Boomkin DPS calculations

[Lorilay 12]

Rescued from the Nostalrius forums, with 2 caveats: 1.) This is based on the warlock dps sheet done by Particles and Cousy. 2.) I'm not a boomkin and think it's a silly spec, but if you're going to do it, you should at least know how to gear for it.

 

The following is the formula for calculating your dps in a raid, and you can use that formula to calculate how much a gear upgrade will increase your dps. Druid is considerably easier to do, since we don't have stupid things like Arcane Power, Improved Shadowbolt, and Ignite to worry about.

 

Thanks mainly to our warlock overlords (all hail the burning legion), here's your overall dps calculation for spamming starfire in a raid (assuming you have nature's grace, and miss is 17-your hit%):

(StarfireBase+spellpower)(1+crit/100)(1-miss/100)/(3-0.5*crit/100)

 

 

Now, there's three variables that can affect your dps here: spellpower, crit, and hit. However, they're all related to each other so it isn't a linear relationship.

The derivative of spellpower (x) to your damage is: (1+crit/100)*(1-miss/100)/(3-0.5*crit/100)

The derivative of crit (y) to your damage is: (StarfireBase+spellpower)(1/100)(1-miss/100)/(3-0.5*crit/100)

The derivative of hit (z) to your damage is: (StarfireBase+spellpower)(1+crit/100)(1/100)/(3-0.5*crit/100)

 

Therefore:

1 crit = y/x spellpower

1 hit = z/x spellpower

 

(StarfireBase+spellpower) Starfire is a 3.5 second base cast, so there is no spellpower coefficient. Your damage is just the base damage of Starfire (this will change when you get the AQ20 book) + your total spellpower bonus.

(1+crit/100) If you have 20% crit, your damage will be increased by 20%, assuming you have 5/5 vengeance.

(1-miss/100) If you have 10% miss, that will be a straight 10% loss to your dps.

(3-0.5*crit/100) This calculation is for dps. Starfire has a (talented) 3 second cast, and your crit % of the time it will be 0.5 seconds faster with nature's grace.

 

Now, what we're really interested in is applying this to gear choices, so it's important to identify how each stat contributes to dps. Not that each contribution depends on the other two variables. This is why you need to use derivatives instead of just algebra.

(1+crit/100)*(1-miss/100)/(3-0.5*crit/100) This is what modifies the contribution of spellpower to damage. (dps/sp)

{(StarfireBase+spellpower)(1/100)(1-miss/100)/(3-0.5*crit/100)}+{(0.5/100)(StarfireBase + spellpower)(1 + crit/100)(1-miss/100)/(3 - 0.5*crit/100)^2} This is what modifies the contribution of crit to damage. (dps/crit)

(StarfireBase+spellpower)(1+crit/100)(1/100)/(3-0.5*crit/100) This is what modifies the contribution of hit to damage. (dps/hit)

 

Using the first derivative above, you should find that 1 spellpower will increase your dps by x (something around 0.35-0.42ish, depending on your gear). To find how much spellpower 1 crit equals, just divide dps/crit by dps/sp. The terms cancel out and you get sp/crit. You can calculate sp/hit in the same way.

 

So, if you wanted to make a spreadsheet of gear upgrades, you would want to first list how much hit (listed on the item), spellpower (listed on the item), and crit (listed on the item + int/60) on each piece of your gear, then add them together to get your total stat values. Then determine the dps increase from each of those 3 stats (using the respective derivative above), and add them together for the total damage provided by a specific piece of gear (dps/sp + dps/crit + dps/hit). Then you can swap in alternate gear to determine the dps increase by it.

 

It's worth pointing out that this is just for maximizing your potential dps, with no regard to silly things like mana regen. There's no way to reliably model that, so I would suggest gearing for maximum dps and then swapping regen items if you're finding yourself perma-oom before the end of a fight.

 

TL;DR: Your dps is affected by your spellpower, crit %, and hit %. The relative value of each stat changes depending on your gear, and you can use the above formulas to determine which upgrades are best for you.

Edited December 8, 2016 by Lorilay

[Rafale 6]

I thought that was Killerduki again, but thx God that's something serious.

[taladril 43]

Calling Keftenk. Help this thread out by data dumping what you've learned.

