"Total" EH  incorporating different damage types into EH
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Re: "New EH"  incorporating different damage types into EH
Vagrant wrote:Now i have not read up on ICC fights. Are these formulae valid or is there more mechanics to circumvent player math (which Blizzard seems to be very much aware of, thus making things like swarm and burrowers and faction champs)?
I'm not sure what you mean here. Nothing about swarm, burrowers, or the Faction Champions encounters invalidate the formula. They may make it more difficult to calculate it properly (by masking X and Y behind other damage), or they may make encounters like Faction Champs where EH isn't a very important metric to use. But none of that changes the formula or makes it invalid.
As a realworld analogy, there are cases where a tape measure is the right tool for the job. When you're measuring things things that are on the scale of inches or feet, it makes a lot of sense.
Then there are things smaller than 1" or larger than 25' (or whatever the maximum length of your tape measure), where a tape measure will work, but be slightly more difficult to use.
Finally, there are things that a tape measure isn't really relevant for. If you want to measure something microscopic, or measure the distance between cities, a tape measure won't do you much good. That doesn't mean the tape measure is measuring things incorrectly, it just means it's not the right tool for the job.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
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theckhd  Moderator
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Re: "New EH"  incorporating different damage types into EH
Earantur wrote:Wrathy wrote:FC  Overall D X and Y
Just my two pence here, but won't EH numbers for FC be somewhat skewed since since their threat table is dependant on damage reduction.
I agree with Theck about the ability to apply the formula on FC, it has applications everywhere, however, people rarely have to worry about gear sets on FC, and even less on survival based on our HP, AC and their AI. When I wrote that, i was in a haze of Nyquil, Sudafed, and a pounding headache, so I went down the Board, however in the end, the real potentials for analysis are as follows:
Gormok Bleeds (possibly Icehowls Ferocious Butt)
Twin's Specials
Anub'arak P3 Freezing Slashes
Going forward, we will have a better situation where we are trying to assemble gearsets to kill content, and ensure survival, and we will have easily acquired data sets (as we will be dying to bosses). At the end of the night, you can just bring up your parses, analyze your death and plug the values into the formula, and as a result, you will be able to adjust your gear choices to improve your survival. We will have a lot more gear choices after a few weeks of ICC, namely Tier pieces versus off set pieces versus Bonus Armor pieces, and we can mix and match according to our findings.
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Re: "New EH"  incorporating different damage types into EH
Update: I have completed the plug and chug spreadsheet utilizing the end formulas that Theck derived. I will be testing them this coming week to ensure that it is giving us accurate numbers. Currently it is just an excel file on my computer but once I feel confident that the spreadsheet gives us the correct values according to Thecks math, I will be uploading it and providing the community with a link.
As for the X and Y value compilation that I have promised from ToTGC, that task go pushed back down to the bottom of the pile after the holidays, some recruiting necessities, as well as a lot of wiping in game. but its still on my list.
As for the X and Y value compilation that I have promised from ToTGC, that task go pushed back down to the bottom of the pile after the holidays, some recruiting necessities, as well as a lot of wiping in game. but its still on my list.
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Re: "New EH"  incorporating different damage types into EH
Nice thread to point out that your actual EH (or NewEH if you prefer) is the weighted average of your damagespecific EH against the hits that you're looking at for people who didn't think of it that way.
If you're not careful though, Theck, someone is going to make you realize that this could easily turn into a "which tank class has the most NewEH for this fight in the same gear" thread, or even "What percentages of Pmit:Pnmit:Mmit:Mnmit damages do each tank have the EH advantage in?" Wouldn't want to leave that nice juicy opportunity unexplored, eh?
Oh, and yes  mark and fort do stack with regards to stam.
@Wrathy if you're looking for more data:
With regards to looking at this for specific fights, specifically Anub'arak main tanking, though, I can offer both some logs from you to draw your own conclusions and my own personal gear/buff changes before the kill. All data is coming from Scions of Destiny  Eredar WoL Reports. The page hasn't been updated for the past week or two, but it has a couple Anub'arak25 HM kills recorded and at least 100 wipes near the beginning of this month and the end of last.
