The version Patch 3.1 currently on the PTR has introduced a few changes that have a decided impact on Resto druid healing in PvE. I wanted to do a quick run through of some numbers and see how the changes might affect healing when the patch drops.
So first, let’s list the changes that I want to discuss:
- Lifebloom: Mana cost of all ranks doubled. When Lifebloom blooms or is dispelled, it now refunds half the base mana cost of the spell per application of Lifebloom, and the heal effect is multiplied by the number of applications
- Living Seed: This talent now accounts for total healing including overhealing.
- Improved Regrowth (Tier 6) renamed Nature’s Bounty. Increases the critical effect chance of your Regrowth and Nourish spells by 5/10/15/20/25%. (Previously increased just regrowth crit by 10/20/30/40/50%)
- Glyph of Nourish: Your Nourish heals an additional 6% for each of your heal over time effects present on the target.
Lifebloom has been the core component of druid pve healing since Burning Crusade introduced the spell. From my own experience, druid healing always starts with a full stack of lifeblooms on a target, which, at very high spell power levels, produces a phenomenal throughput for a minimal expenditure. Once that stack has been established, the healer’s next goal is to analyze how much additional healing is needed and layer additional hots to help compensate for that. For myself, the priority has been rejuv is they just need an extra bit of additional healing, then regrowth if they’ve taken some damage. If more healing is needed on top of that, swiftmend, followed by replacing the consumed HoT or let lifebloom finish and then restack.
Well, obviously the change to lifebloom has the potential to alter that paradigm. Additionally, Regrowth was nerfed and nourish buffed, I believe with the hope of making nourish a viable competitor with Regrowth. Unfortunately, I think Blizzard has positioned the two of them too closely. Ultimately, it looks like either one will be clearly superior when glyphed, or they’ll be equivalent, in which case it’ll be up to the player which they like casting more. In neither case is it a strategic decision whether you use Nourish or Regrowth. They both fill the same role of a rapid cast top up to supplement HoTs. I believe the same holds for Healing Touch when glyphed, though I’m not entirely sure on that one.
I have a whole bunch of number crunching on lifebloom below the fold, but here’s the summary for people who just want to skip to the bottom:
“If the intent of the lifebloom change is to nerf druid efficiency, the intent failed. As shown above, throughput with a slightly different casting style has actually gained, without requiring any more effort on the druid’s part (as measured in, say,GCD usage). Additionally, the increased bloom has improved the efficacy of lifebloom enormously, such that different rotations (fast stack v. slow stack, for instance) can have marked differences on output and efficiency. While I like the change, it doesn’t appear to have addressed the design issue it was intended to.”
Edit: Wowwiki is mildly retarded, and I had to apply a minor fix to the spell power coefficient applied to the HoT and the direct heal. Does not alter final conclusion, does alter some numbers in the analysis.
Edit 2: This is an enormous pain in the ass, but I think I finally figured out the HoT coefficient: 66.9%. Will adjust later.
Let’s examine the cost of maintaining a rolling lifebloom stack versus letting it expire, along with healing output for both scenarios.
Lifebloom’s hot lasts for 7 seconds base, 9 seconds with Nature’s Splendor and 10 seconds with Glyph of Lifebloom. It heals for M * (base + coeff * SP) per tick, where M is the total multiplier on healing from talents, base is the listed amount healed for the spell, SP is the player’s spellpower, and coeff is the coefficient multiplied by spellpower to decide final additional healing.
Assuming Empowered Rejuvenation, coeff = .11422.
Finding M is a bit more complicated, as it involves adding up an assortment of talents we’re assuming a resto druid has taken. In this case, I assume Genesis, Gift of Nature, Master Shapeshifter, and I’ll also include the Tree of Life aura. All of these except Genesis affect every spell resto druids cast, so I could probably leave them out of a comparison between spells…they’d even out in the end. But whatever, I like numbers. With all those, M = (1 + .05 + .1 + .04) * 1.06 = 1.2614.
The base healing value of lifebloom is 371 / 7 or 53.
