"Total" EH - incorporating different damage types into EH

Warning: Theorycraft inside.

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

Postby theckhd » Tue Dec 08, 2009 7:14 am

askraal wrote:
Reynardadin wrote:I've now implemented NEH in TankTotals for arbitrary values of X and Y, defined by the user via the configuration GUI. You can grab it here to play around with the sliders, or via the Curse client if you have it set to download alphas. Should work correctly for all tanks, but...


TLDR

Out of all of the posts in the thread, this is the one you choose to TLDR?

/boggle


Reynard: While the addon looks neat, I really don't need another see-through pane with text cluttering up my UI. Does it support LDB? I'd much rather hide it in DockingStation and only have the information when I mouse over it.
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Re: "New EH" - incorporating different damage types into EH

Postby theckhd » Tue Dec 08, 2009 7:19 am

Jerey-Darkspear wrote:You say that you're solving the d(EH) equation when EH is not changing, i.e. d(EH) = 0. However, if you do that, shouldn't dA be negative?

.....

A gain in armor (positive) would need a loss in health (negative) or vice-versa.

I sort of glossed over this point in the derivation, but yes, I threw out a minus sign there.

A more accurate way of wording it would be to say,

"If we want to know how much armor dA it takes to give the same increase in EH as an amount of health dH, we set the two terms on the right-hand-side equal to one another."

I'll make this change in the OP to clarify.
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Re: "New EH" - incorporating different damage types into EH

Postby Reynardadin » Tue Dec 08, 2009 8:39 am

theckhd wrote:Reynard: While the addon looks neat, I really don't need another see-through pane with text cluttering up my UI. Does it support LDB? I'd much rather hide it in DockingStation and only have the information when I mouse over it.
It will do in the future. For now, rest assured that you can either left-click the title bar to collapse and expand the display, or set it to mouseover mode :)

I've now implemented the first iteration of the NEH damage-tracking module which I mentioned in my previous posts. Basically, this tracks the damage from each source, from the most recent point at which you were at full health to the time you die. It then shows a readout in the chat pane, with the option to export the percentages directly into the NEH calculation.

When I'm somewhat less exhausted, I'll write a more extensive post on the issues which occurred to me while writing the module, but for now here's a couple of screenshots of the new features and a link to the latest version of the addon for people to experiment with.

Image
Image
Image

http://static.curseforge.net/content/fi ... s-r188.zip

PLEASE NOTE: 1. as the changelog says, it's VERY beta. It doesn't throw errors and has operated exactly as expected in my own tests, but it's likely to have several kinks. 2. I've only tried it on my paladin, but it should work fine for all other tanks. Either way, have a go and let me know how you find it.

EDIT: the Record Damage option is off by default, you have to enable it.
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Re: "New EH" - incorporating different damage types into EH

Postby Elsie » Wed Dec 09, 2009 12:34 pm

theckhd wrote:
Jerey-Darkspear wrote:You say that you're solving the d(EH) equation when EH is not changing, i.e. d(EH) = 0. However, if you do that, shouldn't dA be negative?

.....

A gain in armor (positive) would need a loss in health (negative) or vice-versa.

I sort of glossed over this point in the derivation, but yes, I threw out a minus sign there.

A more accurate way of wording it would be to say,

"If we want to know how much armor dA it takes to give the same increase in EH as an amount of health dH, we set the two terms on the right-hand-side equal to one another."

I'll make this change in the OP to clarify.

I'm kind of curious about something, and I'm sorry that this thread is 9 pages so I'm not sure if it's been covered.

You defined EH as originally in terms of physical damage only. The reasoning most people did that was because EH is based on damage taken in intervals. In other words, EH is only a very useful tool in determining if you're going to survive a worst case scenario in a given time interval. So any magic damage taken as part of the worst case scenario was always fairly easy to count discount first, and then use remaining HP for physical EH calculations.

Your post on the front page indicates you're weighting effective HP against the different various damage intake methods (physical, bleed, magic). I'm not sure how this differs any since it was already discounted when referring to how EH has always been used for worst case scenario analysis.

