Spirit/Intellect Relationship 2, understanding up and side-grades

So I am aware that my math post has undergone a lot of updates between its creation and this morning. A lot of that is due to some miscalculations and rounding errors. There are clearly flaws to doing research at 1 in the morning. I have the equation roughly where I would like it to be, though the Intellect portion of the regen may need some more refinement. The reason for this is that my approximations are based off of ” in a perfect world” per-minute int based returns and that isn’t always the case. It is a good place to start for sure.

Some people sent in e-mails inquiring further about evaluating upgrades. It isn’t always going to be about looking into filling an empty slot. There are going to be times when you need to look at evaluating pseudo side-grades or small upgrades. I wanted to help this process along by including some equations that will help you look at how much of an upgrade (regen wise) an item is for you.

Since you probably don’t want to bust out a calculator and type in a long string of information each time, I’ll set this up as a guide for creating your own spreadsheet assuming a fundamental understanding of Excel (or Open Office Spreadsheets).

I like to have labels above each box I set up as a variable to make it easier to edit numbers later. You want to start off by making two boxes labeled: Intellect and Spirit. These are going to be your starting Int. and Spirit stats when you have Mark of the Wild cast. From here on out I’ll be referring to them as INT and SP

You then want to create two more boxes called D[I] and D[S]. These boxes represent the delta (or difference) the new item would give you to those stats. For example if the new item had 40 more intellect and 20 more spirit on it you’d put those values into the boxes. The intellect is a little tricky, you are going to need to multiply the D[I] value by 1.17 to represent all of the bonuses we get to intellect for the spirit section. I made a second box under D[I] that had this new value so I didn’t need to put the 17% increase into the equation later on. I’ll call this new box D’[I] from here on out just so it’s not as confusing.

First let’s look at the theoretical pure intellect based regen.

This is a simple equation to set up: in a new cell setup the following equation (pointing to the appropriate cells for values):

=D[I]*1.22

Since your int regen is just a constant value based on your mana pool it is straight forward. For me this looked like

=(A2*1.22)

Now let’s look at the spirit and intellect portion of your regen

The spirit and intellect portion is a bit more complicated but if you just point it to the right cells for each value it will be a breeze to set up. The equation is as follows:

=0.000125*((D’[I]*SP)+(INT*D[S])+(D’[I]*D[S]))+.55*D[S]

Again, in place of the cell names you need to point to the values in those cells. For me it looked like =(0.000125*((A3*E2)+(D2*B2)+(A3*B2)))+0.55*(B2)

This is useful if you’re looking at a piece of gear that has say 30 more intellect and 20 more spirit and you’d like to know just what that really gets you. This math also works in a situation where you’d like to know how gaining one stat and losing another stat work for you. You can make another cell in your spreadsheet that is the sum of the results of both equations you have entered in. Using this TOTAL cell, you can evaluate situations where you might be gaining 20 intellect but losing 20 spirit. To do so you’d simply put in 20 under D[I] and –20 under D[S].

POWER TORRENT AND HEARTSONG, attempting to understand their benefit through my simplified math

Temporary intellect is extremely difficult to measure because it does not confer any initial starting mana and it does not always line up with innervate. It doesn’t mean we can’t take a crack at understanding how it performs relative to Heartsong. For the sake of argument let’s assume that both enchants have the same uptime (I know that they don’t have the same uptime, but comparing them like this shows at what point their regen output will be equal)

For Power torrent, the 500 intellect with a 25% uptime is roughly 125 intellect all the time or 146.25 intellect after all bonuses are applied. We need to recalculate the pure int based regen to exclude innervate (though you can probably time your innervates to coincide with this buff to further increase its benefit). 146.25 intellect temporarily increases your maximum mana by 2413.13. Over the course of a minute we would regenerate 14% of that increase (revitalize+replenishment) or 337.8 mana. This translates to 28.51 mp/5 or 56.3 mana regen. It’s going to be a lot lower than the per int regen numbers in the last post because you do not get the benefit of starting mana nor are you guaranteed innervate while active. If you can line it up expect an improvement. For a player with 2500 spirit, the intellect from power torrent would grants them an additional 1.8% increase in spirit effectiveness or 45.7 mana regen. This brings us to a total of 102 Mana Regen for this enchant.

Heartsong, using the same 25% uptime yields 60.6 Mana Regen.

If the uptime percents differ from what I have listed but are still the same for both enchants the ratio still holds true with Power Torrent yielding 1.68 times the regen that Heartsong does, for druids that is. We know however that it is not the case and that Heartsong generally has a much higher uptime. Mathematically if the uptime of Power Torrent was 60% that of Heartsong then they would be equal (regen only, throughput and innervate benefit not included!).  From looking at my world of logs it shows Heartsong sitting between 50 and 55% uptime and from reports that I am reading say that Power Torrent sits at roughly 25-30% uptime. This would place heartsong just above Power Torrent for mana regeneration. [need someone to fact check uptimes and ICD’s in case I have missed something or a change]

I’m going to quickly throw in an addendum and look at innervates throughout the course of a fight provided you can line them up with a proc. Let’s say that you can cast two innervates in a fight charged up with the power torrent proc. During each of those innervates you are regenerating 20% of the additional 9652 mana for a total of 3861 mana. This mana broken out over 6 minutes translates into another 53.6 mp/5 or 107.3 Mana Regen.

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6 responses to “Spirit/Intellect Relationship 2, understanding up and side-grades

  1. It’s good to work out the math, but I can’t see spirit competing with intellect unless you have ~2x as much of it.

    Note that spirit and intellect are close to each other in terms of pure regen. However, int has a hidden benefit that is also like regen: you can do the same healing with fewer casts. You thus save the mana from the casts you didn’t make. When you factor that in, intellect looks way better than spirit.

    • There is absolutely no debate in my math whether or not intellect is or is not better than spirit. Blizzard has made the claim from day one that Intellect is a primary stat and should just about always be more important for us.

      The math is purely so you can analyze the effects of choosing one piece of gear over another. Very often these pieces of gear have both intellect and spirit just in varying amounts. Situations like trinkets where you are choosing pure spirit versus Intellect and less spirit are not the most common types of choices that we will be forced to make.

      My goal is simply to offer tools so people can understand what is occurring “under the hood” so to speak. It is not to give the impression that I am surprised by my findings or shocked that intellect is as good as it is because we knew that going in.

  2. Nice math there. Dunno if this helps to take it further but from our 10-man WoL -logs Heartsong’s uptime seems to be 63-64 % for a resto druid, 54-56 % for holy paladin, 62 for holy priest and surprisingly 53 % for resto shamans. The data was quite good .. about 18 wipes on Twilight Ascendant Council (priest’s data was taken from Magmaw+Omnitron+Chimaeron). Also what I gathered from Wowhead it seems that Heartsong’s proc chance is 15 % and Power Torrent’s 20 %. So it even further increases the value of the latter enchant .. according to your calculations at least.

    • That’s good information to be sure! If those proc chances are right all we’d need is the ICD for each enchant.

      As for Power Torrent coming out far ahead, it is the significantly more expensive and higher tier enchant so i’m not super surprised.

  3. Pingback: Lunchtime Napkin Math – Spirit vs Int Regen | Rank 4 Healing Touch

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