Mana Regen: Spirit vs Crit

Update: Since my last post on the Damage Dealing Forums seems to have had some affect. I've posted another thread there to highlight this issue. You can find it here. If you have something to contribute please post it there as well.

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You probably know by know that Blizzard has made some strange choices when itemizing our T8 gear sets. Namely, they more than doubled the amount of spirit on gear from T7 to T8. I bet many of you had the same reaction that I did after seeing this. My first thought was: "What the heck is Blizzard thinking?"

After thinking about it for a little while I can come to only one conclusion. In 3.1. Blizzard is making a lot of changes to the Mana regen system. On top of that all caster DPS are losing 5% crit chance with the Nerf to Improved Scorch and Winter's Chill, and blizzard probably assumes that we will be dropping our 4T7 set bonus and losing another5% crit chance. All in all that is a lot of mana regen going out the door. Therefore, Blizzard must be thinking that we need more Mana Regen, and Spirit = Mana Regen.

Some of you may scoff at this idea since Mana is clearly not an issue right now but that doesn't mean it won't be an issue in 3.1. In fact, I wouldn't be surprised if we do need more regen with the arrival of the next patch, but that doesn't mean it should come from Spirit. In this post I hope to demonstrate why most of that new Spirit should be changed to Crit Rating.

The Spirit Math:

First lets look at how Spirit base mana regen is going to be calculated in 3.1. For this exercise I'm going to assume we all have 3 points in Intensity.

The base formula for In Combat Spirit Based mana regen for moonkin is:

MP5 = (3 * (0.001 + sqrt(Int) * Spirit * Base_Regen)) * 0.5

The Base_Regen coefficient for a level 80 toon is 0.005575, and I'm going to use my stats to calculate the values for Int and Spirit. For Int, I have 925 Int unbuffed and in caster form. With full raid buffs that increases to 1243 ((925 + 60 + 51) * 1.2 = 1243.2). For Spirit I have 411 unbuffed in caster form. With raid buffs that increases to 596 ((411 + 80 + 51) * 1.1 = 596.2).

So my In Combat Spirit Based mana regen can be calculated this way:

IC SB MP5 = (3 * (0.001 + sqrt(1243) * 596 * 0.005575)) * 0.5
IC SB MP5 = (3 * (117.1468)) * 0.5 = 175.7202 Mp5

So, What happens if I increase my spirit by 1.

IC SB MP5 = (3 * (0.001 + sqrt(1243) * 597 * 0.005575)) * 0.5
IC SB MP5 = (3 * (117.3433)) * 0.5 = 176.0150 Mp5

So, by increasing my Spirit by 1, I increase my In Combat Mp5 by 0.2948 (176.0150 - 175.7202 = 0.2943).

The Crit Rating Math:

Now that we know what we are getting from Spirit, how much mana is generated by each point of Crit Rating?

Again, I'm going to use myself as an example. On my armory you can see that I have 17091 mana completely unbuffed. When I add Arcane Brilliance, Mark of the Wild, Blessing of Kings and Furor, my Intellect increases by 318 which translates to 4770 mana. Therefore, fully raid buffed my mana pool is 21861.

As you know every time one of our spells critically hits we regenerate 2% of our total mana. So, every time one of my spells crits I regenerate 437 mana ( 21861 * 0.02 = 437.22).

Now, each additional point of Crit rating gives you an additional 0.02179% chance to crit ( 1 / 4590 = 0.0002179).

Therefore, on average an additional point of Crit Rating will regenerate 0.09522 mana per crit-able spell cast (437 * 0.0002179 = 0.09522).

Now we need to translate this into Mp5 and to do that we need to calculate the average cast time of Starfire and Wrath.

A couple of Assumptions:
1. In raid, I have about 46% chance to crit. In 3.1 one that will shrink by 5% due to the Imp Scorch Nerf, and I will lose another 5% by dropping the 4T7 set bonus. So, I will assume that my crit chance is 36% for Wrath and 39% for starfire in this calculation.

2. I have 16.19% haste from gear. I assume that I will also have 3% from Celestial Focus, 3% from Imp Moonkin Form, and 5% from Wrath of Air. This a total haste value of 29.43% before Nature's Grace.

3. I'm going to ignore the increase crit chance from Eclipse for now.

4. I'm assuming that Starfire will represent 75% of our Damage and Wrath the other 25%.

Now, lets look at the uptime of Natures Grace:

SF NG Up Time = 1 - (1 - 0.39)² = 62.79%
Wrath NG Up Time = 1 - (1 - 0.36)³ = 73.79%

Therefore the average Starfire cast time can be calculated as:

Avg SF Cast Time = (3/(1+0.2943)) * (1-0.6279) + (3/((1+0.2943)*1.2)) * (0.6279)
Avg SF Cast Time = (2.3179) * (0.3721) + (1.9315) * (0.6279) = 2.0753 seconds

The average Wrath Cast time looks like this, but remember that it can't go below 1 second due to the global cooldown:

Avg W Cast Time = (1.5/(1+0.2943)) * (1-0.7379) + (1.5/((1+0.2943)*1.2)) * (0.7379)
Avg W Cast Time = (1.1589) * 1-0.7379) + (1^#) * (0.7379) = 1.0416 seconds
# - Actual value is less then 1, but the GCD sets a floor of a 1 second cast.

So, how much Mp5 is regenerated by each of these spells:

Mp5 from SF = (5 / 2.0753) * 0.09522 = 0.2294 Mp5
Mp5 from W = (5 / 1.0416) * 0.09522 = 0.4571 Mp5

So, by these calculations each point of Crit Rating is worth:

Mp5 per Crit Rating = (0.2294 * 0.75) + (0.4571 * 0.25) = 0.2863 Mp5

Please Note: I do not claim that this number is perfect. In actuality this number should be a little lower. Obviously not every spell we cast has a chance to crit and we are not casting 100% of the time, but I do believe that it is in the right ball park. Please remember that I have also excluded Eclipse from the analysis would would greatly increase the amount of Mp5 generated by Mana on Crit.

Conclusions:

Lets compare the two numbers I calculated. One point of Spirit will increase my In Combat mana regen by 0.2948 Mp5. One point of Crit Rating will increase my In Combat mana regen by 0.2863 Mp5. So, Spirit returns only 2.97% more mana then Crit Rating does by these calculations. Granted the Crit Rating number might be over estimated by a little bit, but the Spirit number may also be over estimated if you ever drop out of the 5 second rule.

If we look at it from a DPS stand point we know that Crit Rating is vastly superior. For my gear level, I've calculated Crit Rating to be worth 0.80 Spell power per point. Each point of Spirit is worth 0.15 Spell power. So, Crit Rating is 433% more powerful in terms of DPS then Spirit.

In short, by itemizing for Spirit instead of Crit Rating, Blizzard is making us give up quite a bit of DPS for a relatively minor amount of mana regen.

I am under no illusion that Blizzard will convert all of the Spirit on the T8 gear to Crit Rating, but I think it would be reasonable to take the spirit off of one of the items and convert it to Crit Rating instead. In my opinion this would improve the set significantly.