Thursday, March 26, 2009

On Replenish / Revitalize

Patch 3.0, with edits on 3.1 changes
Replenish talent. 3.1 will see it become Revitalize.

This talent seems to be one that druids either love or hate. Among those that hate the spell, reasons tend to include:
  • they don't cast rejuvenation that much, or
  • they can't easily see the benefits because it is so passive and uncontrollable, or
  • they do the numbers but judge its worth based on the raw mana cost of rejuv, rather than accounting for all the times they cast rejuvenation WITHOUT this buff anyway, or
  • they PvP so would like to include PvP talents in their build rather than this, or
  • they read bad things about it and never gave it a chance.
Also, they may not've taken into account the upcoming addition of having it proc off of Wild Growth. I loved the talent even before this change; adding Wild Growth just makes it all the more desirable for me, and opens the door to those players who don't cast rejuvenation as often.

(EDIT: the math in this post follows additive probability, which appears to be supported by the gathered WWS data.)

Getting into the math: Rejuvenation

Personally, Rejuvenation accounts for an average of 28% of my healing. If it's proccing energy back to people, all the better! Following/building on Phaelia's work that it has a proc rate of .9 procs/cast, which matchs the 15% proc chance per tick on the tooltip assuming 6 ticks from Nature's Splendor: review of my own WWS reports has confirmed this. For example, in a recent Malygos/Naxx10 combined raid where I was the only resto druid,

  • I cast rejuvenation 820 times.
  • Replenish was gained as a proc 734 times.
  • 734 procs / 820 casts = 0.895 procs per rejuvenation cast.

This proc rate assumes the druid has the Nature's Splendor talent, which adds an additional tick to Rejuvenation, for a total of 6 ticks. The 4-pc T8 set bonus will add yet another tick, increasing Replenish's proc rate by an additional amount (EDIT: unfortunately, the extra "tick" from T8's set bonus does not seem to be counted as a tick of rejuvenation, thus does not proc revitalize, but I will leave the math here for now):

To confirm the 15% proc chance:
  • 6 Ticks w/ Nature's Splendor per cast
  • 0.9 average proc-rate per cast
  • 0.9 procs / 6 ticks = 0.15 procs per tick

Adding a 7th tick with T8:
  • (0.15 procs per tick) * (7 ticks per cast) = 1.05 procs per cast

This means that, in the long run, with Nature's Splendor and 4-pc T8, a rejuv is practically guaranteed to proc at least once every time you cast the spell, unless the RNG is especially cruel! Usually this will play out by getting 2 procs in one spell cast, and 1 or (more rarely) none in other casts. Overall, though, assuming you are getting an average of 2.5k heal ticks, your rejuvenation will now not only heal for 17.5k over 18 seconds (with T8), but also it will most assuredly grant at least a small portion of energy to the target as well.

Per proc, replenish will return:

  • 16 runic power to DKs
  • 8 energy to cats/rogues
  • 4 rage to bears/warriors
  • 1% of total mana pool to mana users

With every 18-second (talented) rejuvenation cast, replenish will return an average of:

  • 14.4 runic power
  • 7.2 energy
  • 3.4 rage
  • 0.9% mana pool

To compare how this stacks up against other energy-returning talents, we can look at the per-minute returns, assuming an 18-second duration that is refreshed immediately, resulting in 3.33 casts per minute:

  • 47.9 runic power per minute
    • Compare to Butchery (Blood), which is 24 runic power per minute.

  • 23.9 energy per minute
    • This has been found by others to be a 4% increase in yellow damage, which would correlate to a 4.6% increase w/set bonus.

  • 11.9 rage per minute

  • 2.9% mana per minute
    • Compare to Replenishment, which is 15% mana per minute. For mana users, this equates to:

    Mana Poolmp5
    6k12 mp5
    8k16 mp5
    10k20 mp5
    13k26 mp5
    15k30 mp5
    18k36 mp5

In graphical form,

(Edit: ignore the yellow line)

So, compared to other sources of energy, Revitalize off of rejuvenation is an amazing proc for runic power, very nice for cats/rogues, okay for any rage-starved bears/warriors, and no where near the power of a true replenishment for mana users.

