Elemental: Crit vs Haste

This is a topic that gets a lot of shamans (and non-shamans, especially those who assign loot in raids) all a-flutter and terribly confused.  Which stat should an elemental shaman prefer – haste rating or critical strike rating?

In the Burning Crusade, shamans loved crit.  It was a great stat for us.  All (two) of our DPS spells could crit, we got a full talented 200% bonus to critical damage, and crits procced clearcasting which improved our mana efficiency.  That was pretty important back then.  Towards the end of TBC, large quantities of haste started appearing on mail gear, and stacking haste became a viable – if much debated – gearing tactic for elementals.  Haste and crit were two different and competing gearing strategies, even though one was broadly proven slightly superior to the other on paper.

Let me be clear right from the start: this is not the case in Wrath of the Lich King.  There is a very clear victor in the war of crit vs haste, and choosing the wrong stat will have an extremely negative influence on your DPS.  Here’s why.

How Critical Strikes work for Elemental

If you look at a typical combat log parse for a raiding elemental shaman, you’ll find that on average crits make up a staggering 70% of the total damage we do.  Clearly crits are important for elementals.  But what about crit rating?  Let’s explore the way critical strikes work for us.

Crit damage bonus

The base modifier for a critical strike is 1.5 * normal hit, or an extra 50% damage.  Using a Chaotic Skyflare Diamond we get a 3% bonus to the base crit bonus.  Then we have talent buffs which stack additively with each other and multiplicatively with the base bonus: Elemental Fury is a 100% increase to all our crits, and Lava Burst then further benefits from a 24% increase through Lava Flows.  The total bonus damage done by a critical strike is therefore:

Base damage: 1.5*1.03=1.545 or 54.5% extra damage

Talent multiplier: 54.5% * (1+100%) = 109% extra damage on all spells except Lava Burst

Lava Burst talent multiplier: 54.5% * (1+100%+24%) = 122.08% extra damage on Lava Burst

Thus a critical Lightning Bolt will do 209% total damage and a critical Lava Burst will deal 222.08% total damage.

Crit scaling

Therefore the first and most obvious thing crit rating does is provide a chance to increase the damage of your spells by 109%.  This is a simple linear increase in damage as more rating is applied, where each point of crit rating is worth precisely the same amount of extra damage in terms of a potential critical strike as the last.  This is very easy to model.

However, crit also has another effect for elemental shamans: it procs the Clearcasting effect from Elemental Focus.  This increases the damage of the two spells following the critical spell by a flat 10%.  Because it affects the next two spells, the chance that any given spell will be affected by Clearcasting is a function of the crit chance of the previous two spells.  That is, if you have a 50% crit chance, the chance that spell number 3 in your rotation will be affected by Clearcasting is 1-(1-0.5)*(1-0.5)=0.75, that is, 75%.  So a small increase in crit chance is actually a large increase in the uptime of Clearcasting.

Lava Burst

Lava Burst has a 100% chance to crit if Flame Shock is on the target.  That means that your two spells following Lava Burst are guaranteed to have Clearcasting active.  Consider the following (hasteless) rotation assuming a 50% crit chance:

Flame Shock > Lava Burst > Lightning Bolt*4 > Lava Burst > Lightning Bolt*3 > repeat

Let’s re-arrange it so that the starting point is the first LB following LvB:

Lightning Bolt*4 > Lava Burst > Lightning Bolt*3 > Flame Shock > Lava Burst > repeat

The first two Lightning Bolts are guaranteed to have Clearcasting active.  The next two and the following Lava Burst have a 75% chance each to have Clearcasting active.  4 out of the 10 spells in the rotation have a 100% CC uptime and 6 out of the 10 have a 75% uptime, making the average uptime 85%.  That’s with just a 50% crit chance, because of the power of Lava Burst‘s guaranteed crit.

Binkenstein has shown that adding more spells to a rotation does not significantly affect the uptime of Clearcasting.  You can click on the image below to see the graph he produced.  The formula used was:

Where C is the crit chance of LB and N the number of spells in the rotation.

Crit buffs

Finally, consider the following sources of crit chance buffs available to a raiding elemental shaman:

• Thundering Strikes (tier 2 enhancement talent) +5%
• Call of Thunder (LB, CL & Thunderstorm) +5%
• Elemental Oath +5%
• Totem of Wrath +3%
• Imp. Scorch and equivalent talents +5%
• Focus Magic +3%
• Blessing of Kings ~+1%

Total 27%.

Thundering Strikes is applied to your character sheet while you stand around Dalaran looking pretty, so you can expect your total raid buffed Lightning Bolt crit chance to be 22% higher than what your character sheet tells you unbuffed.

