Disc stat weights

[Deleted]

I thought I would spend a few minutes recalculating the disc balance points, so I will post the results here:

Using the formula for heals: H = sp*k*(1+M/2)*(1+C*(1+M))*(1+0.6*Mt)*(1+V)*1.3,
where sp = spellpower, k = spellpower modifier, M = mastery, C = crit, Mt = multistrike and V = versatility

we can calculate the partial derivatives for each stat (p/px denotes the partial derivative with respect to x)

pH/pM = 1/2*(1+C*(3+2M))*F(Mt,V), where F(Mt,V) is the heal formula without crit and mastery.
pH/pC = (1+M/2)*(1+M)*F(Mt,V)
pH/pMt = 0.6*F(M,C,V)
pH/pV = F(M,C,Mt)

We can ask what the balance point between crit and mastery is i.e. the optimal combination of crit and mastery that makes the maximum use of your secondary stats for raw throughput.

It can be shown that this occurs when pH/pRm = pH/pRc, where Rm and Rc are the ratings for mastery and crit respectively. I.e. when the partial derivatives of the heal amount with respect to crit and mastery rating are equal

Now this is equation can be converted to pH/pM*pM/pRm = pH/pC*pC/pRc.

pM/pRm is simply the rate at which mastery rating converts to %mastery, which is a constant, so let us denote it as Am. The same holds through for crit so let us say that pC/pRc = Ac

Solving the equation gives us C = [2*Ac-Am+Ac*M*(3+M)]/[Am*(3+2M)] in MoP adding the number in this gives C = (0.4+M*(3+M))/(4.8+3.2*M)

In WoD this changed due to the stat boost that disc gets. Am/Ac is no longer exactly 1.6, it is now 1.522. This means that the new formula is now

C = (0.478 + M*(3+M)/(4.57 + 3.04*M).

Solving a similar equation for Mt and V gives

Mt = [C+1/(1+M)]Amt/Ac - 1/0.6
V = [C+1/(1+M)]Av/Ac - 1

These are the balance points for multistrike and versatility. Notice that both formulas are very similar. The depend on the relative stat weights multiplied by C+1/(1+M) minus an constant factor (either 1/0.6 or 1). Their value increases with crit, but since they depend on 1/(1+M) their value decreases with mastery. Here are some values showing the stats you need at the balance points:

M	C	Mt	V
0.104	0.164	0.035	-0.136
0.114	0.170	0.031	-0.138
0.124	0.175	0.027	-0.140
0.134	0.181	0.024	-0.142
0.144	0.186	0.020	-0.144
0.154	0.191	0.017	-0.145
0.164	0.197	0.013	-0.147
0.174	0.202	0.010	-0.149
0.184	0.208	0.007	-0.150
0.194	0.213	0.005	-0.152
0.204	0.218	0.002	-0.153
0.214	0.224	-0.001	-0.154
0.224	0.229	-0.003	-0.155
0.234	0.234	-0.005	-0.156
0.244	0.239	-0.007	-0.158
0.254	0.244	-0.009	-0.158
0.264	0.250	-0.011	-0.159
0.274	0.255	-0.013	-0.160
0.284	0.260	-0.014	-0.161

Notice that you need more crit to start with but mastery increases in value faster. The multistrike and versatility balance points are also below the level you automatically get for buffs. That means that if you go for the mastery/crit balance point, you don't want any Mt or versatilty.

However as you get more crit the value of Mt and V increases. Here is another table showing the Mt value as you get more crit.

M	C	Mt	V
0.104	0.164	0.035	0.03
0.104	0.171	0.046	0.03
0.104	0.177	0.056	0.03
0.104	0.184	0.067	0.03

Notice that just 2 points of extra crit practically doubled the Mt/crit balance point.

Ultimately due to overhealing you will want some crit above the mastery balance point, which means that multistrike rating will become beneficial. Versatility takes more crit stacking to become useful though.

All in all disc wants crit and mastery once more, but actually you won't lose anything much by having multistrike or haste on your gear. If anything they are theoretical increases (overhealing and mana counteracts that though).

Thus disc is an the enviable (but boring) position, where it is generally better to pick the highest ilvl irrespective of stats (maybe avoid versatility unless you are crit stacking). You pick crit and mastery for same ilvl upgrades.

