Eleanor's theorycrafting - Passive haste for destruction Warlocks.

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The goal of this section is to study the impact of passive haste on a warlock dps. For simplicity's sake, it is oriented toward a shadowbolt-spamming warlock using only Shadow Bolts and Connexions.

Standard considerations

At first we could consider that the dps gained from passive haste would be directly proportionnal from the amount of haste used. The only limitation would be the "haste cap", the point when your main nuke's cast time would be reduced to the Global Cooldown.

However the main nukes of a warlock are known to be pretty mana-inefficients, thus forcing said warlock to make a massive use of connexion. The problem is that connexion is instant, and thus already "haste-caped".

Basic assumptions

As most of the problem here is related to the time lost during "mana regeneration", we can't assume a "mana free" shadowbolts -

spam. However, we will assume an "infinite" health pool, considering hat the life lose via Life Tap is replenished throught HoTs and such.

We will assume that the caster is hit-capped and we won't -for now- consider its critical strike rating. So when refering to a shadow bolt "damage", we will consider that it is its "average" damage.

To improve readability, the formulas used in those pages are using the following conventions:

• manaCost is the cost of the spell, talents and buffs included. For a shadow bolt (rank 11), manaCost=420.
• castTime is the real cast time of the spell, talents and buffs included. For a shadow bolt (rank 11) and using Bane -
  Bane (Rank 5)

  Reduces the casting time of your Shadow Bolt and Immolate spells by 0.5 sec and your Soul Fire spell by 2 sec.
  , castTime=2.5.
• manaGained is the is the mana gained from a life tap. For Life Tap (rank 7), manaGained=580 + 0.8*dmg.
• tapCastTime is the is "effective" cast time of a life tap. It is equal to the Global Cooldown, thus tapCastTime=1.5 sec.

Standard fight

A standard fight could be decomposed in two phases. In the first one, the warlock will be able to chain-cast its shadow bolts without mana considerations.

where Note that this won't help you cast more bolts in phase 1, whis will just reduce the duration of this phase.

In phase 2 however, the gain is lowered, since tapTime is not reduced by the haste rating. The new dps will be:

.

Phase 2 haste-to-dmg conversion

We will have to expand the formula of the previous chapter by remplacing everything inside it and using "real" damage instead of an average value. For consistency sake, here are some new conventions:

• baseDmg is the (average) base damage of the spell, critical strikes non included. For a shadow bolt (rank 11), baseDmg=572.
• dmg is the spell damage used by the character, spell, buffs and talents included (like Demonic knowledge -
  Demonic Knowledge (Rank 3)

  Increases your spell damage by an amount equal to 15% of the total of your active demon's Stamina plus Intellect.
  or Fel armor -
  Fel Armor (Rank 2)

  725 Mana Instant cast

  Surrounds the caster with fel energy, increasing the amount of health generated through spells and effects by 20% and increasing spell damage by up to 100. Only one type of Armor spell can be active on the Warlock at any time. Lasts 30 min.
  ).
• crit is the spell critical rating of the character, buffs and talents included. (22.1 crit = 1% crit chance)
• untalentedCastTime is the base cast time of the spell. For a shadow bolt (rank 11), untalentedCastTime=3.

Using those values, we can define the dps of an unhasted talented hit-capped shadowbolt as:

The formula for an hasted talented shadowbolt becomes:

So, if we want the +dmg equivalent of some haste, we can compare a "damage-amplified" bolt and an "haste-amplified" one:

Where dmg' is the spell damage needed to gain the same dps as haste.

Given this equivalence, we can express the haste as:

Disclaimer

I'm particulary bad at simplifying equations. The haste = f(dmg') above could be wrong. If you want to peek at its development, here it is: sheet1, sheet2. If you find any problem in it, please contact me.

Results

The following table can be used to search the point where haste is better than damage:

haste = f(dmg), with arbitrary base spell damage:

mana cost 420 mana gained from life tap 580 untalented cast time 3 cast time 2.5 base damage 572 damage equivalent \ base spell damage 900 1000 1100 1200 1300 1350 1375 1400 1500 1600 10 13.85 12.82 11.92 11.13 10.44 10.12 9.97 9.82 9.28 8.78 20 27.75 25.67 23.86 22.29 20.90 20.26 19.96 19.67 18.57 17.58 30 41.69 38.55 35.84 33.46 31.38 30.42 29.97 29.52 27.87 26.39 40 55.68 51.48 47.84 44.67 41.88 40.60 39.99 39.40 37.19 35.21 50 69.71 64.44 59.88 55.90 52.40 50.80 50.04 49.30 46.53 44.05 60 83.79 77.44 71.94 67.15 62.94 61.02 60.10 59.21 55.88 52.90 70 97.91 90.47 84.04 78.43 73.50 71.25 70.18 69.14 65.25 61.76 80 112.08 103.54 96.16 89.73 84.08 81.51 80.28 79.08 74.63 70.63 90 126.29 116.64 108.32 101.06 94.69 91.78 90.40 89.05 84.02 79.52 100 140.55 129.79 120.50 112.42 105.31 102.08 100.53 99.03 93.43 88.42 110 154.85 142.97 132.72 123.79 115.96 112.39 110.69 109.03 102.86 97.33

It seems that the borderline where haste begins to be better than pure damage is around +1400 damage. Note that all raid buffs are included in those 1400 damages, so it's not "that" high.

Item Budget

To compare two items, we still need to take something into account: one point of spell haste rating don't have the same "cost" as one point of spell damage. As I don't know the cost of spell haste, I'll evaluate it using two items: [Wristbands of Divine Influence] -

and [Bracers of Nimble Thought] -

Bracers of Nimble Thought

Binds when picked up Wrist

Cloth

103 Armor +27 Stamina +20 Intellect Durability 35 / 35 Requires Level 70

Equip: Improves spell haste rating by 28 (1.8%).

Equip: Increases damage and healing done by magical spells and effects by up to 34.

. Those are convenients because they share the same iLevel, the same item slot, and don't have gem slots.

The [Bracers of Nimble Thought] -

gains 28 spell haste rating, 34 spell damage and 3 stamina over the [Wristbands of Divine Influence] -

Wristbands of Divine Influence

Binds when picked up Wrist

Cloth

103 Armor +24 Stamina +21 Intellect +28 Spirit Durability 35 / 35 Requires Level 70

Equip: Increases healing done by spells and effects by up to 62.

Item Level 141

, but loose 1 intellect, 28 spirit and 62 healing. Assuming the numbers provided by WoWWiki are correct, those 28 spell haste rating are worth 26.139 stat points

1 + 28 + 0.455*62 - (3*0.667 + 34*0.855)

. So, the StatMod of spell haste rating equals 0.934

26.139 / 28

. This means that spell haste is 9.2% more expensive than spell damage.

Converter

As the conversion formula is absolutely atrocious, here is a small javascript tool to convert spell damage to haste rating:

Damage to haste converter:

Current spell damage: Additional spell damage: Equivalent spell haste:

Links

• WoWWiki - Formulas:Item Values [EN] Cost of the different stats on an item.