(1Mt)+G(1Mg)(1Mr) (K+A)*[P(1Ma)(1Mt)+B(1Mt)+G(1Mg)(1Mr)]^2
Again, we equate the first and second terms, and solve for dA:
 Code: Select all
(K+A) P(1Ma)(1Mt) + B(1Mt) + G(1Mg)(1Mr)
dA = **dH
H P(1Ma)(1Mt)
It should be clear by inspection that the second fraction in that expression is simply 1/(1XY), giving us the final forms of dA:
 Code: Select all
(K+A) 1
dA = **dH (21)
H (1XY)
12.54*(K+A) 1
dA = **dS (22)
H (1XY)
Here we finally have an equivalence that accurately relates armor to stamina for a multifaceted fight. We see that as Y>1 (P>0), the second factor blows up. The other way to understand this is that the second term in the differentiated equation goes to zero, removing dA from the equation. This is as expected, since no amount of armor will give you any EH for Y=1.
Alternatively, solving for dS:
 Code: Select all
H
dS = *(1XY)*dA (23)
12.54*(K+A)
So to find out how much stamina an amount of armor is equivalent to, we simply divide by the conversion factor (K+A)/H and multiply by the percentage of damage the armor will help mitigate (1XY). What this means practically is that armor loses effectiveness linearly with the amount of physical damage in the fight. For a fight with 50% physical damage, armor will only be worth 50% as much EH.
Let's check some numbers. For a tank with H=50k, A=30k, Ma=0.6433. For paladins, Mt=0.1686 and Mg=0.1156. Let's see what happens as Y varies from 0 to 1:
I've truncated the graph at 70% since it blows up as Y gets larger. However, here are a few representative points:
 Code: Select all
Y(%) Armor 1/(1Y)
0 11.7 1
10 13.0 1.1111
20 14.62 1.25
30 16.71 1.4286
40 19.49 1.6667
50 23.39 2
60 29.24 2.5
70 38.99 3.3333
So for a purely physical fight, armor seems like a pretty good deal. But for even a fight with 20% magical damage, Armor becomes devalued by 20%. This will generally be enough to make a Stamina trinket provide more EH than an armor trinket.
For an example, let's look at the Glyph of Indomitability, since that's what started this thread. It gives 1792 armor, which is equivalent to 153 stamina. However, for a fight with Y=20%, we get only (1Y)=80% of that, or 123 stamina. For a fight with 30% magical damage, it's only worth 107 stamina, and so forth.
III. Conclusion
It is quite simple to extend the Effective Health calculation to incorporate nonphysical sources of damage. The result is simply a weighted average of one's effective healths vs. "regular" physical, bleed physical, and magical damage. The weighting is determined by the percentages of one's damage intake from bleed and magical sources X and Y respectively. The formulas are:
 Code: Select all
(1XY) X Y
EH = H*D/d = H* + H* + H* (19)
(1Ma)(1Mt) (1Mt) (1Mg)(1Mr)
12.54*(K+A) 1
dA = **dS (22)
H (1XY)
H
dS = *(1XY)*dA (23)
12.54*(K+A)
where Mt and Mg represent talented mitigation factors for physical and magical damage respectively, Mr is the mitigation due to resistances, Ma is the mitigation due to armor (defined below), K is the armor decay factor (also defined below), H is the player's fully raidbuffed max health, and A is the players raidbuffed armor.
 Code: Select all
Ma = A/(A+K)
K = 467.5*L  22167.5
The takehome message of these formulas is that armor loses effectiveness linearly with the percentage of "regular" physical damage intake for a given fight. In other words, for a fight with only 50% nonbleed physical damage, armor is reduced in effectiveness by 50%. If an armor trinket is worth 100 stamina on a purely "regular" physical fight, it will only be worth 60 stamina on a fight with 15% bleed damage and 25% magic damage (60% "regular" physical).
Last edited by theckhd on Fri Nov 27, 2009 10:39 am, edited 6 times in total.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Re: "New EH"  incorporating different damage types into EH
I tend to hesitate before subscribing to any sort of defined stamarmor equivalency ratio.
The problem for me is that I don't think your equation models correctly the part of damage mitigation which I've always considered the most important; the way incoming damage is clustered.
While you can create formulas such as yours if you are basing your assessments of value purely on Damage In, I find that in real situations the relationships between the stats do not remain static depending on damage clustering trends.
Ultimately, what EH theory represents is the answer to the big question "How big a burst can I survive before my next heal lands?". The problem with stam has always been that an extra couple stam gems, or a single or even multiple stam pieces, or even a stam trinket are generally not enough to make a difference in being able to take an additional hit unhealed, and the difference between stam stacking and not is generally lost within the normal variations of damage range.
