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Spiritual Guidance: Shield spam and Divine Aegis, a theorycrafting story

In the beginning there were priests. Then Blizzard said "Let there be other classes!" Things have been a lot more complicated ever since. Fortunately, there is Spiritual Guidance, WoW.com's bi-weekly guide for priests. On Sundays you can enjoy discussion on discipline, holy, and healing in the company of Dawn Moore. We don't have cookies here, but only because we call them biscuits, and serve them with tea, sandwiches, and scones. Did you want one lump, or two?

A couple of months ago I found myself talking to a non-priest about the gems I had slotted on my character. He was of the understanding that disc priests wanted nothing but crit, and thought it was strange that I had gemmed straight spellpower on all my gear. Figuring he was behind on the times, I happily explained to him that I was using the standard gem set up for shield spamming disc priests, which works around the premise that if the majority of what we do is cast shields, then we should stack as much spellpower as possible in order to make our most used spell (Power Word: Shield) absorb more. This is the standard practice advised to shield spammers throughout the priest community, and I've advised it here on Spiritual Guidance before as well.

The non-priest still didn't understand though. He kept insisting "but crit ..." which inclined me to gently stroke back his hair and say "there there, poor little confused non-priest, it's all right." I allowed him his dignity though, and instead went on with my explanation. I told him that alternative stats like crit and haste didn't do much for shield spamming since Power Word: Shield can't crit, and Borrowed Time removes the necessity for haste since the talent carries us down to the 1 second GCD soft cap whenever we cast Power Word: Shield. The non-priest still didn't understand, so I explained to him that a disc priest's primary interest in crit was Divine Aegis, a talent which applies a second shield whenever one of your spells crits. "But shields don't crit," I reiterated. "The heal from the Glyph of Power Word: Shield can, but that would only add say ... 500 extra absorption from Divine Aegis. The spellpower is still better."

As I typed out those last words, they boomeranged back and hit me square in the face. Startled, I peeled the sans serif off my nose and and reexamined the limp letters in my hands. Suddenly I wondered, "is that really true?"

The question

After I pulled the last of the ink from my eyebrows, I quickly set to work at trying to figure out the math for my question. My stream of thinking went like this: The Glyph of Power Word: Shield causes each Power Word: Shield you cast to heal your target for 20 percent of the amount of the shield. If we say the the average absorb amount for Power Word: Shield is 10,000, then the glyph will heal our target for around 2,000 health. If the heal effect crits, then we'll heal our target for 150 percent of your heal, which is 3,000 health. But that critical heal from the glyph will also apply a Divine Aegis. The Divine Aegis will absorb damage equal to 30 percent of the critical heal, even if it overheals. So, if the crit heal from the glyph is 3,000, that means the Divine Aegis would absorb around. 900 points of damage.

I sat back and looked at my numbers. The numbers were inflated but still, I had never really considered just how much extra absorption Divine Aegis could do through Power Word: Shield. I never questioned the validity of spellpower stacking before. After all, I had come to the bubble spam scene late, pursuing a career in tank healing well into early Icecrown Citadel. When I did submit to the good of the raid, I just accepted the methods and shrugged off any benefit from crit as negligible. But now I started to wonder if crit and Divine Aegis had been accounted for in shield spammer throughput. How beneficial might it be to increase my Divine Aegis output as a shield spammer?

My thoughts wandered to the extra spellpower I had on my gear from gems and wondered what they did for me. I had 17 Runed Cardinal Rubies equipped, adding up to almost 400 spellpower. If I swapped those out for spellpower and crit gems, I could get an extra 3.7 percent chance to crit in exchange for about 200 spellpower. If I wanted to drop the spellpower completely and go with straight crit gems, I would be giving up that 400 spellpower for an extra 7.4 percent.

I immediately recoiled at the amount of spellpower I would have to drop to gain a sizable amount of crit. Plus, the gains seemed too small to make a big difference. What could 3 percent really do? Plus, I was still trading off spellpower for a chance to apply extra absorption, not a guarantee. The extra spellpower, on the other hand, would affect every shield I cast. Things seemed doubtful for crit, but I was determined to give it a fair shot.

