Coefficients

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coefficients

Direct (instant-effect) spells

Direct spells are spells that apply all the damage or healing at one time. That is, they have an instant duration. The amount of bonus damage or bonus healing depends on the cast time of the spell before any talents or abilities are applied to them. Spells with a cast time of less than 1.5 sec or greater than 7.0 sec are treated as having a cast time of 1.5 sec and 7.0 sec, respectively.

Direct Damage spells:

C = Cast Time / 3.5

Direct Heal spells:

C = (Cast Time / 3.5) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 42.86% 80.57%
2.0 sec 57.14% 107.43%
6.5 sec 185.71% 349.14%
7.0+ sec 200.00% 376.00%

As of Patch 3.0.2, it is necessary to multiply the results of the standard equations by a factor of approximately 1.88 for all healing spells. This is a proportionality constant introduced to account for the fact that bonus healing behaved differently from bonus spell damage prior to the patch, and took on a different range of values.

Direct (instant-effect) spells

Direct spells are spells that apply all the damage or healing at one time. That is, they have an instant duration. The amount of bonus damage or bonus healing depends on the cast time of the spell before any talents or abilities are applied to them. Spells with a cast time of less than 1.5 sec or greater than 7.0 sec are treated as having a cast time of 1.5 sec and 7.0 sec, respectively.

Direct Damage spells:

C = Cast Time / 3.5

Direct Heal spells:

C = (Cast Time / 3.5) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 42.86% 80.57%
2.0 sec 57.14% 107.43%
6.5 sec 185.71% 349.14%
7.0+ sec 200.00% 376.00%

Example calculation using Rank 11 (L80) of Fire Blast (Mage):

Cast Time = 0.0 (treated as 1.5)

C = 1.5 / 3.5
  = 42.86%

Examples of such spells include: Healing Touch (Druid), Greater Heal (Priest), Shadow Bolt (Warlock)

Some exceptions of this rule are:

Over time spells

Over time spells apply healing or damage over a period of time in ticks. The spell power coefficient depends on the duration of the over time effect.

Damage spells:

C = Duration / 15

Healing spells:

C = (Duration / 15) * 1.88

This coefficient applies to the entire duration of the spell. With a few exceptions, each tick receives an equal bonus. Therefore, the per-tick coefficient can be found by dividing the overall coefficient value by the number of ticks.

Prior to patch 2.0.1, there was a 100% cap on over time spells longer than 15 seconds. This cap has since been removed. There is no minimum duration cap for over time spells.

Table of coefficients

Duration Damage Coefficient Healing Coefficient
3 sec 20.00% 37.60%
6 sec 40.00% 75.20%
15 sec 100.00% 188.00%
18 sec 120% 225.60%
21 sec 140% 263.20%

Example calculation using Rank 15 (L80) of Rejuvenation (Druid):

Duration = 15
Number of Ticks = 5

CTotal = 15 / 15 * 1.88
   = 188.00%

CTick = CTotal / 5
   = 37.60% per tick

Examples of these spells include: Rejuvenation (Druid), Renew (Priest)

Some exceptions to this rule are:

Hybrid spells (Combined standard and over-time spells)

The bonus for spells that have both a direct and an over time component is divided between these components. Currently, the equations are unknown for hybrid healing spells. Several equations have been proposed, but none of them provide correct results for all (or most) hybrid spells. Because there are so few hybrid healing spells, it may be the case that their coefficients are not set by equations at all, but are chosen directly by the developers.

For hybrid damage spells, the equations are:

x = Duration / 15
y = Cast Time / 3.5

CDoT = x2 / (x + y)
CDD = y2 / (x + y)

CTotal = CDoT + CDD

Example calculation using the Rank 14 (L80) Moonfire (Druid) spell:

Duration = 12.0 sec
Cast Time = instant (treated as 1.5 sec)

x = 12.0 / 15.0 = 0.8000
y = 1.5 / 3.5 = ~0.4286

CDot = 0.80002 / (0.8000 + 0.4286)
   = 0.6400 / 1.2286
   = 52.09%

CDD = 0.42862 / (0.8000 + 0.4286)
   = 0.1837 / 1.2286
   = 14.95%

So the DoT portion of Moonfire (4 ticks) has a coefficient of 52.09% (~13.02% per tick). The DD portion has a coefficient of 14.95%. The total coefficient is 52.09% + 14.95% = 67.04%. This agrees very closely with the empirical values of 52% and 15%, respectively.