[Keftenk 0]

I'll come back to this thread when I have time on Friday or the weekend.

[quasexort 4]

I think for the crit derivative you have to use the quotient rule when taking the derivative so instead it becomes:  

[(StarfireBase+spellpower)(1/100)(1-miss/100)(3 - 0.5*crit/100) + (0.5/100)(StarfireBase+spellpower)(1 + crit/100)(1-miss/100)] / (3-0.5*crit/100)^2

 

= (StarfireBase + spellpower)(1/100)(1-miss/100) / (3 - 0.5*crit/100) + (0.5/100)(StarfireBase + spellpower)(1 + crit/100)(1-miss/100) / (3 - 0.5*crit/100)^2

 

This is because the crit variable is in both the numerator and the denominator.  The bold term is what you have but then you can add the italicized term that comes from using the quotient rule.

[Lorilay 12]

Correct. It's been too long since I've had to use calculus, although that still leaves crit% in the derivative, which I was trying to avoid.

Edited December 8, 2016 by Lorilay

[Keftenk 0]

Since I won't be playing on Nostalrius PvP going forward I'm going to dump most of everything that I researched and developed here. You can find most of this back on the Nost forums (http://forum.nostalrius.org/viewtopic.php?f=41&t=36638 and http://forum.nostalrius.org/viewtopic.php?f=41&t=36334) as well. Do not take what I have to say with 100% certainty that it is correct. The tests and validations which I completed weren't completely optimal, especially with everything in Patch 1.9 and onward. It's all speculative after that point. However I did get a fair amount of testing in a high-tempo raid setting with Coalition. I'm fairly certain everything up to 1.8 is more or less accurate.

If someone wants to put together a more appropriate thread that can be stickied. Feel free to do so, just give credit where credit is due.

Additionally, please note that DPSing with Starfire vs Wrath is a completely different mode of play. I never developed Wrath DPS too far, but just from initial tests I could clearly see that you wouldn't want to optimize your gear the same way you do for Starfire. With that said though I think it'd probably be hard to justify Wrath over Starfire due to the lack of damage modifiers for Nature in vanilla.

Before Nostalrius died I was working on a spreadsheet which would give a "sweet spot" between the benefits of SP and Crit. Essentially, I was trying to find a marker as to when Crit started to diminish on its returns. This was never completed for obvious reasons. However, through this research it has led me to believe that Crit isn't the "staple" stat which everyone thinks Moonkin needs to stack. I don't have this spreadsheet anymore but I did find an old image of the initial workings of it on my imgur (http://i.imgur.com/ybicWej.png)

The thing about Moonkin is that it seems no one actually talks about (or maybe they haven't figured out) is that Crit only becomes exponentially better with SP. It needs to scale. You can't just dump a bunch of Crit onto your gear with no SP.

I'd argue that Spell Hit needs to come first over Spell Damage, but you shouldn't ever be aiming for 16%. A threshold should be met first or at least obtaining a number as close as possible. Then you start prioritizing Spell Damage. The reality is you can go with 0% spell hit through most of the game while just purely stacking spell damage. A risk no doubt.
 

The correct stat priority should be: Hit > SP > Crit > Int > M5 > Spi
 

Ideally ~9% spell hit should be suffice, but this really depends on how long the fights are. The longer the fights the better Spell Hit becomes, but as Balance spec we want shorter fights as we are a true-blue burst class* with Starfire.

Spell Hit becomes much more valuable in longer fights. I used to operate in a top guild so our fights were immensely faster than most guilds and because of that I evaluate the need for Spell Hit accordingly. On average I target for a 70-second fight (Blackwing Lair), which is roughly 23 Starfires. So 9% spell hit would theoretically result in only 1 resist, but 8% would result in 2 resists.

TARGET THEORY:


- Starfire 3.0sec with talent
- Starfire 2.5sec after crit with talent
- 70sec target fight duration
- 23 Starfire's
- 9% spell hit target = 1.84 resists

It's probably worth noting that Moonkin isn't ideal in a raid setting because X, Y, Z class out DPS's it. However, if you're going to be viewing raiding in such a way then your raid really should just be class stacking. So, for optimal caster DPS you'd want 1 Shadow Priest and say 9 Warlocks. No Mages, no Moonkins, nothing else. Obviously this would change with Fire Mage being cycled in, but let's just keep it in the current content for now. Raiding generally isn't like this though.