I jotted down more scenarios and considered trading out my haste gear for crit gear, since it didn't require losing any spellpower. I wondered about diminishing returns, raid buffs, and crit from intellect. The more I thought, the more the variables started to pile up around me and it wasn't long before I realized I should get some more qualified help. So, I gathered up my notes and went off to see Zusterke.

The wizard

If you don't know who Zusterke is, no worries. I've mentioned him on Spiritual Guidance before only in passing. Zusterke is a theorycrafter in the priest community, most commonly found working his math magic at PlusHeal.com or even occasionally here at WoW.com, in the comments of Spiritual Guidance. He's also got his own little site, Zusterke's Corner, where you can find lots of useful calculators for priests. He has even been a guest blogger on the legendary World of Snarkcraft, a since retired priest blog run by Joveta and Serianna, the queens of priest blogging in early Wrath of the Lich King. (This is where I first learned of him.) Zusterke also happens to be one of my better friends in the WoW community, and I frequently bounce terrible article ideas off him before going further with them. So technically, you guys already owe him for sparing you a lot of rambling from me. He couldn't spare you this one, however.

Anyway, on a late July morning, I suggested the idea to Zusterke that crit could be better than spellpower, and asked him for his opinion. Immediately he seemed quite doubtful, and moments later provided me with some preliminary math.
Zusterke: Well ... I made a raw throughput comparison. Much like the spirit and int technique I make the formula and derive for both sp and crit. Then compare both.

HPS = (Base + coeff * SP) * (1+Bonus) * (1 + 20% * (1+ crit/4591 * 95%))
d(SP) = coeff * (1+Bonus) * (1 + 20% * (1+ crit/4591 * 95%))
d(Crit) = (Base + coeff * SP) * (1+Bonus) * 20% * 95% * 1/4591

Then we check d(Crit) > d(SP) to know when crit rating is more valuable. (Not being entirely fair since we compare 1 crit to 1 SP and you can get more SP per point of crit) It works out to be: SP > 27146 + crit rating. Which means your SP should be over 27K before crit rating becomes stronger. But I might want to double check this.
Immediately the question flat-lined. My non-priest friend's idea wasn't going to hold up. I watch poor crit scurry off to a corner and whimper like an abused Shadowfiend; my heart swelled sympathetically for it.

For whatever reason, I got it in my head to try advocating for crit from another angle and wondered if there was some sort of compromise I could make on its behalf. I suggested to Zusterke that the rigidness of disc gearing and gemming was a cause for concern to a disc priest who also wanted to tank heal. What would happen if we started to apply the 15 second Weakened Soul debuff to the picture? Zusterke admitted his calculations were strictly for bubble-spamming, and that for tank healing he still recommended balance, something I also suggest here in Spiritual Guidance.

After that, I didn't think much of the failed theory until Zusterke messaged me a week later. I was surprised when he revealed he'd been working on it.
Zusterke: I've been thinking about your crit theory a bit. I thought I'd try something... Investigate whether crit or SP would deliver the biggest contribution to Divine Aegis. It seems this can depend on the spell, but things are looking a bit brighter for crit. Of course, this is restricted purely to Divine Aegis and not the whole throughput of the spell.
Dawn: What's your process?
Zusterke: Well, I worked out a big nasty formula. But it can be brought down to this:

SP = factor * critrating - Base/Coeff

Factor is the difference in stat cost between spellpower and crit rating. (For the stat cost I decided to base myself on WowWiki.)That would be 1.1667. Anyways, this equation shows the balance between both stats in terms of throughput. It is 6/7 in terms of cost. However I need to inverse that (7/6) because for one point of crit rating I can get 7/6 spellpower.

Dawn: What spells have you looked at?
Zusterke: I don't have to see many spells. Check this: imagine we about 40% crit on a target, based on talents, buffs, gear etc... This is the equivalent of 1836.4 crit rating. Our formula becomes:

SP = 2142.5 - Base/Coeff.