Examples of these spells include: Moonfire (Druid), Immolate (Warlock)

Exceptions to this rule include

Channeled spells

Channeled spells, like over time spells, have their benefit distributed over the entire duration of the spell. It is split evenly over each tick assuming that each tick causes the same amount of damage/healing. The duration of the spell cast time is used to calculate the total coefficient:

For damage spells:

CTotal = Duration / 3.5

For healing spells:

CTotal = (Duration / 3.5) * 1.88

For both:

CTick = CTotal / Number of Ticks

Example calculation using Rank 13 (L79) of Arcane Missiles (Mage):

Duration = 5.0
Number of Ticks = 5

CTotal = 5 / 3.5
   = 142.86%

CTick = CTotal / 5
   = 28.57%

Examples of these spells include: Hurricane (Druid), Arcane Missiles (Mage), Hellfire (Warlock). An exception to this rule is:

Area of effect spells

Area of Effect spells receive only 1/2 of the total bonus that they would if they were single-target spells. As with a direct spell, the cast time is used to calculate the coefficient. The 1.5 second minimum and 7.0 second maximum apply to area of effect spells.

Damage spells:

C = Cast Time / 7

Healing spells:

C = (Cast Time / 7) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 21.43% 40.29%
2.0 sec 28.57% 53.71%
6.5 sec 92.861% 174.57%
7.0+ sec 100.00% 188.00%

Example calculation using Rank 7 (L80) of Circle of Healing (Priest)

Cast Time = instant (treated as 1.5)

C = (1.5 / 7) * 1.88
  = 40.29%

Examples of these spells include: Arcane Explosion (Mage), Prayer of Healing (Priest), Circle of Healing (Priest)

In the Burning Crusade and patch 2.0 there is a diminishing return against multiple targets. That is, as the number of targets your spells affect increases, the less damage you will deal to them. The numbers for this mechanic aren’t yet known.

Rules for applying spell damage and healing

  1. Calculate spell time using the base spell cast time before talents and gear. (The in-game tool tip will include those bonuses; refer to WoWWiki’s spells section for base cast times for all spells.)
  2. Spells that take longer than 7.0 seconds to cast are treated as if their casting time was 7.0 seconds, and spells faster than 1.5 sec are treated as if their casting time was 1.5 seconds.
  3. Damage benefits are applied before any talents or buffs that may otherwise increase your spell damage.

Penalty rules

Spells learned before level 20

Many spells have multiple ranks. To avoid abuse of lower ranks to have a similar effect at a negligible mana cost, any spell learned below level 20 receives a large penalty. If such a spell has a shorter cast time than a higher rank, this is also taken in to account. This penalty can be calculated by subtracting 3.75% for each level lower than 20.

(20 - Level Spell is Learned) * .0375 = Penalty

Downranked spells

Main article: Downranking

Downranking, the act of purposefuly using a lower-rank cheaper spell, no longer has any mana benefit as of Patch 3.0.

Spells with additional effects

Spells with additional effects, like a slowing effect, receive a penalty for each effect. Typically the penalty is 5% per additional effect, but can vary according to the developers’ whims. For instance, here is the calculation for Rank 7 (L80) of Insect Swarm (Druid), which is an over time spell with a chance-to-hit debuff:

C = (12.0 / 15.0) * 0.95
  = 76.00%

Examples of these spells include: Blast Wave (Mage), Blizzard (Mage), Insect Swarm (Druid)

Spells that both damage and heal

Some spells, namely Life Drains, both damage the target and heal the caster. The bonus is split between the healing and damaging portion, roughly in proportion to the amount of healing and damage involved. That is, if a spell heals 4 points for every 1 point of damage, 1/5 of the spell’s bonus will go to damage and roughly 4/5 will go to healing. Because bonus healing does not apply to these spells, the 1.88 multiplier is not used for the healing portion.

Thus Drain Life’s bonus is applied 50%/50% to damage/healing, while Devouring Plague’s bonus is split roughly 75%/25%. The exact equations are unknown at this time, but a reasonably close answer can be obtained by:

CDamage = CTotal / (Damage Amount / [Damage Amount + Healing Amount])
CHealing = CTotal / (Healing Amount / [Damage Amount + Healing Amount])

Examples of these spells include: Devouring Plague (Priest), Holy Nova (Priest), Drain Life (Warlock)

How do talents like “Empowered Rejuvenation” Affect Coefficients?
The Empowered Rejuvenation talent reads:
Increases the bonus healing of your heal over time effects by 20%

What this means is that for all HoT effects, you take your current +healing and add 20%. So if you had 1000 +healing, your HoTs would act as though you had 1200 +healing.

Gift of Nature increases the effect of all healing spells by 10%. Does this stack with +healing?
Yes.

For example, if your healing touch would normally heal for 2800, and you had a 1000 +healing, then here’s what this talent would do for you:

 (2800 + 1000) x 110% = 4180

With Empowered Touch (+20% Bonus Healing on Healing Touch) and Gift of Nature, here’s how the math works out:

 [2800 + (1000 x 120%)] x 110% = (2800 + 1200) x 110% = 4400
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