Patch 3.3 Mind Blast, The Definitive Math
by PiousFlea

Introduction
Since the announcement of the T10 set bonus, a lot of people have talked about dropping MB from our rotation. The purpose of this post is to provide some math behind the MB vs MF decision.

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Raw Data

Here are the raw values for shadow spell damage. Coefficients taken from http://www.wowwiki.com/Spell_power_coefficient

MB:
1020 base avg dmg + 42.85% SP
*115% damage (Shadowform)
*110% damage (Shadow Weaving)
*110% damage (Darkness)
*110% damage (Twisted Faith)
*115% spellpower (Misery)

MF (one tick):
196 base dmg + 25.70% SP
*115% damage (Shadowform)
*110% damage (Shadow Weaving)
*115% damage (Darkness + Twin Disc)
*110% damage (Twisted Faith)
*110% damage (Glyph)
*115% spellpower (Misery)

SWD:
810 base avg dmg + 42.96% SP
*115% damage (Shadowform)
*110% damage (Shadow Weaving)
*115% damage (Darkness + Twin Disc)

With all bonuses, expected noncrit damage is as follows:
MB = 1561.26 + 75.427%*SP
MF (per tick) = 345.01 + 52.024%*SP
SWD = 1178.35 + 62.496%*SP

Average damage including crits is approximated by multiplying *(1 + crit). The CSD metagem bonus may affect this by a few percentage points. This bonus was ignored for the purposes of this analysis as it would not significantly change any of the results.

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1) Blast vs Flay, no bonuses

First of all, Haste has nothing to do with this debate. At any value of Haste where your GCD > 1sec, Mind Blast will take exactly one GCD to cast and Mind Flay will tick 3 times over 2 GCDs, for 1.5 ticks/GCD. Haste only affects blast/flay balance after you are GCD capped. Assuming you have raidbuffs (+8.15% haste) but no Bloodlust, you will require 38.7% haste from gear or 1268 Haste Rating to hit the GCD cap. This is an unrealistic amount of Haste even for 3.3.

Therefore, we are comparing the average noncrit damage of one Mind Blast to that of 1.5 Mind Flay ticks.

At 3500 spellpower and 35% crit:
1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.5*MF = 698.65 + 105.349%*SP = 4386 damage
MB advantage = 1409.05 - 3.523%*SP

An average Mind Blast will deal 1286 more damage than 1.5 ticks of Mind Flay. This is a 29% increase in damage! Note that while the advantage of Mind Blast diminishes with Spell Power, you'd need 40,000 spellpower for 1.5 Mind Flay ticks to hit harder than 1 Mind Blast.

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2) Blast vs Flay, T9 4pc

Now let's throw the T9 4pc bonus in the mix. At 3500 spellpower and 35% crit for Mind Blast, 40% crit for Mind Flay:

1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.5*MF = 724.53 + 109.250%*SP = 4548 damage
MB advantage = 1383.17 - 7.424%*SP

At 3500 spellpower and 35%-40% crit, Mind Blast will deal on average 1124 more damage than 1.5 ticks of Mind Flay, for a 25% increase in damage. Note that you'd need over 18,000 Spell Power for Mind Flay to beat Mind Blast.

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3) Blast vs Flay, T10 4pc

The T10 4pc sets the base Mind Flay channel time to 2.5 seconds instead of 3. Therefore, instead of getting 1.5 MF ticks per GCD, you will get 1.5*(3/2.5) =1.8 MF ticks.

At 3500 SP and 35% crit,
1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.8*MF = 838.38 + 126.418%*SP = 5263 damage
MB advantage = 1269.32 - 24.592%*SP

At 3500 Spellpower and 35% crit, Mind Blast will deal on average 409 more damage than 1.8 ticks of Mindflay, for an 8% increase in damage. If you can get 5162 Spell Power or more, 1.8 Mind Flay ticks will hit harder than Mind Blast.

As you can see, at any realistic gear level Mind Blast is still stronger than Mind Flay in terms of pure DPET. Anyone who says otherwise hasn't done the math.

