Shadow Bolt vs Incinerate

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A common debate among warlocks is which is better Fire or Shadow?

It Boils down to simple Mathematics.

First we must ask ourselves "what are we concerned with" and for the topic of this debate I'd say sustained dps in a raid setting

Contents 1 Math 1.1 Common Bonuses 1.2 Incinerate data 1.3 Shadow Bolt data 1.4 Spell Compare 1.5 Conclusions

Math

Common Bonuses

Common Bonuses are things that both spells receive the same bonus from and add multiplicatively with the rest of the equation.

• Hit Rating

• Haste Rating

That's it! Everything else impacts the equations used to determine damage differently

Incinerate data

Incinerate

Deals 479 damage on average Deals 599 damage on average with immolate present 2.5 cast time (talents to 2.25) receives 2.5/3.5 percent of spell damage (talents to .2+2.5/3.5)

Mob Debuff: Misery (+5%)

Mob Debuff: Curse of Elements (+10%)

Mob Debuff: Improved Scorch (+15%)

Self Buff: Emberstorm (+10%)

Self Buff: Imp Demonic Sacrifice (15%)

so an equation modeling Incinerate's DPS would look Something like This (where S is spell damage and C is Crit % represented as a number between 1 and 0)

Where (1+C) is the damage increase caused by your crit rate, C. The 1.XX are the total damage multipliers. These multipliers are then each multiplied against the quantity of the average damage plus the talented spell power coefficient of incinerate times the spell power,(599+(.2+2.5/3.5)S), in order to find the average damage of a hit. The average damage is then divided by casting time to find the dps.

Shadow Bolt data

Shadow Bolt

Deals 572 damage on average 3 cast time (talents to 2.5) receives 3/3.5 percent of spell damage (talents to 1.2*3/3.5)

Mob Debuff: Curse of Elements (+10%)

Mob Debuff: Misery (+5%)

Mob Debuff: Improved Shadow Bolt (+%) Formulas:Shadow Bolt

Mob Debuff: Shadow Weaving (+10%)

Self Buff: Imp Demonic Sacrifice (15%)

so an equation modeling Shadow Bolt's DPS would look Something like This (where S is spell damage and C is Crit % represented as a number between 1 and 0)

Where (1+C) is the damage increase caused by your crit rate, C. The 1.XX are the total damage multipliers while the multiplier for ISB is (1+0.2(-C^4+4C^3+-6C^2+4C). These multipliers are then each multiplied against the quantity of the average damage plus the talented spell power coefficient of Shadowbolt times the spell power,(572+(.2+3/3.5)S), in order to find the average damage of a hit. The average damage is then divided by casting time to find the dps.

Spell Compare

We know Shadow Bolt starts out lower and that if it ever passes Incinerate there must exist an intercept thus any value of Spell Damage/ Crit that exceeds the value at which the interception occurs would be the values at which Shadow Bolt is better than Incinerate.

First set the equations equal to each other.

Then simplify the multipliers except ISB since it includes crit.

The 1+C is common among both so it can be eliminated.

I like not having fractions so multiply the speed of SB on both sides to eliminate it, from this we verify that the faster cast rate of incinerate increases it's dps. I also simplified the spell damage coefficients.

Then just multiply the multipliers against the average damage to find the buffed average damage and the buffed spell damage coefficient.

(lets assume 35% crit since this is sustained dps and most destro locks can obtain this pretty easily)

Using the result from the last section we have:

Then substitute the crit in using C=.35.

Simplify the multiplier of ISB.

Multiply ISB throughout the SB equation.

Find the difference of the spell power coefficients times S and set it equal to the difference in buffed average hit.

Solve for S.

Conclusions

Incinerate is better for sustained personal dps given that immolate is applied for you (until you have 1.3k spell damage).

A good candidate for keeping immolate up is the designated support warlock who has 5/5 Shadow Embrace, 3/3 Malediction, on imp duty and/or has the least spell damage.