It's also worth noting that to be useful you need to consider your role as a DPSer and what the Crit Aura brings to the party you're in. That Crit Aura actually scales differently for yourself, Mages, and Warlocks and that's essentially "added DPS" to YOUR DPS total. It's a way to value the actual aura itself. This also means there is an established DPS threshold that you must meet in order to be more useful than a DPS that could come in and replace you. Initial testings can be viewed here: http://i.imgur.com/5pjfPGD.jpg

You can actually look at Innervate the same way. For instance, when I Innervate our Shadow Priest in our raid he will do roughly ~80 DPS more on Nefarian opposed to not having it. It MUST be understood that you're a support-DPS class that does bring a lot more than what people actually think. Is it worth while though? I wish I had the gear to try and prove it. Unlike the actual Moonkins on our server I can only speculate and crunch numbers :\

I'll share what I've researched and documented through my findings for BiS 1.8.

 

Patch 1.8 BiS Gear (9% spell hit)

-----------------------------------------------------------

Weapon: Lok'amir il Romathis

Off-Hand: Tome of Arcane Domination

 

Head: Mish'undare, Circlet of the Mind Flayer

Neck: Choker of the Fire Lord

Shoulders: Mantle of the Blackwing Cabal

Chest: Bloodvine Vest

Back: Cloak of Consumption

Wrists: Bracers of Arcane Accuracy

Hands: Bloodtinged Gloves

Waist: Firemaw's Clutch

Legs: Bloodvine Leggings

Feet: Bloodvine Boots

Ring 1: Ring of Spell Power

Ring 2: Ring of Spell Power

Trinket 1: Neltharion's Tear

Trinket 2: Briarwood Reed*

 

*: Interchange it with Talisman of Ephermal Power.

All the spell hit gear in the current and upcoming patches:

 

Patch 1.8 Spell Hit Gear

-------------------------------------------

Jin'do's Judgement         2%

Jin'do's Bag of Whammies 1%

 

Bloodvine Goggles 2%

Soul Corrupter's Neckalce 1%

Abyssal Cloth Amice of Sorcery 1%

Bloodvine Vest 2%

Cloak of Consumption 1%

Bracers of Arcane Accuracy 1%

Bloodtinged Gloves 1%

Angelista's Grasp 2%

Bloodvine Leggings 1%

Ringo's Blizzard Boots 1%

Bloodvine Boots 1%

Band of Forced Concentration 1%

Zanzils Band 1% (+3% with set)

Zanzil's Seal 1% (+3% with set)

Neltharion's Tear 2%

 

 

Patch 1.9 Spell Hit Gear

-------------------------------------------

Blessed Qiraji Acolyte Staff 2%

Staff of the Ruins 1%

Royal Scepter of Vek'lor 1%

 

Garb of Royal Ascension 2%

Cloak of the Devoured 1%

Rockfury Bracers 1%

Dark Storm Gauntlets 1%

Ring of the Fallen God 1%

 

 

Patch 1.10 Spell Hit Gear

-------------------------------------------

Lord Valthalak's Staff of Command 1%

Scepter of Interminable Focus 1%

 

Spellweaver's Turban 1%

Star of Mystaria 1%

Diana's Pearl Necklace 1%

Shroud of Arcane Mastery 1%

Ban'thok Sash 1%

Clutch of Andros 1%

Kayser's Boots of Precision 1%

Rune Band of Wizardry 1%

 

 

Patch 1.11 Spell Hit Gear

-------------------------------------------

Brimstone Staff 2%

Sapphiron's Left Eye 1%

 

Cloak of the Necropolis 1%

Seal of the Damned 1%

I've been doing on going tests with Starfire and trying to get a proper stat weight for Balance. I'm not sure if this is the right way to even get them, but I collected a bunch of random green gear which had single stat values on them and went out testing. This is what I've recorded so far, but its frustrating collecting this data and then trying to predict what a certain piece of gear that has, in this instance, INT and SP on it. Only to see the prediction fall short of the actual number SW Stats cranks out.

 

Read the following data as follows: Stat Value = SW Stats DPS increase from base standard test (averages) = DPS breakdown divided by the total Stat Value which was used.

