"Total" EH - incorporating different damage types into EH

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

Postby Reynardadin » Sun Feb 07, 2010 3:58 pm

Awyndel wrote:Hey reynard,

I can see the addon also records the healing received during the burst window. If more physical damage is taken, this health received from healing is once again affected by armor, therefor increasing the value of armor. Does it take that into account as well when calculating the values?

http://maintankadin.failsafedesign.com/ ... 40#p535719

In case you missed that monster of a thread, the basics are in there somewhere.

Hey Awyndel,

The way the figures are calculated is as follows:

(Total unmitigated damage - absorbs - blocks - probabilistic resists) * ((max HP)/(max HP + healing))

Essentially, the EH2 module unmitigates each hit on the fly and "simulates" what would have happened had your health pool included all the healing you received, then scales it down to reflect your actual health pool.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Thu Jun 17, 2010 12:38 pm

Edited the original post to include a section on how EH interacts with healing, and what that means for armor/stamina relations.
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Re: "Total" EH - incorporating different damage types into EH

Postby Rasmfrackn » Wed Jul 28, 2010 6:57 pm

I'm really sorry for not digging through the middle portions of this, but I was curious if you ever added resistance to this more global treatment of EH, Theck. The resistance mechanics in LK are a lot more reliable than they were in BC and Vanilla, and instead of assuming magic damage as a generic "this damage just hurts" model, the 10% incremental breakpoints for resistance (worst-case breakpoints, that is) could definitely be useful. I see you included a provisional variable for resistance gear/buffs via Mr, but it didn't get the same treatment as armor did vs. stamina. Maybe it's a little more complicated to compare, say, the FrR crafted pieces which are nothing but stamina and resistance vs. "real" tank gear that also has avoidance and threat stats on it. Or, maybe it's just an obviously better choice for gear. IME a piece of resist gear is worth probably 5-8% DR per piece, but things get trickier comparing say the 50 resistance flask vs a stoneblood flask.

I can't think of any fights that would warrant resist gear outside of Sindy, but hey, completeness is as completeness does. :)
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Wed Jul 28, 2010 7:53 pm

Rasmfrackn wrote:I'm really sorry for not digging through the middle portions of this, but I was curious if you ever added resistance to this more global treatment of EH, Theck.

Yes, it's accounted for in the mitigation factor Mr.

Code: Select all
d = Dp*(1-Ma)*(1-Mt) + Db*(1-Mt) + Dg*(1-Mg)(1-Mr)         (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
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Re: "Total" EH - incorporating different damage types into EH

Postby kirsty » Thu Jul 29, 2010 3:12 am

theckhd wrote:
Code: Select all
X*P(1-Ma)(1-Mt) - (1-X)*B(1-Mt) +     X*G(1-Mg)(1-Mr) = 0         (14a)
Y*P(1-Ma)(1-Mt) +     Y*B(1-Mt) - (1-Y)*G(1-Mg)(1-Mr) = 0         (14b)


If we multiply (14b) by (1-X)/Y and SUBTRACT it from (14a), we have
Code: Select all
P(1-Ma)(1-Mt) = (1-X-Y)*G(1-Mg)(1-Mr)/Y       (15a)


Similarly, (14b) multiplied by X/(1-Y) and SUBTRACT from (14a) gives us
Code: Select all
P(1-Ma)(1-Mt) = (1-X-Y)*B(1-Mt)/X       (15b)


i think you did a slightly mistake here. you say that you multiply (14b) by (1-X)/Y and subtract it from (14a). but this is not what you are actually doing, you add both together. if you would subtract it, it would look something like this:

-p+2Xp - 2(1-X)b + 2Xg = -(1-X-Y)g/Y

instead of P(1-Ma)(1-Mt) and so on i just wrote p b and g. the same happens at the secont calculation, you wrote you subtract it, but instead you add it.

the endresult is the same, you calculated correctly, but you didn't calculate it in the way you said.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Thu Jul 29, 2010 5:04 am

Oops. Thanks for catching that, it's fixed now.
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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Wed Oct 20, 2010 5:27 am

Seems K might have changed.

http://blue.mmo-champion.com/t/27303223 ... tentional/

Also keep in mind the raid buffed values of health and armor have changed a lot for 4.0.1. Mostly due to 5% extra stamina, and the loss of bonus armor.

I did some initial calculations, without trinkets, and for halion ( no icc buff ). But I still have the number floating around 10 ( without magic damage and extra slow death mitigation ofc ) . Could the changes in raid buffed values make up for the increased K?

I was using K as 21.735. So that makes 12.075*(21735+(A/1.1))/H. If I put in 60K health and 30K armor it rolls out 9.8.

Am I doing something wrong or is armor still doing fine?

I realise that the trinkets I am trying to rate aren't affected by toughness so I should prolly divide the armor on them by 1.1 before I rate them.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Wed Oct 20, 2010 5:48 am

No, I don't see anything wrong with your math. The change to the armor formula should make armor about as good as it was before. I'll try and find some time to update the OP with the proper numbers and formulas for 4.0.1.