A few things to note first  I am an alchemist so Stoneblood is 1950 health and resist flask is +90 to all resists. Second, I reduced my health a bit while tanking this to hit cap myself and cut down on leeching swarm heals. Normally, I'm at a bit over 54k buffed with stoneblood; in my gear for this fight I was at ~50k health, and with a resist flask instead I was at ~48k. Also, at the time, I had ~28k armor unbuffed, and to wipe faster on a few attempts I sat down a few times so there's some melee and even frost strike crits in the data. Those will be obvious, so ignore them.
A few comments on Leeching Swarm while I was main tanking: In my case, with a health flask the max hit size was ~15k premitigation. With only NR aura, 10% resist was guaranteed for a max of ~13.5k hit (minus our magic damage reduction). On the other hand, on our kills I swapped stoneblood for nature resist, which boosts me to 220 NR, guaranteeing a 20% resist, and dropped my max health to 48k for a max of ~11.5k postresist hit(minus our magic damage reduction).
In effect, I traded 2k health to guarantee the maximum hit size I took from this ability was 2k less. Even without running the calculation, I can tell that this didn't provide the most EH for that fight, but it boosts my average resist rate from 20% (NR only) to 30%, which was an extra 151k damage we didn't have to do to the boss on our first kill. That might not seem like much, but after a few sub2% wipes, you might find yourself wishing you used one if you didn't.
If you're not careful though, Theck, someone is going to make you realize that this could easily turn into a "which tank class has the most NewEH for this fight in the same gear" thread, or even "What percentages of Pmit:Pnmit:Mmit:Mnmit damages do each tank have the EH advantage in?" Wouldn't want to leave that nice juicy opportunity unexplored, eh?
Oh, and yes  mark and fort do stack with regards to stam.
@Wrathy if you're looking for more data:
With regards to looking at this for specific fights, specifically Anub'arak main tanking, though, I can offer both some logs from you to draw your own conclusions and my own personal gear/buff changes before the kill. All data is coming from Scions of Destiny  Eredar WoL Reports. The page hasn't been updated for the past week or two, but it has a couple Anub'arak25 HM kills recorded and at least 100 wipes near the beginning of this month and the end of last.
A few things to note first  I am an alchemist so Stoneblood is 1950 health and resist flask is +90 to all resists. Second, I reduced my health a bit while tanking this to hit cap myself and cut down on leeching swarm heals. Normally, I'm at a bit over 54k buffed with stoneblood; in my gear for this fight I was at ~50k health, and with a resist flask instead I was at ~48k. Also, at the time, I had ~28k armor unbuffed, and to wipe faster on a few attempts I sat down a few times so there's some melee and even frost strike crits in the data. Those will be obvious, so ignore them.
A few comments on Leeching Swarm while I was main tanking: In my case, with a health flask the max hit size was ~15k premitigation. With only NR aura, 10% resist was guaranteed for a max of ~13.5k hit (minus our magic damage reduction). On the other hand, on our kills I swapped stoneblood for nature resist, which boosts me to 220 NR, guaranteeing a 20% resist, and dropped my max health to 48k for a max of ~11.5k postresist hit(minus our magic damage reduction).
In effect, I traded 2k health to guarantee the maximum hit size I took from this ability was 2k less. Even without running the calculation, I can tell that this didn't provide the most EH for that fight, but it boosts my average resist rate from 20% (NR only) to 30%, which was an extra 151k damage we didn't have to do to the boss on our first kill. That might not seem like much, but after a few sub2% wipes, you might find yourself wishing you used one if you didn't.
Last edited by Xenix on Tue Dec 01, 2009 7:38 am, edited 2 times in total.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

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Re: "New EH"  incorporating different damage types into EH
Xenix wrote:If you're not careful though, Theck, someone is going to make you realize that this could easily turn into a "which tank class has the most NewEH for this fight in the same gear" thread, or even "What percentages of Pmit:Pnmit:Mmit:Mnmit damages do each tank have the EH advantage in?" Wouldn't want to leave that nice juicy opportunity unexplored, eh?
I think that that area will inevitably be covered, simply because as soon as other classes decide to use the proper formula for EH, they're going to want to know what numbers to plug in.