Therefore the final healing per tick of lifebloom is 1.2614 * (53 + .11434 * SP) = 66.85 + 0.144 * SP.
This implies that a full stack of lifebloom heals for 3 * (66.83 + 0.14397 * SP) = 200.49 + 0.43191* SP
The current list cost of lifebloom is 11.2% of base mana in Tree of Life form. That implies that it will be changed to 22.4%. Therefore, starting a full stack will cost 67.2% of base mana. Lifebloom has a GCD of 1.2 seconds, talented, meaning that in extreme cases multiple stacks may be maintained with a refresh occuring less than a second before expiry for all of them. Let’s assume, then, that lifebloom is refreshed with one second to spare. Obviously the longer it lasts, the more efficient this is. In this case, that leads to a 22.4% of base mana every 9 seconds, or 2.49% of base mana per second. Note that the addition of even a second to the duration is a massive increase in efficiency: refreshing every 8 seconds means spending 2.8% of base mana every second, or ~12% more. The duration increase talent and the glyph add 50% to stacked lifebloom efficiency.
Obviously the changed made halved the efficiency of maintaining a rolling lifebloom stack over present values.
Let’s now take a look at letting lifebloom bloom. The direct heal uses a similar basic equation, and gains all the same modifiers. It’s coefficient is .6453, or .7744 with Empowered Rejuvenation. The base healing value is 970. The final healing value for the bloom is 1.25 * (970 + .7752 * SP) = 1212.5 + .969 * SP. With 3.1, this value will be multiplied by the number of applications on the target when it blooms and refund half the cost of the spell per application. However, the refunded amount is half the cost of the spell before any reductions; that is, half the base cost. The base cost of the spell will be 28% of base mana, so the refunded amount is 14%, bringing the cost of a lifebloom allowed to expire to 8.4% of base mana.
Assuming you allow a single lifebloom to expire before re-applying, that will cost 8.4% of base mana every 10 seconds. It will heal for
10 * tick value + bloom
= 10 * (66.25 + .1428625 * SP) + (1212.5 + .969 * SP)
= 662.5 + 1.428625 * SP + 1212.5 + .969 * SP
= 1875 + 2.397625 * SP.
That in turn equates to 187.5 + .2398 * SP per tick.
Looking at that, we can tell a few things. First, the HoT portion of the spell scales with SP substantially better than the bloom. While this is somewhat offset by the better base healing the bloom grants, we can see that a continually refreshed stack of lifeblooms will rapidly scale to heal for more than a single lifebloom allowed to bloom then refreshed. It is for this reason that maintaining a stack has been more efficient than casting and letting bloom.
Also, the increased duration of the HoT portion minimizes the impact of the bloom on the final healing value. If we remove the glyph and talents, a single lifebloom allowed to expire will heal for 7 * (66.25 + .1428625 * SP) + 1212.5 + .968 * SP = 463.75 + 1 * SP + 1212.15 + .969 * SP = 1676.25 + 1.969 * SP. Obviously, this reduced duration has translated into reduced total healing. However, it hasn’t reduced throughput as strongly as it might due to the bloom…because the addition to the total heal by the bloom is unaffected by the duration of the HoT. That final value equates to 239.46 + .2813 * SP per tick. As you can see, the healing per time for a 7 second lifebloom is substantially higher than a 10 second lifebloom. Also note that the base healing is higher than the base healing for a fullstack refreshed. Obviously, the stack scales better with SP, so eventually it will overtake the throughput of a single lifebloom.
The value of SP at which a stack will overtake a single lifebloom is found thus:
- 239.46 + .2813 * SP = 198.75 + .4285875 * SP
- 40.71 = 0.1472875 * SP
- 276.4 = SP
Obviously, this is level of spellpower is hit by every druid worrying about lifebloom.
As for mana costs, for a 10 second lifebloom, allowing it to bloom expends .84% of base mana every second…less then half the cost of maintaining the stack. For a 7 second bloom, it costs 1.2% of base mana, or 43% less than maintaining a stack.