A perk to a raid heal:

In the long run, you can really see the benefits across the whole group, just from using rejuvenation normally as a raid heal. In a single 3.5-hour raid (10-man), I had replenish tick 734 times across the group out of 820 rejuvenation casts, averaging about 3 procs per minute over the course of the raid. Most of these procs were on tanks because I steadily keep rejuvenation on them, but other raiders saw benefit from these procs as well, since I like popping them a rejuv as a raid heal around wild growths (keeps em swiftmendable and lasts a long time).

Among the replenish numbers from rejuvenation, this resulted in almost 14k mana returned to myself, 13k mana to our often mana-starved prot pally with a relatively tiny mana pool, and 1500 rage to our feral tank. I think that's pretty impressive for a purely passive proc on a spell I cast to heal with, imo.

PTR 3.1: Procs from Wild Growth

Assuming that the revitalize will have the same 15% chance to proc per tick as rejuvenation does on live server, a base of 7 ticks of wild growth per cast results in the same chance to proc per spellcast as does a Rejuvenation with both Nature's Splendor and the 4pc T8 bonus. An important difference to note is that Wild Growth lasts 7 seconds, and Rejuvenation lasts 18 seconds (talented): 62% less time taken to have the same number of ticks occur.

With every 7-second WG cast, revitalize will return an average of:
  • 16.8 runic power
  • 8.4 energy
  • 4.2 rage
  • 1.05% mana pool
...per person hit by the WG.

This is pretty amazing, especially when you then consider that each cast will hit 5 people (or 6 if you have the wild growth glyph), and the casts per minute equate roughly to 8.6 casts, or 10 casts if you have a large group (so that you aren't overwriting ticks on individual people) and you are casting WG on every 6-second cooldown.

Casting chain WGs every 7 seconds, revitalize will return a per-minute average of:
  • 144.5 runic power
  • 72.3 energy
  • 36.1 rage
  • 9.03% mana pool - much closer to the 15% of replenishment.
...per person hit by the WG.

Frankly, I'm worried that they're going to nerf the proc chance on Wild Growth. The PTR tooltip does not say specifically that it has a 15% chance to proc per tick of Wild Growth: that is simply being assumed. (EDIT: Update: the WoWhead PTR tooltip has been updated to re-include the 15% proc chance for rank 3, I noticed as of 4/12/09). I do hope that they will release the exact proc chance after they are done testing on the PTR and release this change on the live servers.

An important PTR note to include is that spirit-based mana regen is being nerfed, which may make these small extra procs to mana users quite more useful when these changes go live.

Short of the Long:

While entirely passive, this talent can return a lot of energy to the people you are healing, provided you actually make use of rejuvenation and have buffed it to have more ticks. It's no innervate, but it is well worth a 3 talent point investment, in my opinion. With the upcoming changes to include wild growth, there is little reason not to take this talent, unless for some obscure reason you rarely cast either rejuv or wild growth at all.

The key to working with this talent is to avoid casting the spells JUST for the purpose of the revitalization. Rejuvenation and Wild Growth are powerful heals if used properly, and together, they make up an average of 50% of my healing. Cast the heals to be heals! Let revitalize do its magic in the background. The spells that the talent affects are still great healing spells, and healing should remain their primary function in your mind.

Of course, in the case that there's not much for you to heal and/or you have plenty of spare mana, you can still decide to throw this around the raid just to grant extra energy to expedite dps. As flexible as druids are renowned to be, we would be remiss to completely ignore that the talent could be used as a small boost to our buddies' energy, even though the mana cost to ourselves is quite inefficient for something that isn't really healing them (again, assuming they aren't taking damage). This usually occurs when you find that your raid is outgearing an instance.

When you do find yourself in this situation, be aware that some classes may be better targets than others based on how useful that amount of energy may be to their class--or their playstyle. My priority as far as replenish is concerned is thus:
  1. Deathknights (but only the DKs that actually USE UP their runic power),
  2. Cat Druids (most of their damage is based on yellow hits),
  3. Rogues (less of their damage is based on yellow hits than cats),
  4. Warriors and Bears (favoring whoever is the most rage-starved),
  5. and then Mana Users (tanks should always have rejuvenation ticking, regardless).
Deathknights in particular receive an amazing amount from its proc, and I've had several DKs thanking me for it. Sometimes I will cast it on DKs before a boss pull so they can tick up the power to buff Horn of Winter. For others, the change is much smaller so they don't usually notice the tick themselves, but it is still a bit of energy that they did not have before.

So, I really like this talent, even before Wild Growth is to be added to it. Wild Growth's addition only empowers this talent further in my eyes.

