Tuesday, January 26, 2010

Discipline Priest Mana Efficiency

Here is a blue post from a few months back that has been festering in the back of my mind:

Power Word: Shield is a really useful tool for Disc priests in particular. We want them using it. However, its utility is balanced by a high cost. If we get to the point where they are spamming it constantly to the exclusion of other spells and without it ever being a decision, that suggests mana regen is still too high.

If I remember correctly this was posted in a thread about how Discipline priests are boring to play because all they do is spam Power Word: Shield. It reads a bit like a "Stop complaining before we nerf you" type of response, but it really makes me wonder if this is what they actually think. In reality, Power Word: Shield does not have a high cost, it has a very low cost. Spamming Power Word: Shield is not something we do because we have too much mana regen and if mana regen were lowered considerably it would be all the more reason to cast Power Word: Shield.

Compare Power Word: Shield to Flash Heal. They have the same coefficient, similar base amounts, the base cost of Power Word: Shield is significantly higher. So from the base spells the comparison made in the blue post is valid. But taking a look at the discipline and early holy tree, we find there are 22 talents that prop up the effectiveness of Flash Heal while there are 27 that prop up Power Word: Shield. What's more, those talents that prop up Flash Heal are mostly in the 1-2% range, with a few being closer to 3% and a few being well under 1% while the talents that prop up Power Word: Shield max out at about 5% increased effect, with a large number of points in the 3% range and a one point 15% cost reduction. And then there's Rapture, which I'll talk about in a moment. The Discipline tree actually has 14 points that either do nothing but increase the effectiveness of Power Word: Shield or have no effect unless you've recently cast Power Word: Shield, there are 3 points devoted in a similar way to Flash Heal. As a point of comparison, Frost Mages have 7 talents that key off Frostbolt in this way. That's right, a class and spec that does nothing but spam one spell1 has less talents specifically designed to prop that spell up than discipline priests have for Power Word: Shield.

And these are our best talents. 5% effect per point for 3 points, 15% cost reduction, 8% spell power coefficient per point for 5 points, mana return that amounts to about 80 mp5 per point for three points as long as shields are cast regularly. With that much invested in this spell, it had better be good enough to spam.

Now I'm the first one to admit that if you want to make something look good, comparing it to Flash Heal will do that. If any other healing class had a spell that after all talents were considered healed for as little as Flash Heal, was as slow as Flash Heal and cost as much as Flash Heal it would not even be on their bars. But for priests Flash Heal is what we've got. I can't readily replace a Power Word: Shield that is meant to backstop health loss with any other spell whether because of cooldowns or because of the very specific application of those spells.

If we naively count the mana returns from Rapture as a cost reduction to Power Word: Shield then it cost me only 414 mana per cast on my last ICC run. This gave it a healing per mana of about 24, factoring in overheal and unused shielding. Flash Heal comes in at 10.4, Penance only got 19.4. Furthermore, it has better throughput than Penance (9714 vs. 9632 healing per second). In fact, the only reason Penance shows up so close is because 69.2% of my Penance casts were made under the effect of Borrowed Time. That means that the fact that I cast so many Shields accounted for about 15% of my Penance throughput. If you factor out the Borrowed Time haste, Power Word: Shield has more healing per cast time than any other spell except for Prayer of Mending. If Borrowed Time were not boosting my other spells, I would be better off spamming Power Word: Shield to deal with AoE damage than I would be casting Prayer of Healing. In reality my maximum output comes from alternating the two.

I subtly admitted, of course, that this is a weak evaluation of the efficiency of shielding. After all, you can only get a Rapture proc every 12 seconds, so casting more shields means more procs, but not in a linear fashion. Basically every shield is more expensive than the last one and spamming it might be costing me more than this analysis lets on.

One of the great things about writing your own log parser is being able to tell it to simulate stuff like this for you. I made some modifications so that it could substitute Flash Heals for Power Word: Shields. It did so at random, first with a 50% chance and then with a 90% chance of substituting so we could see what the effects on my throughput and mana would be. By substituting half my Power Word: Shields for Flash Heals the average cost of a shield went down to only 342 from 414, so shields did get relatively cheaper. On the other hand my net mana went down by about 8 mp5; not a whopping difference, but it went down not up. At the same time my throughput went down about 7%. In the scenario where I cast 90% less shields the average price of a shield was only 22 mana. My net mana went down even further, by another 15 mp5 from the 50% scenario (23 from the real number). And my throughput was about 11% lower than my real throughput. By casting less shields I got more Raptures per shield, but I spent more mana and did less healing. In reality these numbers would not look like that at all. After all, healing done is correlated to damage taken more than to anything else. If I did 11% less healing then either the other healers would be making up the difference or I would be; probably a combination of the two. This means my throughput would be pretty similar and my net mana would be much lower. If I had to cover the cost of that 11% throughput reduction in Flash Heals, then my net mana would be about 10 mp5 lower. These aren't huge differences, but the point is I would have less mana if I cast less shields to the tune of about 10k less mana to spend on a five minute fight.

In fact, it is excessive mana regen that allows us to choose not to cast Power Word: Shield. On Blood Queen Lana'thel I realized after a couple of learning pulls that I should not be using shields to prop up the raid from the persistent AoE damage. Sure, it's my most efficient way of dealing with that damage, but her predilection for shooting a Twilight Bloodbolt a second after casting Pact of the Darkfallen meant that health could drop precipitously and shields were best saved for backstopping that. So I began shielding only when there was a Pact or Swarming Shadows cast. This kept us all alive much better than my typical shield spamming mindset. This, however, left me casting a lot of Flash Heals which is extremely inefficient. The only reason I could afford to do this is because I do have too much mana regen. Lowering mana regen would force me into using more Shields, not fewer Shields, and put me in a position where I can't use Power Word: Shield on the task that I would most like to use Power Word: Shield for, because I am using Power Word: Shield on the tasks for which Power Word: Shield is the spell among my spells I would most like to use; that is, I am using it for everything.

Blue posts like that one scare me. A lot about World of Warcraft does in fact convince me that many of the developers working on it have the ability to do basic math (calculating the expected number of attempts for things like "Mask Task" aside) but that post showed a really shocking inability to multiply a few numbers and notice that Power Word: Shield is our best throughput and most mana efficient single target heal. That is why we cast it so often. Of course, the idea that there are priests out there literally doing nothing but applying shield after shield with no thought to casting any other spell is pretty fictional. Maybe on certain phases of certain fights, but if you want to look at certain phases of certain fights you will find all kinds of odd behaviours that don't reflect the overall state of healing.

1. In PvE where using instant fireballs and ice lances, I understand, is actually a dps loss at good gear levels.