The math on Resto Mastery

[Dundebuns]

No axis labeled, no legend for each line... having trouble reading the graph even if you have stated information in your post...

Anyway, there is no point in arguing which of crit and mastery is better until people realise that Maths can only be done for theoretical and ideal situations. Health bars are incredibly dynamic and it is nigh on impossible to predict what health people will be on, even an average value, because peoples healing styles vary from raid to raid, where some people are adamant of healing everyone up and some let people linger at lower health. Until someone can probably model a boss fight, the health of each person, who the shaman heals, when the shaman heals, will they then be able to get a decent look at how mastery copes with the other stats. Until then, Mastery's value will differ greatly over the course of any fight, and that cannot be quantified with basic excel maths,

[drhay53]

The graph is from mathematica, and for some reason I can't get the axes labels to show up. I just gave up and put it out there, because I was getting tired yesterday. I'm going to figure that out today.

As for getting mastery to a certain magic value, be aware that the more you stack mastery the less health people need to be at before mastery takes over for throughput.

The reason for this counterintuitive result is the interaction of mastery and crit. They work together; and the answer seems to be that mastery-buffed crits are better than more mastery on less crits.

[TobyKenobi]

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.

Thanks for pointing that out. I have a tendency to read through their posts write down numbers and forget where they came from

[drhay53]

I have updated the plot with labels for clarity.

This is how I made that plot; In the OP I described how I make the formula for the expected value of a single heal based on the baseheal value. If you have problems with my results you have to tell me why this equation is wrong. Nothing I've done was based on opinion or anything fancy. I simply used this equation.

So this equation is a function of crit rating, mastery rating, and target HP %. Heal(c,m,HP). To make this plot what I do is calculate the fractional increase in this heal based on adding 179.28 of one rating. For instance:
Fractional increase in Heal due to 1% crit: [Heal(c+179.28,m,HP) - Heal(c,m,HP)] / Heal(c,m,HP)
Fractional increase in Heal due to 1 point of mastery: [Heal(c,m+179.28,HP) - Heal(c,m,HP)] / Heal(c,m,HP)

By setting these two fractional equations equal to each other, and solving for HP, you find the breakpoint where mastery takes over for increasing throughput.

Now, as for the axes on my plot; the y axis is the target hit point fraction. The x-axis is the fraction of your available points that you put into mastery. The different lines are for different total rating points available (i.e. increasing gear level). The overall conclusion to take from this is that at higher gear levels, stacking mastery REDUCES the target HP fraction needed for mastery to overtake crit in throughput.

To me this is saying that a mastery-buffed crit is more important for throughput than a mastery-buffed non-crit. It's counterintuitive because frankly, the equation is a complicated function of HP, crit, and mastery. It's not a simple interaction where you can isolate them from one another.

[Grispin]

The counterintuitive nature of the Crit/Mastery relationship can be explained fairly easily. Larger heals benefit Mastery more. Critical heals = larger heals.

As a simple example, if you critical heal a target at low health, the full heal benefits from the low health Mastery boost. On the other hand, if your first heal doesn't crit, your next heal on the target will more than likely land when the target is at a higher hp %, providing less of a boost from your Mastery.

This is a great discussion. Keep up the good work.

[Whoopsa]

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.

I'm not sure if I'm understanding this correctly, but I want to make sure that you're taking the BASE mastery into account when doing Crit healing equations. Tests healing with Crit at 100% health (ignoring mastery completely) and then healing at various levels on mastery tests would ignore the 8 mastery that comes passive. Just wanna make sure you're taking that into account.

[Strakha]

Resto mastery bothers me greatly, wish they'd just redo it.

[drhay53]

I'm not sure if I'm understanding this correctly, but I want to make sure that you're taking the BASE mastery into account when doing Crit healing equations. Tests healing with Crit at 100% health (ignoring mastery completely) and then healing at various levels on mastery tests would ignore the 8 mastery that comes passive. Just wanna make sure you're taking that into account.

From the OP:
M(m) = 8 + m / 179.28

The '8' is the base mastery which is completely independent of your mastery rating.

[Jynus]

You're doing the same thing as the guy from EJ, and I think I see where your math breaks down, as you're coming to the same conclusions he did..