~ Of course, if you find holes in my math, please let me know :D ~

Kudos to Phaelia of Resto4Life on her original work regarding the Replenish talent.


Dúnadan said...

Nice Text, With the Change that WG also have the proc this talent will be more awesome than now^^

Anonymous said...

It's nice to see someone promoting the replenish/revitalize talent. I used to be specced for it was recently forced to respec when I joined a new raiding guild. They also didn't appreciate my talents in living seed. Any chance you can have a run through that also?

Kae said...

Haven't really looked into the math on Living Seed, but I do know that the patch today (3.1) is fixing one of living seed's most common complaints: that it doesn't account for overhealing. But, if you get even as little as 2% of extra, passive healing out of 3 talent points, when it takes 5 talent points to get 4% (master shapeshifter), then why not?

In some cases, Living Seed's usefulness does depend on your raiding situation. If you're told to sit in a corner and heal the raid while the pallies/disc priests do all the major tank heals, then you're going to be casting many crittable things, and if they do seed, it may wear off before that DPS gets another hit on them.

Make your own judgement, compare to what you'd spend the talent points on otherwise, know how the talent works, and be ready to back yourself up with WWS reports if necessary :)

Kae said...

My proof-reading failed, cuz I was running out the door to go buy dinner. And cake.

"then you're NOT going to be casting many crittable things, and if they do seed, it may wear off before that DPS gets another hit on them."

Saervild said...

Your math is probably off. If the proc is constant at 0.9 per cast, it should not be affected by adding a tick, unless the effect is calculated with each tick. (A hint, with your math you would have a 105% proc each cast, and it would go against your assumption that the proc / cast was constant)
You'd better re-check these calculations, since if we go by a 0.15 proc per tick you'd have a (1-0.15)^6 (or ^7 with T8) = .32 chance of the proc not to occur per cast, which is much higher than the 0.105 gathered from your data.
My math leads me to the proc chance per tick being
(1-x)^6 = 0.105
(1-x) = (0.105)^(1/6)
x = 1 - (0.105)^(1/6) = 0.313 (approx)
and calculating the proc per cast with T8 set bonus is
(1-x)^7 = 0.721 (approx) => proc / cast = 0.928 (approx)

Saervild said...

Last line should be:
(1-x)^7 = 0.0721 (approx) => proc / cast = 0.928 (approx)and nothing else

Kae said...

Thanks for pointing this out.

The 15% proc effect is per tick. It's what the tooltip says, and the base of what we have to go on. In comparison, repeated WWS reports have shown a 90% chance to proc per cast in a large sample size for 6 ticks. I would think it reasonable to imagine that your chance to proc per spellcast would go up if you added a 7th tick to the spellcast.

I'm not particularly a math guru, but I did go poke a math guru about it (<3 Jaemon). After walking me through additive vs multiplicative probabilities, he suggested that the tooltip might be lieing, just as your math suggests. Honestly, my large-sample should've resulted in a .633 procs per cast with multiplicative probability (0.377 chance to not proc), as my rejuv only had 6 ticks (no T8 yet :) )... but it did not. It gave nearly 0.9 per cast, which divides so nicely by 6 to 0.15.

There is certainly something amiss. It may be that the tooltip-writers fail as much as I do at additive vs multiplicative math, and the 0.15 is misleading our math. Hmm.

I want to grab revitalize numbers from WG to compare, but it may be difficult to separate them now in WWS reports, between Rejuv ticks and WG ticks if the two have different ticks per spellcast. I'll have to gather data from raids using only one spell or the other... which will be awkward in the healing department!

Anonymous said...

Each tick is a Bernoulli trial with probability p (15% in this case). If we have n trials (# of ticks per cast) than the expected value (# of successful trials) of the resulting binomial distribution is n*p or 0.15 * 6 = 0.9. You can think of it as flipping a coin a certain number of times. You assume you will get heads half the time, so how many heads would you expect to get in 10 flips (trials). n*p = .5 * 10 = 5.

Kae said...


*nod*, that is the math I was originally going on in the post. The thing is, once you get up to 7 ticks per cast (as with Wild Growth), you now have n*p = 0.15*7 = 1.05, or 105% chance per cast.