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4) Combining Blast and SWD

Some shadowpriests use SW:D to sync their rotation up with MB cooldowns so that they can cast as many MBs as possible. Is this still beneficial with T9? T10? I will compare 3 ticks of Mind Flay (2 GCDs) to one MB and one SWD. With the T10 bonus you will get 3.6 ticks of MF (3/2.5).

At 3500 SP and 35% crit:
MB+SWD = 3698.47 + 186.196%*SP = 10215 damage
3*MF = 1397.29 + 210.697%*SP = 8772 damage
T9 3*MF = 1449.04 + 218.501%*SP = 9097 damage
T10 3.6*MF = 1676.75 + 252.836%*SP = 10526 damage

As you can see, the SWD + MB combo will boost your DPS with T9, but not with T10.

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5) Clipping MF at 2 ticks

Some shadowpriests clip MF at 2 ticks in order to get more Mind Blasts. Is this beneficial? How precisely do you have to clip so that you don't lose DPS? I will compare two scenarios:

I) 3 ticks of mindflay, plus delay, then mindblast.
II) 2 ticks of mindflay, plus delay, then mindblast.

It was rightfully pointed out that you get a similar delay whether you clip with 2 ticks or 3. The question is, how much delay does it take to make clipping counterproductive?

For these comparisons we will use a base haste value of 511 Haste Rating. This translates into 15.58% haste from gear, which multiplied with 8.15% Haste from raidbuffs equals exactly 25% Haste. Therefore, Mind Blast will cast in 1.2 seconds and Mind Flay will tick every 0.8 seconds.

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I) 3*MF+MB = 3504.99 + 312.523%*SP = 14443 damage over 3600ms
II) 2*MF+MB = 3039.23 + 242.291%*SP = 11519 damage over 2800ms

I deals 4012 DPS, while II deals 4114 DPS. It is obvious that clipping mindflay gives a VERY small bonus if any - even with zero delay.

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To solve for the maximum tolerable delay X, we want the DPS to be equal between I and II:
14443/(3600+X) = 11519/(2800+X)

(2800+X) = (3600+X)*(11519/14443) = 2871+0.7975X
0.2025*X = 71
X = 351 milliseconds

This is a fairly high number, meaning that latency should not make clipping counter-productive. However, the point remains that even "perfect" MF clipping provides a vanishingly small DPS benefit. For this reason, if you have any uncertainty about MF clipping (for example, if you mis-clip and wind up with MF1) then you should not do it at all.

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TL:DR summary

1) Regardless of gear, using Mind Blast will always increase your DPS compared to not using it.
2) Using SWD to sync with Mind Blast cooldowns is only worth it if you don't have Tier 10.
3) Clipping Mind Flay to sync with Mind Blast cooldowns is at most a tiny benefit.

Disclaimer: This analysis was performed November 4, 2009. Future patch changes may invalidate the results of this analysis.

sticky...!!

Yes please (and Thx Pious ^^ )

Great post. The only other question I can think of which would be worth answering is how long is it worth delaying casting to wait for MB to come off cooldown?

I would imagine that with no bonuses or with t9 bonus then it would be worth at least a brief delay if MB is about to come off cooldown. But with T10 then MB and MF get very close so the window of opportunity would be miniscule.

Great post, thanks for calculating and clearing everything so smoothly!

I would just like to comment this part :

In the best case scenario for MB, you get that damage advantage every 6.5 seconds.
That means you do 62.92 more dps if you cast MB instead of 1.8 MF.
In a perfect fight where you can chain spells perfectly as soon as their CDs are down, sure MB is to be used as often as possible, but in reality, with all that can happens, I wonder if this "less than 1%" increase in dps is really worthy.

And that has been the discussion over the last month (or since whenever the T10 bonuses came out)

There will probably be people who keep it in their "Rotation" for the sole reason to supply replenishment.
There will probably be people who drop it because the extra DPS isnt worth the extra hassle

Of course, this is assuming that blizzard wont make MB more attractive to cast.

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No set bonus:
At 3500 spellpower and 35% crit:
1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.5*MF = 698.65 + 105.349%*SP = 4386 damage/GCD

1 MB deals as much damage as 1.293 GCDs of MF

If (Delay+MB) >= 1.293 GCDs then MF does more DPS than Delay+MB, thus Delay = 0.293*GCD.