Where stam really starts to have a definite effect on tank survivability is when hits are relatively small, but frequent. A good example would be Algalon.
Armor, on the other hand, contributes in increasing effectiveness as the size of hits go up. The higher the hit, the more damage you are removing from the burst for the same absolute quantity of armor.
Thus, the real stamequivalency of a given amount of armor is directly connected to hit size and the way damage is clustered, and thus cannot be modeled quite as simply as you've done.
The problem for me is that I don't think your equation models correctly the part of damage mitigation which I've always considered the most important; the way incoming damage is clustered.
While you can create formulas such as yours if you are basing your assessments of value purely on Damage In, I find that in real situations the relationships between the stats do not remain static depending on damage clustering trends.
Ultimately, what EH theory represents is the answer to the big question "How big a burst can I survive before my next heal lands?". The problem with stam has always been that an extra couple stam gems, or a single or even multiple stam pieces, or even a stam trinket are generally not enough to make a difference in being able to take an additional hit unhealed, and the difference between stam stacking and not is generally lost within the normal variations of damage range.
Where stam really starts to have a definite effect on tank survivability is when hits are relatively small, but frequent. A good example would be Algalon.
Armor, on the other hand, contributes in increasing effectiveness as the size of hits go up. The higher the hit, the more damage you are removing from the burst for the same absolute quantity of armor.
Thus, the real stamequivalency of a given amount of armor is directly connected to hit size and the way damage is clustered, and thus cannot be modeled quite as simply as you've done.
Arkham's Razor: a theory which states the simplest explaination tends to lead to Cthulu.
 Joanadark
 Posts: 3087
 Joined: Fri May 11, 2007 7:09 pm
Re: "New EH"  incorporating different damage types into EH
Joanadark wrote:I tend to hesitate before subscribing to any sort of defined stamarmor equivalency ratio.
.......
Thus, the real stamequivalency of a given amount of armor is directly connected to hit size and the way damage is clustered, and thus cannot be modeled quite as simply as you've done.
This is my original post:
I would agree that the EH boost of armor fluctuates based off the size of the in coming hit.
.1% worth of armor would be an EH gain of 1 on a 1,000 attack, it would also be an EH gain of 100 on a 100,000 attack.
This is what I found when I tried to prove myself correct:
at 26500 armor you have a 61.43% reduction from a lvl83 attacker
at 27000 armor you have a 61.88% reduction from a lvl83 attacker
500 armor in this case would yeild .45% additional reduction.
500 armor would be 455 armor pretalents, 455 armor is roughly the same as 32.5 stamina in itempoints. 32.5 stamina after talents and buffs would be 406 health.
being hit for 100,000 the .45% reduction would reduce damage by 450
being hit for 20,000 the .45% reduction would reduce damage by 90
Considering that armor reduces the size of EACH hit, the EH boost of armor would be also tied to how many hits one could take before death.
If one could take 2 hits for 100,000 in the above case, then it would be effectively a reduction of 900, 4 hits would be 1800, etc.
With everything else being the same, someone that could take 2 hits for 100,000 could also take 10 hits for 20,000 this would be a reduction of 900......
It would seem that if my logic and math is correct, EH gain of armor would not be tied to the size of the hit as much as one would think, if at all.
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jathitimus  Posts: 95
 Joined: Wed Dec 17, 2008 12:46 am
Re: "New EH"  incorporating different damage types into EH
Armour is only tied to hit size in so much as it affects the effectiveness of block value.
Hit size is irrelevant for armour contribution without Block Value.
(EG you either take 10* as many hits at 1/10 each, or 1 big hit, either way its the same total damage and same total armour contribution. If you are blocking these attacks, however, then if your armour lowers the damage taken to be equal to your BV, you take no damage. This makes the 1/10*10 htis do 0 damage while the one big hit does 9/10 damage.)
Hit size is irrelevant for armour contribution without Block Value.
(EG you either take 10* as many hits at 1/10 each, or 1 big hit, either way its the same total damage and same total armour contribution. If you are blocking these attacks, however, then if your armour lowers the damage taken to be equal to your BV, you take no damage. This makes the 1/10*10 htis do 0 damage while the one big hit does 9/10 damage.)
 Candiru
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Re: "New EH"  incorporating different damage types into EH
Thanks alot Theck

Harlequina  Posts: 229
 Joined: Thu Aug 21, 2008 5:11 am
 Location: Sweden  Earthen Ring EU
Re: "New EH"  incorporating different damage types into EH
Joanadark, Theck also made a thread about hit size vs HP, when more stamina is worth less because of the hit size, if you can't find it, I'll link it when I get home, or maybe someone else can link it.
While tanking new content, one rule is important  it's not about taking less damage; it's about being able to take more.
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