Spirit/Intellect Relationship, evaluating gear choice (math involved)

Disclaimer: Post is rather math heavy but provides useful nuggets of information. This has not been grammar checked yet as my brain is quite tired. Similarly I have not had a chance to super thoroughly double check my math as it is late. Expect this to be reviewed moving forward especially if I get some
really solid feedback on my numbers. I’ve spotted some minor rounding errors due to my open office spreadsheet program settings, as I spot them I will make some modifications to the equations later today. Also the math in this post applies to druid healing for now. Edit text has been removed to clean up the post for now.

Spirit and Intellect are fairly intertwined when it comes to our overall mana regen and it requires some calculations in order to better understand just what is going on under the hood. First i’ll go over some of the assumptions made, then i’ll jump to the equations, and finally I’ll give you the tools you’ll need (though it might take a calculator) to plan out choosing one piece over another if mana regen is something you are concerned with.

ASSUMPTIONS

What we do know is that at any one particular level of intellect, adding more spirit yields a constant amount of mana regen. This was tested and proven accurate.

The value of one point of intellect in terms of mana regen can be approximated by creating a per minute and per 5 second rate of intellect mana return and the value of the initial starting mana over the course of the fight.

The equation, based off of intellect, that governs how much one point of spirit is worth is not a simple linear equation, however around our current gear level it can be approximated by a linear equation  in order to evaluate gear.

EXPERIMENT

I un-forged a couple pieces of gear and took advantage of int only buffs to test my mana regen (spirit based) at a range of intellect levels. At each level I also activated my Darkmoon Card: Tsunami to gage exactly how much my regeneration went up per application of 80 spirit. It did not surprise me that my Mana Regen went up a fixed amount per application per intellect level which allowed me to create a linear equation governing the value of spirit tied to
intellect levels.

EQUATIONS

Through experimental data and creating some charts mapping my results I came to the following linear interpretation of the intellect/spirit relationship:
Mana Regen (spirit) =( (.000125*Intellect)+.55)Spirit

This equation is not 100% accurate as is based purely on my data. I expect to see some variation, possibly deviating + or – up to 50 mana regen per say. Please feel free to check it out with your gear and if you spot anything that needs to be fixed I can tweak my multiplier.

Total Regen=Mana Regen (spirit) + 931

I can only assume this 931 is a base regen as it was constant through every gear check I completed.

FINDINGS

To understand how you would look at two pieces of gear and compare their total regenerative qualities let’s look at how much regen 1 point of intellect alone garners:

Intellect based regen assuming 4 ppm of Revitalize, and 1 point of raw intellect giving 19.28 mana:

Per minute you regen 6% mana from replenishment, 8% mana from revitalize, and 6.66% mana from innervate (glyph not used for this) .2066*19.28=4.05 mana per minute, or 0.34 mp/5.

19.28 additional starting mana over a 6 minute fight translates to 0.27 mp/5. Therefore one point of intellect gives you roughly 0.61 mp/5 or 1.22 Mana Regen

Important Note: This applies to additional raw intellect beyond what is currently on your character sheet. When looking at an item its intellect is not increased by all of the multipliers. I was also erroneously giving too little credit to starting mana. Your character sheet (provided you have Mark of the Wild on you) already includes Leather Specialization, Furor, and MotW, meaning each point of intellect at that stage only gives 16.5 mana. This 16.5 mana translates into 3.41 mana per minute or 0.28 mp/5. The starting mana, 16.5, translates into 0.23 mp/5 for a total of 0.51 mp/5 or 1.02 Mana Regen.

This point of intellect also increases your spirit regen by a small amount as well: 1 point of intellect increases the value of each point of spirit you have by 0.000125. While that isn’t a large number, it does mean that 80 intellect increases the effectiveness of your spirit by 1%.

SO HOW THE HECK AM I SUPPOSED TO USE ALL OF THIS?

The only time you’d really be using these findings is if you were evaluating two pieces of gear to find out which provided you with a larger rate of mana return in the end. These equations aren’t pretty but if you use them they can help (and i’ll throw in an example at the end for reference)

Glossary:

ER – effective overall regen

Int – Intellect (prior to adding any items)

Sp – Spirit

I(Item) = Intellect from an item

S(Item) = Spirit from an item

ER = ((Int+1180)*1.02)+((.000125*Int)+.55)Sp+.931

Note: The 1180 number is a constant I need to review, for right now it will not affect gear comparison as it is a base value

If you want to know what your regeneration is after putting on a piece of gear you’ll need to look at the new spirit and intellect totals you would have with that piece of gear on:

ER = [((Int+1180)*1.02)+(I(Item)*1.22)]+[.000125*(Int + (1.17*I(Item)))+.55](Sp+S(Item))+.931

Sometimes though it doesn’t need to be that complicated. I’ve been meaning to find a way to compare two specific trinkets, one being Darkmoon Card: Tsunami and Jar of Remedies.