You need to stop looking at the increase in heal, and look at the increase in throughput from x amount of stats instead. It's the difference in stats that needs to be the constant value, as essentially thats what we are comparing through reforging. And the breakpoint from mastery is always is always constant when done so.

ie: lets say you have 20% crit and 40% mastery. and get 2 drops, one with +100 mastery or the other with +100 crit. When calculating which gives the most throughput, you'll find the hp breakpoint for single target heals will be 62% (prepatch value)

now lets say you take those exact same values, 20% crit and 40% mastery and get even better drops, so now you have the choice between 200 points of mastery, or 200 points of crit. the hp breakpoint is _still_ 62%.

Now lets say you're in tier 12 so your stats are 30% crit and 50% mastery. And lo and behold, you get again 2 pieces again, on with +100 mastery, another with +100crit. Same thing, 62% breakpoint.

edit: here's a graph from a different poster on EJ who came to the same numbers as I did. He compared adding different values of mastery and crit, and notice a) all hps increases are linear and b) they all intersect at the same breakpoint with different values of stats.

Link to spreadsheet

Now, one of us is right here... I'm just not smart enough to see where/why whos math is wrong and whos is right...

[TobyKenobi]

Jynus, thanks for the link, that graph is a great visualization of crit vs mastery!

[Rashataur2]

Regardless of whether the math is correct or not...mastery is dependent upon the target healed, whether your guild uses healing assignments or does whack-a-mole style (like mine does). With the latter, the odds are someone else (esp a hots healer) has landed a heal before yours can cast, making your mastery worth less and less. There's probably less likelihood of this happening in a 10 man, but in 25 with 6 healers going at it, odds are great that you are getting heal-sniped.

So as it is impossible to model a boss fight and the healing done by all parties on all targets, it is just as impossible to say whether mastery is worth anything at all in a practical sense.

As a certified 7-12 math teacher, tho, I certainly applaud you on your math skills. GJ!

[Jynus]

too add to this, I've been doing some playing myself with different numbers. First here's the formula for figuring out what your heal will hit for for a single target heal including AA.

healAmount = baseHeal * ((1 + crit% * .9) * (1 + masteryValue * (1 - currentHealth%)))

to give an example for a target at 50% hp, 10k base heal, 30% crit chance and 40% mastery bonus, you get:

heal amount = 10000 * ((1 + .3 * .9) * (1 + .4 * (1 - .5)))
which = 15240 healing average


Now when playing with that, I noticed that with I say calculate the heal difference from 5% crit vs 5 mastery rating, mastery hit harder by about 5% at 1hp. However, when I punch in 10% crit vs 10 mastery rating, mastery hit harder by 9%. You can see the upper extent of this sorta in the graph I posted above. I forget the value of mastery they were using, but it was quite large. and mastery was hitting harder vs crit by about 20%.

Now the takeaway I'm getting from this is (and this may be preemptive, as again, i'm not an expert on this sort of thing) mastery itself has diminishing returns with itself the more you stack, buuuttt:

if anything, mastery has _increasing returns_ vs crit the more you stack.

[drhay53]

You're doing the same thing as the guy from EJ, and I think I see where your math breaks down, as you're coming to the same conclusions he did..

You need to stop looking at the increase in heal, and look at the increase in throughput from x amount of stats instead. It's the difference in stats that needs to be the constant value, as essentially thats what we are comparing through reforging. And the breakpoint from mastery is always is always constant when done so.

ie: lets say you have 20% crit and 40% mastery. and get 2 drops, one with +100 mastery or the other with +100 crit. When calculating which gives the most throughput, you'll find the hp breakpoint for single target heals will be 62% (prepatch value)

now lets say you take those exact same values, 20% crit and 40% mastery and get even better drops, so now you have the choice between 200 points of mastery, or 200 points of crit. the hp breakpoint is _still_ 62%.

Now lets say you're in tier 12 so your stats are 30% crit and 50% mastery. And lo and behold, you get again 2 pieces again, on with +100 mastery, another with +100crit. Same thing, 62% breakpoint.

edit: here's a graph from a different poster on EJ who came to the same numbers as I did. He compared adding different values of mastery and crit, and notice a) all hps increases are linear and b) they all intersect at the same breakpoint with different values of stats.

Link to spreadsheet

Now, one of us is right here... I'm just not smart enough to see where/why whos math is wrong and whos is right...

