Disc Priest - Mists of Pandaria - Page 23

Havoc12 · 02/17/13, 1:01 PM

edited to remove potentially wrong info

Szeretlek · 02/18/13, 8:07 AM

Originally Posted by Hamlet

dH/dC = 1.06+2.496M+1.13184M^2
dH/dM = 0.8M+2.496C+2.6368CM

Originally Posted by tib

While in theory this looks like you want to hit the sweet spot i dont think so, the difference between the minimum coefficient (all mastery reforged) and the maximum (some kinda middle ground) is very very low.
Almost always you'd want as much mastery as possible in practice as its more reliable (and then there's PW:S)

Reading the latest posts about atonoment healing and spirit shell it seems to me they should scale the same way as normal healing with respect to crit and mastery effectively making these curves covering all healing except PW:S.

Summirize your ideas (btw, Hamlet, dH/dM = 0.8 + 2.496*C+2.6368*C*M, I fixed it).
To calculate all sweet spots I just solve dH/dM=dH/dC (maximum theoretical HPS).
In raw stats from gear (buffs included):

For example, to hit sweet spot with maximum healing coeff with 7000 crit I need 4000 mastery.

From tib`s graph. to hit sweet spot with K=9900 you need 3750 mastery (9900-3750=6150 Crit)

Hamsda · 02/18/13, 9:43 AM

Even with crit being slightly nerfed by this new implementation I think it was a step in the right direction overall.
The disparity between a non crit and crit was, even without excessive mastery stacking, quite gigantic for disc priests. A heal going from "100%" to something like ~350% was just silly. Even crit stacking wouldn't have been such a nice solution, because our need for spirit will increase with 5.2 rapture changes, which leaves less overall budget for other secondary stats, resulting in still not really high crit percentages (where they start to "feel reliable").
The new mastery implementation keeps closes this huge gap between crit and non crit by also increasing the reliable part of our heals, the heal itself, which is quite nice.
With my current gear (pretty high on int, haste, mastery) average numbers did not change very much when I changed my spreadsheet from the previous ptr formulas to the new ones, but they obviously should have a much smaller deviation from that average.

I still believe that holy will be better if there is continous high raid damage without large spikes (when spirit shell will always be king), but for alternating damage patterns discs buffed penance for atonement healing and increased reliable healing with the new DA implementation seem pretty good overall.

Havoc12 · 02/18/13, 12:09 PM

7000 crit = 11.666666666667% crit + 5% from buff + 7% from intellect = 23.67%

4000 mastery = 10.67%+8% from buff +12.8% base = 31.45%

(1+0.5*0.3145)*(1+0.2367*(1+0.3145)) = 1.517319253087

add 100 mastery --> 31.73% 100 crit = 23.83%

(1+0.5*0.3173)*(1+0.2367*(1+0.3173)) = 1.519922758971

(1+0.5*0.3145)*(1+0.2383*(1+0.3145)) = 1.519753181288

[edited to remove potentially wrong information]

Szeretlek · 02/18/13, 12:26 PM

(1+0.5*0.3173)*(1+0.2367*(1+0.3173)) = 1.519922758971

(1+0.5*0.3145)*(1+0.2383*(1+0.3145)) = 1.519753181288

I give 7k and 4k as approximate value from graph.
Your calculations shows that 1.519 ~ 1.519 - thats what I want to get with that approach.

Havoc12 · 02/18/13, 3:42 PM

Hmmm actually it seems my formula was fortuitously right for the values I used, but it turned out to not be correct either.... I will go back and redo it

ok so

H = (1+0.5*M)*(1+C*(1+M)) = 1+0.5M+C*(1+0.5M)*(1+M) = 1+ 0.5M+C*(1+1.5M+0.5M^2)

where H = heal coefficient, M = mastery, C = crit and both M and C are expressed as fractions i.e. 38.4% = 0.384

using p to denote partial derivatives

pH/pM = 0.5+C*(1.5+M)
pH/pC = 1+1.5M+0.5M^2 = 1+0.5M*(3+M)

if R = mastery rating and CR = crit rating then

M = MR*k*1.6+0.208 (mastery buff + base mastery of 0.128)
C = CR*k+0.12 (crit buff + crit from int of ~7%)

k = 1/60000

dM/dMR = k*1.6
dC/dCR = k

pH/pMR = pH/pM*dM/dMR = (0.5+C*(1.5+M))*1.6*k
pH/pCR = pH/pC*dC/dCR = (1+0.5M*(3+M))*k

pH/pMR >= pH/pCR => (0.5+C*(1.5+M))*1.6 >= 1+0.5M*(3+M) => 0.8+1.6*C*(1.5+M) >= 1+0.5M*(3+M)

