Haste increases the number of casts in a fixed timeframe in a linear manner no matter how much haste you have already. This makes it sublinear with respect to your actual dps but it's still linear to the number of casts:
In a fixed timeframe T, with fixed base cast time C and variable haste H,
each cast is C/(1+H)
so the total number of casts is (1+H)(T/C), and that's linear in H.
I think there is also some consideration as to whether haste is truly sublinear in the short term.
Part of the reason haste is sublinear over 6 minutes is the increased mana output, and thus increased lifetap frequency over an extended duration.
However, during trinkets/heroism, you should be lifetapping 0 times regardless of what your haste level is.
Haste increases the number of casts in a fixed timeframe in a linear manner no matter how much haste you have already. This makes it sublinear with respect to your actual dps but it's still linear to the number of casts:
In a fixed timeframe T, with fixed base cast time C and variable haste H,
each cast is C/(1+H)
so the total number of casts is (1+H)(T/C), and that's linear in H.
"20 sec of both 11.872 bolts @ 1.554"
Total haste = 200+175
with heroism thats 2.5/[(1+375/1577*1.30)] or 2.5/1.609 ie 1.554 for 20 seconds i don't see the issue here. 1 Haste WILL NOT always reduce your cast time(and this is the only thing that determines number of shadowbolts) by the same.
10% haste
2.5/1.1= 2.273
reduction of 0.227
20% haste
2/5/1.2 = 2.083
reduction of 0.189
Unless there was a problem somewhere else that I didnt see or I am totally missing something, the numbers prove using gul'dan during heroism(and coincidently drums aswell) is worse
45 sec of SBs at 2.5/1.3 (1.923) cast time (with r sec overflow) and 20 sec at 2.5/1.11 (2.250) cast time (t overflow) and x at 2.5 =
r = ceil(45/1.923) - 45/1.923 = 0.599
t = ceil(20/2.250) - 20/2.250 = 0.111
ceil(45/1.923) + ceil(20/2.250) + (70-45-20-r-t)/2.5 = 24 + 9 + 1.716 = 34.716 shadowbolts in 70 sec.
Stacking Skull in the first 20 sec of BL you get:
20 sec of SBs at 2.5/(1.3+.11) (1.773) cast time (with r overflow), (25-r) sec at 2.5/1.3 (1.923) cast time (t overflow) and x at 2.5=
r = ceil(20/1.773) - 20/1.773 = 0.720
t = ceil((25-r)/1.923) - (25-r)/1.923 = 0.373
ceil(20/1.773) + ceil((25-r)/1.923) + (70-45-t)/2.5 = 12 + 13 + 9.850 = 34.8508 bolts in 70 sec.
Correct my math if I'm wrong, but while it's a benefit to stack the two, it doesn't seem like much of one.
These assume that you wouldn't pop your trinket until after casting the last bolt affected by the previous haste, of course. the 70 window (instead of 65) was to soak up the overflow, as you techincally get the haste benefit from every spell cast while the haste bonus is up.
Of course, with the right amounts of haste, stacking the two would give an even greater benefit, if you can squeeze that last .72 sec of the last bolt that gets the benefit of both of them down enough to fit another bolt in.
But again, it's really close.
[E] Just realized, my calculation for stacking the two under BL might be off. Is it c/(1+h+.3) for BL, or c/((1+h)*1.3)?
[E2] My fractional times might be off. I'll have to check my units later. Don't have time now, sadly.
I am acting under the assumption it is *1.3 not +0.3 Torq.. I tried to get a shaman to heroism me 4 times but apparently there is some sort of bug where heroism wasnt hitting me.. If it is +0.3 then it is even more clear not to stack them tho.
Torq, you should do two of those graphics you do Torq with total bolts casted vs passive haste 0-400 one for trinket during hero, one for trinket after hero. Curious where the inflection points are.
Edit: Fixed my original numbers for a mistake(wrote bolt count down off by 1second), would seem as tho stacking is still better, at 200.. and the gap changes so insignificantly that it is probably always better to stack them.
Last edited by Flamingcloud : 04/28/08 at 6:39 PM.
Could you make your math any less readable? Your math seems to be identical to mine tho, and I plugged in real numbers and got those results. The simple fact is the more haste you have the less useful it is. (the whole 1% haste is 1% off your cast but 100% haste is only 50% off your cast mechanic, thus 30% haste all the time is better than 60% haste half the time.)
You seem to be mixing 2 mechanics here. Haste and increased spell casting speed are not the same. While abilities like Heroism and Icy Veins increase spell casting speed where yes, 100% would just cut your casting time in half because it would cause you to just cast at 200% casting speed, haste however keeps a relatively linear haste to dps progression (until you hit the GCD, then it follows the GCD down for that spell). So in all actuality 100% haste would make every spell instant but keeping the GCD at 1s, though that would take 1577 haste rating to achieve. Basically increased spell casting speed well it increases your spell casting speed (duh), whereas haste rating lowers the time your spells take to cast.
Now keeping that in mind, the skull actually adds raw haste to your standing haste for 20s. The question is, depending on how it is all calculated together, is the Heroism calculated after or before the skull? Seems like this would depend if the skull is just being added to your gear haste rating for calculations or if its being taken into account after things like Heroism.
Please tell me if i missed something here because every resource i have seen, including the spreadsheet, says this is how haste rating works.
100% haste means your spells cast in half the time it normally takes to cast if you ignore the global cooldown. Haste rating acts the same way as heroism.