Ok, a couple of things about that spreadsheet:
1) They are using essentially a tiny portion of the parameter space that my plot encompasses. First, they are using a discrete method using 10% intervals of HP%. My equation is a function of HP%, which is a continuous parameter in all calculations. Second, they only consider stacking crit, stacking mastery, and mixing the 2 completely equally.

2) If you consider the portion of my plot where the 2 are mixed equally, i.e. at an x-axis value of about 0.5, you can see that all of my lines intersect there. If you were to look at all of these lines only in this region they would look very linear, not deviate from each other very much at all, and always have a HP breakpoint of nearly 0.7. This is very very near the HP breakpoint shown in the spreadsheet you linked.

Essentially the result in the spreadsheet and my result are the same; theirs is just simplified.

[Jynus]

Makes sense, I didn't even see your spreadsheet in the first post..

I sense here a few things now that I'm looking at this.
1) Both our math is right, I was just confused (i easily am)
2) mastery and crit both have diminishing returns the more you stack
3) hp breakpoints remain constant regardless of your stats
4) (and what you're missing from that graph) when you compare mastery directly to crit point by point, mastery will have increasing returns the more you have in regards to throughout vs crit. (assuming you're under the breakpoint for your heal, if you're above the breakpoint, the inverse is true.)

4) I think explains why our coefficients were so gimped for resto at the start of cata. Basically the more mastery we have, the more exponential our throughput becomes. The blizz theory was that this would carry our heals in the end to be on par with other classes.. (essentials our mastery is a % increase of healing on a %, so we scale hard). the problem is twofold. we are weak out of the gate for mastery and stats, so we can't see the benefit of this until in later tiers really. And the concept of real triage in raids like blizz promised it would be is false. (ie: people always low and not in danger) The triage issue is the real killer as while granted we have increasing returns the higher mastery vs crit when you heal someone below the breakpoint, the inverse is also true, and we become weaker the more healing we do with people above the breakpoint vs other stats. Since in a raid, we're healing people of all HP levels, in the end it tends to even out a lot of the time for average hp value. So we just don't ever get a chance to really see this scaling mastery healing.

Which seems to now that I think about it, further solidify my stance on crit vs mastery. If you're single target healing for the most part, haste/crit is best. But if you're HR+CH raid healing (where the HP breakpoint is like 90% so you're always under it) then mastery stacking will work best. And since it seems to be exponential increasing returns the more you stack vs crit, then HR+CH is going to get VERY powerful in later tiers I'm thinking...

[drhay53]

Here is another plot looking at the fractional increase in crit versus mastery. Essentially this is the 'STAT WEIGHT'. Whichever one is higher on the plot is more valuable to throughput.

stat weight plot

This plot may be overwhelming at first. Here is the overview:
1) Mastery indeed has diminishing returns the higher you stack it.
2) Crit has a very slight but still perceptible increase in value the more mastery you stack.
3) The mastery line that intersects the crit line is the one for 70% HP.

As a rough base for my stat evaluation in the future, I am going to estimate the level of health that I will be healing people at, and if it's less than 70% I will prefer mastery over crit. If it's greater than 70% I will prefer crit over mastery for throughput. Notice that these lines are falling at approximately 0.8% increase, just below the 1% increase due to haste. However you can see that if your target is below 60% HP, the fractional increase due to 1 point of mastery is greater than 1% and 1 point of mastery will be more valuable for throughput than 1% haste. Since the rating values are a little bit different, I do not know exactly what the turnover point is.

I will update the OP in a little bit and add this analysis, but it appears for alot of raiding scenarios mastery will be very valuable, even with diminishing returns.

---------- Post added 2011-02-17 at 07:15 PM ----------

Makes sense, I didn't even see your spreadsheet in the first post..

I sense here a few things now that I'm looking at this.
1) Both our math is right, I was just confused (i easily am)
2) mastery and crit both have diminishing returns the more you stack
3) hp breakpoints remain constant regardless of your stats
4) (and what you're missing from that graph) when you compare mastery directly to crit point by point, mastery will have increasing returns the more you have in regards to throughout vs crit. (assuming you're under the breakpoint for your heal, if you're above the breakpoint, the inverse is true.)

