Greetings priests and other spirit healers,

With the start of WotLK we have seen recurring questions regarding our mana regen, the value of spirit vs the value of intellect and how they affect our mana regen in raids. Many theorycrafts (including some of my own) seemed intent in finding a magic value for intellect or spirit to find the best regen stat. What's surprising is that different research yields different results (even in my own theorycrafts). This inconsistency has always puzzled me and had pushed me to believe that the value of intellect and spirit changes with the quantity of, and the ratio between those stats.

We examine this by calculating the regen for variable amounts of both spirit and intellect. In these calculations I took into account:
- spirit regeneration
- replenishment
I chose to neglect Shadowfiend and Hymn of hope as I deem their impact to be small.

I also assume:
- 85% FSR which I believe is a good average.
- 95% Replenishment. Any interruption can ruin a 100% replenishment and I find 95% far more realistic.
- 30% regen while casting.

We do this for a range of spirit (say 300 to 1500) and a range of intellect (300 to 1500) and obtain a big table with a blur of numbers. Then we do the following for each value in the table:
- we add 100 spirit and calculate the new regen value.
- we add 100 intellect and calculate the new regen value.
If adding 100 spirit yields more regen than adding 100 intellect, we color the original regen value red. If adding intellect would yield more mana than adding spirit, we color the original regen value blue. So red numbers are best improved with spirit and blue numbers are best improved with intellect.
We obtain the following table:


We can clearly see that:
- the 'best' regen can be found on the border between the red and blue zone.
- endlessly stacking intellect or spirit is never the best option
- a comparable amount of spirit and intellect yields the best regen
- at first, intellect is a tad stronger than spirit, but spirit becomes slightly better at higher numbers.

So, what is the best choice of stats? Balance. A healthy 1:1 ratio will yield the best regen value per stat point. For progressed raiders, spirit may yield a tad more regen in the end with a 14:12 ratio.

It is possible that spirit/intellect bonusses from talents may skew this graphic and slightly move the balance. However, these can never have such an impact that one stat will particularly dominate the other and a 1:1 ratio will remain very close to the optimal regen value per stat.

Now that's impressive

Although - do you guys really spend as much as 85% of the time out of casting? Surely many boss fights require more spamming than that, in which case spirit becomes far less valuable. Or am I reading it wrong - you mean 85% of the time casting, with therefore 15% of the time enjoying full regen?

I meant 85% inside the FSR, or five second rule. This means that 15% of the time I enjoy the full mana regen.

Sounds very reasonable - I shall be pointing priesties and trees I know in this direction.

A lot to think about, good job. I like the chart.

Considering the 5spi/2mp5 disc relationship how would this effect the 1:1 ratio? Clearly Spirit has less value for me as a disc priest, roughly 1/2 the value now.

These calculations did not include Rapture, nor the mental strength bonus or spirit of redemption. This is just a study of adding spirit and replenishment and checking the balance.

However.. I can tell that the spirit bonus from SoR and intellect bonus from metal strength don't skew the graphic all that much. I've done the works but the difference in results is rather subtle so I didn't bother to throw in endless charts to show a minimal difference.

Rapture on the other hand... that is hard to tell. I haven't examined that enough to give you an answer. Admitted.. I was only keeping holy priests in my head.
Vigil... I'll try to work Rapture out and add a chart with it.

I've published the tool I used to make that chart and added a few options:
- % stat modifiers for int and spirit
- % FSR selection
- % regen while casting
- % replenishment
- MP5 value

It's available here:
http://zusterke.orderoftheathanor.eu/to ... =intspirit
(edit: New Link!)

And this link gives you the settings I used:
http://zusterke.orderoftheathanor.eu/to ... &sb=0&ib=0

If you check the MP5 option, you'll see half your table go green. But if you add a 15% bonus to spirit and 10% to intellect ('blessing of kings' and 'spirit of redemption') you can see how these buffs dramatically increase the value of intellect and spirit:
http://zusterke.orderoftheathanor.eu/to ... b=10&mp=mp

I'm still working on a feature to include rapture but I'm still investigating how to model it...

Enjoy

and thanks

Rapture is interesting because it is active regen rather than passive regen. It works more like a variable reduction in mana cost.

This is very similar to some maths I did last month. My approach was to solve for the optimal proportion spirit, assuming you could divide some total of stat points between spirit and intellect. I considered spirit-based regen and replenishment and shadow fiend.

It's possible to solve the whole thing. It's not a pretty expression, though. I'll copy it here for posterity, but Z's nice tables give the same answers, via a more graphical method.

optimal-proportion-spirit = 1/(r^2 s smult^2)(-23.6392 imult + 0.666667 r^2 s smult^2 - 23.6392 Sqrt[ imult ( imult + 0.0282017 r^2 s smult^2 ) ] )

where

r is effective spirit regen rate ( = p(0.3) + (1-p)(1), where p is proportion of time inside 5sec rule)
s is total amount of stat points to divide between spirit and intellect
smult is the multiplier of spirit (1.1 with BoK, (1.1)(1.05) with SoR, etc.)
imult is the multiplier of intellect ( (1.1)(1.15) with Mental Strength and BoK, e.g.)

