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[Derivation] Armor/Mastery/Avoidance Calculations

Warning: Theorycraft inside.

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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby tlitp » Fri Aug 12, 2011 7:37 am

It follows the same distribution as in WotLK :
Code: Select all
Ra = min(R/(R+k),0.75)
k = L^2-127.5*L+4200, for L>60 (587.5 @85)
Pi = 2.5*max(0.2-abs(Ra-Ri),0), for Ri=0:0.1:1
Rmin = ceil(10*max(Ra-0.2,0))/10
Rmax = floor(10*min(Ra+0.2,1))/10

R = total resistance
k = resistance parametric constant
L = level
Ra = average resisted amount (%)
Ri = resisted amount thresholds (from 0% to 100%, in 10% steps)
Pi = probability of the thresholds
Rmin = minimum resisted amount (%)
Rmax = maximum resisted amount (%)

Obviously, the Prismatic Elixir is useless (as far as the EH metric is concerned) when R=0, R=400 (IoI), R=497 (MotW/IoI). When at least one of the MotW/RA buff classes is active (IoI inactive) or when both RA/IoI are active, PE will shift Rmin :
Code: Select all
MotW : 0% -> 10%
RA : 10% -> 20%
RA/IoI : 30% -> 40%
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby Hrobertgar » Fri Aug 12, 2011 8:17 am

For me, rather than run thru all the detail calc and models, I look at typical amount of dmg mitigated given the fight mechanics.

The armor elixir will usually boost my physical mitigation by like 0.5% to 1%, but since I'm already at about 60% mitigation, its like a 2%ish reduction in recieved physical dmg between using the elixir and not using it.

The primstaic elixir will reduce magical dmg by like 24%ish.

Anytime magic dmg is more than about 10%, then I consider using prismatic over armor. I usually check my dmg intake on recount if I am uncertain. On some fights like Nef I actually change, starting with prismatic for ph1 + ph2, and shifting to armor to kite the adds in ph3 as the magic dmg is something I mitigate thru CDs. Most of the time however I stick with the guild cauldron.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby tlitp » Fri Aug 12, 2011 9:15 am

Hrobertgar wrote:The primstaic elixir will reduce magical dmg by like 24%ish.

It's all fine and dandy, except it's physically impossible. PE only grants a maximum of ~13.3% (absolute) average resisted amount.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby theckhd » Mon Aug 15, 2011 6:58 am

If you're looking for guaranteed (anti-burst) reduction, you need specifics as in tlitp's analysis. At certain resistance values, the prismatic elixir doesn't give enough to bump you up to the next guaranteed level of mitigation.

If all you care about is overall damage reduction, then you can make a fairly simple estimate that ignores on-use trinkets and effects. Assuming you have resistance aura (195 resist), the elixir reduces magic damage taken by an additional 8.92%:

resist=R/(R+724)

Aura: R=195, resist=0.2122 (21.22%)
Aura+Elixir: R=285, resist=0.2825 (28.25%)
relative reduction: 1-(1-0.2825)/(1-0.2825)=8.92%

Another way to see this would be to define a magic mitigation factor Fm in the same way we did for the armor mitigation factor Fa, with

Code: Select all
Fm=(1-R/(R+724)) = 724/(R+724)


In that case, the relative reduction is just (1-Fm'/Fm), where Fm' is evaluated with the aura+elixir and Fm is evaluated with the aura only.

The armor potion will just change Fa, the armor mitigation factor. That's also easily calculable, assuming Ar=40k (and K=32573):

Fa=K/(Ar+K)

No elixir: Fa=0.4488
Elixir: Fa'=0.4433
Relative Reduction: 1-Fa'/Fa = 0.0122, or 1.22%.

For a mix of physical damage P and magical damage M, as measured by WoL (so post-avoidance/resist), the armor elixir will reduce your overall damage taken by 0.0122*P, and the prismatic elixir will reduce it by 0.0892*M. Setting these equal to one another and using the constraint M+P=1 (all damage is either magical or physical), you find that the break point is P=0.8797 (87.97%, or M=12.03%). So once more than about 12% of the damage you're taking is magical in nature, the prismatic elixir will mitigate more overall damage.

With only MotW/Kings, the magic elixir increases to 9.88% relative reduction and the break point shifts to 11% magical damage.

Again, this is only looking at overall damage taken. Often burst concerns are a bigger factor, and one should choose elixirs accordingly based on the encounter.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby Awyndel » Tue Aug 16, 2011 5:17 am

For block capping the flask still gives the most EH, since the armor elixir is under budget for EH, and the resist elixir doesn't push you over a soft cap.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby Kihra » Tue Aug 16, 2011 9:25 am

Awyndel wrote:For block capping the flask still gives the most EH, since the armor elixir is under budget for EH, and the resist elixir doesn't push you over a soft cap.


Don't forget about Scroll of Stamina IX. It counts as a Guardian Elixir and provides 150 Stamina. 225 Mastery + 150 Stamina vs. 450 Stamina is actually a good tradeoff, since you're getting 0.75 Mastery per Stamina as opposed to the usual 0.667 that swapping gems and trinkets would give you.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby tlitp » Tue Aug 16, 2011 12:56 pm

Awyndel wrote:For block capping the flask still gives the most EH, since the armor elixir is under budget for EH, and the resist elixir doesn't push you over a soft cap.

