The 2.4 Mana Regen Series
Note: The Graph, decision tree, and calculator have been updated as of 3/17/2008 to correct a couple of logic errors and to add the marginal values for Spirit and Intellect vs. MP5.
To help you determine the value of your personal MRC and resulting base mana regeneration. I’ve created a JavaScript-based mana regeneration calculator. It determines how you can optimize your Intellect vs. Spirit ratio by taking into account the following variables:
- Current Intellect and Spirit (raid-buffed)
- %FSR
- Fight Length
- Number of times Innervate is used
- Cast Frequency (for determining proc rate on the two trinkets included)
- Intensity (or Meditation) and Dreamstate
- [Darkmoon Card: Blue Dragon], [Bangle of Endless Blessings], and [Primal Mooncloth] set bonus
From these variables, we can determine the following:
- Mana Pool
- Spirit/Intellect-based Mana Regeneration (excluding the effects of additional MP5 from gear)
- Recommended Spirit if Intellect is held constant
- Recommended Intellect if Spirit is held constant
- Returned mana during Innervate and whether Innervate will completely refill the mana pool
- What type of weapon is recommended during Innervate
Table of Contents:
- Using the Calculator: An Example
- Sample Graph with Regions of Significance
- Behind the Scenes: Decision-Making
- Behind the Scenes: Formulas
Using the Calculator: An Example
As an example of how to use the calculator, I’ll use the hypothetical Restoration Druid, Thaelia:
Thaelia is a member of the questionably-Latin-named guild "Aegis Vesta." Ever the trendsetters, AV is currently working its way through Serpentshrine Caverns but is stalled out on the Morogrim Tidewalker encounter. Thaelia estimates that the fight — if ever successful — will last approximately eight minutes. Raid buffed, Thaelia has 450 Spirit and 575 Intellect. Naturally, she has Intensity and plans to use Innervate once in this time period (and to scowl at the Holy Paladins for asking for it). To boost her mana return during Innervate, she wears the Bangle but does not have the Darkmoon Card: Blue Dragon. She thinks that she casts every 2.0 seconds. Using the RegenFu addon, she determines that she spends about 85% inside the Five Second Rule on this encounter.
Plugging these values into the Mana Regeneration Calculator, she sees that her current estimated mana regeneration is 321 MP5. She can also see that Innervate will return more mana than she has and that she should be using a High Intellect weapon during Innervate. From the optimization recommendations, she can see that she can either choose to optimize by decreasing her Spirit from 450 to 378 or by increasing her Intellect to 628. She opts for the latter option which will boost her overall mana regeneration under these conditions from 321 MP5 to 339 MP5.
In the above example, Thaelia chose to optimize by increasing her Intellect rather than decreasing her Spirit. This may seem like an intuitive choice, but keep in mind that had she opted to scale back her Spirit (and thus mana regen), she could have shifted those points more toward +Healing.
Sample Graph with Regions of Significance
Using the conditions described above (8 minute fight, 1 Innervate, Intensity, Bangle, 85% FSR, 2.0 sec cast frequency), we can generate a graph of the relative value of Intellect to Spirit and the resulting MP5 when these are optimized. Please keep in mind that this graph is under very specific conditions and should not be used to make gear decisions unless your conditions happen to match those described above. This graph is intended to help demonstrate significant trends among these stats.
I have color-coded three significant bands on the above graph, each of which represents a change in the way you optimize mana regeneration:
- Yellow
In the first band, Innervate does not yet completely fill your mana pool so Intellect is not especially valuable. - Purple
At the start of the second band , Innervate has caught up to your mana pool. As you progress through this band, your best option is to increase Intellect so that Innervate will continue to max out your mana pool. During this band, Intellect is significantly more valuable than Spirit. In this example, 330 Spirit is worth 540 Intellect. - Orange
Because Innervate essentially gives you a second (or third) mana bar when it’s used at these higher values, the value of Intellect is significantly higher than Spirit for most of this band. The value of Spirit does approach it at the uppermost values (900+), however, as the extra mana regeneration outside of Innervate begins to outweigh the contribution to mana regeneration from Intellect during Innervate. At this level of gear, if you continue to stack Intellect to maximize Innervate, you will actually hurt your mana regeneration outside of Innervate to such a degree that you will be disadvantaged overall. Should we increase the number of Innervates used during the same time period, this band will shift slightly to the right.