 

 

1 int = .03dps = .03dps

2 int = .05dps = .025dps

3 int = .08dps = .0266666666666667dps

4 int = .11dps = .0275dps

5 int = .14dps = .028dps

6 int = .17dps = .0283333333333333dps

7 int = .20dps = .0285714285714286dps

8 int = .23dps = .02875dps

9 int = .26dps = .0288888888888889dps

10 int = .29dps = .029dps

11 int = .32dps = .0290909090909091dps

12 int = .35dps = .0291666666666667dps

13 int = .38dps = .0292307692307692dps

14 int = .4dps = .0285714285714286dps

15 int = .43dps = .0286666666666667dps

16 int = .46dps = .02875dps

17 int = .49dps = .0288235294117647dps

18 int = .52dps = .0288888888888889dps

19 int = .55dps = .0289473684210526

20 int = .58dps = .029dps

 

1 sp = .29dps = .29dps

2 sp = .59dps = .295dps

3 sp = .89dps = .2966666666666667dps

4 sp = 1.18dps = .295dps

5 sp = 1.48dps = .296dps

6 sp = 1.78dps = .2966666666666667dps

7 sp = 2.07dps = .2957142857142857dps

8 sp = 2.37dps = .29625dps

9 sp = 2.67dps = .2966666666666667dps

10 sp = 2.96dps = .296dps

11 sp = 3.26dps = .2963636363636364dps

12 sp = 3.56dps = .2966666666666667dps

13 sp = 3.85dps = .2961538461538462dps

14 sp = 4.15dps = .2964285714285714dps

15 sp = 4.45dps = .2966666666666667dps

16 sp = 4.75dps = .296875dps

17 sp = 5.04dps = .2964705882352941dps

18 sp = 5.34dps = .2966666666666667dps

19 sp = 5.64dps = .2968421052631579dps

20 sp = 5.93dps = .2965dps

 

 

Multiple Stat Test 1: 7 int 20 Sp

Prediction: 166.57dps

Actual: 166.58dps

 

Multiple Stat Test 2: 18 int 14 sp

Prediction: 165.11dps

Actual: 165.13dps

 

Multiple Stat Test 3: 100 int 0 sp

Prediction: 163.34

Actual: 163.36dps

 

* 100 int = .292dps = .0292dps

 

 

Below is complete theory with NO TESTS conducted:

 

Starfire R6 + Moonglow R3

baseDPS = 160.44dps

1m/5 = .1121958041958042dps

Hit trials. The only way I'll be able to test 13-16% is if I acquire more gear. Unfortunately ZG doesn't seem to ever drop the Gloves, Cloak, or other Zanzil ring, rip. We may not need that data anyways. Here are those results:

 

1 hit = 1.94dps = 1.94dps

2 hit = 3.89dps = 1.945dps

3 hit = 5.83dps = 1.943333333333333dps

4 hit = 7.78dps = 1.945dps

5 hit = 9.73dps = 1.946dps

6 hit = 11.68dps = 1.946666666666667dps

7 hit = 13.62dps = 1.945714285714286dps

8 hit = 15.57dps = 1.94625dps

9 hit = 17.52dps = 1.946666666666667dps

10 hit = 19.47dps = 1.947dps

11 hit = 21.42dps = 1.947272727272727dps

12 hit = 23.37dps = 1.9475dps

13 hit = ?dps = ?dps

14 hit = ?dps = ?dps

15 hit = ?dps = ?dps

16 hit = ?dps = ?dps

 

Again, numbers were acquired under the assumption that the above INT and SP values are CORRECT. So, if they aren't correct then this makes these tests completely invalid.

 

Bloodvine Vest Test 1: 13 int 27 Sp 2% hit

Prediction: 172.72dps

Actual: 172.95dps

 

Bloodvine Leggings Test 1: 6 int 37 Sp 1% hit

Prediction: 173.52dps

Actual: 173.69dps

 

Something seems a bit off. The discrepancy gets larger than expected with every test I do. It has to be some sort of scaling with Hit:SP. I'm assuming Crit will react the same. This might warrant even further testing with gear that is strictly just Hit and strictly just SP. Does such gear even exist? I can use items like Soul Corrupter's Neckalce, but that has INT on it..

