csi

Basically I wanan figure out where the cut off point is for when warlocks that are spamming shadow bolt should be gemming for haste over spell damage. Basically gonna throw out calculations and tell me if things look correct, or what can be changed.

first off, calculation of 1 spell dmg for shadow bolt.

-> With Shadow and Flame, shadow bolt's spell coefficient is up from 85.7% to 105.7%. This puts 1 spell dmg equivalent to 1.057 actual dmg for a shadow bolt.

-> Now factoring all the damage multipliers (they are additive, not multiplicative).
* Curse of Shadows: 10%
* Shadow Weaving: 10%
* Misery: 5%
* Demonic Sac: 15%
* Improved SB: 20% (assume it is up)
* 4 piece Malefic: 6%
* Total: 66%
* For the sake of arguement, we can have two extreme cases, one without ISB and one assumign its up.

-> modify the dmg modifiers to the 1.057 spell dmg we have from before by multiplying the modifiers with 1.057.

* Maxima (assuming ISB is up): 1.75462 dmg.
* Minima (assuming ISB is not up) : 1.54322 dmg

So from this, Spell dmg is ALWAYS linear, 1 spell dmg will always add either 1.54322 or 1.75462 damage per shadow bolt, depending whether ISB is up or not. Now we have to model an equation that calculates the damage of shadow bolt.

-> the dmg range of Shadow bolt is 541 to 603 damage. The Average dmg is 572.

* Assuming ISB is up:
#Shadow Bolt Base Average(572*1.66): 949.52
* Assuming ISB is not up:
#Shadow Bolt Base Average(572*1.46): 835.12

-> Now we can model the equation to figure out how much damage on AVERAGE your Shadow Bolt will do if you have x shadow damage:

* Assuming ISB is up: 949.52 + 1.75462x
* Assuming ISB is not up: 835.12 + 1.54322x
(where x is the amount of shadow damage you have)

Ok, Now that we have figured out how spell damage effects your Shadow bolts, lets move onto the haste aspect to see at which point, 1 point of haste will be better than 1.2 points of spell dmg (10 haste gem vs 12 spell dmg gem).

-> Blizzard already gave us the equation for how haste conversion works:
* Cast Time = (Base Cast Time) / (1+Spell Haste Rating/Conversion Factor/100)

-> the converstion factor is 15.7 haste rating = 1% haste.
* Cast Time = (Base Cast Time) / (1+Spell Haste Rating/1570)

-> Now lets plug in the values for 1 spell haste rating, and base shadow bolt cast time of 2.5 seconds.
* Cast Time = (2.5) / (1 + 1/1570) = 2.4984
* [1 - (Cast Time) / (Base Cast Time)] * 100 = % cast increase, or % shadow bolt spam dps increase.
* (1 - 2.4984/2.5) * 100 = 0.064% damage increase from 1 haste rating.

Since We are comparing 1 haste rating to 1.2 spell damage, we need a cutoff point for when haste overtakes 1.2 spell dmg. 1.2 spell damage translates into:

* 1.2 * 1.66 = 1.992 actual damage (with ISB up)
* 1.2 * 1.46 = 1.752 actual damage (without ISB)

so at which point will 1 haste rating translate to more than 1.992 damage (with ISB up), and more than 1.752 damage (without ISB up).

-> We know 1 haste rating = 0.064% damage increase. So for our 2 cases, we have the following question and equation:
* With ISB up: at which value of x will...
0.00064 * (949.52 + 1.75462x) >= 1.992
* Without ISB up: at which value of x will...
0.00064 * (835.12 + 1.54322x) >= 1.752

-> Not gonna guide step by step through how you solve common Algebra. Feel free to solve it yourself or take my word for it:
* With ISB up: 1 haste rating >= 1.2 spell dmg at 1232.7 spell dmg
* No ISB up: 1 haste rating >= 1.2 spell dmg at 1232.7 spell dmg as well.

-> So we can see 2 things form this actually,
* 1) regardless of damage modifiers, it appears spell haste will over take spell damage at the same cut off point.
* 2) After you reach 1233 spell dmg, you should be going for haste.



Just gonna throw in a shortened version of the same process i did for Incinerate (for fire locks)

-> Coefficient for Incinerate: 91.4%, or 1 spell dmg = 0.914 actual dmg.

