Thursday, December 18, 2008

Holy Theorycrafting: Revisiting BoK vs. BoW

So, in the PlusHeal thread where I originally posted my Blessing of Kings vs. Blessing of Wisdom theorycrafting, several questions came up about what was included (or omitted) in my calculations. Those questions were:
  1. Doesn't Blessing of Kings also have the added benefit of increasing one's chance to crit, and shouldn't that be factored in to the mana regeneration comparisons due to the Illumination talent?
  2. Due to the above, wouldn't the Divine Illumination talent (different from Illumination) further push Blessing of Kings' advantage?
  3. Blessing of Kings also increases the total mana available, since each point of Intellect also grants 15 mana. Shouldn't this be taken into account as a "variable mp5" stat which varies based on the length of the fight?
In addition, it was pointed out that Holy Guidance also converts each point of Intellect into a point of spell power at a 20% rate, and this should be factored in. Finally, some of the arguments above were counter-theorycrafted based on a 1000 Intellect model and a 5-minute fight. So, let's revisit the topic and take all of the above into account.

Alright, so let's compare Blessing of Kings and Blessing of Wisdom with 1000 Intellect and see what that gets us. I'll also try to factor in the additional mana regeneration from the added crit, although I'd like to point out that I didn't factor it in earlier because not only is it difficult to model without assuming certain playstyles or going crazy with theoretical maximums, but also because I was trying to tilt the scale in favor of Blessing of Kings as much as possible. WhileBlessing of Kings will net you 0.6% crit with 1000 Intellect (since current consensus is that it 100 Intellect grants 0.6% crit, and a fully talented Blessing of Kings with 1000 Intellect will provide exactly 100 additional Intellect), it also has the significant opportunity cost of 3 talent points in Sanctified Seals, which grants 3% crit. In other words, spending the 5 points to max out Blessing of Kings instead of 2 points to max out Blessing of Wisdom essentially results in a net loss of 2.4% crit at 1000 Intellect.

Also before we begin, I'd like to note that I'm not going to factor in the additional 1500 mana at the start of each fight as mp5, because the length of each fight is too variable to simply assume a 5 minute duration. 1500 mana is definitely a bonus, but it amounts to 5 Flash of Light casts or 1 Holy Light and 1 Flash of Light cast or 1 Beacon of Light. Also, the usefulness of 1500 mana really depends on how you view that mana added to your total mana pool. For example, someone who sees that mana added to the top of the mana pool may cast a Beacon of Light prior to the fight and think "Wow, Blessing of Kings gave me a free Beacon!", whereas I see the the mana as added to the bottom of my mana pool, so I don't see it as a real factor unless it becomes the difference of having the mana to cast a spell or not having the mana to cast the spell.

That said, let's make the assumption that maxing out Blessing of Kings doesn't force you to choose between Beacon of Light and Sanctified Seals, and you somehow manage to max out all 3 talents (though this is impossible without being level 83). Since we're pretty much riding the Hypotheticalmobile to Impossibleland anyway, we'll make a few more completely unrealistic assumptions. One such assumption is that each crit would yield the maximum mana return possible—the amount returned from a Holy Light crit. Correct me if I'm wrong, but Holy Light should cost about 1274 mana at level 80, which means each Holy Light crit restores 764.4 mana. Thus, 0.1% crit would give about 0.7644 mana per cast. We continue our voyage into Crazyville and assume we have so much haste that Holy Light is now limited by the minimum global cooldown of 1 second. So, 0.1% crit would yield 0.7644 mps. Multiply this by 6, since the additional 100 Intellect from Blessing of Kings would give 0.6% crit, not 0.1%, and then multiply by 5 because we want mp5 and not mps, resulting in a maximum of 22.932 mp5 for 1000 total pre-Kings Intellect.

As for Divine Illumination, let's also model it in a best-case scenario for Blessing of Kings. Basically, this would be to assume that when Divine Illumination is up, we chain cast our most expensive heal to maximize mana return. Our most expensive heal is Holy Light, and since we've assumed that we've capped haste to the point where you are now limited by the 1 second minimum of the global cooldown above, we'll make the same assumption now, which gives us a maximum of 15 Holy Light casts in a single Divine Illumination duration. Using the Holy Light cost of 1274 mana above, Divine Illumination would reduce this cost to 637 mana, and a Holy Light crit would restore 764.4 mana as mentioned earlier. This gives us a net gain of 127.4 mana in an additional 0.6% (or 6 out of each 1000) of Holy Light casts, averaging to a gain of about 0.7644 mana per cast. Since we assumed we can cast 15 Holy Light per Divine Illumination, we get an average of 11.466 mana each Divine Illumination. As Divine Illumination has a 3 minute (or 180 second) cooldown, this yields 36 5-second periods per cast, resulting in approximately 0.3185 mp5 (or a meager 19.11 mana over the course of the hypothetical 5-minute fight).

The equation you'd get would essentially be as follows:
BoK vs BoW
= [additional mp5 of DP + MTT + replen from BoK] + [additional mp5 of crit from BoK] + [additional mp5 from Divine Illumination + Holy Light crits] vs 109.2mp5
= [1000 * 0.057] + [22.932] + [0.3185] vs 109.2 mp5
= 80.2505 mp5 vs 109.2mp5
So, even with numbers that are completely impossible in-game (not to mention at a 1000 Intellect gear level), fully improved Blessing of Wisdom gives you about 28.9495 more mp5 with 1000 Intellect. With 1000 Intellect, Blessing of Kings gives you 1500 more mana and 20 more spell power (and 0.6% crit if you want to make that argument, although it still has an opportunity cost of 3% crit from Sanctified Seals), health equal to your pre-Kings Stamina, attack power equal to 20% of your pre-Kings Strength, a small amount of block value from Strength, a small amount of dodge and armor from Agility, a small amount of Spirit-based mana regeneration, and quite possibly a partridge in a pear tree (but only if you've been a good little boy or girl). :P

1 comment:

  1. First of all, I want to say completely unbuffed, I have 1329 intellect, and I'm by no means that well geared. That being said, you make a couple of mistakes in your post.
    First of all, I lose 5% crit if you I BoK (which will no longer be a question starting tomorrow), since I use this: . In 3.1, I have absolutely no idea what to take instead of infusion of light in the holy tree, so I don't really see your point about maxing out BoW.
    Second of all, intellect _is_ mp5. 100 intellect gives you (with kings):

    * 126.5 Intellect, with BoK and Divine Intellect
    * 1897 Mana at the start of the fight
    * 39.5mp5 from Divine Plea, if it's used on CD.
    * 21.3mp5 from Replenishment, with 90% uptime.
    * 4.7mp5 from Arcane Torrent, if you are a Blood Elf.
    * 25.3 Spell Power
    * 0.759% Spell Crit

    Intellect is a much better stat than you think.

    Also. You say it's unlikely to ever get the Perfect Storm for using DI, something I don't agree with. You usually use DI when you get bloodlust, so 1s cast for HL is not that far fetched.

    In the end, though, it depends a lot on your gear, which of the two is better. For my gear, there is no question, BoK is vastly supperior to improved BoW. For blues/greens, BoK might be inferior.