There is still a chance that it might not tick, even though you have 105% chance. The RNG is fickle and cruel and evil (it has burnt me many a time, don't get me started on the Giant Sewer Rat), so you might not get a revitalize proc out of a single cast, even though the additive probability (.15 + .15 + .15 etc) is 105%. That is what is wrong with the math... it goes over the 100% maximum of chance, and yet it still might not proc. It works as a rough estimate over a large sample size, but is not statistically sound PER CAST.

It's getting into some pretty deep statistics, but... in order to really be able to present this talent well and get the true chance to proc per spell cast, I want more data. And to get data, I need more raids and WWS reports. And to get raids and WWS reports... I need the instances to stop crashing and dropping my treedruid in limbo-land :D

If anyone does have a sample wws report with number of times you cast the spell vs number of times revitalize procced, let me know. Just keep in mind that data with both a 6-tick rejuv and a 7-tick wild growth will not let us easily separate where those revitalize ticks procced from.

Anonymous said...

It's not 105% chance to proc per cast. It's that you expect it to proc 1.05 times per cast.

Anonymous said...

If you look at the example of flipping a coin (which is what this ultimately boils down to), after 20 flips you expect to have gotten 20*.5 = 10 heads. Even though you expect for that outcome to occur 10 times, there is still a .5^20 chance that you will get 20 tails.

Anonymous said...

The probability that it will proc at least once over the course of 7 ticks is 1 - probabilty of it not proccing, or 1 - (1-.15)^7 = 0.68 = 68%

puckster said...

You are looking for the *expected value* of independent events. You only care about "how much mana will be returned on average". Not "what is the probability that revitalize will proc at least once".

The probabilities are independent.

1 - It procs
0 - It doesn't.

= (1*.15) + ... + (1*.15)
= 7*.15
= 1.05.

Casting it to a simpler example. If Revitalize had a 50% chance of proccing on each tick of a spell that ticked 20 times. How many average ticks would get? That number is 10, not something less than 1. We could just as easily say it could tick 1,000 times with a .9999% probability.

Anonymous said...

Dude...yr original calculation is wrong. You stated that you got 734 procs out of 820 CASTS. This is incorrect - you got 734 procs out of 4920 TICKS (820 x 6)which works out to be 14.91%. So it seems out of the largish data sample you had the Blizz math bears out (in fact you were slighly(0.9%)unlucky when it came to procs)

Anonymous said...

further to the above - lets assume that the 15% proc rate is accurate and see how this pans out:

Keeping Rejuvenation on a target permanently in a 9 minute fight (I'm using 9 mins 'cos it keeps the math simple) you get:

9 mins = 540 secs
Rejuv (NS) = 18 secs
Rejuv ticks every 3 secs
therefore 180 ticks total

15% of 180 = 27 procs of Revitalize

27 x 8 energy = 216 energy over 9 mins
27 x 4 Rage = 108 rage over 9 mins
27 x 16 runic power = 432 runic power over 9 mins
27 x 1% mana (lets assume 20k) = 5400 mana over 9 mins

That's what you could 'reasonably' expect to get for your investment.

Kae said...

Saying I got x procs per cast is the exact same thing as saying I got x procs per 6 ticks... assuming I never over-wrote the spellcast to loose a tick. However, we can't assume that I got always 6 ticks per every cast, because it does get over-written when renewing it to keep it from falling off the tank or others (for purposes of swiftmend, etc). It is safer to average it out per cast using data from a live raid, rather than assume the most ideal situation where we'd only ever renew the spell the instant it made its last tick on the target... only in that perfectly ideal situation can you then assume that there would have been 820x6 ticks. Raids are never ideal situations.

Wild Growth gets overwritten before the final tick often enough, as well.

Work's kept me too busy to dig back into the math as of yet, but I do plan to.

Pathis said...

Great information Kae! I am a big fan of the talent as anything which makes the spells I already use better without any effort on my part is a bit of a no brainer. Thanks for coming to its defense.

Just to clarify though, your math presumes that none of the ticks for either Rejuvenation or Wild Growth were complete over-heals, correct? It has been my observation that Revitalize doesn't proc unless some healing was applied on the underlying tick.

Kae said...


Revitalize will still proc even if the healing wasn't applied. You can see this effect by dropping a rejuv on players who are out-of-combat (and full health); it is likely to proc once before it wears off, and makes a little graphic effect and sound effect when it procs, and if it was a warrior or DK, you should see their power bar reflect their gain.

I used to use this to the raid's advantage when buffing for a pull, by dropping the DKs some RP for Horn of Winter (before the buff was changed to not cost RP).