I'm sure you understand, but incase others don't: When talking about worst case scenario, you're giving a set amount of damage intake from select sources that are probable to occur. Since we already have a time interval, and all values are subtractive, then the order in which they are discounted has no meaning. That's why non-physical damage was always shaved off first. Or have I simply been doing it differently than most the whole time?


The only unique thing I can tell from the original post, with this in mind, is that EH values cannot be given a value until you designate weights where-as originally people used purely physical EH, assuming zero non-typical physical damage intake, as a method for comparison (something still capable in your formula if you simply set the weights to 1, 0, 0).
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Re: "New" EH - incorporating different damage types into EH

Postby Reynardadin » Thu Dec 10, 2009 4:03 am

Once again I'm going to have to put off writing a more extensive post about some of the relevant issues I encountered while implementing this, but the latest alpha of TankTotals has a couple of new features which I think people would be interested in trying out (and which I could use some feedback on). If the tank chooses to adopt the NEH percentages from a particular death as I described above, the addon will now show two new values. The first is a "Lower" bound, i.e. the amount of NEH which the tank would have needed to survive assuming that he dodged, absorbed, blocked, resisted and was healed for the same amounts as observed during combat. The second value is an "Upper" bound, that is, the amount of NEH the tank would have needed to survive if he didn't get healed or block, absorb, avoid or resist (aside from guaranteed resistance) any of the damage. To test this, I went and died to Gormok in ToC 10N several times.

Here's my NEH before combat, with X = 0, Y = 0. I had Fire Aura, GBoS and Plea active; normal rotation, Holy Shield up 100%. Note that all the following are calculated with the AD Heal ready, since it was up when I started the fight:

Image

I then went and fought Gormok until I died, and got the following data:

Image

Note that "Damage" is the total unmitigated damage including all absorbs, blocks, etc; "Absorbed" is the total of blocked, resisted, absorbed, etc. Notably, it also includes avoided physical attacks, estimated as the number of avoids times the average unmitigated hit for that specific attack.

Here's how the addon looks once the above figures are accepted:

Image

As you can see, my current NEH (i.e. the NEH with which I fought Gormok) is coloured red, since it is very slightly below the Lower bound. The similarity of the two numbers is unsurprising, since the hit that killed me was small:

Image

I can now play around with my buffs to see how they affect my NEH relative to what I would have needed to survive. If I switch from Fire to Devo Aura, I get the following:

Image

It's enough to put me over the Lower bound, and so my current NEH turns yellow. It's still a bit close for comfort, though, so let's see what happens when I use my Impeding Scarab (and Heart of Iron, although that's not relevant here):

Image

That's a bit more of a buffer. Here's what happens when I take an Indestructible Potion and pop Bubble Wall:

Image

My current NEH is now above the Upper bound and turns green, meaning that I would have been able to survive everything Gormok threw at me even without avoiding, resisting, blocking, absorption or healing.

Comments and feedback welcome! I'm particularly interested in getting some non-Paladins to test it out, since I haven't had the opporunity to do so. It should work identically for all tanks, but I'd rather not upload a Release version until it's been more widely tested.
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Re: "New EH" - incorporating different damage types into EH

Postby theckhd » Thu Dec 10, 2009 7:50 am

Elsie wrote:I'm sure you understand, but incase others don't: When talking about worst case scenario, you're giving a set amount of damage intake from select sources that are probable to occur. Since we already have a time interval, and all values are subtractive, then the order in which they are discounted has no meaning. That's why non-physical damage was always shaved off first. Or have I simply been doing it differently than most the whole time?

Well, you're using it more effectively than most. But it's still not giving you the whole picture.

The primary reason I bothered to approach this topic was armor trinkets. Now, I don't want to knock armor - I love armor as much as the next tank. But I was seeing an increasing number of people posting things like this:

"Well, [Armor Trinket A] gives me more EH than [Stamina Trinket B], so anyone who uses B is just a stam-stacking whore."

Beyond the implicit derogatory tone (which was present in a number of these posts, sadly), the fundamental argument is flawed. Sure, an armor trinket can give you more EH against pure physical damage. But if the burst scenario includes magic damage, it is very likely that the armor trinket does not give you more overall effective health.