The next rotation of interest is quickly stacking two lifeblooms and allowing the stack to expire. Because an expiring lifebloom heals per application, this becomes a much more interesting situation. Due to the cost changes, stacking two costs the exact same as maintaining an existing stack. For a talented and glyphed duration lifebloom, this should amount to slightly less mana usage per second. Let’s look a the final healing throughput: we know that it’ll take a second to refresh once started. That means it’ll tick once for the base HoT tick, before ticking 10 times for twice that and then bloom for twice normal bloom value. That is, the total heal will be
66.25 + .1428625* SP + 10 * 2 * (66.25 + .1428625* SP) + 2 * (1212.5 + .969 * SP)
= 66.25 + .1428625* SP + 1325 + 2.85725 * SP + 2425 + 1.938 * SP
=3816.25 + 4.94 * SP
That equates to 340.737 + .441 * SP per second (11.2 seconds). As we can see, the throughput of this cycle has surpassed a refreshed stack.
What about for a 7 second lifebloom? Substituting 7 for 10 in the last equation, we get:
66.25 + .1428625* SP + 7 * 2 * (66.25 + .1428625 * SP) + 2 * (1212.5 + .969 * SP)
= 66.25 + .1428625* SP + 927.5 + 2 * SP + 2425 + 1.938 * SP
=3418.75 + 4.081 * SP
As the first cast had a GCD of 1.2 seconds, plus a 7 second duration on the lifebloom for 8.2 seconds, this equates to 416.92 + .498 * SP per second (a lifebloom tick is one second, but I think second probably should be used as its a bit more generic). The scaling of two lifeblooms allowed to bloom on their target has far surpassed a 3 stack
As for efficiency, recasting two lifeblooms every 11.2 seconds at 8.4% per lifebloom equates to 1.5% of base mana per second. Two lifeblooms every 8.2 seconds costs 2.05% of base mana per second. Two 7 second lifeblooms, then, heals for more than a stack of three maintained and yet costs less to maintain.
A question of interest is the efficiency of the healing: how much does one point of healing cost? I’ve been attempting to keep specific stats out of the question, and I think we can continue to do this by using base mana as a unit (denoted bm). Since base mana pools are often rather large, though, we probably ought to use some fraction of a BM as our unit. Looking to the matric system, a centibasemana (cbm) would be 1/100th of a base mana, or 1% of base mana. That unit would make a great deal more sense, given that all spells cost some % of base mana. Two 7 second lifeblooms costs 16.8 cbm and heals 3418.75 + 4.081 * SP health. That amounts to 203.49 + .2429 * SP health/cbm. As expressed above, maintaining that will cost 2.05 cbm/sec.
Looking at efficiency for rolling stacks of lifebloom, we see the most efficient version heals for 198.75 + .4285875 * SP per second, at a cost of 2.49 cbm. We end up with 79.82 + .172 * SP health/cbm. Thus we see that, with these changes in 3.1, casting and allowing to expire 2 lifeblooms is more efficient AND has a higher throughput than the rolling stack of lifeblooms.
Finally, let’s take a look at 3 lifeblooms cast one directly after another and allowed to expire. First up: the 10 second lifebloom:
66.25 + .1428625* SP + 2 * (66.25 + .1428625* SP) + 10 * 3 * (66.25 + .1428625* SP) + 3 * (1212.5 + .969 * SP)
= 66.25 + .1428625* SP + 132.5 + 0.285725 * SP + 1987.5 + 4.285875 * SP + 3637.5 + 2.907 * SP
= 5823.75 + 7.6214 * SP
For a 12.4 second total duration (including stacking times), this amounts to 469.66 + .615 * SP health per second.
And if we use 7 second lifeblooms? Substituting:
66.25 + .1428625* SP + 2 * (66.25 + .1428625* SP) + 7 * 3 * (66.25 + .1428625* SP) + 3 * (1212.5 + .969 * SP)
= 66.25 + .1428625* SP + 132.5 + 0.285725 * SP + 1391.25 + 3.0001 * SP + 3637.5 + 2.907 * SP
= 5227.5 + 6.3357 * SP
Over 9.4 seconds, that’s 556.12 + .674 * SP per second.