First let’s look at Jar of Ancient Remedies. This trinket gives 515 spirit 75% of the time and returns 6420 mana every two minutes. Over the course of a fight
its average spirit based on uptime will be 386. The mana return is 6420 mana every two minutes, or 3210 mana per minute averaging out to roughly 268 mp/5 or flat 535 Mana Regen.

If someone with 5000 intellect and 2000 current spirit is looking to fill an empty slot their stats are 3281 Mana Regen and 8271 Effective Regen. This trinket adds a flat 535 Mana Regen from the on use, and 454 Mana Regen based on the addition of spirit at that intellect level. This gives a total of 4270 Mana Regen and 10511 Effective Regen.

Now if that same person (using 3281 Mana Regen and 8271 Effective Regen) wants to use Darkmoon Card: Tsunami they are looking to add 321 Intellect and 400 spirit. These stats change the players Mana Regen to 3863 and their Effective Regen to 10497.

You’ll notice that while the regular mana regen is significantly different between the two items, the Effective Regen is actually not. This is a situation where you need to figure out if the added spellpower gained from the intellect is worth the slight mana regen loss. This also assumes theoretical intellect based return, please note that fight mechanics, timing, and RNG will play a factor in your total Effective Regen returns.

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12 responses to “Spirit/Intellect Relationship, evaluating gear choice (math involved)

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  4. hhhhmmmmmmm thnx for the equasions dude. Luckily my priest is getting to a point where regen isnt as much of an issue as it was a few weeks ago but having some actual numbers I can use for my druid alt will come in handy.

    Panzee

  5. Thanks for the aweesome post. These equations are defiantely close enough to gauge the effeectiveness of each stat.

    • I’m glad that it helped you out some. The more tools people have when looking at gear the better. With the hotfixed Rejuvenation cost reduction and the 4.0.6 patch changes to add Nourish into the AoE healing tool set we may be able to reevaluate how much pressure we put on ourselves to have tons of regen. I’m not saying that Spirit is going to drop out of the equation, but once we hit a certain point we may be swapping some spirit for some haste/mastery/crit and it will help to know just how much we’re giving up from item/gem to item/gem.

  6. Hello,
    This math is good. I think it would be helpful in addition to give formulas for the instantaneous regen contributions of int and spirit (that is, their values at a state of intellect and spirit rather than looking at specific upgrades). Let R, S, and I be effective mana regeneration, spirit, and intellect respectively. Then (distributing your formula)
    R = 1.02*I*S + 1.02*1180*S + I*S/8000 + 0.55*S + 931
    With some basic calculus, we can derive in terms of I and then in terms of S to find each instantaneous mana regen contribution.
    dR/dI = 1.02*S + S/8000
    dR/dS = 1.02*I + I/8000 + 1.02*1180 + 0.55
    I hope this is helpful.

    • I think you multiplied the equation through a little off. It should read:
      R = 1.02*I+1203.6+(I*S)/8000+.55*S+931
      Evaluating the derivatives of the equation with respect to each variable you get:

      dR/dI=1.02+(S/8000)
      or dR=(1.02+(S/8000))dI

      dR/dS=(I/8000)+.55
      or dR/=((I/8000)+.55)dS

      double checked these in a spreadsheet using a dS of 1, and dI of 1 to get a per unit delta and they checked out. While I understand this gives you more information for evaluating how the stats scale relative to each other, I figured giving players an application to use the math (e.g. comparing gear) would prove more useful.

      You can use the math to say “how much spirit or int is needed to hit this benchmark of theoretical regen” or something like that. For that purpose knowing the instantaneous delta is useful.

      • Whoops, I misread your parentheses. It is definitely more practically useful to be able to compare upgrades; I just thought it might be interesting to see the value of each at a given point. You could also set them as an inequality and see when, generally, one gives more regen than the other.
        Regards, and thanks for the insightful math.

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  9. Thanks for all the information, I plugged in all the numbers, and finally (after an hour) decided an upgrade was worth it even with the 62.1 mp5 loss

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