4) I think explains why our coefficients were so gimped for resto at the start of cata. Basically the more mastery we have, the more exponential our throughput becomes. The blizz theory was that this would carry our heals in the end to be on par with other classes.. (essentials our mastery is a % increase of healing on a %, so we scale hard). the problem is twofold. we are weak out of the gate for mastery and stats, so we can't see the benefit of this until in later tiers really. And the concept of real triage in raids like blizz promised it would be is false. (ie: people always low and not in danger) The triage issue is the real killer as while granted we have increasing returns the higher mastery vs crit when you heal someone below the breakpoint, the inverse is also true, and we become weaker the more healing we do with people above the breakpoint vs other stats. Since in a raid, we're healing people of all HP levels, in the end it tends to even out a lot of the time for average hp value. So we just don't ever get a chance to really see this scaling mastery healing.

Which seems to now that I think about it, further solidify my stance on crit vs mastery. If you're single target healing for the most part, haste/crit is best. But if you're HR+CH raid healing (where the HP breakpoint is like 90% so you're always under it) then mastery stacking will work best. And since it seems to be exponential increasing returns the more you stack vs crit, then HR+CH is going to get VERY powerful in later tiers I'm thinking...

I don't agree with your point that the HP breakpoint is always constant. The slight increase in crit's value and the diminishing returns on mastery's value as you add more mastery causes the breakpoint to vary by ~10% if you stack all the way into one or the other.

[TobyKenobi]

The one thing that still leaves me uneasy about Mastery is that it does not effect everything. To my knowledge the spells it currently does not effect are: Riptide HoT, Earthliving HoT, Earth Shield, and Healing Stream Totem.


What this means is that for these 4 spells you get the flat graphs. While for everything else you get the nice sloped graphs.

End result is what Jynus's point 4 says: As gear gets better our Mastery is going to start scaling a lot. But... I think the unwanted side effect will be that these 4 spells are going to become trivial for heals in comparison to our other Mastery buffed heals.

[Thunder Blue]

Resto mastery bothers me greatly, wish they'd just redo it.

Agreed, I wish they would just change it to a sliding scale where your heals become more effective as your target's health drops. Making an arbitrary health % where the mastery kicks in is just wonky and unattractive.

[TobyKenobi]

Agreed, I wish they would just change it to a sliding scale where your heals become more effective as your target's health drops. Making an arbitrary health % where the mastery kicks in is just wonky and unattractive.

Actually it is a sliding scale where your heals become more effective as your target's health drops. The breakpoint is where Mastery Rating becomes more effective that Crit Rating. So Your Mastery still makes your heals more effective at 80% target health. It just doesn't give as much of a boost as Crit does at that percentage.

[Jynus]

I don't agree with your point that the HP breakpoint is always constant. The slight increase in crit's value and the diminishing returns on mastery's value as you add more mastery causes the breakpoint to vary by ~10% if you stack all the way into one or the other.

I'm still unsure of how you calculate this.

Basically what I did was one set of calculations at 30% crit and 60% mastery.
then another at 23% crit and 77.5% mastery.

The difference between the 2 heals was 30hp. total heal was ~15.6k for both. Thats like a .19% variance, which more than likely is from the 62% breakpoint not being calculated to it's proper decimal point. I just can't see how the breakpoint lowers the more mastery we have...

[drhay53]

I'm still unsure of how you calculate this.

Basically what I did was one set of calculations at 30% crit and 60% mastery.
then another at 23% crit and 77.5% mastery.

The difference between the 2 heals was 30hp. total heal was ~15.6k for both. Thats like a .19% variance, which more than likely is from the 62% breakpoint not being calculated to it's proper decimal point. I just can't see how the breakpoint lowers the more mastery we have...

Because mastery increases the stat weight of crit when you stack it, while suffering from it's own diminishing returns. All I did was mathematically solve the fractional increase equations:

Fractional increase in Heal due to 1% crit: [Heal(c+179.28,m,HP) - Heal(c,m,HP)] / Heal(c,m,HP)
Fractional increase in Heal due to 1 point of mastery: [Heal(c,m+179.28,HP) - Heal(c,m,HP)] / Heal(c,m,HP)

For when they were equal, as a function of HP for how much mastery you stack. The plot in question is a contour plot showing the regions of parameter space where the fractional increase in crit is equal to the fractional increase in mastery, using the target HP.

---------- Post added 2011-02-17 at 07:39 PM ----------

Updated OP with the following:

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.

Fractional increase (stat weights) plot
This plot shows the fractional increase in 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%