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#1 Myowndk

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Posted 11 March 2010 - 12:42 PM

ADDED A SECTION ON HASTE VS SPELL POWER

SECTION ONE: HASTE SCALING

I figured there wasn't a thread focused on the math behind haste yet, and as there are *alot* of misconceptions about haste(such as the value of it during Bloodlust, or during eradication), I decided to make this thread.


Some general information about haste:

The first thing about haste you should know, is that it stacks multiplicatively. That means if you have 20% passive haste, and you gain an Eradication proc you then have:
1,2*1,2=1,44 --> 44% haste.
This means, the more haste you have, the better the scaling is with bloodlust and eradication.

The effect of Curse of Tongues(-30% haste) on your target's total haste:
For the same reason as above, the more haste your target has, the better it gets to use Curse of Tongues on them. When using Curse of Tongues your target's haste is divided by 1,3 , thus costing him massive ammounts of haste.

For those who don't know it yet:
The haste formula:
New cast time = Old cast time/(1+(Haste%/100))



That means that with 20% haste, your corruption's cast time would be:

18/(1+20/100)=18/(1,2)=15 seconds

The ammount of haste you need for 1% is 32,79 at level 80.


Some calculations involving haste:

Situation A: "Lol I laik haste"-setup
Affliction warlock specced into Eradication, using full haste off set gear and some haste gems to match sockets.
Around 750 haste with spellstone, around 23% haste.
Teamed with a shaman, for Bloodlust.
Using Black Magic on weapon, Hyperspeed Accelerators on gloves.

Maximum haste in an ideal situation:
750 passive haste + 250 from Black Magic + 340 from Hyperspeed Accelerators = 1340, ~41% haste.
Now, we add an Eradication proc:
1,41*1,2=1,692 so that makes 69,2% haste.
Now we add in Blood Lust:
1,692*1,3=2,1996 so just about 120% haste.

Now it's a bit hard to say what your average haste would be during a match, so I'll just make a comparision between the passive haste(23%) of this situation, and the maximum haste(120%)
For the medium value we'll take 1000 haste, and an Eradication proc, which is almost 57% haste.


Global cooldown:
Max 1,5/(1+(120/100))=0,68 seconds
Med 1,5/(1+(57/100))=0,96 seconds
Min 1,5/(1+(23/100))=1,22 seconds
It's too bad the global cooldown however is capped at 1.00 seconds, so you are sadly wasting some haste here.

Corruption:
Max 18/(1+(120/100))=8,18 seconds
Med 18/(1+(57/100))=11,46 seconds
Min 18/(1+(23/100))=14,63 seconds

Fear*:
Max 1,3/(1+(120/100))=0,59 seconds
Med 1,3/(1+(57/100))=0,83 seconds
Min 1,3/(1+(23/100))=1,06 seconds

*Note: when calculating the new cast time, you have to use the base cast time. With the 4 piece PvP set bonus this new base cast time is 1,3 seconds.

Shadowbolt:
Max 3/(1+(120/100))=1,36 seconds
Med 3/(1+(57/100))=1,91 seconds
Min 3/(1+(23/100))=2,43 seconds

Unstable Affliction cast time:
Max 1,5/(1+(120/100))=0,68 seconds
Med 1,5(1(57/100))=0,96 seconds
Min 1,5/(1+(23/100))=1,22 seconds

Drain Soul:
Max 15/(1+(120/100))=6,8 seconds.
This means it ticks every 1,36 seconds.
Med 15/(1+(57/100))=9,55 seconds
Which means it ticks every 1,91 seconds.
Min 15/(1+(23/100))=12,19 seconds
Which means it ticks every 2,44 seconds.

Drain Life / Drain Mana*:
Max 5/(1+(120/100))=2,27 seconds
Med 5/(1+(57/100))=3,18 seconds
Min 5/(1+(23/100))=4,06 seconds

*Note: for Drain Mana this means that you are draining 15% of your targets mana in 2,27 seconds assuming 0 resilience.
If the target has capped resilience(1414), and therefor has -33% Mana Drains and Critical Strikes, you would be draining 10% of his total mana in 2,27 seconds.
At this rate, you can oom your target in 22,7 seconds.