This isn't solved by your method either. If you discount the magic damage by subtracting it out, and then apply the old EH formula, you still erroneously find that the armor trinket is worth more EH than the stamina trinket.

The only way to get the correct answer is to weight the armor contribution according to the percentage of damage intake that it helps mitigate. I suspect many of us already had this intuition, and made our choices accordingly (including yourself). But it falls right out of the mathematics if you formulate the EH equation properly, and gives us a solid justification for our choices.

More importantly, by having the equation developed accurately, we can make more informed decisions about other comparisons, not just Armor. A few obvious examples are in the first few pages of the thread:
  • At what Y-value (% magical damage taken) does a resistance flask give more guaranteed EH than a Stoneblood flask. Alternatively, how much stamina is each point of resistance worth for a given fight? (link)
  • Given two talents, one that reduces magic damage by A% and one that reduces all damage by B%, which one gives more EH for a given fight? (link)
It's not too hard to think up some others. How much mitigation does Aura Mastery provide on a given fight compared to Divine Guardian (speccing decision for ret perhaps)? What's the value of resistance on a fight with a mix of spellfire and single-domain magical damage? I'm sure there's others we'll encounter that we haven't even though of yet.


On a more philosophical level, I'm a physicist. I regularly encounter the question, "Why do we care to know the fine details of this phenomenon when we already have a reasonably good model that the engineers can use to do their thing?" The answer I like the best is that it's always to our benefit to know as much as we can about the inner workings of something. Even a good model can lead you astray if you use it in situations that start to push the edges of its validity, and some of the more important scientific breakthroughs in the last century came from people who dug deeper to figure out exactly how stuff works in finer detail.

If it's at all possible, there's no good reason not to have the full derivation fleshed out somewhere, just because eventually someone might notice something significant that others have overlooked.
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Re: "New" EH - incorporating different damage types into EH

Postby Elsie » Thu Dec 10, 2009 8:12 am

This isn't solved by your method either. If you discount the magic damage by subtracting it out, and then apply the old EH formula, you still erroneously find that the armor trinket is worth more EH than the stamina trinket.

Well, I disagree, because you're still dealing with the percentage remainder of the total burst. The method I used historically is the same net result, just stepped. I guess I was just unaware so many people discounted non-physical hit damage.

There's no net difference between the two except for discussion purposes, which I can see merit to your approach since it can be a simpler explanation to some people.
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Re: "New" EH - incorporating different damage types into EH

Postby theckhd » Thu Dec 10, 2009 8:54 am

Elsie wrote:Well, I disagree, because you're still dealing with the percentage remainder of the total burst. The method I used historically is the same net result, just stepped. I guess I was just unaware so many people discounted non-physical hit damage.

There's no net difference between the two except for discussion purposes, which I can see merit to your approach since it can be a simpler explanation to some people.

I may be misunderstanding what you posted - I read your post as "take the magic damage as a given, and lower the EH threshold you're shooting for, using the old formula to calculate EH." That would still give the wrong answer, because the EH formula doesn't care what target you're aiming for.

However, you might be doing something more sophisticated. But fundamentally, to get the right answer, you need to somehow modify the EH formula to include percentages of damage types, whether you do it phenomenologically at the end, or include them in the beginning.

Example:
For simplicity, take a tank with 59k health, 30k armor, giving 1 Stam = 10 Armor for EH purposes and Ma=64.33%. Assume a 100k post-mitigation burst damage scenario with 60% physical and Y=40% magical (no bleeds or fancy stuff). I'll use the values for Mt, Mg, and Mr from the first post.

"Old" version:
A trinket with 1200 Armor is more EH than a trinket with 100 stamina.
EH = H*(1+A/K)/(1-Mt) = 197.76k for the armor trinket, 196.91k for the stam trinket. Armor trinket wins.

"Subtract magical" version:
Lowering the EH target doesn't change the formula, so plugging in the values gives you exactly the same result. Armor trinket wins.

"New" version:
Y is 0.4, X=Z=0, so EH = H*(0.6/(1-Mt)(1-Ma) + 0.4/(1-Mg)(1-Mr)). Plugging in values, we get 151.36k for the stam trinket, and 151.17k for the armor trinket. Stam trinket wins.