Note: You can build a personalized graph by specifying your own conditions and then graphing input Spirit as it increases vs. the recommended Intellect and resulting mana regeneration.
Behind the Scenes: Decision-Making
Thanks to insight from readers MK and Concillian, I discovered that Intellect was more valuable due to the fact that Innervate will eventually completely refill your mana pool. This required a significant rethinking of the way optimal values were calculated. The following is a decision diagram (gg, ISDS 3100) that will hopefully help you visualize some of the logic involved in optimizing Spirit (the same logic was used for optimizing Intellect):
Those with programming experience (or insatiable curiosity), are welcome to examine the JavaScript code itself to see how the many decisions interact with each other. I’ve tried to name functions and variables in a clear manner and to provide comments at important decision.
Behind the Scenes: Formulas
Building upon the math presented in 2.4 Mana Regen - Part 1: The Basics and with a few key adjustments in which the effects of Innervate were completely isolated from the calculation of MRC, here are the formulas used in the calculator. Heavy theorycrafters are encouraged to take a look and point out any perceived inaccuracies:
Let:
- c = 5 * 0.009327
- MRC = Mana Regeneration Coefficient, without Innervate
- m = MP5
- t = fight length in ticks
- S = Spirit
- I = Intellect
- d = Dreamstate (0 or 1)
- b = Bangle (0 or 1)
- n = number of Innervates
The last formula derived above is for determining the value of Spirit relative to Intellect, assuming Innervate doesn’t completely fill your mana bar. To determine the value of Spirit relative to Intellect when Innervate does completely refill your mana bar, the following formula is used:
29 Comments
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March 16th, 2008 at 7:06 pm
I tried the calculator - pretty cool! Where does mp5 from gear figure in?
March 16th, 2008 at 7:08 pm
I just looked at that equation after working today, and now my brain hurts. However, this is an excellent read for all those classes who like regen mana.
March 17th, 2008 at 3:11 am
I use CasterWeaponSwapper to bring in the Ethereum Life-Staff with a spirit enchant whenever I get innervated or my Darkmoon Card procs. Is there any way to account for this in the calculator? Is that what “Innervate Weapon” Means? Which spirit/intellect value should I include in the calculator, the one that applies during innervate/Blue Dragon proc, or my spirit/intellect the rest of the time?
March 17th, 2008 at 6:53 am
I’ve been trying to comment, but either your website is eating my comment or just not displaying it…
I had a few questions, etc.: The “mana pool” it says my character has does not match on the live realms. I’d love to go through the math on that formula, but I cannot discern all the variables (What is “i”? Should it be “I”?). What formula did you derive for dm/dI? You said that the mana regen model is for priests and druids, but you account for innervate only, not shadowfiend (probably too many variables in that).
I’m a little worried people will take the values from your calculator and use them directly to make decisions about how to gear themselves. For example, priests get 1/4 spirit converted into +heal. That is very significant, and increases the overall benefit of spirit for priests. Your calculator just deals with mana regen. Hopefully people realize that it isn’t a singular solution to everything, just one aspect of being a healer.
Anyways, nice job with the calculator. It looks like you spent a lot of work on it.
March 17th, 2008 at 9:44 am
@Aurth: I believe that CWS lets you specify the weapon you want to swap to during Innervate? (I’m not sure; I use Evocation2 right now.) If it does, you should swap to the weapon type recommended for your current values. So if it says “High-Intellect” you may want to look at getting a weapon that focuses on Intellect and enchanting it with +20 Intellect, too. You should include your normal, raid-buffed Spirit/Intellect values while not under any temporary effects. As far as Darkmoon Card, that’s a cool idea to swap weapons during its effects. However, that’s something I can’t build in directly. Basically when your DMC procs, as long as your Spirit is less than double your Intellect and you aren’t full mana, you will want to swap in a Spirit weapon, even though you will probably often be swapping in an Intellect weapon during Innervates to get the extra mana.