Though after this exchange, I think I may want to take this in a different direction. Instead of writing it up just as a formal derivation of the proper form of EH, I may want to write a guide for what EH means and how it should be applied, with the derivation added as an appendix.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
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Re: "New EH"  incorporating different damage types into EH
On a similar note, what I mentioned above would be rather easy to do. Just get a representative gear set for each class for health/armor values, plug it into your formula with their class damage reduction abilities and create a plot with Xaxis for Mitigatable Physical damage, Yaxis for NonMitigatable Physical damage and Zaxis for resistible magic damage. A fourth axis isn't necessary due to the Pmit% + Pnmit% + Mmit% + Mnmit% = 100% constraint which means it's actually a 3variable system. Then for each point on this plot, calculate the EH of each class, and color that point orange for druid, red for DK, pink for paladin and brown for warrior.
You'd then have a pyramid (the part of the cube under the X+Y+Z=100 plane) representing the whole spectrum of damage possibilities and you could take a slice across any plane (e.g. Pmit = 50%) to get a useful plot showing where each class is best (although you might have to take druid out or have a completely orange box). Furthermore, you could replot this for various levels of armor/health, etc to get some trends. Lots of potential for flamebait but even more potential for showing off some really sexy plots  I'd do it myself but I'm too lazy to put together the gear sets.
On the other hand, the same approach could be used with a color bar to show your own EH vs. every possible combination of damage types. It'd be the same plot, but you'd color the points from red to green (or whatever you prefer) going from your minimum to maximum EH limits. Now that would be a useful thing to know, since you could then change your armor/health/resistance and replot it to see the exact effect the change had. Hmm... That could be worth a whole new thread and might just be enough to motivate me to go code something.
Edit:
Not going to post a new thread for this yet since it needs some cleaning up, but here's the preliminary results:
First, the code, of which I have two files:
NewEH calculator function: neh.m
Main calculations: main.m
Two things to note: First, the NEH calculation is for a PALADIN ONLY and considers only minimum resists not average resist (e.g. going from 0 to 50 resist does nothing for your NEH because it doesn't GUARANTEE any higher resist rate). Second, I am unfamiliar with plotting volumetric scalar data in MATLAB, so the second half of the main.m code has a lot of room for cleaning up by someone who actually knows what they're doing in that respect. I had to truncate the data to approximately 3% of the total by considering only a plane where Mnmit = C while plotting in order to get something that would plot in a reasonable amount of time.
Now, as for what it does:
This calculation takes in two sets of (health,armor,resist), then calculates the change in NEH between those two values for EVERY possible combination of physical damage affected by armor (Pmit), physical damage unaffected by armor(Pnmit), magical damage affected by resistance (Mmit) and magical damage unaffected by resistance (Mnmit). In my plots, Pmit is Xaxis, Pnmit is Yaxis, Mmit is Zaxis and slices are taken across the plane where Mnmit = C, where C is some constant.
So, let's say I'm looking at a fight like Twin Valkyr where Mnmit = 0, and I want to see if a resist flask is worth more EH than a health flask. I would then plug in my buffed numbers of (31500 armor,54600 health,130 resist) for the health flask and (31500,52650,220) for the resist flask. (yes, I trade 1950 health for 90 resist since I'm an alchemist). Doing so gives the following plot:
Once again, as I'm not that familiar with plotting this type of data in Matlab, I have a fairly granular color bar. Looking at the legend, each color represents all EH changes between the two numbers next to it (red is a +6381 to +3789 EH change, etc.), so pink/red are a noticeable EH increase and blue/cyan are a noticeable EH decrease, with green being a wash for this particular plot.
In this fight, we also happen to have zero Pnmittype damage as well, which means the possibilities for EH lie along the line on the PmitMmit plane. Let's reorient it to look at the plot from that side:
The points we're interested in for Twin Valkyr are where Pmit + Mmit = 100% or the diagonal edge. From the point I have highlighted, you can then see that if 60% of the incoming damage was Mmittype that switching to a resist flask would be a noticable NEH increase. Also, we can see that if the boss applied a bleed instead that swapped all Pmit for Pnmit, then the value of resist would go up enough that resist would be a better choice if only 40% of the incoming damage was Mmittype. (That would be looking at all points along the Pmit=0 line.)
You can do a similar analysis for any possible gear change and for any combination of PmitPnmitMmitMnmit damage, and this program will provide a clear visual picture of the regimes that gear change will increase your NEH.