For holy the process is really straitforward since all stats are independent, so it is not worth writing a post about it. You simply want to stack multistrike as much as you can.

[Deleted]

This is an excellent resource. I'll assume your math is correct since I cba'ed going back to derivatives math for now. I'll put them on excel.



What's the equation for mastery?

- - - Updated - - -

What's the value of Am?

[Deleted]

Ac	             Am	          Amt	         Av
0.00952381	0.014492754	0.015151515	0.007692308

I got these from https://docs.google.com/spreadsheets...gid=1207425635

The values work out. I put them in excel and making small deviations from the balance points reduces the healing.

You can either solve the equation for crit in terms of mastery or for mastery in terms of crit. Solving mastery requires solving the quadratic equation and reject one solution, but you don't get clean results, so I solve for crit instead.

[Deleted]

I'm a bit confused right now. How does adding mastery diminish the return of the tertiary stats? Even if crit stays the same.





PS. It 'appears' at exactly 23.4%, mastery and crit reach a parity but the tertiary stats complicate it. It might need a more inclusive relationship, or the consideration of a final average heal.

[Deleted]

The formula for the balancepoints for Mt and V is dependent on the factor C+1/(1+M), so the more mastery you have the weaker the tertiary stats and the more crit you have the stronger the tertiary stats.

This is crit raises in value faster than any other stat with mastery. At the same time crit has diminishing returns so its value is lowered the more crit you have.

That is why having more mastery makes crit stronger and the tertiary stats weaker, while having more crit makes crit weaker and hte tertiary stats stronger.

If you stack crit and mastery at the balance point the you will keep multistrke and versa weaker than crit. If you go above (and you probably will want to) then multistrike will become useful. Versatility is only useful if you are massively crit stacking.

[Deleted]

Regardless of their relations, don't we need a more summarized way to figure out what we need? e.g. say I stack critical strike chance to make multistrike stronger. How do I know I didn't diminish the overall result by omitting mastery?

[Deleted]

The optimal point for raw throughput is achieved when the stats are as in table one. That means if you are optimising for raw throughput you don't want any multi strike or versatility. However this does not account for overheal. To do so you need to take crit above the balance point to calculate it you need to apply a correction to Ac and Am that accounts for overheal and recalculate. Depending on how much crit above the balance point you get you may need more multi. Basically you first need to decide how much extra crit to take and then you can decide if multistirike becomes useful.

[Deleted]

if you are optimising for raw throughput you don't want any multi strike or versatility.

Did you conclude to that by thinking the weights of the tertiary stats are smaller?



Oh wait, they are also negative at a point. Does it mean they do harm?

That would sound weird and wrong.

[Deleted]

The equations take into account the fact that if you get any secondary stat you have to sacrifice a little rating from some of the others. The value in the table is the threshold you need to reach before the stat is no longer useful. Since multistrike and versatility are below the level you automatically get from buffs, when you are at the crit/mastery balance point their value is already lower than more crit/mastery. The optimum values for raw throughput are those in table 1. That means any versatility or mulstrike rating you have on gear instead of crit/mastery is actually reducing your raw throughput.

[Evry]

Edit: the value of Ac is correct for the rating on gear, i was looking at rating in character pane, which reflects the passive 5% increase to rating. Values below have been updated to reflect this.

I'll try to explain what he's doing. It makes a little more sense if you convert the percents to stat ratings (using the values from the 2nd post).

Mastery	         Crit	Mt	V
-166 (0.104)	1198	234	-1766
-97 (0.114)	1256	207	-1793
-28 (0.124)	1314	181	-1819
41 (0.134)	1372	156	-1844
110 (0.144)	1429	132	-1868
179 (0.154)	1486	110	-1890
248 (0.164)	1542	88	-1912
317 (0.174)	1599	68	-1932
386 (0.184)	1655	48	-1952
455 (0.194)	1711	30	-1970
524 (0.204)	1767	13	-1987
593 (0.214)	1822	-4	-2004
662 (0.224)	1877	-19	-2019
731 (0.234)	1932	-34	-2034
800 (0.244)	1987	-48	-2048
869 (0.254)	2041	-60	-2060
938 (0.264)	2096	-72	-2072
1007 (0.274)	2150	-83	-2083
1076 (0.284)	2204	-94	-2094
1145 (0.294)	2257	-103	-2103

I put in the mastery effect in parenthesis so you can compare to Havoc12's chart.
The first lines are a negative mastery rating because we have 12.8% base mastery.