Note that this isn't the same value if you just multiply your total armor by 0.6 either. I.e., plugging in 0.6*(31200) for armor doesn't give you 151.17k, it gives you 146.16k. Nor is it the value you get if you multiply armor by P=0.7806, which is the percentage of raw damage that's physical.

That's because the proper multiplication factor is a function of both your physical mitigation and your magical mitigation, and the weights of both types. This makes it fairly difficult to just put an obvious and intuitive multiplication factor in the EH formula.

Of course, it's very simple in the formula for dS, because that contains all of those factors and has distilled it down into just the part you're interested in, with a lot of convenient canceling going on along the way. There you can just multiply by (1-Y), since it's linear in that relationship.
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Re: "New" EH - incorporating different damage types into EH

Postby Elsie » Thu Dec 10, 2009 12:12 pm

First order of business: screw school computers for deleting my longer post because I wasn't logged in. This'll have to be shorter since I have a finals project due in 4 hours. This was typed up hastily. I'm sure I could describe the process I'm talking about better in a cleaner manner given enough time, but this should do.

What I was saying:
    f(0) = HP
    f(1) = f(0) - Magic Dmg*(Magic Reductions)
    f(2) = f(1) - Physical Dmg*(physical reductions)
    Real EH = f(1)*(1 + physical reductions) + (f0-f2+f1)*(1 + magical reductions)

What I'm describing
    1. Start at HP
    2. Modify for Expected Magic dmg taken
    3. Modify for Expected physical dmg taken
    4. Total > 0 => you survive
    5. Calculate Real EH as a function of the previous steps
What I believe you are doing
    1. Calculate EH based physical only
    2. Calculate EH based on magic damage only
    3. Calculate weights based on percentage of magic/physical dmg of total expcted damage
    (Magical weight = expected magical dmg / total expected dmg)
    (physical weight = expected physical dmg / total expected dmg)
    4. Sum EHs based on the absolute conditions adjusted by weights
    (Real EH = Physical EH*Physical Weight + Magical EH*Magical Weight)
    5. If Real EH > Total expected damage => you survive
I guess my only implication was that we've been doing this all along, but only when emphasizing the encounter. Even your analysis requires an expected encounter. Weights can easily be expressed in numerical terms.
    E.g. 50% magical weight, 50% physical weight = 100% total damage.
    If total damage = 100,000, then:
    Physical dmg = 50,000
    Magic dmg = 50,000
The only difference is process, which is mostly due to what you want to emphasize. Something like armor, or any plugged in 'constant,' into 'physical damage reduction' so the net effect is viewable in both methods.

t;dr: Basically, I was just curious if there was anything new in this besides the obvious process difference.
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Re: "New" EH - incorporating different damage types into EH

Postby Xenix » Thu Dec 10, 2009 1:21 pm

There's only really two differences from what you posted:

First, the damage is separated into four damage types (and with the general equation can be generalized to any number of damage types):

Physical, affected by armor
Physical, unaffected by armor
Magical, affected by resistance
Magical, unaffected by resistance

The other thing is your "real EH" formula is wonky. That doesn't give you an EH.
Last edited by Xenix on Thu Dec 10, 2009 1:39 pm, edited 1 time in total.
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Re: "New" EH - incorporating different damage types into EH

Postby Elsie » Thu Dec 10, 2009 1:37 pm

First, the damage is separated into four damage types (and with the general equation can be generalized to any number of damage types):

Physical, affected by armor
Physical, unaffected by armor
Magical, affected by resistance
Magical, unaffected by resistance

If you look closer, I was simplifying things by using 2 types like what I was replying to.

The other thing is your "real EH" formula is wonky. That doesn't give you an EH.