Situation B: "I don't want to go over the global cd cap during Eradication"
This situation assumes a warlock who doesn't want to hit the global cooldown cap with just Eradication up. Therefor this warlock does not use Black Magic and the Hyperspeed Accelerators, and stacks a bit less haste.

Ammount of haste needed to cap your global cooldown with just Eradication up:
To hit the global cooldown cap, you'd need 50% haste.
Eradication is 20%, so you need an ammount equal to 1,2*x=1,5
The x here, would be 25%. So you need 25% passive haste to just hit the global cooldown cap with Eradication up. This equals to 25*32,79=819,75 haste rating.

So a person with 819,75 haste rating would have the following cast times, the Max value assumes Eradication and Bloodlust, Med assumes just Eradication and Min is just the passive haste.
Max is 95% haste, med is 50% and Min is 25%.

Global cooldown:
Max 1,5/(1+(95/100))=0,77 seconds
Med 1,5/(1+(50/100))=1,00 seconds
Min 1,5/(1+(25/100))=1,20 seconds


Corruption:
Max 18/(1+(95/100))=9,23 seconds
Med 18/(1+(50/100))=12,00 seconds
Min 18/(1+(25/100))=14,40 seconds

Fear:
Max 1,3/(1+(95/100))=0,67 seconds
Med 1,3/(1+(50/100))=0,87 seconds
Min 1,3/(1+(25/100))=1,04 seconds

Shadowbolt:
Max 3/(1+(95/100))=1,54 seconds
Med 3/(1+(50/100))=2,00 seconds
Min 3/(1+(25/100))=2,40 seconds

Unstable Affliction cast time:
Max 1,5/(1+(95/100))=0,77 seconds
Med 1,5/(1+(50/100))=1,00 seconds
Min 1,5/(1+(25/100))=1,20 seconds

Drain Soul:
Max 15/(1+(95/100))=7,69 seconds
This means it ticks every 1,54 seconds.
Med 15/(1+(50/100))=10,00 seconds
Which means it ticks every 2,00 seconds.
Min 15/(1+(25/100))=12,00 seconds
Which means it ticks every 2,40 seconds.

Drain Life / Drain Mana:
Max 5/(1+(95/100))=2,56 seconds
Med 5/(1+(50/100))=3,33 seconds
Min 5/(1+(25/100))=4,00 seconds



Curse of Tongues:
This section is dedicated to Curse of Tongues, as it has a rather destroying effect on your opponents haste, and therefor in some situations can be vital to keep up.
I'm not doing the entire math for every spell again here, but I'll just give an indication on the % dps loss on corruption and shadowbolt.

Curse of Tongues becomes more valuable the more haste your opponent has, so therefor it's probably a good idea to keep it up 100% during the opponents Bloodlust. I'll show you why down here:

Max haste from Situation A: 120%
Now, let's see how much that is after Curse of Tongues:
2,2/1,3=1,69 now it's only 69%
As you see, the target now lost 51% haste.
This is roughly a 25% nerf to corruptions dps, aswell as an equal nerf to his Shadowbolt spamming dps.


Now we take a normal situation with the average lock, who is running with the 750 haste from Situation A, without any buffs or procs.
Before CoT he has 23% haste. After CoT he suffers from a negative 5,5% haste.
Now, what means this for his corruption and shadowbolt? The effect is a bit less than before, it's around a 22% nerf to both.

Now, corruption is usually about 45% of my dps, and shadowbolt around 15%.
If we assume that a 25% dps nerf to both, this would mean I'd lose a total of around 15% dmg.
Ofcourse, this does mean that you would lose the around ~12% overal dmg of CoA, but the devastating effects of CoT are definitely something to keep in mind when you need to limit the opponent warlock's damage.

*Note: the effects on shadow priests and mages are even greater, as they have more spells that benefit in a direct damage way off haste, so it would mean an even bigger damage nerf for them.


Advantages of Haste:
Utility: faster casts mean it's easier to controll targets due to your reduced fear cast time.
Raw damage: in burst scenario's haste provides a lot of extra damage, specially when under the effect of Blood Lust or/and Eradication.
Drain soul: Haste particularely is awesome for Drain Soul, as it makes the first tick come A LOT sooner, therefor giving you a much better chance for a solid Drain Soul Execute.