Feel free to fix my extremely slow plotting method, ask any questions, or take this even further if you want.
You'd then have a pyramid (the part of the cube under the X+Y+Z=100 plane) representing the whole spectrum of damage possibilities and you could take a slice across any plane (e.g. Pmit = 50%) to get a useful plot showing where each class is best (although you might have to take druid out or have a completely orange box). Furthermore, you could replot this for various levels of armor/health, etc to get some trends. Lots of potential for flamebait but even more potential for showing off some really sexy plots  I'd do it myself but I'm too lazy to put together the gear sets.
On the other hand, the same approach could be used with a color bar to show your own EH vs. every possible combination of damage types. It'd be the same plot, but you'd color the points from red to green (or whatever you prefer) going from your minimum to maximum EH limits. Now that would be a useful thing to know, since you could then change your armor/health/resistance and replot it to see the exact effect the change had. Hmm... That could be worth a whole new thread and might just be enough to motivate me to go code something.
Edit:
Not going to post a new thread for this yet since it needs some cleaning up, but here's the preliminary results:
First, the code, of which I have two files:
NewEH calculator function: neh.m
Main calculations: main.m
Two things to note: First, the NEH calculation is for a PALADIN ONLY and considers only minimum resists not average resist (e.g. going from 0 to 50 resist does nothing for your NEH because it doesn't GUARANTEE any higher resist rate). Second, I am unfamiliar with plotting volumetric scalar data in MATLAB, so the second half of the main.m code has a lot of room for cleaning up by someone who actually knows what they're doing in that respect. I had to truncate the data to approximately 3% of the total by considering only a plane where Mnmit = C while plotting in order to get something that would plot in a reasonable amount of time.
Now, as for what it does:
This calculation takes in two sets of (health,armor,resist), then calculates the change in NEH between those two values for EVERY possible combination of physical damage affected by armor (Pmit), physical damage unaffected by armor(Pnmit), magical damage affected by resistance (Mmit) and magical damage unaffected by resistance (Mnmit). In my plots, Pmit is Xaxis, Pnmit is Yaxis, Mmit is Zaxis and slices are taken across the plane where Mnmit = C, where C is some constant.
So, let's say I'm looking at a fight like Twin Valkyr where Mnmit = 0, and I want to see if a resist flask is worth more EH than a health flask. I would then plug in my buffed numbers of (31500 armor,54600 health,130 resist) for the health flask and (31500,52650,220) for the resist flask. (yes, I trade 1950 health for 90 resist since I'm an alchemist). Doing so gives the following plot:
Once again, as I'm not that familiar with plotting this type of data in Matlab, I have a fairly granular color bar. Looking at the legend, each color represents all EH changes between the two numbers next to it (red is a +6381 to +3789 EH change, etc.), so pink/red are a noticeable EH increase and blue/cyan are a noticeable EH decrease, with green being a wash for this particular plot.
In this fight, we also happen to have zero Pnmittype damage as well, which means the possibilities for EH lie along the line on the PmitMmit plane. Let's reorient it to look at the plot from that side:
The points we're interested in for Twin Valkyr are where Pmit + Mmit = 100% or the diagonal edge. From the point I have highlighted, you can then see that if 60% of the incoming damage was Mmittype that switching to a resist flask would be a noticable NEH increase. Also, we can see that if the boss applied a bleed instead that swapped all Pmit for Pnmit, then the value of resist would go up enough that resist would be a better choice if only 40% of the incoming damage was Mmittype. (That would be looking at all points along the Pmit=0 line.)
You can do a similar analysis for any possible gear change and for any combination of PmitPnmitMmitMnmit damage, and this program will provide a clear visual picture of the regimes that gear change will increase your NEH.
Feel free to fix my extremely slow plotting method, ask any questions, or take this even further if you want.
Last edited by Xenix on Tue Dec 01, 2009 12:26 pm, edited 1 time in total.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

Xenix  Posts: 244
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Re: "New EH"  incorporating different damage types into EH
Wow my head hurts... You guys are so far above me its not even funny...
It seems as though my spreadsheet is working relatively well. I still want to get some more data from the raid tonight to see if everything works out well, but I wrote a little post on my blog about the spreadsheet with a screen shot and everything, so if you are interested go ahead and take a look. I'd say i'm about a week or two out from uploading it.