 

It could be just a small margin, but I'm worried when say, I pop a Flask of Supreme Power and then 1 Hit acts completely different than what I've tested. Or it might not, who knows haha... Also, how does this all react to things like Power Infusion and Nightfall, etc. Is it just a straight % increase? Aghhh!!

 

Quite frustrating results.

 

A brief note on the M/5 stat weight. I did not do any testing on it. I just theorized 1mana every 5 seconds coming back on a Rank6 Starfire under Moonglow R3 and converted it into potential DPS increases (assuming you ran out of mana). When Rank7 comes out, this value will decrease to  .1038446601941748dps. If that is even accurate. It would be completely different for Wrath and even the inclusion of Moonfire in a rotation (if your guild would even allow it).

 

It needs to be understood that M/5 and SPI are only "dps increases" if and only if you run out of mana. Otherwise the stats are useless and don't contribute to an actual DPS increase.

I'm actually just going to submit my Crit findings now. They're incomplete as of now...

 

1 crit = 1.75dps = 1.75dps

2 crit = 3.51dps = 1.755dps

3 crit = 5.27dps = 1.756666666666667dps

4 crit = 7.04dps = 1.76dps

5 crit = 8.81dps = 1.762dps

6 crit = 10.59dps = 1.765dps

7 crit = 12.37dps = 1.767142857142857dps

8 crit = ?dps = ?dps

9 crit = ?dps = ?dps

10 crit = ?dps = ?dps

11 crit = ?dps = ?dps

12 crit = ?dps = ?dps

13 crit = ?dps = ?dps

14 crit = ?dps = ?dps

15 crit = ?dps = ?dps

16 crit = ?dps = ?dps

17 crit = ?dps = ?dps

18 crit = ?dps = ?dps

19 crit = ?dps = ?dps

20 crit = ?dps = ?dps

 

- Tests were done with 0 SP.

- Any tests that were done with >0 SP were then subtracted from previous test results.

- A scaling issue was determined with Hit AND Crit. It was documented when testing various gear checks.

- Even INT has a different scaling mechanism, but it's incredibly small compared to the Hit/Crit scaling.

Patch 1.8 BiS Gear (9% spell hit)

-------------------------------------------

Lok'amir il Romathis

Tome of Arcane Domination

 

Mish'undare, Circlet of the Mind Flayer

Choker of the Fire Lord

Mantle of the Blackwing Cabal

Bloodvine Vest

Cloak of Consumption

Bracers of Arcane Accuracy

Bloodtinged Gloves

Firemaw's Clutch

Bloodvine Leggings

Bloodvine Boots

Ring of Spell Power

Ring of Spell Power

Neltharion's Tear

Briarwood Reed





PURELY-SPECULATIVE STARFIRE BIS
 

 

 

Patch 1.9 BiS Gear (836sp 417int 37%crit 11%hit)

-------------------------------------------

Lok'amir il Romathis

Royal Scepter of Vek'lor

 

Mish'undare, Circlet of the Mind Flayer

Amulet of Vek'nilash

Mantle of the Blackwing Cabal

Bloodvine Vest

Cloak of the Devoured

Rockfury Bracers

Dark Storm Gauntlets

Eyestalk Waist Cord

Bloodvine Leggings

Bloodvine Boots

Ring of the Fallen God

Ritssyn's Ring of Chaos

Neltharion's Tear

Briarwood Reed

 

 

Patch 1.10 BiS Gear (836sp 417int 37%crit 11%hit)

-------------------------------------------

Lok'amir il Romathis

Royal Scepter of Vek'lor

 

Mish'undare, Circlet of the Mind Flayer

Amulet of Vek'nilash

Mantle of the Blackwing Cabal

Bloodvine Vest

Cloak of the Devoured

Rockfury Bracers

Dark Storm Gauntlets

Eyestalk Waist Cord

Bloodvine Leggings

Bloodvine Boots

Ring of the Fallen God

Ritssyn's Ring of Chaos

Neltharion's Tear

Briarwood Reed

 

 

Patch 1.11 BiS Gear (933sp ---int --%crit 9%hit)

-------------------------------------------

Brimstone Staff

 

