Raw HPS of Rapid Rejuv Glyph

There is much debate on the real benefits of the Rapid Rejuvenation glyph for druids.  It goes back and forth on how you can't blanket a raid as well with it, or how it all goes to overheal, or how it is worse for tank healing because it causes you to cast Rejuv on the tank more, and thus be able to cast fewer nourishes.

Most of the debate is all anecdotal and hand waving, without any math to back it up. Sooo, let's look at some numbers!

First, I will assume effective healing, and not count overhealing.  This will help make the comparisons a bit more straight forward.

I will use the healing numbers from myself on the last raid we had done that was uploaded to WOL.

My Rejuv healed for 877.0, with an overheal of 66.1%

Since 877.0 is the effective healing done, that means that 877 = total healing * (1-.661).  Total healing done is then 877/.339 or 2587 per tick

Using the same math on the other spells we come up with the following

Regrowth Direct Heal: 2761.3/(1-.628) = 7422.8 per cast

Regrowth HoT: 469.9/(1-.628) = 1263.2 per tick

Wild Growth: 270.7/(1-.671) = 822 per tick

Nourish: 4838.5/(1-.472) = 9163.8 per cast

Lifebloom HoT: 257.2/(1-.590) = 627.3 per tick

Lifebloom Bloom: 833.6/(1-.802) = 4210.1 per bloom

Now, at least when I'm hotting a tank, I will slow roll lifeblooms to three stacks, while keeping regrowth and rejuv up on the tank.

For a moment, let's pretend I have awesome reflexes, and recast every spell exact when it needs to be done, while also living in a frictionless vacuum.  We will also assume haste cap, even though not many people are there yet.

Thus, in a 5 minute fight, on a single tank, we would come up with the following HPS without the Rapid Rejuvenation glyph.

Rejuv = 2587 / 3 seconds = 862 HPS
With 18 second duration, it will be cast 17 times (with some splash over beyond the end of the fight).

Regrowth Direct Heal = 7422.8 per cast.
Regrowth duration is talented to 27 seconds.  Thus we will have to cast this 12 times to keep the HoT up full time.  This equates to 27*12*7422/300 or 296.9 HPS

Regrowth HoT = 1263.2 per tick or 421 HPS

Lifebloom will be cast once every 9 seconds, and bloom every 27 seconds.  That is 34 casts of Lifebloom, and 11 blooms.

The HPS for this one is difficult to model, simply due to the fact that the average numbers above, are from lifebloom being rolled already, and not really a uniform stack size at any given time.  However, for the sake of this excersize, it is really only important that these numbers (and the number of casts) are consistent.

Lifebloom HoT = 627.3 per tick, thus 627.3 HPS

Lifebloom Bloom = 4210.1 per bloom or 168.4 HPS

Now, in our 300 second time window, we will cast:

17 Rejuvs x 1 second cast time = 17 seconds
12 Regrowths x 1.33 second cast time = 16 seconds
34 Lifeblooms x 1 second cast time = 34 seconds

17+16+34 = 67 seconds spent casting HoTs

This keeps our HoTs up and rolling on our tank, thus allowing us to take full advantage of the Nourish Glyph.

In a 300 second fight, this leaves us with 300-67 = 233 GCDs left available for Nourish Spam.

Now, Nourish gives us 9163.8 HP per cast.  9163.8*233/300 = 7117.2 HPS for the duration of the fight.

This gives us a total of:
    7117.2 (nourish)
    862 (rejuv)
    296.9 (regrowth direct)
    421 (regrowth hot)
    627.3 (lifebloom hot)
+ 168.4 (lifebloom bloom)
=================
9491.9 single target HPS without RR glyph.

Now, to add the RR glyph, we simply need to tweak the HPS for rejuv and the number of casts for rejuv and nourish.

Rejuv = 2587 / 2 seconds = 1293.5 HPS

With 12 second duration, it will be cast 25 times

25+16+34 = 75 seconds spent casting HoTs

This leaves us with 225 Nourish's to cast now.

At 9163.8 HP per cast, 9163.8*225/300 = 6872.25 HPS for the duration of the fight.

This gives us a total of:
    6872.25 (nourish)

    1293.5 (rejuv)

    296.9 (regrowth direct)

    421 (regrowth hot)

    627.3 (lifebloom hot)

+ 168.4 (lifebloom bloom)

=================

9679.35 single target HPS with RR glyph.

This is an increase of 9679.35/9491.9 = 1.0197, or about 2%.

If we take into account Living Seed, I suspect the numbers would converge back closer to being the same.

Thus, unless I've completely missed something, the RR glyph for tank healing is essentially up to personal taste from a raw HPS standpoint.  Now of course in practice, and depending on fight mechanics, it could shine more or less (we all know healing is not simply an HPS game).