@MK: The function used to determine mana pool size is called “getManaPool(intIntellect)”. This is the formula used:
var intLess20 = intIntellect - 20;
if (intLess20 > 0) {
return 20 + (15 * intLess20) + dblManaAt70;
}
else {
return intIntellect + dblManaAt70;
}
I pulled this from WoWWiki, and dblManaAt70 is 2374; can you see a problem with it?
dm/dI is the third line down in the formula. I am not sure what “little i” you are referring to, but little i is generally used as a counter variable for looping.
Shadowfiend is unaffected by either Intellect and only slightly affected by Spirit if you are deep Discipline-specced (from the additional spell damage from Improved Divine Spirit). So it will essentially have no affect on Int/Spirit since it’s extra, free mana, kind of like a Pot.
I see what you’re saying about the additional benefits for Spirit (Druids experience something similar). However, given the same number of itemization points, it’s best to spend them in such a way that the two stats are balanced to maximize your return. Then you could spend the remaining itemization points on bolstering your +Healing directly. Of course, this is in a perfect world where you have access to any number of items at a given time (I would like to live in this world).
One day, I hope to include a +Healing comparison in this calculator, but for now users will have to consider those factors on their own.
March 17th, 2008 at 10:15 am
wow, will have to try it from home tonite. Great work, your dedication to helping droods analyze their gear and play style should be rewarded….
March 17th, 2008 at 10:30 am
@Sibohan: I’ve added a comparison of Int/Spirit to MP5 (I assume that’s what you were asking for). Thank you for requesting that as it helped us find and correct a few important bugs with one of the ways that optimal Spirit was being calculated!
@Crythia: Ty =) I hope your brain feels better soon!
@Aurth: You will want to switch to whatever weapon is recommended by the Weapon Swap result for your current stats. This is going to cause a problem for the Evocation2 addon since I think it automatically selects the highest Spirit combination it can find in your inventory. Hopefully the author is taking this into consideration. You should use your raid-buffed values for Intellect and Spirit and not include any temporary effects that buff either. And great idea to do a weapon swap with your Darkmoon Card; that’s something I hadn’t thought of. Something like that would be difficult to build into the calculator directly, but you will probably want to keep swapping to a Spirit-based weapon during those procs (unless you’re full mana).
@MK: I too have been having difficulties commenting. =( I had written a very long reply to your comment, but my site ate it! T_T
The function used to determine your mana pool is getManaPool and is a function of Intellect. It’s based on a formula from WoWWiki and looks like this:
var intLess20 = intIntellect - 20;
if (intLess20 > 0) {
return 20 + (15 * intLess20) + dblManaAt70;
}
else {
return intIntellect + dblManaAt70;
}
Where dblManaAt70 = 2374 (this is our free, base mana regardless of Intellect). Do you see any problems with this formula? It’s an easy change if I can tell what’s wrong.
The formula for dm/dI should be the third line down.
Shadowfiend, while an important regen tool for Priests, is unaffected by Intellect and mostly unaffected by Spirit (the only exception being heavily Discipline-specced Priests who have Improved Divine Spirit, affording slightly more spell damage and making their Shadowbuddy hit a bit harder). Since it isn’t tied to Int or Spirit, it didn’t seem appropriate to include here, and as you say, there are too many variables involved to really add it, even as a static contributor.
What you say about +Healing is true and Druids actually experience something similar, however, this calculator is intended to help people make direct decisions about how they should gear, gem, and enchant. After all, given a static number of itemization points, if you optimize your Intellect and Spirit in the best ratio to maximize your mana regeneration, you will have more “free” points to spend on directly bolstering your +Healing (which is always going to be cheaper than bolstering it via increasing your Spirit for the same purpose). This is of course in an ideal world where you have access to an infinite number of items and gems at all different values (I would like to live in that world!), but it’s nonetheless a good guideline. I would eventually love to include a +Healing comparison with this analysis, but in the mean time, people will have to determine this separately and based on their own needs and experience.
@Falina: Thank you! I hope that it’s as helpful to everyone as it has been for me. =)
March 17th, 2008 at 5:23 pm
oooooooo! What a fun little toy! A very slim easy to understand calculator for those of us that don’t like equations like THAT!
One note for those of us that do give away our innervates to a friendly neighborhood priest or what have you, this is an excellent link for them so that they might make a more informed decision on their choice of innervate weapon. Just something I was thinking on.