C*1.6 >= (0.2+0.5M*(3+M))/(1.5+M) = (0.4+M*(3+M))/(3+2M)

C >= (0.4+M*(3+M))/(4.8+3.2*M)

Thus the correct breakpoints past which crit is less valuable than mastery are:

crit			5.2	5.1
0.195269321		0.208	0.325
0.205436921		0.228	0.35625
0.215514874		0.248	0.3875
0.225506222		0.268	0.41875
0.23541387		0.288	0.45
0.245240597		0.308	0.48125
0.254989059		0.328	0.5125
0.264661797		0.348	0.54375
0.274261242		0.368	0.575
0.283789725		0.388	0.60625

The question is are these the maxima?

If we want to find the maxima then we need to calculate dH/dM and dH/dC

dH/dM = pH/pM+pH/pC*dC/dM

since you can only have a certain amount of rating allocated to CR and MR it is necessary that CR+MR = TR

i.e. C/k+M/k/1.6 = TR --> C = TR*k - M/1.6 --> dC = -dM/1.6 --> dC/dM = -1/1.6 and conversely dM/dC = -1.6

dH/dM = 0 --> pH/pM = pH/pC*1/1.6, which is the same as above thus the maxima are the breakpoints.

To verify

dH/dM = 0.5+C*(1.5+M) - 1/1.6 - 1/3.2*M*(3+M)

the maximum requires that dH/dM = 0 --> 0.5+C*(1.5+M) = 1/1.6+1/3.2*M*(3+M) --> C*(1.5+M) = 0.125+M/3.2*(3+M) --> C = (0.4+M*(3+M))/(4.8+3.2*M)

So the answer is that the maxima do indeed lie at the breakpoints

Thus the equation above will calculate how much crit you need to have for a particular value of mastery in order to hit the optimum value.

I verified it by taking the optima and adding +100 rating to one stat while subtracting -100 from the other in both cases the value is reduced by the exactly the same value compared to the optima. I am now certain that this formula works.

The equation can be easily converted to mastery rating and crit rating.

Perkeyone · 02/19/13, 12:46 AM

Do your graphs assume some sort of baseline crit chance from intellect? (and the class specific baseline chance?)

Szeretlek · 02/19/13, 1:05 AM

C*1.6 >= (0.2+0.5M*(3+M))/(1.5+M)

I repeat all your calcs and after that sentence I lost your point.

You go from %Crit and %Mastery to CritRating and MasteryRating. Buffs included. But anyway your table shows %Crit and %Mastery. Hows that?

And btw, Crit% for Int users:
Crit% = 1.2% (base) + Int/2400 (approx) + 5% (raid buff) + CritRating/600
For offensive spells it supressed by ~2.5% against 93lvl boss.

Szeretlek · 02/19/13, 2:02 AM

Ehm. We were so excited about Mastery and Crit and totally forget about SpellPower.
Lets refresh our knowledge:

AvgHeal = (BASE + SP_Coeff*SP) * HealCoeff

HealCoef = (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2)

C and M - raid buffed Crit% and Mastery Points (not %)
(BASE+SP_Coeff*SP) = BASE * (1+SP_Coeff/BASE * SP)
And SP_Coeff/BASE = const = K = 0.000096449 for all spells.

So
H = AvgHeal/BASE = (1+ K*SP) * (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2)
C = CR/60000 + 0.15
M = MR/60000 + 0.13 (this is mastery points, not%)
Truly value of
dH / dCR = dH/dC * dC/dCR = (1+ K*SP) * (1.06 + 2.496*M + 1.3184*M^2)/60000
dH / dMR = dH/dM * dC/dMR = (1+ K*SP) * (0.8 + 2.496*C + 2,6368*C*M)/60000
dH / dSP = K * (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2)

For CR=7000 (C=0.267), MR = 4000 (M=0.197 this is points, not %) and SP=35000
dH / dCR = 1.168e-4
dH / dMR = 1.169e-4
dH / dSP = 1.528e-4

