The math on Resto Mastery

[drhay53]

EDIT (2-17-11)Added a new plot showing the fractional increase (essentially stat weighting value) of mastery and crit

EDIT (2-17-11):Fixed plot to include axis labels, and an explanation of each line

Current best conclusions:
1) Mastery is more throughput than crit when your average heal occurs on a target whose HP is less than 65-75%
2) Stacking mastery causes mastery's value to suffer from some diminishing returns. This this causes the range of HP breakpoints listed above
3) Stacking mastery very slightly (almost imperceptibly) increases the value of crit.

WARNING: MATH
179.28 crit rating / 1% crit
179.28 mastery rating / 1 point of mastery
My crit + mastery (rating) = 1661

Healing done including both Mastery and Crit
Significant portions of this were aided by elitist jerks, as I was figuring out the equations: http://elitistjerks.com/f79/t110263-...discussion/p2/

definitions:
BH: Base Heal
M(m): points of mastery as a function of mastery rating
MI: The effect of mastery as a function of target HP
C(c): Crit chance as a function of rating, assuming 10% base crit chance from INT/raid buffs
Hc: Value of a crit heal
AA: Value of an AA proc from a crit heal
EHc: Expected value of a heal taking crit into account only
Heal: expected value of a heal based on mastery effect

M(m) = 8 + m / 179.28
MI = M(m) * 0.03 * (1 - HP)
C(c) = 0.1 + 0.01 * c / 179.28

Hc = BH * 1.5
AA = Hc * 0.286
EHc = (1 - C(c)) * BH + C(c)*(Hc+AA)

Heal = EHc*(1+MI)

The following plot shows the effects of putting mastery vs. crit.

image posting doesn't appear to be working, so here is a link
Mastery Plot

The x axis is the percentage of your available itemization points you put into mastery, with other points going into crit. For instance, for my toon I keep 916 haste, and never reforge spirit. So I end up with approximately 1600 rating to split between crit and mastery.

The y axis is the percentage HP of the healing target.

The displayed lines are the breakpoint where below this, mastery is higher throughput than crit. The different lines indicate the total amount of rating you have available, from 1600 to 4000. The more total points you have, the worse mastery is when you stack it.

Fractional increase (throughput) plot
This plot shows the fractional increase in healing for crit and mastery for a range of HP% values, versus how much mastery you stack (from 0 mastery rating to full mastery rating). Interesting conclusions:
1) Stacking more and more mastery has significant diminishing returns.
2) Stacking mastery has the effect of very slightly increasing the value of crit.
3) At around 70% HP for your normal heal, mastery is more valuable than crit. Stacking crit moves this breakpoint towards 75% and stacking mastery moves it towards 65%

[Gistwiki]

WARNING: MATH
My Crit rating is 1391 (7.76% chance) = 179.253 crit rating / 1% crit
My Mastery rating is 270 (1.51 points) = 178.808 mastery rating / 1 point of mastery

This is a bit off due to rounding in the tooltips.

http://elitistjerks.com/f15/t29453-c..._85_cataclysm/

Both Crit and Mastery take 179.28 points of rating to get an actual % crit or point of mastery.

[drhay53]

This is a bit off due to rounding in the tooltips.

http://elitistjerks.com/f15/t29453-c..._85_cataclysm/

Both Crit and Mastery take 179.28 points of rating to get an actual % crit or point of mastery.

Fixed. Doesn't really affect any of the other numbers though.

[Radux]

Definitely appreciate the support for Mastery. I'm good enough at math to follow your calculations and it seems good. However, I'm not an uber math wizard to be able to tell you if there is a flaw or not.

On one note, though. This is looking at a throughput only glass. One needs to consider that Crit has a secondary effect of being an incredible longevity stat because of IWS.

Great work though.

[Gistwiki]

Also, are you taking ancestral awakening into account? That varies the final numbers based upon your spell usage.

[Daetrin]

Out of curiosity, has anyone done the numbers for when the HPS per mastery for shaman equates to the HPS Per mastery for priests or pallies? I'm aware that's a bit more complicated but it just seems by mechanics resto mastery has to have a line where it intersects the more static masteries.

[drhay53]

Also, are you taking ancestral awakening into account? That varies the final numbers based upon your spell usage.

