Numbers discussion for upcoming Disc changes

90 Blood Elf Priest
10625
Just some musings based on something someone said to me re: bubblespam becoming viable again.

A disc priest in (non-upgraded) full BIS t14 gear has roughly 13,000 Spirit, which equates to 13,336 mp5 and 19,500 mana return from each Rapture.

At 18 seconds between Raptures, Rapture equates to 65,000 mana per minute.

Power Word: Solace on CD returns 3000 mana/cast. At 5 casts per minute, that's 15,000 mana per minute.

Shadowfiend restores roughly 90,000 mana per cast.

So in a 7-minute encounter, a priest has the following amount of mana available:
3 * 90,000 + 7 * 15,000 + 7 * 65,000 + 7 * (60/5) * 13,336 + 300,000 = 2,250,224 total mana.

Assume the priest casts Spirit Shell 6 times and casts PoH 6 times in each Spirit Shell, for a total of 36 casts at 13,500 mana/cast or 486,000 mana. That leaves 1,764,224 mana.

At 75% of its current cost, in Inner Will, PWS will cost 11,647 mana. So the priest can cast about 151 Power Word: Shields.

Assuming the priest has about 15% haste, the casts of PoH, Solace, and Shadowfiend have occupied 128 seconds, leaving 292 seconds free. Of those 292 seconds, the priest has enough mana to fill 197 with Power Word: Shield. In other words, casting nothing but Spirit Shell, Power Word: Shield, and Solace is sustainable enough in t14 gear that the priest only needs to be idle for about 95 seconds, or 23% of the encounter.

That's not quite at the level of "Wrath-style bubblespam is viable", but it's clearly approaching it.

How much Spirit would a priest need to reach 100% activity with just SS and bubblespam? Well, they'd need enough mana to cast 224 Power Word: Shields plus the SS PoHs, so they'd need 3,094,928 mana. 504,000 of that is free from base regen, 300,000 from base mana pool, 270,000 from Shadowfiend, and 105,000 from Solace, so they need 1,915,928 from Spirit.

So:
Rapture + Spirit regen = total mana from Spirit
23 * 1.5 * x + 1.1287 * x * 7 * (60/5) * .5 = 1,915,928
x (23 * 1.5 + 1.1287 * 7 * (60/5) * .5) = 1,915,928
x = 23,393

If I haven't done something terribly wrong with my arithmetic here, it looks like a priest with roughly **EDIT: 23,000** Spirit has "infinite mana" in the Wrath sense: they can literally start an encounter, begin spamming PWS (with SS PoH on CD), and continue until the end of the encounter. I think 23,000 is going to be attainable in t15 gear, at least the heroic tier, and probably t16 normal gear at the latest.

And you don't really have to hit 23,000 for the situation to affect how you play; even a priest in t14 heroic/t15 normal gear is going to be able to do an awful lot of blanketing.

Needless to say, I do not think this is a good thing. Please check my arithmetic if you can. My overall impression of the PTR changes is that they're probably going in a good direction, but there's reason for concern.
Edited by Kaels on 1/16/2013 11:39 PM PST
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90 Gnome Priest
12440
So what you're telling me is to go Spirit/Mastery and bubblespam all day errday.

On the serious side, I'm not convinced that bubblespam is a good option.

In terms of preventing damage spikes, you're better off with Spirit Shell PoH-spam. Higher cap, more APS, more forgiving if you attempt to do so too late (I'd much rather have a ~40k shield on two groups than a ~85k shield on 3-4 people) and more efficient too. For sustained HPS, you'll still get more healing out of PoH, nerfed as it is, for similar reasons.

I get that other healers could pretty easily beat us down with the nerfs as they are and bubblespam lets us provide something other healers can't, but in terms of just sheer throughput? It falls behind in a lot of ways.