It costs 2.03 cbm per second to maintain the 10 second lifebloom, and 2.68 cbm per second for the 7 second lifebloom.
As for efficiency, the 10 second lifebloom puts out 231.1 + .302 * SP health/cbm. The 7 second lifebloom puts out 207.4 + .251 health /cbm.
Some more observations can be made on this analysis. First, the changes to lifebloom have made it more efficient to allow stacks to bloom that to maintain them. That means that taking the talents and glyphs which increase lifebloom duration increase efficiency, but at the cost of throughput. As lifebloom stands currently on live, however, the because stacking more lifeblooms minimizes the impacts of the final heal, particularly for longer duration lifeblooms, it is generally no big sacrifice to add additional time on the lifebloom. As I recall from my old BC theorycrafting, it was always better to maintain 3 stacks that never fall off, both from the efficiency and the throughput perspectives. Now, this is no longer the case. In the new system, once you stack 2 lifeblooms, regardless of their duration, it is both more efficient and higher healing to let them fall off and then restore them as opposed to recasting on the stack.
Additionally, we see that adding more lifeblooms increases efficiency. Why is this? The first tick of the first lifebloom. We get that first tick of our initial cast while building our lifebloom stack essentially “free”, because the next cast will refresh the duration of the stack, while keeping the health benefits of the first cast for all those ticks. In fact, I suspect we would see even greater efficiency, at the cost of healing per second, if we allowed each HoT, as we built up to 2 or three, tick for nearly its full duration.
What probably interests me most, though, is how this compares to the current king of throughput and efficiency: a 3 stack at half the cost. First, the changes going on to the PTR haven’t changed the healing per second of maintaining a stack on your target. Therefore, we can say that we have actually gained additional healing out of lifebloom from this change. Assuming a refresh every 9 seconds, costing 11.2 cbm, we are spending 1.24 cbm/sec and healing 198.75 + .428325 * SP health/sec. That indicates an efficiency of 160.282 + .345 * SP health/cbm. That is indeed more efficient than any of our high throughput casts (at least, it scales more rapidly, so at some level of SP it will surpass them in efficiency. Eyeballing the efficiency scaling tells me it’s likely at least at current gear levels).
Well, let’s see what Blizzard has given us in terms of high efficiency lifebloom. The most efficient lifebloom sequence we can cast, as noted above, is a 10 second lifebloom stacked to 3, waiting until the last tick to cast the next lifebloom, and, once 3 are stacked, allowing it to expire. That would heal like so:
9 * (66.25 + .142775 * SP) + 9 * 2 * (66.25 + .142775 * SP) + 10 * 3 * (66.25 + .142775 * SP) + 3 * (1212.5 + .968 * SP)
= 596.25 + 1.284975 * SP + 1192.5 + 2.56995 * SP + 1987.5 + 4.28325 * SP + 3637.5 + 2.904 * SP
= 7413.75 + 11.042175 * SP
Since this lasts 9+9+10 = 28 seconds, we’re looking at 264.78 + .394 * SP health/sec.
To maintain this, the caster will spend .9 cbm/sec.
Efficiency: 294.2 + .438 * SP h/cbm
What we see is that at some value of spell power, the Live version of 3 lifebloom stacks will do more healing than the PTR version. However, the PTR version starts out more efficient and gains rapidly.
Here’s the spell power level where the rolling stack of lifeblooms catches up in healing per second done:
198.75 + .428325 * SP = 264.78 + .394 * SP
.0343 * SP = 66.03
SP = 1925.07
Well, it looks like resto druids have essentially received a lifebloom buff. Only druids over 1925 spell power will lose any throughput with the new lifebloom, and that’s only if they use the most efficient new lifebloom rotation. By simply refreshing earlier, they will make that up, at the cost of efficiency.
More interestingly, the efficient version is a DRAMATIC gain in efficiency.