SECTION TWO: HASTE VS SPELL POWER

By popular demand: an added section on haste vs spellpower.

Now, this is a fair bit harder than the previous calculations, as alot of the power of haste cannot be meassured by exact numbers.
(Being faster cast times on Fear, UA, faster dotting etc.)
However, some factors can be exactly measured, such as the dps difference on Corruption, Drain Soul and Shadow Bolt.

Let's make three different sets of gear, keeping in mind the stat budget of haste vs spellpower.
20 haste equals 23 spell power in terms of budget, so 1 haste = 1,15 spell power

The first set up, is one of a warlock wearing crit pieces, gemming purely for Spell power, which brings him to about 3800 sp, and around 30% crit. And only 60 haste(Spell Stone)

The second set up, uses full haste off gear, and has around 750 haste with his Spell Stone, while still having 3800 sp and 15% crit.

The third set up, uses full haste off gear, aswell as sacrificing a fair bit of extra Spell power for more haste. This set up has 1000 haste, 3513 sp and still 15% crit.

Ofcourse, these scenarios are a bit flawed, as normally the bulk of your haste comes from sacrificing crit and not spell power, but for this comparison it's close enough.

Also, these calculations are done, assuming you specced for Nightfall, aswell are using the Corruption glyph, for a total of 7,84% to proc an instant Shadow Bolt of every Corruption tick(4%+4%, minus the chance they both proc at once, which is 0,16%)

Formulaes used:

Corruption:
Formula: 1080+(162% of Spell Power)*Multipliers
Multipliers:
Improved Corruption: 10%
Siphon Life: 5%
Shadow Mastery: 15%
Contagion: 5%
Malediction: 3%
Haunt: 20%
Spell Stone: 1%
Damage reduction: resilience: around 25%
Final formula: (1080+(1,62*Spell power))*1,1*1,05*1,15*1,05*1,03*1,2*1,01*0,75


Shadow Bolt:
Formula: 730+(85,71% of Spell Power*Multipliers
Multipliers:
Shadow Mastery: 15%
Malediction: 3%
Damage reduction: reslience: around 25%
Final formula: (730+(0,8571*Spell power))*1,15*1,03*0,75


Drain Soul:
Formula(per tick): 710+(42,86% of Spell power)*Multipliers
Multipliers:
Sub 25% hp: 400%
Soul Siphon: 18%
Shadow Mastery: 15%
Haunt: 20%
Malediction: 3%
Damage reduction: resilience: around 25%
Final formula: (710+(0,4286*Spell power))*4*1,18*1,15*1,2*1,03*0,75


Set up 1: 3800 sp, 30% crit, 60 haste.

Corruption:
Damage and dps table:
Damage per tick(non crit) 1574,77
Damage per tick(critical) 2204,68
Average damage per tick: 1694,45
Total damage: 10166,72
Duration: 17,68
Dps: 575,15
Dps including Nightfall: 676,09

Additional Corruption related dps*:
Nightfall procs:
An average of 6*0,0784=0,47 procs per 17,68 seconds
Adding 0,47*3568,5=1784,2 to Corruptions total damage, which equals to 1736,18/18=100,94 dps.
*Note: this is not taking in to consideration the burst a nightfall proc generates, just the overal dps. Not does it consider the posibility of having Corruption on multiple targets.

Shadow Bolt:
Damage(non crit): 3541,93
Damage(critical): 3719,03
Average damage: 3568,50
Cast time: 2,95
Dps(spamming) 1201,90

Drain Soul:
Damage per tick: 11767,67
Total damage: 70606,00
Cast time: 14,73
Dps: 4791,79


Set up 2(750 haste, 15% crit, 3800 sp)

Corruption:
Damage and dps table:
Damage per tick(non crit) 1574,77
Damage per tick(critical) 2204,68
Average damage per tick: 1631,46
Total damage: 9788,78
Duration: 14,65
Dps: 668,19
Dps including Nightfall: 789,06

Additional Corruption related dps:
Nightfall procs:
An average of 6*0,0784=0,47 procs per 14,65 seconds
Adding 0,47*3541,6=1770,8 to Corruptions total damage, which equals to 1736,18/14,65=120,87 dps.

Shadow Bolt:
Damage: 3541,60
Damage Critical: x*
Cast time: 2,44
Dps(spamming) 1450,52

*Note: Shadow Bolt most likely isn't going to crit in an arena setting with only 15% crit.