If you count AA as an increase in the crit modifier to 1.6, it does change the numbers slightly. It lowers the HP breakpoints by a couple % for the high mastery scenarios, and 5-6% for high crit scenarios.

The new equation taking into account AA as a 1.6 modifier to crit is:
HP breakpoint = (6 - 0.00111557*c + 0.00557787*m) / (8 + 0.00557787 * m)

Edit: This is not precisely correct, but it is an initial estimate. I'm still working on this stuff and will update the OP as I get time.

[TobyKenobi]

A few things that look a bit off to me:

1) Crits also have the AA bonus
H(c) = (1 - Crit) * AH + Crit * ( 1.5 * AH + .286 * 1.5 * AH)
H(c) = baseHeal + Crit * baseHeal * (.929)

2) Mastery effects the crit heals. Your formula calculated mastery based on 'AH' which you said was an average non-crit/non-mastery heal.
It should be based on average heal with a factor accounting for crit added. You should be using H(c) instead of AH in the mastery calculation.
H(m, HP) = H(c) * (1 + (0.24 + 0.3*m)(1-HP))

Something for people to keep in mind:
- Crit increases throughput, efficiency and regen
- Mastery increases throughput and efficiency
- Haste increases throughput (can improve regen through TC)

I've been a big fan of crit, but have been doing a lot of math lately, and will probably start focusing more on Mastery.

[drhay53]

A few things that look a bit off to me:

1) Crits also have the AA bonus
H(c) = (1 - Crit) * AH + Crit * ( 1.5 * AH + .286 * 1.5 * AH)
H(c) = baseHeal + Crit * baseHeal * (.929)

2) Mastery effects the crit heals. Your formula calculated mastery based on 'AH' which you said was an average non-crit/non-mastery heal.
It should be based on average heal with a factor accounting for crit added. You should be using H(c) instead of AH in the mastery calculation.
H(m, HP) = H(c) * (1 + (0.24 + 0.3*m)(1-HP))

Something for people to keep in mind:
- Crit increases throughput, efficiency and regen
- Mastery increases throughput and efficiency
- Haste increases throughput (can improve regen through TC)

I've been a big fan of crit, but have been doing a lot of math lately, and will probably start focusing more on Mastery.

Where does the 0.286 come from in the AA bonus section?

Also, essentially both Crit and Mastery equations currently ignore the other. The crit equations should also have mastery effects taken into account. I haven't quite reconciled the effects they have on each other yet in my equations, but I'm working on it. It seems to me that there is really only one equation for healing done, which is a function of Crit, mastery, and HP; ignoring other effects like SP and such obviously.

Your input is appreciated and I definitely appreciate any help to improve the estimates done here.

[TobyKenobi]

Ancestral Awakening heals 30% of the amount healed (including the crit) to another the lowest health target within 40 yards. I think in practice it comes out a bit less so 28.6% or .286

http://elitistjerks.com/f79/t110263-[resto]_cataclysm_raiding_discussion/p2/

Cyfir has some great math here. The equations I posted are pretty much the same but have some values changed for 4.0.6.

[Deleted]

The new equation taking into account AA as a 1.6 modifier to crit is:
HP breakpoint = (6 - 0.00111557*c + 0.00557787*m) / (8 + 0.00557787 * m)

It is 30% of 1.5 => 1.95

I think we can assume the 30% because it is a smart heal - It says "instantly healing the lowest percentage health friendly party or raid target within 40 yards for an additional 30% of the amount healed", so it can also heal the tank. I cannot think of many scenarios in which everyone is topped off the whole time - i think we can just assume the whole 30%...

[Jynus]

Nice job. I'm happy to see people coming to the same numbers I did back in November. I figure the more independent sources on the math the better. I still get flamed on a daily basis saying my math is wrong in some fashion or another.

[drhay53]

Significant changes to OP, and a plot download is included.

You cannot isolate crit and mastery. The interaction of the two is what makes the big difference. The Mastery breakpoint for HP drops rapidly from ~75% into the 60% range the more mastery you stack over crit.

I caution that this doesn't necessarily mean crit is BETTER than mastery for overall throughput, which still will depend on the amount of HP people have. I will work on this in the coming days and see if I can come to any conclusions.