Theck, I read that thread that you posted over on WoW dot com, and It never ceases to amaze me that our community is usually one step ahead of the the curve. I am so glad that I am a paladin and not another tank class, because I would have never found half the stuff that we have on the other sites! I think redefining effective health beyond the blanket statement would be highly beneficial to some of the tanking community, from a basic training stand point.
It seems as though my spreadsheet is working relatively well. I still want to get some more data from the raid tonight to see if everything works out well, but I wrote a little post on my blog about the spreadsheet with a screen shot and everything, so if you are interested go ahead and take a look. I'd say i'm about a week or two out from uploading it.
Theck, I read that thread that you posted over on WoW dot com, and It never ceases to amaze me that our community is usually one step ahead of the the curve. I am so glad that I am a paladin and not another tank class, because I would have never found half the stuff that we have on the other sites! I think redefining effective health beyond the blanket statement would be highly beneficial to some of the tanking community, from a basic training stand point.
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Re: "New EH"  incorporating different damage types into EH
One other thing I just realized this tool could be used for  answering the question of "When is the badge Armor trinket better than the Stam trinket", or just in general "When will XX armor help me more than XX health"? Normally, you have to say that it increases your EH by XX but that's only for fights where pure EH matters, and if you're taking magic damage it's not quite as good..
Using my code, though, we can instead plug in those exact numbers, color every point where it's an NEH increase green, every other point red and say "The armor trinket is better when your fight falls in the green region" for an exact ability to show when it's better. I will do that calculation and post a plot of it as soon as I get back to a computer with Matlab on it.
This is the main use of the code I posted  it's nothing new compared to what Theckd did, but rather a visualization of exactly what fights a certain stat swap gives you more NEH in. Every stat swap will generate a unique NEH plot and every fight will be at some Pmit/Pnmit/Mmit coordinate on that plot.
Using my code, though, we can instead plug in those exact numbers, color every point where it's an NEH increase green, every other point red and say "The armor trinket is better when your fight falls in the green region" for an exact ability to show when it's better. I will do that calculation and post a plot of it as soon as I get back to a computer with Matlab on it.
This is the main use of the code I posted  it's nothing new compared to what Theckd did, but rather a visualization of exactly what fights a certain stat swap gives you more NEH in. Every stat swap will generate a unique NEH plot and every fight will be at some Pmit/Pnmit/Mmit coordinate on that plot.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

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Re: "New EH"  incorporating different damage types into EH
I think it's just about to the point of a simple "plug 'n chug" action, at least after we gather data from fights. God knows some of my offtanks could use a program to bypass all of the formulas here so far
Xenix, couldn't you just lump Pnmit and Mnmit into Nmit? If it can't be mitigated by either resistances or armor, then we can just have a baseline of damage reduction from talents and/or buffs/cooldowns.
Makes me wonder how the new block will fit in when Cataclysm rolls out.
Xenix, couldn't you just lump Pnmit and Mnmit into Nmit? If it can't be mitigated by either resistances or armor, then we can just have a baseline of damage reduction from talents and/or buffs/cooldowns.
Makes me wonder how the new block will fit in when Cataclysm rolls out.
 Iselian
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Re: "New EH"  incorporating different damage types into EH
But what about things which specifically reduce damage of a magical type without it being done via resistsances (powers such as AntiMagic Shell or talents which specifically reduce magical damage by a set percent)? Those need to be calculated separately unless they completely bypass all effects including passive talents.Iselian wrote:Xenix, couldn't you just lump Pnmit and Mnmit into Nmit? If it can't be mitigated by either resistances or armor, then we can just have a baseline of damage reduction from talents and/or buffs/cooldowns.
 Alixander
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Re: "New EH"  incorporating different damage types into EH
Iselian wrote:Xenix, couldn't you just lump Pnmit and Mnmit into Nmit? If it can't be mitigated by either resistances or armor, then we can just have a baseline of damage reduction from talents and/or buffs/cooldowns.
No  paladins have 6% more passive damage reduction against magic, and thus an equivalent extra amount of EH against that type than physical so it has to be separated.