The value of Crit Rating

So let’s put this all together for crit rating:

• It does not affect Lava Burst, which accounts for 20-30% of our damage (or the DoT of unglyphed Flame Shock);
• It has a slightly increased effect (16.5%) on Lightning Bolt due to Lightning Overload (and marginally more with 4t8);
• Clearcasting uptime suffers rapidly diminishing returns against adding more crit rating;
• We already have a vast amount of crit from raid buffs and talents, pushing CC uptime well into the high 70-percents even in entry level gear;

Conclusion: While critical strikes are extremely valuable to elemental shamans, critical strike rating is not.  There is no minimum crit level needed to sustain our crit-powered buffs due to Lava Burst.

How Haste works for Elemental

Haste is a fair bit harder to model than crit as our rotation depends upon a fixed duration spell (Flame Shock) and a fixed cooldown spell (Lava Burst).  In addition, haste can be affected by procs or buffs which may differ from moment to moment.  Thus adding more haste produces a linear increase in DPS most of the time, with sudden more dramatic variations as a point is reached at which another spell can be inserted between Lava Burst’s cooldowns.  Haste is also affected by your latency (the lag between your client and the server) and the ability (since patch 2.3.0) to instruct the server to queue up the next spell before your last spell has finished casting.

One curious effect of haste is that it actually effectively reduces the cooldown of Lava Burst.  Consider that the cooldown begins when you finish casting the spell, so if you finish casting it sooner, the cooldown starts sooner and is finished sooner.

Haste affects our cast times by allowing more spells in a given window of time: for example, 1% haste means you can cast 1% more of any given spell in the same time.  The formula is:

Haste % = Haste Rating / 32.78998947

Hasted Casting Time = Base Cast Time [inc. talents] /( (1+ Haste % /100) * (1+ Haste Effect % / 100) )

So with 600 haste rating and Wrath of Air Totem for 24.2% total haste, Lightning Bolt would cast at 1.61 seconds:

2/((1+(600/32.79)/100)*(1+5/100))=1.61

Simply put, This Means More Spells™.  In our case, it means Lava Burst casts and thus cools down 0.3 seconds faster:

1.5/((1+(600/32.79)/100)*(1+5/100))=1.20

The more haste we have, the less we “clip” the cooldown of Lava Burst while casting filler Lightning Bolts.  Eventually it reaches the point where we can start casting another Lightning Bolt before Lava Burst cools down, but at the cost of pushing back the next cast of Lava Burst by the duration of that spell – but then adding yet more haste reduces the amount of “clip” until the process repeats itself.

The global cooldown is reduced by haste to a cap of 1 second.  While haste can reduce our cast times below that, this means that the limiting factor in more casts becomes the 1 second GCD.  It’s also worth noting that the haste effect of Bloodlust/Heroism does potentially “GCD cap” Lava Burst, but Lightning Bolt doesn’t cap out until 1386 haste with Bloodlust, Wrath of Air and Improved Moonkin Aura.

Conclusion: Haste rating and effects favourably affect all our spells and are consistently valuable to elemental shamans, though the precise value varies slightly.  Haste values above 1386, fully buffed, are of reduced value during heroism/BL.

So Crit vs Haste..?

Haste rating is always better than an equal amount of crit rating.  If you want to know by exactly how much, try a spreadsheet or check out Wowhead’s starter DEP values.  As for napkin math, I tend to regard haste rating as worth twice as much DPS as crit rating, and spellpower as worth half as much again.  That’s a very rough and horribly inaccurate figure, but it’s ballpark enough to know that haste wins the war against crit.

Please note that this does NOT make crit a “bad stat” for elementals.  Yes, it’s worse than haste – that is, in any situation where you have a choice between either crit or haste, haste will result in better DPS.  But we still love to get crit on our items that also have haste and spellpower on them, and a big enough amount of crit rating will still be superior DPS to a small enough amount of haste rating.

Do I gem for haste?

Point for point, Haste is still not as valuable for DPS as Spellpower in most circumstances.  This is further exaggerated by the fact that spellpower costs less on the item budget than haste, so you only get 20 haste on a gem but you get 23 spellpower.  Spellpower is still the clearly superior stat for gems and enchants and so forth.  However, if there’s a yellow socket that comes with a nice big spellpower bonus, using an orange Spellpower/Haste gem (Reckless) to get the socket bonus is better than just gemming for pure spellpower and missing the bonus entirely.

Do I gem for crit?

Please don’t, it’s a choice between 10 haste or 10 crit and 10 haste is always, always, always better.

Conclusion The upshot of all this is: Effects that increase your critical strike bonus damage are very valuable (CSD, talents, etc) – though less so if they only affect one spell (e.g. 4t7) Crit rating is of moderate value Haste rating is of good value Spellpower is of excellent value Hit rating is of the highest value until capped.

So prioritise Hit (until capped) over Spellpower over Haste over Crit.