Mish'undare, Circlet of the Mind Flayer

Gem of Trapped Innocents

Rime Covered Mantle

Crystal Webbed Robe

Cloak of the Necropolis

Rockfury Bracers

Dark Storm Gauntlets

Eyestalk Waist Cord

Leggings of Polarity

Boots of Epiphany

Ring of the Fallen God

Band of the Inevitable

Neltharion's Tear

The Restrained Essence of Sapphiron



Thoughts about Spell Penetration (source: http://vanillagaming.org/forum/index.php?topic=16983.0)

 

According to a few Elitistjerks posts from vanilla it seemed to be generally accepted that a Curse of Elements or Shadows removed all boss resistance besides 20 "unpenetrable" resistance.

 

This means that we're looking at a total of 75 spell penetration that would be required for boss encounters, quite a lot to say the least. Those who have a guild rocking a Thunderfury are lucky and will "only" have to aim for 50 spell penetration.

 

Many of the same Elitistjerks posts tell us that each point of resistance accounts for approximately 0.25% damage reduction and therefore, while many elemental shamans will want to gear up like they would gear any other caster class they should actually be aiming a lot more for spell penetration.

 

As other classes do not have to gear towards spell penetration to such an extent many might think the stat not worth going for as you're "sacrificing too much". But before you steer clear of spell penetration let me give you an example:

Ring of Swarming Thought vs Band of Forced Concentration

These items should be quite comparable as something a shaman would carry through AQ vs something a mage or warlock would carry through the same instance. Both provide you with about the same amount of spell damage but here the shaman is "sacrificing" 1% hit for 20 spell penetration.

 

Using a rough formula I'm going to value the 1% hit vs 20 spell penetration:

 

(base_damage+spell_damage*spell_dmg_coefficient)*chance_to_hit*(1+crit_chance)*(0,8125+(0,0025*spell_penetration)) = DPS

 

So if we apply basic theoretical values for a normal caster to the formula:

 

(100+100*1)*0,85*(1+0,2)*(0,8125+(0,0025*75)) = 204

 

And then we add an extra chance to hit:

 

(100+100*1)*0,86*(1+0,2)*(0,8125+(0,0025*75)) = 206,4

 

We'll see that DPS was increased by (206,4-204)/204*10=1,17%.

 

Now if we apply the same basic theoretical values for a shaman with no spell penetration (or curse, obviously) to the formula:

 

(100+100*1)*0,85*(1+0,2)*(0,8125+(0,0025*0)) = 165,75

 

And then we add an extra chance to hit:

 

(100+100*1)*0,86*(1+0,2)*(0,8125+(0,0025*0)) = 167,7

 

We'll see that the 1% hit again resulted in (167,7-165,75)/165,75*100=1,17% DPS increase. But what happens if we exchange that 1% hit for 20 spell penetration?

 

(100+100*1)*0,85*(1+0,2)*(0,8125+(0,0025*0)) = 165,75

 

And then we add 20 spell penetration:

 

(100+100*1)*0,85*(1+0,2)*(0,8125+(0,0025*20)) = 175,95

 

So now we can calculate that 20 spell penetration resulted in (175,95-165,75)/165,75*100=6,15% DPS increase.

 

With that said we can return to the problem: The lack of a curse. It's quite obvious that the only thing you can do to combat this is get more spell penetration. Problem solved right?

 

Maybe. But perhaps the problem wasn't a lack of a curse to begin with.

 

It could be said that the real problem is the unwillingness of some to sacrifice good items for spell penetration items or perceive doing so as a huge hindrance to the entire success of the spec. I am therefore going to address this "hidden problem" now.

 

Obviously it doesn't have a solution so to speak. It's a fact that you're going to have to gear towards spell penetration and doing so does require steering from "better" items. What's needed is a way to put the mind at ease over these losses.

 

Here's my proposed solution to that problem: Think of the amazing talents as a counterweight.

 

Although mages do come pretty close in regards to additional spell hit, spell crit, increased damage and reduced cost of spells granted by talents no one comes close when it comes to reduced cast time of their main spell and when you think about it -1.0 seconds is pretty absurd.

 

So there it is. They get a curse, you get an extra -0.5 seconds off of your main spell, almost a fair deal. But only almost because it prompts another problem.

 

 

Edited December 10, 2016 by Keftenk