EDIT: Oh and yeah. That breakpoint fits with some of my old napkin math. I was probably less mana efficient about it (I tried to do some figuring based around a 5x PoH - PW:S rotation), but it came out around the same: 16k with 200% Rapture.
Edited by Skootalloo on 1/16/2013 10:57 PM PST
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90 Blood Elf Priest
10625
Well, I built in the assumption that you're Spirit Shelling to max capacity very nearly on CD (6 times in 7 minutes).

PoH may have more raw throughput, but in terms of actual effectiveness, without DA, I suspect PWS spam will win out in most situations (excluding when people actually take enough AoE damage to get a mostly-full PoH cast off). PWS has significantly better throughput, and, I believe, now slightly better efficiency than current full-overheal PoH spam at 50% DA - and people still do that instead of waiting for the damage to happen.
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90 Blood Elf Mage
15120
This is just in heroic tier 14, not including upgrades or, for example, a spirit flask. Seems like folks could well approach the 17K number even before tier 15 gear.
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90 Blood Elf Priest
10625
** I did the arithmetic wrong in the final calculation. I forgot the Meditation modifier in both parts and forgot to correct for the base mana pool in the final calculation. The actual 'breakpoint' for 100% activity is closer to 23k Spirit, which is probably something we'll approach somewhere between late t15 and early t16, not in early t15. Corrected in the OP.

EDIT: Oh and yeah. That breakpoint fits with some of my old napkin math. I was probably less mana efficient about it (I tried to do some figuring based around a 5x PoH - PW:S rotation), but it came out around the same: 16k with 200% Rapture.

Yeah. I'd like to point out that it's not actually a 'hard' breakpoint - we approach something that feels very much like 'infinite mana' and heavy spamminess when we get up to around 85-90% activity with our highest-throughput rotation. That's going to be pretty easily achievable when people start getting t15 gear. We can already hit over 75%.

As a point of comparison, a paladin who wanted to keep up their highest-throughput rotation (HR HS HR LoD) at 100% activity for 7 minutes at 15% haste would need 3,189,120 mana, of which 144,000 comes from Divine Plea, 300,000 from base mana pool, and the rest from normal Spirit regen, so they'd need 2,745,120 / (1.1287 * 7 * (60/5) * .5) = about 57,900 Spirit (i.e. not happening. Ever.)
Edited by Kaels on 1/17/2013 12:30 AM PST
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90 Pandaren Priest
7670
Do you know what the new formula for SS/PoH will be with the DA change? I'm assuming that it'll be the same as that for our direct heals, but can anyone confirm this?
Edited by Ceddya on 1/17/2013 7:07 AM PST
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90 Troll Shaman
13250
Shouldn't you use HoH in the equation as well?
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90 Blood Elf Priest
10520
01/17/2013 07:18 AMPosted by Harpoa
Shouldn't you use HoH in the equation as well?


HoH doesn't technically have to return spirit to the priest, so I suppose Kaels could play around with it either way. I'm okay with him excluding HoH if it makes his napkin math easier.
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01/17/2013 07:18 AMPosted by Harpoa
Shouldn't you use HoH in the equation as well?


I assume he didn't because we aren't guaranteed to receive any benefit from our HoH.
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90 Blood Elf Priest
7430
01/17/2013 07:35 AMPosted by Morenn
I assume he didn't because we aren't guaranteed to receive any benefit from our HoH.


Stoopid Warlocks and Arcane Mages. D:
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01/17/2013 07:46 AMPosted by Qùess
Stoopid Warlocks and Arcane Mages. D:


Indeed!
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90 Blood Elf Priest
10625
I assume he didn't because we aren't guaranteed to receive any benefit from our HoH.


Stoopid Warlocks and Arcane Mages. D:

Yep :(

I usually leave out HoH from priest mana calculations because it's unreliable, and while it does buff Shadowfiend returns reliably, the overall contribution is pretty trivial. (We're talking 13500 mana from increased Shadowfiend and 24000 from HoH, so about 3 additional PWSs per cast if you get all 4 ticks. That means in a 7-minute fight my figures are off by at most 7 PWSs, probably more like 4 on average.)