Alixander wrote:But what about things which specifically reduce damage of a magical type without it being done via resistsances (powers such as AntiMagic Shell or talents which specifically reduce magical damage by a set percent)? Those need to be calculated separately unless they completely bypass all effects including passive talents.
Anything that increases your damage reduction against magical damage gets added into the magic damage reduction part of the NEH equation. NEH is the sum of (%of total damage damage)*Health/(1%(reductions on that type of damage)). If you had more reduction against magic damage, you'd simply multiply that in to your "%Reduction against that type of damage". That's why I said the neh.m function I posted is valid for paladins only, as I included all paladin talents in it only.

On to the armor trinket vs. stam trinket as an example of using this to test a simple gear change over the entire range of fights. I will use my own raid buffed values and change main.m to color positive points green and negative ones red (this type of plot is probably more useful than the colorbartype one I showed previously, unless you're comparing multiple plots at once). Since replacing one of my current stam trinkets would actually decrease even my Pmit EH, I'll consider replacing my i245 stam trinket (2.2k health) with a theoretical ICC one that gives 2.2k armor. Plugging these numbers in gives the following plot for Mnmit = 0, Pnmit = 0 and Mmit=0 (code in main_binary.m):
So, anywhere in the green and it's an EH upgrade. Where does that happen? Looking at the plot, it's an EH upgrade in the area with axisintercepts at Pnmit = 20%, Mmit = 17% and Mnmit = 19%(calculated by looking at the Pmit = Mmit = 0 axis).
Putting that together, you get approximately the Pmit > 82% plane (it's rotated slightly towards the Pnmit), or you can say definitively that (for my gear) trading 2.2k health for 2.2k armor provides more NEH when physical damage affected by armor is at least 82% of the incoming damage, with slight variations depending what axis your fight leans toward. This kind of plot is to be expected, of course, since armor loses its value as the amount of the damage type it can reduce goes away, but you could do similar plots for trading health for resist or armor for resist for your specific gear and a specific fight.
Also, two other things  I should really multiply all these EH values by the effective health boost that AD gives us, but I haven't yet. It won't affect the qualitative calculation any, but it will effect the total EH, so I'll update my NEH function with that multiplier if I upload it again. And lastly, for fights with multiple sources of magic damage that you have different resists against (e.g. Hydross), I'd need to update the NEH formula to take in multiple magic resistance values. I won't bother doing so unless there's really a need for it though.

Edit: Wow  just had a /facepalm moment after realizing all this analysis just shows something I should have realized in the first place. This could easily turn into the beginning of a new thread titled:
"Practical use of NewEH in gear choices"
All right, let's look at what we know about NewEH:
1. The formula is simply Sum over all damage types of (% of total damage)*(Health)/(1(%damage reduction against that damage type)).
2. This is EXACTLY equivalent to Sum over all damage types of (% of total damage)*(damagetypespecific EH)
3. The EH function is completely linear with regards to changing the percentages.
What does this mean? Instead of doing a massive calculation like my previously posted code does, we can simply calculate your NEH for the four limits of the pyramid: 100% Pmit, 100% Pnmit, 100% Mmit and 100% Mnmit, then do a linear interpolation to determine all points in between. Furthermore, for any gear change, you can once again calculate the change in EH for 100% Pmit, Pnmit, Mmit and Mnmit, then calculate the exact equation of the plane separating increased NEH from decreased NEH, which is the final thing we care about anyways.
Let's take a look at how to do this:
First, I will call your 100% damagetype NEH values, PNEH, PnNEH, MNEH and MnNEH. (Yes, PNEH is the same as normal EH). I will further assume we are talking about a gear change and the values of dPNEH, dPnNEH, dMNEH and dMnNEH represent that change in damagespecific NEH with that gear change. This means there will be some plane of Pmit,Pnmit and Mmit values such that the change in NEH is zero.