At 511 haste (GCD=1200), Delay = 352ms.

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T9 set bonus:
At 3500 spellpower and 35% crit:
1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.5*MF = 724.53 + 109.250%*SP = 4548 damage/GCD

1 MB deals as much damage as 1.247 GCDs of MF

If (Delay+MB) >= 1.247 GCDs then MF does more DPS than Delay+MB, thus Delay = 0.247*GCD.

At 511 haste (GCD=1200), Delay = 297ms.

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T10 set bonus:
At 3500 spellpower and 35% crit:
1*MB = 2107.70 + 101.826%*SP = 5672 damage
1.8*MF = 838.38 + 126.418%*SP = 5263 damage/GCD

1 MB deals as much damage as 1.078 GCDs of MF

If (Delay+MB) >= 1.078 GCDs then MF does more DPS than Delay+MB, thus Delay = 0.078*GCD.

At 511 haste (GCD=1200), Delay = 93ms.

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You're correct, with the T10 bonus the difference between MB and no MB is very small. However, it is still a damage increase. A non-meta gem is worth less than 62.92 DPS but you wouldn't raid with a socket ungemmed.

What's even crazier is people who argue that you should stop using MB with a T9 set bonus. As the math shows, you'd give up over 150 DPS by never using MB. That's a difference on the order of flasking versus not flasking.

In addition, unless you royally mess up your rotation, there is not a major risk of decreasing your DPS by using Mind Blast. If you're not that good at using MB you might not use as many Mind Blasts as you could, but as long as you're not unintentionally clipping MF or failing to recast DoTs you won't decrease your DPS.

This is in stark contrast to TBC-style intentional MF clipping. With perfect reaction times, MF clipping can also yield a theoretical DPS increase of 60-odd DPS at level 80. However, every time you misclip you're losing several thousand damage.

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Let me end my walls of text with a brief tirade about statistical significance. "Personal experience" with target dummy DPS parses are completely meaningless because of the inherent variations of Crit and trinket procs.

A very simple minded analysis:

A +20 Crit Rating gem gives exactly 0.4358% crit. Let's say your crit chance is 30% without the gem, 30.4358% with. What sample size do you need to get a statistically significant difference between 30% and 30.4358%?

Using Pearson's chi-square formula, you would actually need n = 42,459. This would give you an expected:
12,923 crits and 29,536 noncrits at 30%
12,738 crits and 29,721 noncrits at 30.4358% (p=0.05)

Assuming you hit the target once per second, you would need to DPS a target dummy for nearly 12 hours straight to achieve this level of significance. Presumably, you'd take much longer than this due to running OOM.

The point of this thought exercise is: Target dummy DPS parses are utterly useless for measuring small DPS differences. No one would argue that you should stop gemming your gear. However, you could leave quite a few gems out and not be able to tell the difference based on target dummy parses.

This is why simulation (with >=1000 simulated dps runs per datapoint) or direct computation are the proper way to tell which rotations yield superior DPS.

Thanks Pious!

also..



made me lol very hard

3,500 spell power will not be anywhere near accurate in Patch 3.3. Please consider that 25-person buffed raids will near 3,800 in short order. Depending on the off-pieces, we may finish this expansion at 4,200+.

Thanks Pious, excellent posts that clear up a ton of questions.

Sticky this!

Also, Pious, nice name. I catch the reference.

Great post thank you

Well that 8% is not 8% increase in dps. Its 8% more on that GCD only.

What this means: Haste very very much affects the % of damage that MB will add in your total DPS - Depending on the amount of GCDs that you can fit between mind blasts

How much dps increase is MB at 1000 haste ? 1.5% ? 120-150dps ?
How much that becomes when you delay MB? (assume that you delay it instead of clipping since clipping is bad!)

Edit: since MB is about 10% of damage that makes is 0.8% increase in dps at the gear of http://code.google.com/p/simulationcraf ... eOutputPTR (at 600haste | 10kdps+ is about 80dps)
At higher haste and/or when you delay MB its even less.