  • In terms of itemization points, the claim that EoDE is under budget is void of substance. Do remember that 1 Armor costs 4 itemization points in Cataclysm.
  • As previously mentioned, there are specific resistance thresholds where PE does shift Rmin.
  • Let's see some numbers. Taking the T12H set (yeah, Theck slacks like a pro), we expect the following stats under full raid coverage : ~220k HP, ~43k Armor, 98.8% CTC (ignoring both flask and elixirs). Therefore the 225 mastery rating granted by EotM is only partly converted to stamina (at the usual 3/2 ratio); 98 rating is still needed to reach full CTC. Using a script that solves the TEH intake thresholds :
    Code: Select all
    ehsolve

    ans =

        0.7234    0.6474    0.4425
        0.8383    0.7845    0.6115
        0.4849    0.3980    0.2222
        0.6512    0.5673    0.3617

    Assumptions :
    • As already mentioned, full CTC is maintained in all cases.
    • ES is always active.
    • The usual 3/3 Toughness and 3/3 Sanctuary are always active.
    • Any cooldown that has the same effect on both melee/magic intake is ignored.
    Analysis of the results :
    • The rows indicate no (relevant) cooldowns/HS/glyphed DivProt/HS+gDP, respectively.
    • The columns indicate R=97/R=195/R=595, respectively. (MotW/RA/RA+IoI)
    • The values are the magical damage thresholds [%] (nota bene : the values are normalized for WoL parsing) for which PE overpasses FoS in the (relevant) burst windows.
    • It should be fairly obvious that the effect of PE scales well with the gear level. Under the same initial assumptions (which will hold only if block-capping is not made "impossible" in a future patch), the Stamina gains emphasize PE over FoS.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby pfunkmort » Thu Aug 18, 2011 7:34 pm

I mean...those are relatively high levels of magic damage it would require in a burst window to favor PE over FoS, right? 50%-70%? I feel like it might be more constructive though to look at the problem as though the mastery elixir isn't wasted and gets the full use for CTC, no? In that in most situations you can itemize out of mastery somewhere else (maybe I'm just being self-centered in that I'm an alchemist and have the stone).
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby tlitp » Fri Aug 19, 2011 12:08 am

Oh, the numbers change dramatically when :
  • one can fully convert EotM's 225 itemization points into Stamina.
    Code: Select all
    ehsolve

    ans =

        0.5228    0.4382    0.2572
        0.6847    0.6073    0.4070
        0.2828    0.2192    0.1108
        0.4388    0.3576    0.1982
  • maintaining full CTC is a non-issue (overwhelming proportion of magical attacks/damage coupled with weak physical attacks/damage, or physical attacks/damage that can't be blocked). In this case one can ignore blocking (with or without HS) altogether when computing the TEH.
    Code: Select all
    ehsolve

    ans =

        0.3428    0.2708    0.1415
        0.3428    0.2708    0.1415
        0.1581    0.1179    0.0560
        0.1581    0.1179    0.0560
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby pfunkmort » Fri Aug 19, 2011 6:15 am

epic. thanks so much. It was just so hard for me to stomach that PE could be so weak, when it can make you gain a step in Rmin both with IoI/RA and simply RA.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby Awyndel » Sat Aug 20, 2011 5:34 am

I just meant when you put the armor elixir into the stamina<>armor formula for EH, it doesn't compare to the stamina flask. Perhaps a personal consideration, being an alchemist, this difference gets bigger through my perk. Also because of the perk, the stamina scroll isn't attractive.

I'm a bit confused with the resist soft caps you're using. http://elitistjerks.com/f15/t44675-resi ... ics_wotlk/ points out that for example an average resist of 50%, would rule out 30% rolls. Making 40% the minimum. Putting that into http://elitistjerks.com/f15/t29453-comb ... cataclysm/ I get the following soft caps:

10%: 181.0
20%: 310.3
30%: 482.7

Is that correct?
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby tlitp » Sat Aug 20, 2011 11:19 am

Let R* be the minimum amount of resistance that corresponds to a given Rmin :
Code: Select all
R* = ceil(k*min(2*Rmin,0.1+Rmin)/(1-min(2*Rmin,0.1+Rmin))), for any Rmin<0.7

At k=587.5 (i.e. level 85) :
Code: Select all
   Rmin      R*
    0.0        0
    0.1      147
    0.2      252
    0.3      392
    0.4      588
    0.5      882
    0.6     1371
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby Awyndel » Sat Aug 20, 2011 2:54 pm

And what about 88? Aren't we supposed to plug in the mobs level?
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby jere » Sat Aug 20, 2011 3:27 pm

Awyndel wrote:And what about 88? Aren't we supposed to plug in the mobs level?


Calculated for level 88, I get the same values as yourself.

specifically, I get:
Code: Select all
Min %   Rvalue        Rounded
0.1     181           181
0.2     310.2857143   311
0.3     482.6666667   483
0.4     724           724
0.5     1086          1086
0.6     1689.333333   1690


I couldn't calculate past that as that would require 80% average resist which is higher than the 75% cap, so I don't think there is a 70% min resistance value.
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Re: [Derivation] Armor/Mastery/Avoidance Calculations

Postby pfunkmort » Sun Aug 21, 2011 5:02 am

so then even as an alchemist, against lvl 88 mobs PE won't push your Rmin to the next threshold?
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