Drain Soul:
Damage per tick: 11767,67
Total damage: 70606,00
Cast time: 12,21
Dps: 5783,57


Set up 3(1000 haste, 3513 sp, 15% crit):

Corruption:
Damage and dps table:
Damage per tick(non crit) 1473,59
Damage per tick(critical) 2063,02
Average damage per tick: 1526,64
Total damage: 9159,81
Duration: 13,79
Dps: 664,09
Dps including Nightfall: 784,58

Additional Corruption related dps:
Nightfall procs:
An average of 6*0,0784=0,47 procs per 13,79 seconds
Adding 0,47*3323,09=1661,55 to Corruptions total damage, which equals to 1736,18/13,79=120,49 dps.

Shadow Bolt:
Damage: 3323,09
Damage Critical: x*
Cast time: 2,30
Dps(spamming) 1445,54

*Note: Shadow Bolt most likely isn't going to crit in an arena setting with only 15% crit.

Drain Soul:
Damage per tick: 11148,72
Total damage: 66892,32
Cast time: 11,49
Dps: 5819,63


Recap:
Dps - Set up 1 - Set up 2 - Set up 3
Corruption - 676,09 - 789,06 - 784,58
Shadow Bolt - 1201,90 - 1450,52 - 1445,54
Drain Soul - 4791,79 - 5783,57 - 5819,63

Notes:
The damage difference between running with 750 haste, and 1000 haste is neglible on these spells. Ofcourse you will lose additional ammounts of dmg, when we factor in the other damaging abilties.
Set up 1 is clearly inferior, but we all knew that already as haste>crit anyway.


To show how the numbers would be, if we do factor in Bloodlust, I'll show a quick table of the dps per spell while having both Bloodlust and Eradication up.
I'm not going to back this up with my extensive calculations, I'm using the exact same ones as for the figures above.

Calculations including Bloodlust / Eradication:
Dps: - Set up 1 - Set up 2 - Set up 3
Corruption - 1045,11 - 1222,96 - 1212,74
Shadow Bolt - 1877,22 - 2268,98 - 2255,27
Drain Soul - 7484,24 - 9046,98 - 9079,52


Remarks on Spell Power vs Haste:
On the spells I have compared(those spells that benefit from Haste), the damage and dps difference between Set up 2 and 3 is neglible.
The extra factors that do need to be taken in to consideration however, are the damage losses off Unstable Affliction, Haunt and Curse of Agony.
These factors might be properly compensated though, by having faster Fear casts, and the ability to dot up targets just a bit faster.
It's really hard(read, probably impossible) to give an exact value to the utility haste gives in this area. Personally however, I feel like it's worth sacrificing a tiny bit of Spell Power for some Haste, but just don't go all overboard.


I really hope this thread helped any of you out :)

Ps. If you notice any flaws in spelling or grammar, please do tell me, so I can correct them. English isn't my first language, but I tried my best.
Corrections on flawed math are more than welcome as well.
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#2 orion12314

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Posted 11 March 2010 - 12:51 PM

Jawsus sticky please.
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#3 Drye

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Posted 11 March 2010 - 12:55 PM

wow, good job there
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#4 Guest_Shizzle_*

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Posted 11 March 2010 - 12:56 PM

Good job indeed, reppin
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#5 Myowndk

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Posted 11 March 2010 - 12:58 PM

Thanks for the kind words :)
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#6 Trikso

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Posted 11 March 2010 - 01:11 PM

Sticky please
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2.7k nonglad Warrior commenting on RMP

overpowered

warrior reporting in

there are so many bad players at high ratings right now because they got a skill boost with 4.0.6 x.X


#7 oogleboogle

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Posted 11 March 2010 - 04:29 PM

+3 internets
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#8 Myowndk

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Posted 11 March 2010 - 04:30 PM

Trying to add a comparison of spellpower versus haste somewhere tomorrow.
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#9 Myowndk

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Posted 11 March 2010 - 04:33 PM

If I can find the time somewhere that is, as that's quite a bit harder in terms of calculations than all off this =/
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#10 Jugg

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Posted 11 March 2010 - 07:12 PM

Now, we add an Eradication proc:
1,41*1,2=1,692 so that makes 69,2% haste.
Now we add in Blood Lust:
1,692*1,3=2,1996 so just about 120% haste.