What he's looking at is, for a given amount of Mastery rating, what rating of stat 'X' do we need where an increase of 1 rating to either stat gives the same throughput increase. So, at a given line in the chart, if you had the ratings shown, an increase/decrease of any of the stats should have the same effect on your throughput (of non-absorb spells, ie excluding PWShield and CoW). A negative rating means, effectively, you should be avoiding that stat, not that the stat itself is harmful, but you just don't get enough out of it.

There are a couple of things to notice here. The first is, even with around 0 mastery on gear, you need a decently large amount of crit before adding any mastery is better than adding more crit. The second is, multistrike should be better than mastery (for non-absorb spells) up to a decent amount of crit (about 1400). Here's the chart based around 0 mastery on gear:

Mastery	         Crit	Mt	V
-345 (0.078)	1046	311	-1689
-276 (0.088)	1104	280	-1720
-207 (0.098)	1163	251	-1749
-138 (0.108)	1221	223	-1777
-69 (0.118)	1279	196	-1804
0 (0.128)	1337	171	-1829
69 (0.138)	1394	146	-1854
138 (0.148)	1452	123	-1877
207 (0.158)	1508	101	-1899
276 (0.168)	1565	80	-1920
345 (0.178)	1621	60	-1940
414 (0.188)	1678	41	-1959
483 (0.198)	1733	23	-1977
552 (0.208)	1789	6	-1994

Hopefully this makes it a little bit more clear what's happening here.

Remember that PW: Shield and CoW will scale better with Mastery than Holy Nova/Atonement/T90, so depending on your anticipated spell usage, it may be better to avoid the multistrike for mastery even early on.

Edit 2: fubar'd the baseline 5% crit chance.

[Deleted]

Edit: the value of Ac is correct for the rating on gear, i was looking at rating in character pane, which reflects the passive 5% increase to rating. Values below have been updated to reflect this.

did you include crit sources other than rating on gear when converting to rating? The values in my spreadsheet are for full raid buffs. So basically the amount of multistrike you need for its value to dip below crit and mastery when you are the raw throughput balance point is below the value you already get from the multistirke buff. That means if you are at the raw throughput balance point you don't want any multistrike or versatility. Only if you have more crit than the balance point do you actually want to have any multistrike.

[Myllior]

Minor corrections, but the values used to calculate Ac and Am were rounded and so they're not exact. The exact values are,
Ac = (1.05/110) = 0.00954545...
Am = (1.6/110) = (1/68.75) = (2/137.5) = 0.01454545...

I'm comparing my results to those posted here but I'm too tired to sort out where they're different and, if they are, why. I'll try again later but until then, here's the optimal distribution of stats I get as a function of total available secondaries. It's for pure normal/aegis healing, with no overhealing, with all raid buffs accounted for (it's also for a Worgen, so it may be slightly different because of that). You can find it here if you remove the space: imgur.com/ aiohKZz

[Deleted]

Can we tl;dr that as "stack crit until at least 23.4"? And then look for multistrike. By the way, is that the same for level 90?

[Deleted]

tl dr is stack crit until 18% then start adding mastery. If there is any haste or multistrike in your gear its ok.

[Deleted]

Why 18?

10char

[Evry]

did you include crit sources other than rating on gear when converting to rating? The values in my spreadsheet are for full raid buffs.

I did not include raid buffs (or racials) when calculating the rating on gear. I've added the option to show the rating taking raid buffs into account.