Due to the linearity of the function, that plane's intercepts with the axes can be calculated as:
 Code: Select all
Pmitintercept (Xaxis) = (dMnNEH)/(dPNEH  dMnNEH) = Xo
Pnmitintercept (Yaxis) = (dMnNEH)/(dPnNEH  dMnNEH) = Yo
Mmitintercept (Zaxis) = (dMnNEH)/(dMNEH  dMnNEH) = Zo
From linear algebra, we also know that we can calculate the equation of any plane given three points. In this case, our points are (Xo,0,0),(0,Yo,0) and (0,0,Zo). The method to do so is as follows (determinants made much easier since the points are on the axes):
 Code: Select all
Plane of equation Ax + By + Cz + D = 0 from the given three points:
Xo 0 0 
K = 0 Yo 0  = Xo*Yo*Zo
0 0 Zo
D 1 0 0  D*Yo*Zo D
A =  * 1 Yo 0  =  = 
K 1 0 Zo Xo*Yo*Zo Xo
D Xo 1 0  D*Xo*Zo D
B =  * 0 1 0  =  = 
K 0 1 Zo Xo*Yo*Zo Yo
D Xo 0 1 D*Xo*Yo D
C =  * 0 Yo 1 =  = 
K 0 0 1 Xo*Yo*Zo Zo
This then gives us the final equation of the plane (D cancels out):
 Code: Select all
x y z
1 =  +  + 
Xo Yo Zo
or (when converted so percentages can be input)
dMnNEH  dPNEH dMnNEH  dPnNEH dMnNEH  dMNEH
100 = (%Pmit)* + (%Pnmit)* + (%Mmit)*
dMnNEH dMnNEH dMnNEH
An alternate form of this equation is:
dPNEH dPnNEH dMNEH
0 = (%Mnmit) + (%Pmit)* + (%Pnmit)* + (%Mmit)*
dMnNEH dMnNEH dMnNEH
Which is in an extremely elegant differential form that shows I could have just taken the summation and differentiated with respect to MnNEH and gotten the equation of the plane. (nice to know after the fact)
Now, this is the equation of the plane where your deltaNEH is ZERO. What you want to know is where the deltaNEH will be positive, which means the = needs to be changed to a < or a >. To find that, you'll just plug in one of your points and use that to determine the operator.
By now your eyes might be glazed over, so I'll give an example of exactly how to do this. First, download my NEH function. Using that and taking dH, dA and dR to be the health, armor and resistance changes you're looking at respectively,
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dPNEH = neh(100,0,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dPnNEH = neh(0,100,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dMNEH = neh(0,0,100,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dMnNEH = neh(0,0,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
Let's say that gave us the following values:
dPNEH = 200, dPnNEH = 100, dMNEH = 100, dMnNEH = 200. In that case, plugging the values into the above equation gives the split plane at:
 Code: Select all
100 = %Pmit*2 + %Pnmit*1.5 + %Mmit*.5
To determine whether the points we want lie on the > or < side of this plane, we plug in a point we know such as 100% Pmit is an increase (which is what we want). I this case, 100% Pmit gives
 Code: Select all
100 ?= 200
which means we want a <. As such, our final formula for those dNEH values is
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100 <= %Pmit*2 + %Pnmit*1.5 + %Mmit*.5
And we can say that any valid combination of Pmit%, Pnmit% and Mmit% that satisfies the inequality will cause the gear change that produced those values to be an upgrade.
TLDR:
Steps to use NEH effectively:
 Determine the change in stats between the two gear sets you want to examine.
 Calculate the following values using my NEH function as a paladin or your own as another class:
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dPNEH = neh(100,0,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dPnNEH = neh(0,100,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dMNEH = neh(0,0,100,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
dMnNEH = neh(0,0,0,health + dH,armor + dA,resistance + dR)  neh(100,0,0,health,armor,resistance)
 Plug them into your preference of the following equations:
 Code: Select all
dMnNEH  dPNEH dMnNEH  dPnNEH dMnNEH  dMNEH
100 ?= (%Pmit)* + (%Pnmit)* + (%Mmit)*
dMnNEH dMnNEH dMnNEH
dPNEH dPnNEH dMNEH
0 ?= (%Mnmit) + (%Pmit)* + (%Pnmit)* + (%Mmit)*
dMnNEH dMnNEH dMnNEH
 Pick one of your four calculated dNEH's that is not zero. Plug that point into the previous equation. If that dNEH was positive, set the ?= so the equality is true, else set ?= so the equality is false.
 Plug in any valid combination of %Pmit, %Pnmit and %Mmit to your newly minted inequality. If the inequality is true, your gear change is an NEH upgrade for that fight, otherwise it is an NEH downgrade.