It does. f(1)*(1+Phys reduction) is equivalent to weighted physical EH. The second half is equivalent to weighted magical EH.
edit: Ah, I see in my haste I made an error in the formula.
Last edited by Elsie on Thu Dec 10, 2009 1:42 pm, edited 2 times in total.
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Re: "New" EH - incorporating different damage types into EH

Postby Xenix » Thu Dec 10, 2009 1:38 pm

Elsie wrote:
First, the damage is separated into four damage types (and with the general equation can be generalized to any number of damage types):

Physical, affected by armor
Physical, unaffected by armor
Magical, affected by resistance
Magical, unaffected by resistance

If you look closer, I was simplifying things by using 2 types like what I was replying to.

The other thing is your "real EH" formula is wonky. That doesn't give you an EH.

It does. f(1)*(1+Phys reduction) is equivalent to weighted physical EH. The second half is equivalent to weighted magical EH.

Edited this into the previous post while you were posting - I'll re-post it here and take it out there:

As an example, let's say you have 50k health and have 50k incoming melee and 25k incoming magical. You've also got 10% reduction against magic and 60% reduction against physical.

By your formulas:
f(0) = 50k
f(1) = 50k - 25,000(0.9) = 27.5k
f(2) = 27,5k - 50,000(0.4) = 7.5k
Real EH = 27.5k*(1 + .4) + (50k-7.5k+27.5k)*(1 + 0.9) = 171.5k <-- Edited to correct
If you divide instead:
27.5k/(1 + .4) + (50k-7.5k+27.5k)/(1 + 0.9) = 56.48k

Actual EH (calculated from raw damage percentages):
50k/(66.666%*.4 + 33.333%*.9) = 88.24k

Edit:
Just to show it's the same - Actual EH (calculated from post-mitigation percentages):
50k*47.06%/0.4 + 50k*52.94%/0.9 = 88.24k

The main thing is that this formulation of everything in one step allows you to come up with a simple closed-form formula for armor vs. health vs. resist equivalences based on the fight using either raw or post-mitigation damage values. Your method will still tell you if you survive the same series of hits (EH calculation aside), but it won't easily show you how much armor or resistance would be equivalent to a certain amount of health, for example.

I'm sure you can also see that it is much simpler to look at since everything can be done in one line of calculations, as well.
Last edited by Xenix on Thu Dec 10, 2009 2:04 pm, edited 2 times in total.
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Re: "New" EH - incorporating different damage types into EH

Postby kysu » Thu Dec 10, 2009 1:54 pm

I'm not going to number crunch with you but I saw something were you wanted to see a parse.

http://www.worldoflogs.com/guilds/26839/

http://www.wowmeteronline.com/browse/gu ... 0#calendar

Feel free to look at them I normally tank it all.
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Re: "New" EH - incorporating different damage types into EH

Postby Elsie » Thu Dec 10, 2009 2:00 pm

I'm sure you can also see that it is much simpler to look at since everything can be done in one line of calculations, as well.

It's still technically multiple steps in finding your weights and EH values, etc, and requires the same inputs. I already said it's probably easier for many to understand.

Secondly, the formula I posted is wrong, but even as written, your numbers are wrong.
Real EH = 27.5k*(1 + .4) + (50k-7.5k+27.5k)*(1 + 0.9) = 56.48k
27.5k*(1 + .4)= 38500
50k-7.5k+27.5k)*(1 + 0.9)=133,000
That's definitely not ~56,000.

At any rate, I've determined that you couldn't find EH from this if you end up with a value greater than zero. You'd only be left with a given HP that you would have remaining - that is, you can only calculate EH used or required - unless you calculate some additional damage dealt or partition the remaining HP as the original post. I added on calculating the Real EH on what I described as an after-thought. The analysis portion of 'live or die' still appears equivalent, though.
Last edited by Elsie on Thu Dec 10, 2009 2:07 pm, edited 2 times in total.
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Re: "New" EH - incorporating different damage types into EH

Postby Xenix » Thu Dec 10, 2009 2:03 pm

Yeah, I divided instead of multiplying out of habit. You're right - yours gave 171.5k EH. I edited my post to reflect that.

As I said above though - your method is completely valid (barring the EH calculation) for seeing if you can survive a series of hits. It will not, however, allow you to create any generalized formulas for which stats give you more EH, which is what an actual EH formula is for.
Last edited by Xenix on Thu Dec 10, 2009 3:21 pm, edited 1 time in total.
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