Mastery	         Crit	Mt	V
-345	0.158	991	-242	-2302
-276	0.168	1048	-263	-2323
-207	0.178	1104	-283	-2343
-138	0.188	1160	-302	-2362
-69	0.198	1216	-319	-2379
0	0.208	1272	-336	-2396
69	0.218	1327	-352	-2412
138	0.228	1382	-367	-2427
207	0.238	1437	-381	-2441
276	0.248	1491	-395	-2455
345	0.258	1546	-407	-2467
414	0.268	1600	-419	-2479
483	0.278	1654	-429	-2489
552	0.288	1708	-439	-2499

edit: some values if you move crit above the Mastery - Crit balance point

Mastery	         Crit	Mt	V
0	0.208	1272	-336	-2396
0	0.208	1481	-127	-2187
0	0.208	1691	83	-1977
0	0.208	1900	292	-1768
0	0.208	2110	502	-1558
345	0.258	1546	-407	-2467
345	0.258	1755	-198	-2258
345	0.258	1965	12	-2048
345	0.258	2174	222	-1838
345	0.258	2384	431	-1629
690	0.308	1814	-457	-2517
690	0.308	2024	-247	-2307
690	0.308	2233	-38	-2098
690	0.308	2443	172	-1888
690	0.308	2652	381	-1679
1035	0.358	2078	-489	-2549
1035	0.358	2287	-279	-2339
1035	0.358	2497	-70	-2130
1035	0.358	2706	140	-1920
1035	0.358	2916	349	-1711

this is from a jsfiddle, you can play with it here:
jsfiddle net/Amortise/rkpwdsx5/

If these are correct, we'll want mastery + crit. MS isn't much of a loss if we can't get mastery. We'll be short on crit, where mastery looks better for Holy Nova, and should be better for PWS/CoW as well

[Deleted]

Why 18?

10char

At about 18% you are above the balance point with base mastery, so you can start adding mastery. The question ofc is how far above the balance point you want to go. That will depend on overheal. You can model overheal, by decreasing Am by a certain factor to give mastery a reduced value and seeing how the balance points are shifted.

@Evry you need to be stacking some crit above the balance point, which means that multistrike will probably have a positive value above the multistrike raid buff. Also the value of multistrike and crit/mastery are actually pretty close.

Here is a list of the stat values at the balance point with just the 5% Mt buff and the 3% versatility buff.

M	      C	         M/C value	   Mt value
0.128	0.17513765	0.01569   	0.01551
0.134	0.180617136	0.01589   	0.01565
0.144	0.186069934	0.01611   	0.01583
0.154	0.191496528	0.01632   	0.01601
0.164	0.19689739	0.01654   	0.01619
0.174	0.202272982	0.01676   	0.01637
0.184	0.207623753	0.01698   	0.01656
0.194	0.212950143	0.01720   	0.01675
0.204	0.218252582	0.01743   	0.01694
0.214	0.223531489	0.01765   	0.01713
0.224	0.228787272	0.01788   	0.01733
0.234	0.234020333	0.01810   	0.01752
0.244	0.239231062	0.01833   	0.01772
0.254	0.24441984	0.01856   	0.01792
0.264	0.249587042	0.01879   	0.01813
0.274	0.254733033	0.01903   	0.01833
0.284	0.259858168	0.01926   	0.01854

As you can see there is hardly any difference. If you are just a couple of % points above the balance point Mt overtakes mastery. Basically you would pick the highest ilvl item available (unless it has versatility). If it is the same ilvl upgrades you pick crit and mastery.

[Deleted]

Oh I see what you mean, you value crit higher than the math. I want to see how wod encounters are balanced though. Blizzard said they want to change healing and encounters so that people go back to the era there was more 'regular' damage, less full-health raids and less sudden deaths.

[Jimjam38]

Suddenly my "Partial Differential Equations in Engineering" course seems relevant xD Thank you for settling this debate, it's been getting on my nerves, as the stat priority section of my satiric disc guide may have indicated :|

That being said, and I hate to throw a spanner in the works here, but in doing dungeons the last few days I have been noticing that CoW (and PWS to a lesser extent) are coming dangerously close to capping, and I only have ~620 ilevel at the moment, so this can only be expected to increase as we get more stats.

Absorbs are still restricted to a % of the caster's maximum health, so wouldn't mastery, multi and crit have a diminishing value as we get enough of them that we hit the cap in a single cast? In MoP, this problem still existed except it wasn't really possible to reach the levels of crit/mastery necessary to make it happen, but when you throw multi strike in the mix, and the insane SP co-efficients on CoW and PWS, it's seems to be a real possibility now.