Oh and also looking in on whether or not the priest trinket is overkill. I noticed that on the bangle and card description with higher int. Maybe putting such a trinket in the calc would be nice for priests but this IS a resto blog. /shrug just my off topic thoughts.
March 17th, 2008 at 5:37 pm
Hi Phae, thanks for the reply. Shadowfiend is affected by spirit with the Spiritual Guidance talent which most healing priests take, but it is a pain to model as you’d likely want to know the total spell damage number, too. I see dm/dI now (don’t know how I missed it)! I still don’t understand what “i” is in your top formula. I’m not sure what is wrong with the mana pool number, but I’ll see if I can figure it out.
March 17th, 2008 at 7:24 pm
@Zackoria: That was exactly what I was hoping to achieve. Something that didn’t require you to download a file or enter a bunch of values or apply an equation. There’s just so much involved with this calculation that I’m ecstatic to be able to share this! Once I’m sure that everything with this is A-OK, I plan on sending it to a few of the Priest blog authors, as well, with the hopes that they’ll share it with their readers, too! And … great idea about that trinket. I’ll have to see what Mr. Phae thinks! It won’t affect your MRC value, but the 300 Spirit will really be nice during Innervates, at least while you’re “undergeared” (that includes me, sadly).
@MK: Oh I’m very sorry. I misunderstood which “i” you were talking about. The “i” in the formulas above has been corrected to “I” as was originally intended. If you can quantify the effects of Shadowfiend and its interaction with Spirit, then we could look at adding it in. I just know that Priests often lament the unpredictability of the returns from SF. And thank you very much for your help with mana pool; I really appreciate it! =)
March 17th, 2008 at 7:50 pm
Ooh, is it possible to up the fight length to 25 minutes? Illidan’s enrage timer is set to 25, and while I don’t think we’ll run into the timer much (We just got our first kill yesterday, we beat the game eee!) it might be useful for others as well to calculate in the 20-25 minute range.
Amazing work on the caculator — that’s all kinds of crazy work I’d rather not have to do myself. Thank you.
March 17th, 2008 at 9:08 pm
@Kaera: Oh, sorry about that! I didn’t actually realize that the Illidan takes so long to complete (and to think I get tired after a 4 hour raid). The maximum time limit is now 45 minutes and you can specify the use of Innervate up to 10 times. Note that there is no validation preventing you from specifying a number of Innervates possible within a given time period. Please click responsibly.
And you’re quite welcome. I’m honored to be of assistance to those who are progressed so far beyond where we are. =)
March 19th, 2008 at 12:59 pm
Hey Phae,
Excellent work here! The next logical step, IMO, would be to take your previous work on equating +heal to mp5 and add healing breakdown (percentage of lifebloom vs. rejuv, & regrowth) to the calculator, so gear item points could be developed based on an individual’s playing style. Having the ability to sort prospective gear based on playing style and individual fight dynamics would be the ultimate tool!
March 19th, 2008 at 7:33 pm
Hello Phae, nice work on the calculator~
Got a question..I’ve tried plugging in the values from your example, but it doesn’t return me the values that its supposed to. I’ve put in 85% 5SR, 8 mins, 1 Innervate, 2s cast freq, Intensity+Bangle, 575 Int, 450 Spi. I got back a result of:
Mana Regeneration (Spirit/Intellect): 321 MP5
Mana Pool: 10719 mana
Mana Return from Innervate: 13196 mana
Innervate Weapon: High Intellect
I/S Ratio: 1.278
1 MP5 Equals: 2 Int OR 2.1 Spi
MRC: 0.434
[Bangle of Endless Blessings] Active: 23.1%
The recommendations didn’t tally either. It asked me to increase my int to 628 or reduce my spirit to 378.
March 19th, 2008 at 8:03 pm
@Flynx: That is pretty much exactly what I plan to do in the next few weeks! I am really excited to see how things turn out!
@Erwinde: Eek. Thanks for pointing that out. I updated the example’s parameters when we discovered an error in one portion of the code, but I forgot to update the results! Correcting that now. =) Ty!
March 20th, 2008 at 12:59 pm
Phae, the calculator is great! I’m assuming it is supposed to show 2.4 mana regen numbers? Maybe I’m assuming wrong.
But… it doesn’t match what my character has on the PTR.