One thing I think comes out of this lifebloom discussion is that the lifebloom glyph has been indirectly nerfed from this. While it used to be a major efficiency boost, it appears from the above analysis that many resto druids can now replace it and actually see a boost. In fact, any druids who, in 3.1, find themselves with excess mana may be inclined to remove the glyph as it is effectively limiting their available throughput. The same holds for nature’s splendor, though that one is tougher to call for cutting as it also impacts rejuvenation and regrowth. Please also keep in mind that I have used a rather generous analysis of stacked lifebloom. I have completely ignored the initial stacking costs. Depending on how long the stack is maintained and how good the druid is at not letting the stack fall off, these become minimized by the ongoing cost of maintenance, but they certainly aren’t negligible. This change effectively eases the restoration druid’s job, by giving them buffer room around their lifebloom.
Before ending the lifebloom discussion, I’d like to put in some concrete numbers for the healing druid. That often helps make more “real” all the variables.
First, let’s just talk healing output. Let’s assume a druid with 2000 SP and 0 crit. The rolling lifebloom heals for 198.75 + .428325 * SP, so this druid will be putting down 1055.4 h/sec. With the proposed PTR changes, the most efficient lifebloom will heal for 264.78 + .394 * SP, so 1052.8 h/sec. Not a terribly big difference, using the slightly fewer GCDs per second.
A level 80 NElf Druid has 3,496 base mana. The rolling lifebloom stack costs 11.2cbm, or 391 mana, and they end up spending 43.4 m/sec. They therefore see an efficiency of 24.3 h/m. On 3.1, using the most efficient lifebloom, this same druid will spend 31.46 m/sec, for an efficiency of 33.5 h/m. That’s 38% more efficient…wow. Just wow.
In addition, this NElf druid may now experiment with a much higher throughput lifebloom: the 7 second lifebloom, stacked rapidly to 3, let bloom, reapply. This druid’s new lifebloom has the potential to output 556.12 + .673 * SP, or 1902.12 h/sec. That is an 80% gain over the prior lifebloom main method. At 2.68cbm, they’ll be spending 93.7 m/sec at an efficiency of 20.3 h/m. For a 65% loss in efficiency, they’d gain 80% throughput.
I admit, I’m excited by the change. This introduces a lot of options in the use of lifebloom as a druid healer.
However, this change constitutes, I’d say, a class design failure. Here is Ghostcrawler on the intent of the change:
“Rolling Lifeblooms on 2-3 tanks is just hands down one of the most — probably the most — efficient heals in the game. We didn’t want to nerf the amount Lifebloom heals, but we were concerned druids would jump to the top of the healer stack pretty quickly with the recent mana changes.
We added the bonus to the bloom to improve its use in PvP, where you can’t always keep 3 stacks rolling, and for say throwing a single spell on a rogue where you don’t plan on keeping it rolling.
Keep in mind that yanking the hot removal of DKs is also a druid buff for PvP.
Edit: I meant to add that we discussed getting the same effect by having the 2nd or 3rd application of the spell on the same target increase in mana cost. But that becomes pretty complex to explain in a tooltip and might be too mathy for quick calculations when deciding whether you want to roll blooms or not.
[…] We think rolling is a fun part of the spell. It’s just too efficient and makes Lifebloom the best heal per second and heal per mana. We don’t want you to change the way you use the spell, at least in terms of single tank healing. The bonus on a bloom or dispel is just supposed to be a bonus.
If the numbers aren’t right, we’ll continue to tweak them. It may be that the cost needed to go up by 75% instead of 100% for example.”
If the intent of the lifebloom change is to nerf druid efficiency, the intent failed. As shown above, throughput with a slightly different casting style has actually gained, without requiring any more effort on the druid’s part (as measured in, say, GCD usage). Additionally, the increased bloom has improved the efficacy of lifebloom enormously, such that different rotations (fast stack v. slow stack, for instance) can have marked differences on output and efficiency. While I like the change, it doesn’t appear to have addressed the design issue it was intended to.