<edit>
Wait, why are you dividing armor by 1.1? Are you trying to solve for the effective stamina of an armor trinket?

If so, just use

dA = 12.075*(K+A)/H * dS

with the new K and your raid-buffed H and A to figure out dA/dS, which should come out around 10 (I get 10.4117 for A=30k and H=60k). To figure out how much "effective stamina" an armor trinket is worth, just divide the trinket's armor value by that number.

In other words, a trinket with 2000 armor would be roughly equivalent to 2000/10.4117=192 stamina in a situation without healing. All the usual disclaimers about armor being better with the presence of significant amounts of healing still apply, though it should be noted that due to the Vengeance mechanic, Stamina is actually a reasonable threat stat for us now (about as good as Strength in ICC thanks to the 30% buff).
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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Wed Oct 20, 2010 6:38 am

theckhd wrote:Wait, why are you dividing armor by 1.1? Are you trying to solve for the effective stamina of an armor trinket?


Toughness.

I'll account for the fact that it's bonus armor on the trinkets seperately by dividing their armor value by 1.1. I don't want that to influence the formula coz I wanna use it for different gear too. But this is a seperate issue.

Sorry I can see how that could be confusing.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Wed Oct 20, 2010 7:29 am

The A in that formula is not the trinket's armor, it's your total armor as read off of the character sheet. Toughness should already be encapsulated in A by default. Also, if my memory serves, toughness doesn't affect bonus armor on items, just base armor.

If you want to account for it for a specific item, you'd do it by modifying dA.


Example #1: Bonus armor trinket (same as before)

Trinket A gives 2k armor, at 10.4 armor/stam that's effectively 192 stamina.


Example #2: Bonus armor non-trinket

Items A and B both have 1500 base armor, but A has 500 bonus armor and B has 40 more stamina than A. Which gives more physical EH?

500/10.4 = 48 effective stamina, so the armor is still more EH (again, ignoring healing which makes the armor even better).


Example #3: Items without bonus armor

Item A has 1500 base armor and 100 stamina, Item B has 1400 base armor and 110 stamina. Which is more physical EH?

A has 100 more armor, but since base armor is affected by toughness, that's actually 110 more armor. 110/10.4 = 10.6 effective stamina, still slightly higher than Item B.


Example #4: Item with bonus armor and a base armor difference

Item A has 1500 base armor and 300 bonus armor. Item B has 1700 base armor, 0 bonus armor, but 10 more stamina.

B has 200 more base armor, which thanks to Toughness is really 220 more armor. Thus, you're comparing 80 armor from item A to 10 stamina from item B, and item B comes out about 2.5 stamina ahead.
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Wed Oct 20, 2010 3:35 pm

I've updated the OP with new numbers for 4.0.1, but note that it doesn't include block. Block is irrelevant for the dA/dS relations (it cancels just like 1-Mt does), but it will have an effect on calculations that consider magical damage.
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Re: "Total" EH - incorporating different damage types into EH

Postby Kihra » Wed Oct 20, 2010 3:40 pm

theckhd wrote:I've updated the OP with new numbers for 4.0.1, but note that it doesn't include block. Block is irrelevant for the dA/dS relations (it cancels just like 1-Mt does), but it will have an effect on calculations that consider magical damage.


"Since for paladins, talents, mastery, and BoK give us f=12.075, then:"

I think you meant "plate specialization" rather than "mastery."
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Re: "Total" EH - incorporating different damage types into EH

Postby theckhd » Wed Oct 20, 2010 3:44 pm

Kihra wrote:I think you meant "plate specialization" rather than "mastery."

Yup. Fixed.
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Re: "Total" EH - incorporating different damage types into EH

Postby Awyndel » Thu Oct 21, 2010 12:43 am

Thnx for those examples Theck. They will certainly make it easier for me to apply the formula to different kinds of items.

I was however not trying to solve the trinket with the formula. The formula I was using is supposed to solve the relationship between 1 stamina and X armor on gear, just like the original one. I merely took some health and armor numbers without wearing trinkets, since I was most interested in using it for those later, but ppl can put in any numbers they like. Forget about what I said about trinkets please, that was confusing, my bad.

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

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

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

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

Sorry I'm not trying to be a wise guy or anything. I am notoriously bad at explaining my thought process. I hope this makes more sense. Let me know your thoughts.

P.S. :

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

I also took some optimistic numbers for buffed health, yesterday I only reached 57500. Adding all this changes my armor number to about 10.8. Still not too bad.
Last edited by Awyndel on Thu Oct 21, 2010 1:24 am, edited 1 time in total.
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Re: "Total" EH - incorporating different damage types into EH

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

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


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

For me armor degraded slightly with the new formula by about a point. My 284 Petrified Twilight Scale is now worth ~220 Stamina instead of ~243 Stamina. In general you should see a slight degradation in the value of armor trinkets with the new formula, but not so much that it really changes anything.
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