2.3 I have: 443 int, 396 spirit and that works out to 345 regen in combat and 157 regen out of combat. The mana regen calculator gets a number pretty close to this.
2.4 I have: (Same int, spirit) 465/193 regent out/in combat.
So if it is supposed to show 2.4 regen, then it doesn’t seem to be working right. If it is showing 2.3 regen then ignore me, it works fine.
March 20th, 2008 at 1:39 pm
@Zute: The numbers shown here are intended to be effective numbers and will not match those numbers you find on your character sheet since those numbers do not take into account variables like like trinket effects, how much time you spend in the 5SR, the benefit you derive from Innervate, fight length, etc. Does that make sense?
March 21st, 2008 at 5:49 pm
I was wondering how the on use effect of The Bangle is affected during an innervate. Also since the on use effect has a 2 minute cooldown (so you can potentially use it 3 times for every innervate), how would the temporary spirit affect these calculations?
March 26th, 2008 at 1:52 pm
@George: The on-use effect of the Bangle adds 140 more Spirit and adjusts the base mana regeneration formula that’s multiplied by 5 during an Innervate. And, while you could theoretically use it 3x/Innervate, you’d probably stick to using it only twice to avoid it not being available to you when you needed it. Were you doing this, it would bias you slightly toward a higher Intellect (though not much since its on-use effect is going to be much less potent outside of an Innervate since you are under 5SR most of the time and not getting 500% regeneration).
March 29th, 2008 at 2:07 pm
The values do not match what I see on the live realm even if I eliminate all the factors you mention (100% inside 5SR, no innervates, none of the regen trinkets…). The difference is not huge (less than 5 mp5) but in any case it is not completely accurate.
March 29th, 2008 at 4:30 pm
@Nighcol: I was worried when I read about the discrepancy you seemed to spot, so I logged on and detailed all the MP5 from my gear. I get the exact same numbers when I account for MP5 on gear, enchants (including 4 MP5 from Vitality to boots), gems, and socket bonuses. Of course, it took me twice of inventorying to get everything, but I’m pretty sure it’s accurate now that I have. Are you sure you also happened to catch everything?
April 3rd, 2008 at 3:36 pm
[...] tips, information and general healy goodness I can usually find here. Phaelia has some excellent theorycrafting and she will take the time to answer questions. I can’t say enough great things. Go. [...]
May 7th, 2008 at 1:01 pm
[...] There are some links to some lootrank sets that probably covers what you’re going for. As for spirit vs. int, generally spirit is the way to go first, you’ll get enough int incidentally that the marginal returns on spirit are consistently better when you have a choice. If you really want to know though, try out the regen calculator at: Resto4Life Blog Archive 2.4 Mana Regen: The Mana Regen Calculator [...]
May 9th, 2008 at 7:00 am
Very nice artible.
It would be great to cover mages too, and especially arcane mages.
May 9th, 2008 at 5:22 pm
@Kolvir: I have been meaning to get to that, actually. Mr. Phae plays an Arcane-specced Mage. Check back on Monday, and I’ll see what we can do.
May 21st, 2008 at 12:01 pm
Mr Phae, i found
“dblManaAt70 is 2374″
is incorrect for a Tauren Druid at 70 it is infact 2370.
you may calculate base mana for yourself very easily with
BaseMana = ManaPool - (20+((Intellect-20)*15))
luckily for druids there are only two races you can be, however i think other factors affect base mana, this has complicated me trying to make your calcuator (addon)useful for other classes.
I have also included Mage functionality into the addon, but without Evocation so far (looks preety easy to do).
ETA on addon has been extended further since i have exams, i had some problems with the addon interfering with the wow interface and also i made a mistake somewhere and the code is too messy for me to work out what i did wrong XD.
so im redoing the calcuating side of the addon with some new skillz i learnt!
i shall keep you and your viewers updated.
May 22nd, 2008 at 1:00 pm
@Gararf: I’m very excited to see what you come up with. It would be quite convenient to have available in game since the paperdoll mana regeneration can be sort of misleading.
May 22nd, 2008 at 1:31 pm
@Kolvir: Sorry I’ve been slow to update this for Arcane Mages. It’s something I am working on along with an article specifically related to them. I hope you can be a little patient with me. =)
May 27th, 2008 at 4:25 am
Thanks for the mage update!