Thats real value of 1 Crit Rating, 1 Mastery Rating and 1 SpellPower.
If we talk about gemming, then we should compare 2 Crit vs 2 Mastery vs (1.334*SP + 0.2369*Crit) = 1Int

so for gemming
2 * dH / dCR = 2.34e-4
2 * dH / dMR = 2.34e-4
1.334 * dH / dSP = 2.04e-4

And If 1 int gives you 1.334SP and 0.2369Crit, so 1 Int value = 2.04e-4 + 1.168e-4 * 0.2369 = 2.32e-4

So with 7k crit, 4k mastery and 35k sp:
Mastery gems and Crit gems and Int gems are even.
Only difference is mastery gives you 0 dps.

Any thoughts?

Updated: Int gems value recalculated. My mistake

Havoc12 · 02/19/13, 3:11 AM

I don't convert to rating:

pH/pMR = pH/pM*dM/dMR = (0.5+C*(1.5+M))*1.6*k
pH/pCR = pH/pC*dC/dCR = (1+0.5M*(3+M))*k

Its still C and M not CR and MR. The equation is pH/pM, which is in terms of C and M not, CR, MR and dM/dMR which is a constant. I am basically finding pH/pMR in terms of C and M not instead of CR and MR.

The breakpoints and the equation refer to total raid buffed crit and mastery and not to crit/mastery rating. These are the target you need to hit including racials, baseline int from intellect and buffs.

I am using 12% as the base value for crit before crit rating. This value only matters for the conversion of the formula to CR and MR, and it is included as part of C in the posted equation.

k is different for damage spells and heals, so atonement has a different benefit from int.

Szeretlek · 02/19/13, 3:25 AM

Originally Posted by Havoc12

I don't convert to rating:

pH/pMR = pH/pM*dM/dMR = (0.5+C*(1.5+M))*1.6*k
pH/pCR = pH/pC*dC/dCR = (1+0.5M*(3+M))*k

Its still C and M not CR and MR. The equation is pH/pM, which is in terms of C and M not, CR, MR and dM/dMR which is a constant. I am basically finding pH/pMR in terms of C and M not instead of CR and MR.

The breakpoints and the equation refer to total raid buffed crit and mastery and not to crit/mastery rating. These are the target you need to hit including racials, baseline int from intellect and buffs.

I am using 12% as the base value for crit before crit rating. This value only matters for the conversion of the formula to CR and MR, and it is included as part of C in the posted equation.

Then we get same results.

one of many sweet spots from my graph (I took them approximately from graph): 7k crit and 4k mastery = 23.67% crit and 19.67 Mastery Points (49.17% in 5.1)

one of many sweet spots from your table (you took them accurately from calculations):

Crit%                   Mastery% in 5.1
0.23541387		0.45
0.245240597		0.48125

Our results are near. So I think my graph is right.
Causes of little difference are:
1) You dont calculate metagem effect
2) I took my values from graph

Szeretlek · 02/19/13, 8:56 AM

Ok. So I worked with Spellpower a bit more and realize that I dont need to perform a 3 dimensional optimization, but I can solve 2 tasks of 2 dimensional optimization.

for example:
dH / dCR = dH / dMR = dH/dSP

dH / dCR = (1+ K*SP) * (1.06 + 2.496*M + 1.3184*M^2)/60000
dH / dMR = (1+ K*SP) * (0.8 + 2.496*C + 2,6368*C*M)/60000
dH / dSP = K * (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2)

dH / dCR = dH / dMR = (1.06 + 2.496*M + 1.3184*M^2) = (0.8 + 2.496*C + 2,6368*C*M)
(1+K*SP) - is gone from both part. So Mastery/Crit optimization should be performed w/o SP in mind. We already did that.

After we hit some sweet spot between Mastery and Crit and their derivative are even, we can perform second optimization task:
dH / dCR = dH / dSP
or
dH / dMR = dH / dSP

it doesnt matter, because we assume that dH / dCR = dH / dMR.

So I do:
dH / dCR = dH / dSP

(1+ K*SP) * (1.06 + 2.496*M + 1.3184*M^2)/60000 = K * (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2)

SP ={ [K * 60000 * (1 + 1.06*C + 0.8*M + 2.496*C*M + 1.3184*C*M^2) / (1.06 + 2.496*M + 1.3184*M^2)]-1 } * K

C and M are linked to be in sweet spot from condition dH / dCR = dH / dMR.