As such, for any reasonable amount of SP, crit is likely still to be the most valuable stat. The base heal and coefficient will combine to a negative number, in benefit for crit. So... Even if the base heal would be 0, any amount of SP above 2142 would imply crit is better than SP.
I stared stupidly at Zusterke's formulas. He had told me many times that people often misinterpreted his theorycrafting, then made it worse by trying to use their incorrect conclusions to support their own theories. This was the first time I saw for myself just how easy it was to misunderstand this stuff. Fortunately, to help me understand, Zusterke later gave me a tour through his daunting spreadsheet, and let me play with some of the crit values to see how the numbers worked with each other. (He even worked in some extra variables for me, like overhealing.) It certainly was impressive to look at.
The new math intrigued both of us. Since I'd been rooting for it, I was pleased to see how influential crit was to the Aegis (something to keep in mind when us disco priests get back to tank healing.) Zusterke seemed to appreciate the working relationship between the two, commenting that crit took on a role very similar to hit, in that the Divine Aegis needed it to function.

Unfortunately for crit, the new formulas weren't enough to coax the little stat from its corner. Zusterke's formula determined crit was only stronger when Divine Aegis was isolated. Once the throughput of Power Word: Shield is added back in, crit no longer holds up against spellpower. I made a graph to illustrate this (read: not a spreadsheet.)
I used 100 Power Word: Shields as my foundation, since it would allow an amount of Divine Aegis obviously proportional to the percentage of crit. 100 is also a good number to estimate for a normal fight. (To give you an idea how many shields us spammers use, in the heroic Lich King fight I might cast between 300 and 400 shields during the 15 minute fight. And that is casting shields for the first 2 phases at very specific points in the fight.) The absorption amount for Power Word: Shield is determined using the normal formula. The absorption amount for Divine Aegis is determined by multiplying the glyph crit amount by 30%. You get the total amount of throughput from absorption by adding up both totals.

The conclusion

So what did we learn out of all this? Well for one, that my non-priest friend was wrong. The theory I proposed on his behalf didn't hold up, and the spellpower stacking that the community and myself, however blindly, have advocated was the correct choice. Overall it's a nice feeling for me. I felt satiated to come out where I started, but now with the understanding that I've explored different routes as a spammer. Hopefully this exercise has done the same for any other disc priests who might have wondered why spellpower was the thing to do over everything else.

That said, between my talking with Zusterke and my own simplified math, I now have a more tangible understanding of the trade off between crit and spellpower. Min-maxers will recoil when I say this, but the difference honestly isn't that large. Over 100 Power Word: Shield casts, you lose a little from each shield by taking crit, but you can see in my graph it only adds up to about about 3 shields. It makes me think to myself that if you're interested in flexibility (e.g. the ability to swap to tank healing without regemming your gear) then you're not losing much to take a more balanced approach to gear. (Alternatively, you could also say you don't gain much by taking a little extra crit, but I have to draw the line somewhere.) Again, if you're a min-maxer then this probably sounds like appalling advice, but I think it's a fair trade.

I could be wrong, but I have in my mind an idea that most disc priests don't play the way I'm used to in my progression guild, assembly line raids. I rarely have to cross heal in a guild raid, but back in the day when I played with more pugs and less progressed guilds, I remember everyone cross healing more to cover each other. It's up to you really. Typically, I really like to advocate min-maxing as a way of getting the most out of what you do, but I understand it's not always applicable or needed. Plus, true min-maxing must be considered on a fight per fight basis. You can't necessarily pick one set up and be truly min-maxed for an entire dungeon. Spellpower stacking is no exception. If you do switch roles a lot, feel free to balance your stats a little. The crit will help out your normal casts and in turn your Divine Aegis output. So in that sense, my non-priest friend wasn't wrong about crit being what us disc priests want. We do want it, just so long as we do more than push the Power Word: Shield button on occasion.

Want to find more great tips for carrying out your priestly duties? Spiritual Guidance has you covered with all there is to know. Check out Holy 101 or Disc 101 for an introduction to healing as a priest; for the party-minded healer, check out a priest's guide to tanks.

Filed under: Priest, (Priest) Spiritual Guidance

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