Lunchtime Napkin Math – How much mana do we REALLY have in a fight?

This was a fun mathy rant that I threw together for your enjoyment here at lunch time. It is not necessarily spell checked or anything so take it for what it is and be gentle with the grammar police 🙂

I thought I’d take a look at some numbers from world of logs and gain a rough understanding of just how much mana we really do have access to over the course of a fight. I think this will help me quantify stats in an empirical way in order to compare them to what I’d expect to get.

I’m going to use our recent Majordomo Staghelm kill as it lasted a good  9.5 minutes (longer than it should I know) with my lifebloom uptime in an acceptable spot (95.5%). Right now my base intellect is 6102 and spirit 2690. Raid buffed (+380 flask +90 food multiplied by 1.17) my intellect is ~6957 I believe and spirit jumps to 3090 with Tsunami active. Raid buffed my mana is at ~140,000. I don’t have any heroic firelands gear and am predominantly 378 items. None of this is meant to be bragging, simply setting the stage for the observations ahead.

So let’s look at what I actually got for regeneration.

Spirit Regen + Base Regen

Based on the equation that still holds true, ER =((.000125*Int + .55)*Spirit )+931

This puts my raid buffed in combat regen at 5317.64, or ~2659 mp/5

In all fairness I’m going to discount the first 10 seconds of the fight as negligible mana is spent giving us a total of 9 minutes and 20 seconds (9.33 minutes). Over this time my spirit regenerated 297,681 mana.

Intellect Based Regen

I have cited theoretical numbers for intellect regeneration in the past so it’s probably a good idea to put some real world numbers to the test and make some observations.

Revitalize

Theoretical – 4 procs per minute for 104,496 mana (not including increases from gloves/power torrent)

Actual – 113,998 mana

Replenishment

Theoretical – 6% gain per minute for 78,120 mana

Actual – 77,355 mana

Innervate

Theoretical – 6.66% per minute for 86,993 mana

Actual – 59,797 mana

Over the course of the fight my intellect based regen gave me 251,150 mana. I know my intellect regen is usually listed higher in the math you may be familiar with, please bear in mind that distributes the starting mana intellect provides over the course of a fight in order to equate it to mp/5. That is not displayed here.

Gear Based Regen

Heartfire – T12 2-piece bonus

Actual – 44,168 mana (~395 mp/5 or 789 mana regen)

Observations

The first order of business is looking at intellect based regen. Clearly my Revitalize math does not do any justice to temporary large intellect buffs or higher procs per minute due to things like lust/hero and Nature’s Grace. Due to this my actual Revitalize return is roughly 9% higher than my theoretical number. My replenishment data looks spot on coming in at 99% of the theoretical value. Innervate on the other hand was clearly way off! Distributing innervate out over the duration of the fight as a per minute return does not accurately represent situations where innervate was is not optimized. During this fight I spent significantly more mana in the second half as opposed to the first and with mana tides and cat phases my first ‘vate was delayed quite a bit as it wasn’t necessary. As such only two were cast in a 9.3 minute fight giving me only 69% the theoretical yield.

Overall my actual intellect based regen was 93.2% of the theoretical yield which I think is actually pretty good.

Purely for fun:

The spirit regen number is pretty much what I expected as it is the workhorse of our mana replenishment. What I thought would be fun to do is break down how much raw intellect that equates to as far as starting mana and intellect regen.  My mana regen from spirit only (without base regen) is 245,564 mana over the course of the fight (4386 mana regen). For this length of a fight, 65% of intellect regen comes from revitalize etc. and 35% is due to starting mana pool – 0.63 mana regen and .34 mana regen per point of intellect respectively. Doing some additional math this gives us 4515 modified intellect or 3860 raw intellect. This isn’t really significant but it does show you that it would take 3860 raw intellect to replace 3090 spirit indicating that one point of intellect provides, very roughly, 80% or so of the regenerative properties of 1 point of spirit (in a real world setting).

Overall my total mana over the course of the fight was: 140,000 initial + 297,681 static regen + 251,150 int regen + 44,168 gear regen for a total of 732,999 mana. This amount is nearly 424% larger than my normal maximum mana and represents everything I’d have access to over the course of the fight.

While I did have to make some corrections to my old math due to the fight length being so long and innervate return being so different, I didn’t really learn that much new that we didn’t already know. What I did like to see is just how much mana we ultimately have access to. I was looking hard at this data and I thought hey, why don’t I try to take a look at how these numbers would change if I had one less point in moonglow versus one more point in furor. This would simply be for fun, as a single fight is not enough data to base any definitive conclusions off of.

If we have access to a total of 732,999 mana, then effectively we would be spending 805,493  mana of un-cheapened spells (being 91% of what we actually had to spend on un-cheapened spells). With only two points in moonglow we’d have 779,786 mana to spend on un-cheapened spells. The difference between the two is 25,707 mana. This is a quantified, but not definitive, value of the 3rd point of Moonglow in this situation. Also note this mana value is highly theoretical as it is not mana you ever actually have at any time, simply mana savings. If you did not have this point of moonglow you would have to spend this mana from your fights overall mana pool.

If we had one more point in Furor we would increase our maximum mana by 5% more of the amount we’d have without Furor as well as increase our intellect regen by the same amount. This is actually a 4.55% increase in mana from 2/3 Furor values.  Our max mana would go up to 146,370 and our intellect regen would go up to 262,577 for a gain of 6,370 + 11,427 = 17,797 mana.

Not surprising, the 3rd point of moonglow still beats out the 3rd point of Furor by 7,910 mana total over the course of the fight. Clearly victorious.

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2 responses to “Lunchtime Napkin Math – How much mana do we REALLY have in a fight?

  1. This was really interesting, thanks!

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