I am getting 4-piece, 1000haste and I am skipping MB

First, thank you Pious for the number-crunching - it is most beneficial as a "base" to begin a conversation like this. I have always held that because general MB theory assumes the "every 6.5s" optimal situation, and that said situation in-game never happens even among the most skilled/lucky SPs, then you have to get to the meat of the matter to see just what kind of a benefit we are talking about in the first place. I'll share my personal opinion on MB-or-no later, but first the math...

Your analysis shows a net 63 dps increase comparing MB to T10 4pc MF 1:1 over x time. This is with the conditions of 3500 SP and a haste amount below the hasted 1s GCD (1268 from gear as you state) in a raid setting. Thus to me there are a couple clear exceptions to note that would cause the increase to be less:

1) > 3500 SP - I took a quick glance at my shadow set (I'm Disc main now) and calculated I roll with 3635 SP (3745 with the 3.3 shadow glyph change) in a 25 man static already, before any short term buffs (Lightweave cloak for example). This is with 1 258 piece and a few 245 heroic items. Therefore as griemak posted earlier it is reasonable to assume that we will cross the 4k barrier in 3.3. In addition, every time a SP proc hits, that further closes the gap during that buff duration. Lightweave/trinkets/the new 3.3 rep caster ring will all provide these, bringing you one step closer to the 5162 SP "break-even" point you mentioned.

2) Haste procs/Heroism - Again, I'll use your 1268 self rating to reach GCD. With haste tracking equal to or greater in relative value to SP in early 3.3 calcs, it is certain many people will stack haste in 3.3. In addition, +haste effects become very valuable as well, especially in conjunction with the SW:P behavior of retaining the initial value (this might not make it to live, we'll see). Regardless, I see situations where a priest with stacked haste (1kish maybe?) + haste trinket breaks the GCD and therefore enters the realm of MF superiority. This is only for the buff duration of course, but it should still be noted (a 20s duration/2 min CD trinket would mean 1/6 of active time at least). Heroism is certainly in this category as well, and while it is only once per fight, it is nonetheless a considerable portion (40s).

So a cursory look here at the above points. If you substitute 4000 for 3500, approaching the magic number of 5162, that is roughly 30%, so would it be fair to say we can lower 63 dps number to 43, or is that not a linear relation? After this you would have to consider the effects of any SP procs and how they further lessen the gap during the duration. Furthermore, if you can break the GCD barrier with a trinket, then you must take that amount of time + heroism time as not only break-even, but on the + side of things for MF vs. MB. You can either try and calculate this vs. the MB favored times, or simply write it off as a moments where you simply switch your priority mindset from MB to MF, then back again when the buff wears off.

Either way, this brings me to my personal opinion on MB priority casting - it never matches up in-game to the math on paper, and now with the T10 4pc, we have a situation where the benefit shrinks to the point where we can realistically say statistically it is a bit of a wash. With the math so close, you begin to think about how MB-obsessive behavior (clipping a MF/waiting a fraction of a second for MB to finish CD) hurts you in the long run. My own personal "stress free" rotation I developed a while back may very well become my standard rotation in 3.3 - cast MB after every VT cast. This is an easy way to make sure Replenishment stays refreshed, and will guarantee MB is always off of CD when you reach for it, leaving you to MF to your heart's content the rest of the time. This also makes Improved Mind Blast a non-mandatory talent, freeing some points for the shadow "extras" later in the tree that may or may not be nice to have depending on the encounter you are working on, but that's a topic for another thread

can we get simulationcraft results with purity's rotation vs 'standard' rotation?

I'm not 100% sure how to mod priorities in simulationcraft...

Nice thread,

Im still new to all these simcrafted number stuff.

But If I had to be honest, clipping mind flay for mind blast i am personnaly seeing no major increase in DPS. Also I am finding myself going ooom and having to use dispersion sometimes, which I try to avoid generally during a few of the TOGC 25 fights due to multidotting.

So yeah personally lose a little DPS but at least you wont go ooom, as purity said, mind blast gives replenishment so that a raid utility buff given by us and ret palas so its important as well.

Definately keep MB in rotation even in next patch.