-> Damage Modifiers for Incinerate:
*Curse of Elements: 10%
*Misery: 5%
*Improved Scorch: 15%
*Demonic Sac: 15%
*Emberstorm: 10%
*4 piece Malefic bonus: 6%
*Total: 61%

-> 1 spell dmg = 1.472 actual damage

-> Average Damage for Incinerate (with zero spell dmg): 963.585

-> Average Damage for Incinerate: 963.585 + 1.472x (where x = fire damage)

-> At which point will: 0.00064 * (963.585 + 1.472x) >= 1.7664

-> 1 spell haste overtakes 1.2 spell dmg at 1220.4 fire dmg

Obviously this isnt including immolate.

Please check over my math and logical reasoning and make corrections as needed. If these hold true, then I should be socketing all spell haste.

This is only as far as theorycrafting takes you however (and for Shadow Bolt Exclusively). If you incorporate immolate, curse of dooms in your rotation, I'm not sure waht the cutoff point for those spells are. I assume spell dmg works much better for Curse of doom since its a 400% coefficient. It will also depend on the nature of the fight as well. But as far as pure Shadow bolt spamming goes, these calculations should be correct.

Also crit may or may not effect these calculations at all, but if anything, I would think haste would favor crit more, more casts you get into a fight, more crits you should get (theoretically), and more ISB uptime. Also Haste seems like it would favor trinkets more too than flat spell dmg.

The more haste you have, theoretically, you shoudl be able to get more use out of a trinket activation, such as hex shrunken head. with a 2.5 second cast, you can only get in 8 shadow bolts within the 20 second duration. If you can push your shadow bolt down to 2.22 seconds (which takes roughly 200 haste rating, give or take), that gives you 9 casts within that 20 second window. ( you can say the same for destruction potion).

 

Varrah

Hmmm... I don't see hastes effect on lifetap in there? Or does it cancel out, because you have X lifetaps to Y shadowbolts? Though that wouldn't be quite true, as haste doesn't affect your static MP5...

Seems like a job for spreadsheets?

 

csi

well since haste effects gcd...i guess 1 haste rating increases your mana gain rate by 0.064%, i'm not quite sure what the conversion rate for spell dmg -> mana returned is for life tap though. I believe its around 70%, but until someone gives me an actual coefficient, I dont wanan jump to any conclusions.

 

Prinsesa

From the Theorycrafting Think Tank, Life Tap has an 80% spell damage coefficient.

That is, 100 spell damage will cause your Life Tap to drain an additional 80 HP and restore an additional 80 mana.

If talented, 100 spell damage will cause your Life Tap to drain an additional 80 HP and restore an additional 96 mana.

"We do want Sanctuary to be the tanking seal"

- Ghostcrawler

 

noster

Hi, I'm actually at work and don't have the time to check your maths in detail but the first thing i realized is that you didn't take critrating into the calculation.

100% Crit would double the use of Spelldmg. So not regarding crit is falsifying the result.
And while we are at the subject of critrating. Although you need much more crit- than hitrating to raise your dps by 1 percent, crit has other benefits too.

1% crit while pushing your overall dps also raises your dpm by 1 percent and helps sustaining the ISB debuff.
Haste just raises the dps at the cost of dpm.

Nevertheless for gems i personally prefer Reckless Pyrostones as long as i don't want the socket bonus.

At the end I think you should find a balance between crit/haste/dmg and not just push one value at the cost of the others

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François

As far as I know, they are multiplicative. However, I've always considered it to be of no impact on the spell damage vs spell haste vs spell crit balancing.

Damage per second on spam bolt fight is
Multipliers x (base + coef x spell damage) x (1 + spell haste / 1570) x (1 + crit effect x 0.01x(base crit + crit score / 22,7))

I mean every stat has an affine effect (except crit when talented with stuff like ISB), and those affine effects are multiplicative.

As you augment your spell damage, spell haste becomes more powerful, and as you add spell haste, spell damage becomes even more powerful. The 1232 spell score you get is only valid for the first spell haste item.

 

fletch578

I think you forgot to include the spell coefficient (0.8571+0.20) = 1.0571. Doing so means 1.992 actual damage (with ISB up) becomes 2.1057, and the resulting damage break-even point goes from 1232.7 to 1334.0. It's interesting to note that this break-even number doesn't distinguish between +dmg from gear and that from raid buffs and consumables. Fel armor, a flask, weapon oil and a food buff are worth 130+80+42+23=275 dmg. This makes the +dmg needed from gear 1059.0.

