Holy Theorycrafting: Mana Regen of Kings vs. Wisdom

Back in the Burning Crusade era, there seemed to be a wide variety of ways one could build a Holy Paladin. Some players went Holy/Prot, others Holy/Ret, and still others Holy/Prot/Ret (I myself used a 47/7/7 build). However, since Wrath of the Lich King launched, it seems that two Holy builds have become dominant: the Holy Kings build (51/5/15) and the Holy Critadin build (51/0/18 + 2 points wherever). The primary difference between these to builds boils down to just 5 points. The Holy Kings build spends these 5 points in Blessing of Kings and Improved Blessing of Kings, and the Holy Critadin build spends 3 points in Sanctified Seals and has 2 points left over. These 2 points can be invested in a variety of different talents, but for the sake of this post, we'll invest them in Improved Blessing of Wisdom. So, ultimately, our trees will look something like this: Holy Kings (51/5/15) and Holy Critadin with Wisdom (53/0/18). (As a side note, choice between Improved Judgements and Improved Blessing of Might in tier 2 of Retribution is irrelevant, and either build can take either talent).

So, with the above 2 builds being the most dominant, the question of which is better will almost invariably arise. As the issue was brought up by a supporter of the Holy Kings build, and I myself favor the Holy Critadin with Wisdom build, I figured I would stack the deck in favor of the Holy Kings build and see when it would surpass the Holy Critadin with Wisdom build. Since Intellect is now one of the most valuable mana regeneration stats for Paladins (thanks to Divine Plea, Replenishment, and other mana restoration abilities that scale based on total mana, such as Mana Tide Totem) and Blessing of Kings added stats scale based on gear, whereas Blessing of Wisdom remains a static bonus, the former will certainly overtake the latter at some point. The question deals with where exactly that point is, and whether or not it is obtainable. Now, on with the post!

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Question:

How much Intellect is needed for a fully improved Blessing of Kings to equal the mana regeneration of a fully improved Blessing of Wisdom? For the purposes of this example, I'll be stacking everything possible in favor of Blessing of Kings, with the exception of improving Blessing of Wisdom via talents.

Assumptions:

1. Blessing of Kings would replace Blessing of Wisdom on the target.
2. Replenishment is up on the target 100% of the time (though this is not a particularly realistic assumption).
3. The target is a Paladin who happens to be grouped with a Restoration Shaman, and thus has access to both Divine Plea and Mana Tide Totem, so that mana regeneration due to Intellect is maximized.
4. Blessing of Wisdom and Blessing of Kings are both fully improved by their respective talents.
5. [Glyph of Mana Tide Totem] is used, but other glyphs are not taken into account.
6. Relics are not taken into account.
7. The highest rank of each spell is used.
   

Abbreviation Key:

• BoK: Blessing of Kings
• BoW: Blessing of Wisdom
• DP: Divine Plea
• MTT: Mana Tide Totem
• replen: Replenishment
• INT: Intellect, after other multiplicative modifiers have been taken into account
• mps: mana per second
• mp5: mana per 5 seconds
  

Given:

• (improved) Blessing of Kings = 1.1 * base stat (after other multiplicative modifiers)
• (improved) Blessing of Wisdom mana regeneration = 91mp5 * 1.2 = 109.2mp5
• mana restored per Divine Plea cast = Intellect * 15 * 0.25
• Divine Plea cooldown = 60 seconds
• mana restored per Mana Tide Totem cast = Intellect * 15 * (0.06 + 0.01) * 4
• Mana Tide Totem cooldown = 300 seconds
• mana per second restored from Replenishment = Intellect * 15 * 0.0025 = Intellect * 0.0375
  

Theorycrafting:

First, let's convert everything into mp5, so it's easier to compare:

mps of DP = [mana restored per DP cast] / [DP cooldown]
= [INT * 15 * 0.25] / [60]
= INT * 0.0625

mp5 of DP = [mps of DP] * 5
= [INT * 0.0625] * 5
= INT * 0.3125

mps of MTT = [mana restored per MTT cast[ / [MTT cooldown]
= [INT * 15 * (0.06 + 0.01) * 4] / 300
= INT * 0.07 * 0.2
= INT * 0.014

mp5 of MTT = [mps of MTT] * 5
= [INT * 0.014] * 5
= INT * 0.07

mp5 of replen = [mps of replen] * 5
= INT * 0.0375 * 5
= INT * 0.1875

Thus, we can say that the mp5 given by DP + MTT + replen is:

mp5 of DP + MTT + replen = [mp5 or DP] + [mp5 of MTT] + [mp5 of replen]
= [INT * 0.3125] + [INT * 0.07] + [INT * 0.1875]
= INT * 0.57

Since INT will increase by 10% with BoK, we can conclude that the mana regeneration of the above will also increase by 10% with BoK, since they scale with INT. Thus, they would yield an additional mp5 of:

additional mp5 of DP + MTT + replen from BoK = [mp5 of DP + MTT + replen] * 0.1
= INT * 0.57 * 0.1
= INT * 0.057

So, how much INT would be needed for BoK to equal BoW on the mana regeneration front?

additional mp5 of DP + MTT + replen from BoK = BoW
INT * 0.057 = 109.2
INT = 109.2 / 0.057
INT = 1915.79 (rounded up to 1916)

Now, even if you stack full INT and have access to all obtainable gear, items, item enhancements, and buffs, you'd still be hard pressed getting to 1916 INT.

As I see it, Blessing of Wisdom allows me to worry less about mana regeneration stats and instead focus on stats that give me a bit better return, such as haste and spellpower. Blessing of Kings, while nice, still functions best when you stack base stats. Don't get me wrong—it can certainly be a life-saver when the extra health, dodge, armor, crit, etc. etc. it provides means the difference between life and death, but that extra mana regeneration from Blessing of Wisdom can also prove to be the difference between a victory and a wipe.

Ultimately, I think my biggest issue with Blessing of Kings is probably that I still see it as a buff which essentially works to mitigate the effect of bad luck, whereas Blessing of Wisdom does more to allow you to play at your best. I can't speak for anyone else, but personally, I'd rather be good than lucky.