Although including it would make a 16-second difference in the priest's active time. Combined, those effects might be worth including...let me see. Including the buff on 2 Shadowfiends plus 2 effective ticks per cast, and reducing the time we need to fill by 16 seconds, changes the Spirit requirement for 100% activity to about 21k. So yes, that's meaningful.
Edited by Kaels on 1/17/2013 9:08 AM PST
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90 Blood Elf Priest
14305
At 75% of its current cost, in Inner Will, PWS will cost 11,647 mana. So the priest can cast about 151 Power Word: Shields.

Assuming the priest has about 15% haste, the casts of PoH, Solace, and Shadowfiend have occupied 128 seconds, leaving 292 seconds free. Of those 292 seconds, the priest has enough mana to fill 197 with Power Word: Shield.


If that 15% haste is from gear/raidbuff, you forgot Borrowed Time. Chain-casting PW:S will take less time than that.
Edited by Nerfheals on 1/17/2013 9:40 AM PST
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90 Blood Elf Priest
10625
At 75% of its current cost, in Inner Will, PWS will cost 11,647 mana. So the priest can cast about 151 Power Word: Shields.

Assuming the priest has about 15% haste, the casts of PoH, Solace, and Shadowfiend have occupied 128 seconds, leaving 292 seconds free. Of those 292 seconds, the priest has enough mana to fill 197 with Power Word: Shield.


If that 15% haste is from gear/raidbuff, you forgot Borrowed Time. Chain-casting PW:S will take less time than that.

I just pulled 15% out of my !@#. I guess with Borrowed Time you're never really going to be below about 25% when you're chain-casting.

The difference wouldn't be huge. Keep in mind that at least in 10m (and probably also in 25 with more than one Disc) there's sort of a hard cap on how fast you can spam PWS anyway. You're not getting much more than 10 of them every 14 seconds (with the Weakened Soul glyph) no matter what.
Edited by Kaels on 1/17/2013 9:52 AM PST
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90 Gnome Priest
17125
on the ptr right now PW:S costs a little bit over 9k mana, and you put it down as 11k mana, that will probably make a difference
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90 Blood Elf Priest
10625
01/18/2013 10:06 AMPosted by Zolvolt
on the ptr right now PW:S costs a little bit over 9k mana, and you put it down as 11k mana, that will probably make a difference

The PTR is one build behind the most current patch notes. It has the 50% cost reduction and 100% Rapture right now; the most current notes have updated that to 25% reduction and 150% Rapture.
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90 Gnome Priest
17125
Oh i must have missed that =o
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90 Human Priest
16625
So there are a couple of things when looking at this problem that hopefully won't arise.
How much mana is required?
What are the spells being cast?
What does next tier's itemization look like?

We can definitively answer 2 of those questions.
I do agree that power word: solace would be the talent of choice for bubble spam. And I would also agree that inner will is the preference. With a 25% reduction in the current PW:S cost, it will cost 11666.25 mana in inner will.

Some other initial conditions to consider: is this for 10 or 25 man? Because in a 10 man, you will have 13 seconds (remember the new glyph) to wait on a target before casting another shield on them. I would say any haste past 1.3 seconds per cast would be wasted, but if you add the pw:solace cast into the mix, that number becomes 1.18 seconds per cast. Here's something cool about the new solace: it doesn't consume borrowed time. So if you account for borrowed time, you wouldn't want to go over 5.93% haste raid buffed or you will be waiting for your weakened souls to expire in a 10 man. This haste wasn't accounting for the 5% haste in a raid, so you'll want 0.888% haste on your toon for this style of play. Basically, avoid any and all haste gear. The OP originally had 15%. Even with these considerations, there will be a 'dead' global eventually because weakened soul is 13 seconds and pw:solace is 10 seconds. You can say that this will probably not happen due to latency, arguably, or that your broadband will suck up that dead global.