I agree with François, the break-even number is a function of your current haste rating as well. The more haste you have, the higher the break-even point is. After working the equations, the expression I get for the break-even point is:

BreakEvenDmg = (12 / 10) * (1570 + haste) - (base / (0.8571 + 0.20))

where:
haste = current haste rating
base = spell base dmg = 572

With a haste rating of 0, the BreakEvenDmg evaluates to 1342.9 dmg.

Another point of note is that while simplifying the equation, the factor for crit divided out of both sides of the problem. This is due to the fact that while crit doubles the effect of spell damage, it also doubles the effect of spell haste.

The damage multipliers (for CoS, Sac, Misery, etc.) also divided out of both sides of the equation. I believe them to be multiplicative as well, but in this case, whether they add or multiply didn't make a difference.

 

csi

I did think about that. However, Haste effects Crit as well as I mentioned at the end. If you have 100% crit rating, Haste will also cause you to crit more casts in a given time period. Realistically, you won't have 100% crit, probably roughly around the 35% crit range give or take.

So spell damage gives you larger crits, while haste will give you more crits (more ISB up time as well). The question is which one is stronger?

 

csi

They are additive because there was a patch where Blizzard clearly changed it from Multiplicative to Additive.

I did include the Spell Damage Coefficient if you read the first section, (1 * 1.0571 * 1.66) = 1.992.

And for what Francois says, it makes a lot of sense. So the 1232 spell damage just means at that point, we should be stacking haste as well as spell damage?

I never liked the idea of gemming for crit, on most fights, your actual crit for the fight will be off from your character sheet. In a typical fight, the amount of spells a caster casts does not give you a large enough sample size for crit to always average out, where melee dps swings enough to have a very large sample size of attacks.

Case and point: I've had Brutallus fights where my crit percent was 27% for the entire fight, or sometimes 45%, when my character sheet says it should hoover around 35%. Basically crit just doesnt seem like a reliable enough stat to invest in, but with haste, it may allow you to cast enough spells to create a large enough sample size for crit to be a bit more reliable.

 

Trickykid

Can you cite this change in patch notes? Most of the work done here assumes these multipliers are multiplicative.

Also the fact that actual and expected crit differ from fight to fight does not change the benefit it yields on the average. Increasing DPS comes from increasing the expected yields from the different stats, counting one out that relies on probabilities is unnecessarily simple.

As far as your break-point for haste and spell damage, you're probably better off using the spreadsheet which already accounts for the nuances of warlock buffs and spell choices. You're doing mostly redundant work here that is found in seconds on Leulier's sheet.

 

Pstar

Seems like they have to be multiplicative... how else would you get destro locks in T6 hitting 10-11k crits?... to work backwards, that'd be a 5k normal hit, on a (572 + bonusdamage) * 1.66 *1.05 cast? No way. These casters don't have 2500 bonus damage, even buffed with trinkets popping.

Multiplicative: would give you a 1.86 multiplier (572 + x ) * 1.86 *1.05 = 5000.... X comes out to 1973, which seems much more reasonable (although would require a trinket proc, raid buffs, etc)...

More generally, the poster who stated that the effects are affine is correct. Here's how I'd look at it

1) Assume a set of buffs and debuffs (as you're doing), as well as a cast rotation
2) Create a function DPS = F(bonusdamage, crit, haste)
3) Backdoor a 3d matrix by taking a stat of interest and make some 2d table slices... like such

15% Crit 0% Haste 2%H 4%H 6%H 8%H 10%H
1000dmg DPS DPS DPS DPS DPS DPS
1050dmg DPS DPS DPS etc....
1100dmg
1150dmg
1200dmg
1250dmg
1300dmg

Reproduce for 10% crit and 20% crit, or maybe 16% and 17% as you see fit, depending on how narrow or broad of a range you want to take the derivatives over... You could change the axes to hold damage or haste constant and compare crit and something else if you wanted...

You're essentially solving for partial derivatives with respect to the 3 stats. If you were better than me at calculus, you could probably derive a symbolic solution and just plug in #s, but I'm much better at using Excel than PDE's on a blackboard.

Finally, I'm not much of a lock theorycrafter (I'm a rogue) but I suspect there's probably a spreadsheet that already does this, and will even download your gear from the armory and tell you what items will be upgrades and by how much. This is likely what Trickykid alludes to. I do find it rewarding to work thru the math myself, but I'm not sure I'd create a seperate thread to do it