Ah yes.. it resembles a strategy I tried as well a while ago. I ended up trying to make a 3D plot of the spirit vs intellect graph and attempted to extract the optimal line using (partial) derivatives. Unfortunately I got lost. The numbers my calculations yielded weren't very descriptive and I found myself trailing into a increasingly difficult calculations.. till I backtracked and jumped back to the basics: a table where the regen is just calculated. Amidst the blur I looked for patterns that should be there till it hit me I could just let the calculator check those out for me
The color indication was the next logical step. The border between the int and spirit-zonde is actually the line I tried to calculate directly.

Regarding Rapture.
I feel somewhat odd trying to include this talent in the calculator. As it depends on an action or spellcast to take place, my instincts would tell me to include this in a healing efficiency calculator. On the other hand... it relies on your manapool which means it depends on your mana regen strategy as well.
To include rapture properly, I would need to include parameters for cast speed, overheal and lost absorption.
I would calculate it as follows:
- Give rapture spells cast per 5 seconds -> <rapture spells per 5 seconds>
- Give effective healing or absorption done by these spells -> <effective healing/absorption %>
Conclusion:
Rapture = <rapture spells per 5 seconds> * <effective healing/absorption %> * 2.5% <mana pool>

Does that sound right?

That sounds like a good approach. I remember seeing some math on Rapture over on Elitist Jerks. There are subtle issues with exactly how Rapture returns mana to different spells. But given some parameterized average rate of return, and a series of examples using actual rates, it should be easy to include Rapture in an approximate way. But if you had exact proportions returned for each spell and let the user just input casts-per-minute and an effective absorb rate, then yes, you could get exact answers for a wide range of casting scenarios.

My thinking has been that Rapture makes intellect super powerful, through a feedback. First, it encourages casting. Then, casting diminishes the usefulness of spirit, because you spend more time outside the 5sec rule. This in turn makes time outside the 5sec rule less valuable, encouraging more casting.

Given that a Disc priest will have a (1.1)(1.15)---BoK and Mental Strength---multiplier on intellect, seems like intellect is going to beat spirit by a kilometer for Disc priests.

Doesn't Rapture also make spellpower a regen stat? Including that could get complicated.

My memory is also that Rapture counts total healing, including overheal, to compete mana returned. So you can leave out overheal. But that may be different now, and I have not played Disc since beta.

Ahh yeah... I forgot that it scaled with the amount healed, not just the effective % done. Well I clearly haven't examined Rapture enough.. To be honest, that's a whole lot of factors working on the mana regen model

I'll look up more details about the talent and see how I can integrate it. It might take a while though

I'll happily wait.

I'm about to ding 80 this weekend (I hope) and I'm starting to see drops or rewards that I could consider an upgrade. For now I'm favoring Int well over Spt but trying not to let the gap between them get to great. On EJ threads I've read almost everyone is saying get Int, forget Spt. But the math they use is way beyond what I can grasp.

So I'm going with trial and error approach grabbing gear with Int in it and trying to get Spt on enchants or gems which are more easily replaced. I'm afraid if I go to much on Int side and later I see I need more Spt I'll have an hard time getting that Spt back. I also hate to be rolling on gear I'm not sure it's the best for me when someone else might be better off with it.

So far I've noticed that my regen dropped a lot when I hit 75 but since my mana pool is growing obscenely fast it has not been a problem so far.

If you need raw data, let me know what I can use to gather it and I'll send it your way.

My beta notes on Rapture (copied from some play tests posted to EJ) have it returning (for direct heals):

R = min[ (H/9330)(0.025)M , (0.025)M ]

where

R is the amount of mana returned
H is the total amount healed
M is total mana pool (max-mana)

Mana return is capped at 2.5% of your mana pool for each heal, so that is why the min function is there. So assuming a mana pool of 20k, you can get a max of 500 mana returned per cast.

Consider a Greater Heal landing for 9330 (easy to do these days), to make the math easy. Then with a 20k mana pool, you hit the mana return cap exactly (500). If you heal more than 9330, the extra healing results in no extra regen.

This does indeed make it hard to model. Discontinuous functions are a pain in the butt. But I can still infer one thing right away: Intellect is better than spellpower for Rapture. Once you've hit the mana return cap (0.025*M), spellpower provides no extra regen. Intellect is the only way to do it (through this talent, at least).

Despite the complexities of the imagined global function in this case, it's easy to do napkin-math estimates for single casts. Suppose we are chain casting Greater Heal. Suppose it lands for an average of 9330 (to make the math easy---I already average about this, with blue 80 gear and a few BT epics) every 2.5 seconds. The gain in mp5 from each point of intellect will be:

Delta-R = (0.025)(15)(1)(1.1)(1.15) = 0.47 mana => 0.94mp5.

With BoK and Mental Strength, you get 19 mana from each point of intellect. You can cast 2 GHs in 5 seconds, so it's almost 1 mp5 gain per point of intellect (but only if you are casting).

Those are some golden formula's. That's exactly what I'm looking for. Do you believe the rapture formula is still accurate?

Also, is H the raw healing done or effective healing done? I'm guessing the latter.
Given that info, I might ask Disc priests to check out some values of their healing style on WWS and use those as parameters. Should be doable I think.

As far as I know, that's still the right formula. But I really haven't kept up Disc mechanics, to be honest.

The H is total healing, not effective healing. You can test this by speccing into Rapture and healing yourself while at full health. You still get mana back (or at least you did back in beta!).

Or, to save some gold in re-spec, I can do that for you.
Since I'm the one pressing for Disc results it seems only fair (and I'm already specced for it).

Recounts stats ok or do you prefer other data source?

Ehm, Recount sounds like an excellent start. We'll see if we can do the works with just that.