Patch 3.3 changed the Black Magic weapon enchant to a haste proc effect: 35% chance to proc 250 haste rating for 10 seconds, with a 35 second internal cooldown.  When the change first appeared on the PTR and at intervals since as more information has emerged, various Elemental Shaman folks at Elitist Jerks have done the maths and concluded that it’s not worth using over the Mighty Spellpower option.

Despite this, a lot of other folks are suddenly suggesting all over the interwebs that it’s “best in slot” and that Elementals should be using it instead of Mighty Spellpower.  Argh!  Which is it?!

To the testmobile Batman!  Let’s see both (a) how we can check the equivalent potency of each enchant and (b) which actually comes out on top.

How to test

Averaging the proc

The first and easiest method of testing the proc is to average it out into a constant haste figure that we can use to compare to the 63 spellpower from the competing enchant.  First, we need something to give us equivalency points for haste and spellpower: I’ll use my own spreadsheet for this.  Equivalency points differ depending on what the user’s precise stats, buffs/debuffs and other settings are, but for my own shaman – Chayah – with the default settings, the DEP of a single point of haste is 1.733 and spellpower is 1.650.

Secondly, we need to figure out how often the proc will trigger.  We know it’s a 35% chance each time we fire off a spell, so we can work out how many seconds we’ll wait – on average – for a proc by working out how many spells we fire a second, then multiplying that by 35%, then dividing a second by that.  With Chayah’s stats this is an average proc time of 3.33 seconds (!).  Add that to the internal cooldown and you get a proc once every 38.33 seconds.

Thirdly, we average out the proc duration over the time between procs.  The internal cooldown triggers as soon as the proc does, so this would be 10 seconds divided by 38.33 seconds or 26.09% of the 250 haste proc, which is 65 haste.

Finally, we multiple the two competing values by their respective DEP totals:

Black Magic as 65 haste rating on average: 65 * 1.733 = 112.45 DEP

Mighty Spellpower as 63 spellpower on average: 63 * 1.650 = 103.95 DEP

Using this method, it looks like Black Magic is coming out on top for Chayah by 8.7 DPS.  But what if a proc goes off at an inopportune time?  Let’s assume that one in every four procs will be totally wasted and that we’ll get the maximum benefit for the other three.  This results in the average haste coming to only 49, and the DEP drops to about 85, which is 19 DPS less than the spellpower enchant which does not suffer the limitations of the proc.  Suddenly instead of being a tiny bit better than Mighty Spellpower, it’s a lot worse!

This reflects something of the fragility of a proc effect versus a static effect and is why Black Magic is generally advised against by the theorycrafting community.  But of course, once we start making assumptions like the one above, we’re moving beyond what simple DEP values from a spreadsheet can do for us.  So we move on to the second method:

Modelling the full proc

Another way of working out the relative values is to model the full effect of the Black Magic proc, but then to apply that effect for only a portion of the fight based on the “uptime” as defined by the proc chance maths we did earlier.  This is better than averaging out the proc because it reflects what really happens to our spell rotation with the extra haste.

So firstly we need a model for normal elemental DPS: once again, I’ll use my own spreadsheet for this.  Secondly, we need to change the model to subtract 63 spellpower from the entire fight, but to add 250 haste temporarily at certain points.  Then we can subtract the values produced by this new model from the values produced by the old model, with the same stats and settings, to get the Damage Equivalency Points (DEP) of the Black Magic enchant as compared to the Mighty Spellpower enchant.

Finally, we want to see how different situations affect this relative DEP.  First we can try fiddling around with haste values.  The graph below reflects what happens to the relative DEP of Black Magic when, using Chayah’s current stats with default settings, we vary the amount of haste rating she has:

The zero line is where it breaks even with Mighty Spellpower; above zero means Black Magic’s better, below zero means it’s worse.  We can see that with Chayah’s other stats remaining intact, Black Magic looks a tiny bit better at very low haste rating values, but gets dramatically worse as haste gets higher.  We can also see that factoring in “movement” (a regular short period of no spellcasting) nearly always results in worse performance for Black Magic as compared to Mighty Spellpower.

Now of course, nobody is going to have only 200 haste rating with Chayah’s 50% crit chance and 3k spellpower.  So let’s establish two gear profiles:

1. “base” gear for a shaman who’s just reached level 80 and is part-way through farming heroics.  We’ll call this gear level 0.
2. “best” gear for a shaman who’s completed farming tier 9 25-man heroic content to the very gills.  We’ll call this gear level 10.

(29/12: those links don’t work anymore because I had to delete the profiles to make room for Icecrown BiS fiddling.  However you can still see the stats used on the google docs spreadsheet linked at the end.)

The exact gear choice isn’t that important – what is important is the difference in stats that it gives.  We can take these differences and then average them out equally over an arbitrary number of “upgrades” and use them to plot a meaningful “gear level” where each stat increases incrementally from the ‘base’ level to the ‘best’ level.  This should result in a fairly realistic distribution of stat increases at each arbitrary gear upgrade stage.

Doing this – again using full raid buffs, heroism etc, but this time not using any set bonuses or relics – from level 0 through to level 10 resulted in the following relative DEP values for Black Magic:

Again, zero is the break-even point for Mighty Spellpower.  This time we can see that Black Magic is clearly worse than Mighty Spellpower for nearly every gear level, and that even when the “No movement” line does peek above zero, the “movement” line is well below.  Furthermore the maximum gain from Black Magic peaks at only around 3 extra DEP, but the maximum loss is down near 30 DEP.

Conclusions

So, what do these tests suggest?

Firstly, it’s pretty clear that Black Magic does not react well to circumstances other than standing-‘n-nuking.  Emulating even the slightest amount of movement or casting delay dramatically decreases its relative value for nearly all circumstances.

Secondly, we see that even when the value of Black Magic does seem to exceed the value of Mighty Spellpower on paper, it’s by very very small amounts – it never gets much above 10 extra DPS, and even then only briefly and in the least realistic model.

Thirdly, we see that the value of Black Magic is both variable and “fragile” and peaks and dips based on all of our other stats and the circumstances of the fights.  These dips are always far lower than the peaks, which means that the average DPS loss of Black Magic is always greater than the average DPS gain.  While enchanting Black Magic may give you 5 or 10 extra damage in one fight, in the next fight it may cost you 20 or 30 DPS.  That’s not a good trade if the fights where it’s costing you are the fights that demand the highest DPS.

And all this is only for a single target: start factoring in AoE and the use of fire DPS totems and the verdict would swing even more in Mighty Spellpower’s favour.

Of course, as with our Big Four glyphs, the actual difference between Black Magic and Mighty Spellpower is so small (at worst and assuming the player doesn’t get horribly confused by the proc and screw up his or her rotation entirely, the difference is no more than 100 DPS) that using the “wrong one” won’t have that big an impact on your DPS.  So if for some reason anyone really wants to use Black Magic, don’t let me stop you.  But for serious, maximum, robust PvE DPS, stick with Mighty Spellpower.

Where Black Magic does perhaps look quite nice is for PvP, but as this is a blog about PvE that’s as much as I’ll say.

(You can see the google docs spreadsheet wherein I collated the results here.  The modified version of ZAP! which I used for modelling the haste proc is available here.)