But this has a pretty major problem if you spec power infusion. Speccing power infusion not only goes over the haste soft cap of 50% when accounting for borrowed time, power infusion, and the 5% raid buff, but it leaves a lot more dead time while you're waiting for weakened soul to fall off. So perhaps for this example, we should stick with 25 man, where you wouldn't have this problem of waiting for weakened soul to come up.

But power infusion is still a good thing because it reduces the mana cost of our shields. And it's a multiplicative reduction, so 0.85*0.8 = pw:s cost during power infusion with inner will. In laymen's terms, pw:s costs 9333 mana during pi.

To say that shadowfiend will be used to close to its 3 minute cooldown is a good assumption because each melee swing will not cap your mana pool if you're casting shields at the same rate or faster than the sfiend swing because of borrowed time, so you can cast it right away and try to maximize it on cooldown. If you follow my advice above, you won't have any haste rating. This means, you will not have any additional shadowfiend melee swings unless you happen to use it during a bloodlust (for the record, shadowfiend get's an additonal swing at 12.5% haste). To say that Power Word: Solace will be used on cooldown is not a safe assumption. It will be close, but outside of power infusion, you will be able to fit 8 shield casts in between each solace. So it's actually a solace every 10.62 seconds.

And we know how spirit works. The formula is mp5 from spirit =300000*0.02+(1.1287*0.5*spirit). There are some 'ifs' with it though. Temporary spirit procs exist and have internal cooldowns, and Jade Spirit becomes 750 more spirit if you're under 25% of your mana. Each proc averages well, but if you run oom before the internal cooldown is done, that can work both for and against you. Also, these procs do not count for the new rapture refund.

And speaking of rapture, we know that the new rapture is going to be 150% of your static spirit. Whether or not this gets used close to cooldown is going to vary by encounter, but I believe that the proposed 18 second cooldown is reasonable as that's what I'm currently getting on the actual encounters in 5.0-5.1.
Edited by Twistedmind on 1/18/2013 11:07 PM PST
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90 Blood Elf Priest
10625
That's going to be a long post... :)
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90 Blood Elf Priest
10625
Thank you for the input!

I was going more for 'napkin math' than precise calculations because of the issues with trinket procs, fight variability, GCD clashes, Rapture timing variability, etc. If we can establish a 'ballpark' figure for the amount of Spirit necessary to support spam, we can then get an idea of how PWS-heavy actual play is likely to be.

Some other initial conditions to consider: is this for 10 or 25 man? Because in a 10 man, you will have 13 seconds (remember the new glyph) to wait on a target before casting another shield on them.

It's actually closer to 14 seconds because of the often-forgotten lag between when PWS is applied and when WS is applied. I was thinking more about 25s; encounter design so far has been sophisticated enough that pure shield spam is not likely to be desirable in 10s except perhaps on some 3-heal fights, which have been in the minority so far. Even 10s may still support quite a lot of bursts of spam, however, depending on how sustainable it is.

I hadn't though about Power Infusion, which would have some interesting interaction. Come to think of it, PI (to be used with brief bursts of shieldspam) is actually likely to be a very solid talent choice for Disc in the next tier in any case. But it's another factor mucking up constant shieldspam in 10s.

To say that Power Word: Solace will be used on cooldown is not a safe assumption. It will be close, but outside of power infusion, you will be able to fit 8 shield casts in between each solace. So it's actually a solace every 10.62 seconds.

Yes, I figured that - that's why I assumed 5 Solace/minute instead of 6.

The 10.62 second interval would actually give you 5.65/minute, but I don't like assuming perfect use of CDs.

And speaking of rapture, we know that the new rapture is going to be 150% of your static spirit. Whether or not this gets used close to cooldown is going to vary by encounter, but I believe that the proposed 18 second cooldown is reasonable as that's what I'm currently getting on the actual encounters in 5.0-5.1.

Yes, 18 seconds has historically been a pretty decent guesstimate for Rapture frequency for a skilled priest (or any priest with heavy PWS use).
Edited by Kaels on 1/19/2013 12:28 AM PST
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