From my understanding, your calculations are off. For a combination of 41% haste and 20% haste you get 52.8% haste, not 69.2% (0.59*0.80=.472 1-.472=.528). Adding in all 3 effects is (.59*.8*.7=.3304 1-.3304=.6696%) results in 66.96% haste, not 120%. Stopped reading after this point, but I lawlstack haste as much as possible.
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#11 Saracens

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Posted 11 March 2010 - 07:17 PM

at 120% haste does the world explode? ;)
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#12 dubroya

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Posted 11 March 2010 - 07:20 PM

Pretty nice, glad to see someone good at mathematics. Rep + :)
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#13 Myowndk

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Posted 11 March 2010 - 07:33 PM

From my understanding, your calculations are off. For a combination of 41% haste and 20% haste you get 52.8% haste, not 69.2% (0.59*0.80=.472 1-.472=.528). Adding in all 3 effects is (.59*.8*.7=.3304 1-.3304=.6696%) results in 66.96% haste, not 120%. Stopped reading after this point, but I lawlstack haste as much as possible.


The way haste scales is multiplicatively, meaning that it scales in the way off (1+(Passive haste/100)*(1+(Haste from Proc 1/100)*(1+(Haste from Proc 2/100) ... etc.

The way you calculated it is very odd, but according to all sources(and my own experience related to Shadow Bolt spamming with all procs up) that is absolutely not the correct way to calculate it.

Thanks for your input though.
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#14 Filovirus

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Posted 11 March 2010 - 07:37 PM

+1
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#15 Nadagast

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Posted 11 March 2010 - 08:11 PM

Pretty nice, glad to see someone good at mathematics. Rep + :)

Jesus fucking christ this makes me emo.

Basic multiplication = good at math?

Don't get me wrong I can somewhat appreciate what he's trying to do but this is not difficult math. Anyone who has passed middle school should be able to do this easily
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#16 yoyot

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Posted 11 March 2010 - 08:13 PM

[B]
Now, we add an Eradication proc:
1,41*1,2=1,692 so that makes 69,2% haste.
Now we add in Blood Lust:
1,692*1,3=2,1996 so just about 120% haste.




Except it's not added like that. It should be 1.41/1.2/1.3 for total haste. Really sad that you're wrong in this kind of post.
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#17 yoyot

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Posted 11 March 2010 - 08:16 PM

Just from reading the start, your math is wrong. 20% + 20% Haste don't stack to make 44% Haste, they stack to make 36%

It'd be .8 * .8 = .64 => 1-.64=.36 => 36% Haste


Jesus fucking christ this makes me emo.

Basic multiplication = good at math?

Don't get me wrong I can somewhat appreciate what he's trying to do but this is not difficult math. Anyone who has passed middle school should be able to do this easily


And he even failed at doing it correctly :D
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#18 Jugg

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Posted 11 March 2010 - 08:18 PM

The way haste scales is multiplicatively, meaning that it scales in the way off (1+(Passive haste/100)*(1+(Haste from Proc 1/100)*(1+(Haste from Proc 2/100) ... etc.

The way you calculated it is very odd, but according to all sources(and my own experience related to Shadow Bolt spamming with all procs up) that is absolutely not the correct way to calculate it.

Thanks for your input though.


You're wrong.
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#19 Nadagast

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Posted 11 March 2010 - 08:21 PM

And he even failed at doing it correctly :D


What kind of an anti-intellectual culture do we live in when someone can post basic multiplication and division on the internet and get someone calling them good at math?
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#20 Myowndk

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Posted 11 March 2010 - 08:36 PM

I'm sorry, but my way to calculate it IS correct. Having 23% passive haste, 30% from Bloodlust and 20% from Eradication gets me a 1,56 second Shadow Bolt, I know for sure as I just checked while in arena. This is EXACTLY the value my calculation under these conditions said it would be ...

1,23*1,3*1,2=1,92 --> 92% haste
This makes for a 3/(1+92/100)=1,5625 seconds...

Also, I do agree this isn't AWESOME math or anything. I just thought it would be useful.

More coming up on Spell power vs Haste.
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