[Radux]

Ok the longer this thread goes on the more I <3 you guys. This is the reason the Shaman community is great. People coming together and posting things (correct or not) and gain feedback (correction, even) from others and move on to a good consensus.

Seriously --

Keep up the damn good work.

[zshikara]

A few things that look a bit off to me:

1) Crits also have the AA bonus
H(c) = (1 - Crit) * AH + Crit * ( 1.5 * AH + .286 * 1.5 * AH)
H(c) = baseHeal + Crit * baseHeal * (.929)

2) Mastery effects the crit heals. Your formula calculated mastery based on 'AH' which you said was an average non-crit/non-mastery heal.
It should be based on average heal with a factor accounting for crit added. You should be using H(c) instead of AH in the mastery calculation.
H(m, HP) = H(c) * (1 + (0.24 + 0.3*m)(1-HP))

Something for people to keep in mind:
- Crit increases throughput, efficiency and regen
- Mastery increases throughput and efficiency
- Haste increases throughput (can improve regen through TC)

I've been a big fan of crit, but have been doing a lot of math lately, and will probably start focusing more on Mastery.

I have been stacking mastery since I did my first initial test healing back when I first hit 85. I admit I wasn't in the beta or anything so all my info is based on my own healing style and experiments, but I strongly prefer a mastery heavy setup over a crit heavy one. If you do it right (and not just spam heal like a retard) then mastery far outweighs crit imho. You still need crit, but by default you should have 15 to 20%. Even with me reforging away as much crit as I can I still have 19% I think right now and 1400 mastery. My guild hasn't progressed too far into raids yet due to lack of attendance and stuff like that, but for the fights I have done I almost always come out on top or second only to our top holy pally. And even when I come in second its very close. (9 to 11K HPS depending on fight)

[Jynus]

Significant changes to OP, and a plot download is included.

You cannot isolate crit and mastery. The interaction of the two is what makes the big difference. The Mastery breakpoint for HP drops rapidly from ~75% into the 60% range the more mastery you stack over crit.

I caution that this doesn't necessarily mean crit is BETTER than mastery for overall throughput, which still will depend on the amount of HP people have. I will work on this in the coming days and see if I can come to any conclusions.

I'm unsure how you get this. each point is linear, so doesn't matter if you add 1 point or 1k of mastery or crit, each one will have the same breakpoint of hp.

[Radux]

His point was that as Mastery goes up and, as a result, Crit going down, Mastery may have a lower break point. When you and others' did math in the past, you didn't take other stats into account.

I may be wrong here (please prove me wrong if I am), but I'm not sure how adding more Mastery (with the lowering of crit) can lower the break point of health levels. Like I said previously, I'm not an uber expert in math, but I guess I don't see where/how this can happen.

[SuperNick]

I have around 21% unbuffed crit and 500 mastery.. Overall i'm happy with these numbers.

I think generally the target to shoot for right now is 20% crit and 1000 mastery, thus complementing each other to a good end.

The days of stacking one stat only while ignoring others is kinda gone; it's really all about the spread of stats while focusing more on what you feel you need most. That said, my personal opinion is that stacking haste upto 1500+ is nowhere near worth getting your crit or mastery to that amount.

Good post anyway.

[ChrisKoe]

I'm truly lacking in the math department and get nervous twitches whenever I see graphs.
I understand Mastery gets worse the more of it you stack in relation to crit. Can you really name a certain number of Mastery rating to aim for as SuperNick did? Say "Get 1000 Mastery, then stack crit" or does the value of Mastery depend on other variables?

I'd be happy about any clarification. I'm really hopeless in understanding and interpreting math .

[Rabidkoala]

* Unlike indicated by the tooltip, only heals for 27% of the initial crit. (Yes, this is a known bug)
* Double dips from Spark of Life. At 3/3 Spark of life, will heal you for 32.91% of the original heal or someone else for 28.6% of the original heal.

From over at EJ, thats why the you can expect to use .286 as the additional healing done by a crit from AA IF you are healing yourself, you should probably expect to use the .27 modifier to cover most cases, or you can proportionately weigh it based on your logs of how often you heal yourself and others with direct heals.