Last edited by Xenix on Tue Dec 01, 2009 5:39 pm, edited 7 times in total.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

Xenix  Posts: 244
 Joined: Thu Jun 25, 2009 4:56 am
Re: "New EH"  incorporating different damage types into EH
Xenix wrote:One other thing I just realized this tool could be used for  answering the question of "When is the badge Armor trinket better than the Stam trinket", or just in general "When will XX armor help me more than XX health"? Normally, you have to say that it increases your EH by XX but that's only for fights where pure EH matters, and if you're taking magic damage it's not quite as good..
Using my code, though, we can instead plug in those exact numbers, color every point where it's an NEH increase green, every other point red and say "The armor trinket is better when your fight falls in the green region" for an exact ability to show when it's better. I will do that calculation and post a plot of it as soon as I get back to a computer with Matlab on it.
This is the main use of the code I posted  it's nothing new compared to what Theckd did, but rather a visualization of exactly what fights a certain stat swap gives you more NEH in. Every stat swap will generate a unique NEH plot and every fight will be at some Pmit/Pnmit/Mmit coordinate on that plot.
Yes, but there's a much simpler answer to that question, since the value of armor only depends on armormitigated physical damage. The formula from the original post is
Theck wrote:
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H
dS = *(1XY)*dA (23)
12.54*(K+A)
(1XY) is just the percentage of intake that's armormitigated physical.
"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: 7984
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: "New EH"  incorporating different damage types into EH
Heh, yeah, but I always use rambling about new ways to calculate stuff we already can do to think about new ways to do stuff we can't do, and in this case it worked out to get a really elegant differential NewEH equation valid for all fights that shows whether any gear change is an upgrade with five lines of calculations, as shown in the edit to my last post.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

Xenix  Posts: 244
 Joined: Thu Jun 25, 2009 4:56 am
Re: "New EH"  incorporating different damage types into EH
Xenix wrote:Heh, yeah, but I always use rambling about new ways to calculate stuff we already can do to think about new ways to do stuff we can't do, and in this case it worked out to get a really elegant differential NewEH equation valid for all fights that shows whether any gear change is an upgrade with five lines of calculations, as shown in the edit to my last post.
But as far as practical gearing questsions go, there are really only two questions we'd want to consider:
 Is dA armor better than dS stamina for a given fight?
 Is dR resistance better than dS stamina for a given fight?
Both of those have relatively simple formulas that I've already posted (one in the OP, the other somewhere on page 2 or 3).
Questions about mitigation talents are better treated by just calculating EH with and without the talent to see the effect.
"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: 7984
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: "New EH"  incorporating different damage types into EH
theckhd wrote:But as far as practical gearing questsions go, there are really only two questions we'd want to consider:
 Is dA armor better than dS stamina for a given fight?
 Is dR resistance better than dS stamina for a given fight?
Both of those have relatively simple formulas that I've already posted (one in the OP, the other somewhere on page 2 or 3).
Questions about mitigation talents are better treated by just calculating EH with and without the talent to see the effect.
There are, however, some times where the question is "Is dA armor + dR resistance overall better than dS stam for a given fight" (e.g. the Onyxia resist ring), or similar questions for resist vs. armor, resist + health vs. armor, etc. In that case you need a coupled formula between all three variables, which is one use for the formula I posted.
Also, the point of this thread was consolidating all the EH, MEH, etc. formulas into one single value. Similarly, I've made a formula that encapsulates the health vs. armor vs. resist (or rather the change in EH, MEH, etc. variables) into a single equation, which lets you see the interplay between them for any fight type much better than separating it out, and means you don't have to have a giant set of formulas to calculate these values.
The main thing to use it for, though, is a bigpicture visualization of exactly what types of fights a certain gear change is suited to. That, and I'm sure someone will eventually use the singledifferential form for some kind of calculation eventually.
Edit: Another very good reason to include mitigation talents in NEH  a Death Knight could take his current gear, calculate the NEH from speccing into each tree, and see for what types of fights he would get the most EH from which spec. It's something you could do now with a lot of calculation, but this tool would make it much simpler.
Kimurellia  Holy/Protection Paladin  Scions of Destiny  EredarUS

Xenix  Posts: 244
 Joined: Thu Jun 25, 2009 4:56 am
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