Basically it would happen when MaxHp*0.66 < sp*k*(1+M/2)*(1+C*(1+M))*(1+0.6*Mt)*(1+V)*1.3
where MaxHp is the disc priest's max health and it's capped at (I think) 66% of our hp.

I'm not very confident with the maths here, but essentially it's likely to happen whenever you crit AND multistrike at the same time, or when you multistrike twice, or when your multistrikes crit or any combination of these, so (I think) the chance of it happening is essentially your crit*multi + multi*multi + multi*crit*multi*crit and so on (i'm really not sure about the math there when it comes to the interactions between crit and multi, because i'm not sure if Multi crits independently or if it's based on the crit of the original spell, but what I am confident about is that it can happen in a number of ways, which means there are a number of events which can result in capping, meaning that the probability of any event happening is additive ("or" events), meaning that frequency of it occuring is much higher, ie, it's not going to be that rare for us to cap compared to MoP when we didn't have multistrike. Mastery obviously contributes by increasing the potency of the crits/multistrikes.

PWS alone is less problematic because of Weakened Soul, but CoW, with it's larger Coefficient and ability to refresh/stack I've been finding I'm capping out, occasionally in a single cast, but quiet often in 2 casts if the tank has some of their own, smaller absorbs up. Furthermore, PWS is going to start experiencing this problem just as much once we hit t18, maybe even mythic t17. I'm also wondering how Divine Ageis would be affected by this problem.

Now, good gameplay can minimize this problem, by making sure you're not close to the cap when you recast it, but it's just an extra thing to have to manage, and it's still very RNG and hitting the cap is purely wasteful overhealing. Also, during Archangel it's even more likely to happen, and if you have any other healing buffs present then it's quiet probable.

What I'm wondering is whether we're going to get to a point where we should consider stacking haste or even stamina over mast/mult/crit to avoid frequently capping our absorbs.

Haste is strange, it only partially addresses the problem; by allowing more, weaker casts we're less likely to hit the cap in a single cast, but we still need to be careful not to stack up to the cap with successive casts; essentially it reduces the likelihood while blanketing (since we usually won't cast on the same target twice in a row), but does little while focusing a single target such as tank healing in raids or 5man healing (since faster casts means we may be refreshing/stacking CoW before it is consumed, potentially reaching the cap).

Stamina, is also strange, by increasing our max hp, we make it harder to reach the cap, however it doesn't contribute to our throughput in any other way. We'll always be getting increased stamina with each upgrade, so it's not like our MaxHp isn't going to scale up passively, but what's important is the ratio between the rate at which throughput stats and MaxHp scale. Even though they increased player Healthpools relative to everything else, I wonder if they've also adjusted the scaling rates relative to the scaling of healing. This is a problem unique to disc, as no other healer has absorbs with the potential to reach cap before being consumed, and true heals don't have a cap, so it's fairly likely they haven't considered this (also, its disc, they don't consider anything anyway). Anyway, as it currently stands at ~heroic dungeon level, I'm already coming close to capping on a noticeably often basis, and I can't imagine that Health is going to passively scale ahead of healing by any really significant amount with higher ilevels, so it's pretty safe to assume that this problem is going to persist, and increase, with higher ilevel. So, we consider whether it's worth stacking stamina at all. Obviously the scaling of the stamina passively available on 'regular' healing gear isn't enough to prevent this from occurring in the first place, however, what I want to know is whether the stamina available on trinkets and from gems contributes a significant enough amount of extra health that it's worth seeking them out. You'd also need to be very frequently capping and unable to reduce it any more through gameplay and/or shifting stats into haste/spirit before it was even worth considering using stamina. However, I suspect we may get there by the later tiers.

TLDR - Strong potential for capping absorbs with higher crit/multistrike levels, manage through gameplay and shifting stats towards haste, potential need for stam stacking in the late tiers of WoD.

- - - Updated - - -

Oh and also, Havoc, would you be able to make a script macro that uses this math to work out the balance point based on the player's current gear?

[Noradin]

While not a stat that we would look for anyway, I find it worth mentioning that lifeleech is another mechanic that does not work with absorbs at all.
Seems like Blizzard went all out trying to beat on absorbs any chance they got. We only need to get back to absorbs preventing tanks abilites to work properly and we are done.