I get these data:

CR+MR   SpellPower Threshold
3824	49543
4724	49441
5621	49346
6516	49260
7409	49182
8300	49111
9189	49047
10075	48991
10960	48941
11843	48898
12723	48861
13602	48830
14479	48806
15355	48787
16228	48774
17100	48766
17970	48764
18839	48766
19706	48774
20571	48787
21435	48804
22297	48826
23158	48852
24017	48882
24875	48917

What does it mean? If you have for example Crit Rating + Mastery Rating = 10 000 and you balanced them to be equally good for maximum theoretical hps; 1 pure spellpower will be more valuable then 1 crit or 1 mastery right before the threshold. After that secondary stats will be more valuable (1vs1vs1). And in that boundary all these stats will be even.

This is not Intellect. I got another table for gemming, where I compare (2 crit vs 2 mastery vs 1 int) and SP threshold in that situation is near 34500-35000. That threshold number explain why I got all stats as equal to each other in my previois post. I calculated Int value for gems right near its threshold. If I drop 3000sp from that example, Int would be more valuable then secondary stats.

ADDED: Btw, I noticed that "SpellPower Threshold" has a minimum around 18000 stat sum. Interesting.

Havoc12 · 02/19/13, 11:34 AM

I am not incuding the crit meta, because I assume everyone will be using the legendary one. The 3% value is not going to change anything much.

Lets derive a more general formula for int optimisation.

pH/pI = pH/pSP*dSP/dI = pH/pSP*1.33*g. where g is a factor for intellect from gems, which we will deal with later.

We already know that the optimum ratio of mastery to crit is fixed so C = F(M) = (0.4+M*(3+M))/(4.8+3.2*M)

pH/pI = 1.33*g*k*(1+0.5M)*(1+F(M)*(1+M)), where k is now the spellpower scaling factor

pH/pMR = pH/pM*dM/dMR = (1+(1.33*I*g+baseSP)*k)*(0.5+C*(1.5+M))*1.6*z = (1+(1.33*I+baseSP)*k)*(0.5+F(M)*(1.5+M))*1.6*z, where z = 1/60000 and baseSP is non-intellect dependent spellpower, including the bonus from IF and SP buff.

Setting pH/pI = pH/pM, which we assume to be the optimum as the proof should be the same as for crit and mastery, we get

1.33*g*k*(1+0.5M)*(1+F(M)*(1+M)) = (1+(1.33*I*g+baseSP)*k)*(0.5+F(M)*(1.5+M))*1.6*z

The g factor is there to correct for the fact that each gem you have changes the relationship between dI/dCR, dI/dMR, which are important in the optimization. Sadly you cannot consider each gem in isolation and make a different table. You have to consider how each stat scales relative to the other and that relationship changes with every gem you have. Thus SP = 1.33*(int_gear + int_gems/2) = 1.33*(int_gear + int_gems/2)/I*I = 1.33*g*I, where g = (int_gear + int_gems/2)/I is the gem correction factor. This is an approximation and it is not strictly correct. The reason why we are doing this is because the optimisation equation is actually, not

pH/pI = pH/pMR, but

pH/pI = pH/pMR*dMR/dI, due to the fact that we are working with variables that are not independent (the dangers of working with partial derivatives). For gear dI/dMR = 1, but for gems it is not. g is just there to account for that and to save. I can instead do the correct partial derivative calculation to get a more exact solution. I think I will see if it takes too long.

I will solve the equation after I purify my PCRs.

Szeretlek · 02/19/13, 12:07 PM

Yeah, I got that in mind too when I already wrote the post, but consider to post it anyway.
It should be calculated as derivative of complex function.

=(

• Hamlet · 02/19/13, 1:09 PM

Spell changes contain all the already-announced stuff:
5.2 PTR - Build 16597 - Spell Changes and More - Wowhead News

Notably, the new DA tooltip describes the PWS crit as "Power Word: Shield has a chance equal to your critical effect chance to absorb twice as much." If that's literal then it clarifies what we were wondering above, although we can check soon enough.

It also says that Solace will "atone" for Holy, which is pretty interesting.