All haste effects work the same, +100% haste is a -50% casting speed change. All haste gained through haste rating gets lumped together additively, all other haste effects get multiplied separately. So a 30% bloodlust with the skull active will make you cast 30% caster than a non-lusted skull activation. Hasting the haste nets you a minor cross-multiplicative term that makes them better to stack than to use independently.
Math: Let's say you have two equal amounts of time, two haste activations, and for the sake of simplicity you can either haste one interval than the other, or double-haste on and have the other be unhasted. Haste, as should be evident, multiplies your damage done in that interval by a percent. Let's look at the sum of damage multipliers.
Stacking them is better than not stacking them, by an amount equal to the cross-term. Which is 30% of however much haste you get from the skull.
Note that this is only true because of bloodlust being done by percent instead of haste rating. If you had two haste rating activations (or a proc and a clicky or whatever) there is no benefit to stacking them. Because the benefit of haste rating is linear it doesn't matter if you use them together or not.
Hueristics: 100% haste doubles your cast speed, giving you double damage. 200% haste triples it, tripling your damage. The second 100% was the same increase as the first 100% (compared to your base damage).
All haste effects work the same, +100% haste is a -50% casting speed change. All haste gained through haste rating gets lumped together additively, all other haste effects get multiplied separately. So a 30% bloodlust with the skull active will make you cast 30% caster than a non-lusted skull activation. Hasting the haste nets you a minor cross-multiplicative term that makes them better to stack than to use independently.
Math: Let's say you have two equal amounts of time, two haste activations, and for the sake of simplicity you can either haste one interval than the other, or double-haste on and have the other be unhasted. Haste, as should be evident, multiplies your damage done in that interval by a percent. Let's look at the sum of damage multipliers.
Stacking them is better than not stacking them, by an amount equal to the cross-term. Which is 30% of however much haste you get from the skull.
Note that this is only true because of bloodlust being done by percent instead of haste rating. If you had two haste rating activations (or a proc and a clicky or whatever) there is no benefit to stacking them. Because the benefit of haste rating is linear it doesn't matter if you use them together or not.
Hueristics: 100% haste doubles your cast speed, giving you double damage. 200% haste triples it, tripling your damage. The second 100% was the same increase as the first 100% (compared to your base damage).
Ah, thank you for clarifying. I guess it all goes by the old standard that we locks abuse as it is to get top dmg in raids. Percent buffs are always better to stack a bunch of than stacking a bunch of set number buffs.
You seem to be mixing 2 mechanics here. Haste and increased spell casting speed are not the same. While abilities like Heroism and Icy Veins increase spell casting speed where yes, 100% would just cut your casting time in half because it would cause you to just cast at 200% casting speed, haste however keeps a relatively linear haste to dps progression (until you hit the GCD, then it follows the GCD down for that spell). So in all actuality 100% haste would make every spell instant but keeping the GCD at 1s, though that would take 1577 haste rating to achieve. Basically increased spell casting speed well it increases your spell casting speed (duh), whereas haste rating lowers the time your spells take to cast.
Now keeping that in mind, the skull actually adds raw haste to your standing haste for 20s. The question is, depending on how it is all calculated together, is the Heroism calculated after or before the skull? Seems like this would depend if the skull is just being added to your gear haste rating for calculations or if its being taken into account after things like Heroism.
Please tell me if i missed something here because every resource i have seen, including the spreadsheet, says this is how haste rating works.
Extended example:
final_cast_time = talented_cast_time / (1 + total_haste_rating_in_percent) / 1.3 (bloodlust) / 1.1 (berserking) / 1.2 (icy veins)
Lets say I use a talented shadowbolt and 10% passive haste
x = 2.5 / (1 + 0.10) / 1.3 / 1.1 / 1.2
In other words, spell haste rating is additive, and haste effects like bloodlust, icy veins, power infusion, berserking, focus proc are multiplicative.
Note that this is only true because of bloodlust being done by percent instead of haste rating. If you had two haste rating activations (or a proc and a clicky or whatever) there is no benefit to stacking them. Because the benefit of haste rating is linear it doesn't matter if you use them together or not.
This is not totally true. Stacking haste effects is not a linear effect. In the grand lines of things it is, but in practice it is not fully true. If you take into account that spell cast time is determined upon time of casting and not 'as they leave your hand' (which wouldn't make much sense, but ignoring that), stacking more/less haste can be a benefit.
If, for example, you had a 200 haste / 20s trinket, and one that gives 400 haste / 20s, then stacking them together would allow you for:
conclusion: stacking 200 haste with 400 haste trinkets together is detrimental.
PS: using different values I can also show that stacking them is to your advantage; the point is that the gain is not linear, and stacking/unstacking can be beneficial depending on what your haste is at.
I am using haste due to my group synergy (Spriest + ele sham 100% of the time, so definitely always for brut.)
I am currently at 11% haste not counting skull, with 2.25 second SB.
The reason for using haste to me, instead of spinels/straight +dmg, is that my haste multiplies the effects of the totem of wrath and wrath of air by 11% tooltip, 10% in real time, thus slightly edging out +dmg in what I have sacrificed for haste.
I have deviated from a few leulier spreadsheet non-haste upgrades due to their rather weak (5-15) dps improvement numbers, based on my personal calculations.
Each Cast will need to be 1.92857 seconds to achieve our target.
Calculate the difference between our target time and current time
(1.93 / 2.25)*100 = 85.7%
The Reduction required:
100 - 85.7 = 14.3%
The End Result
14.3 x 15.7 = 224.51 ~ 225 Haste
The ultimate question: Does it worth it to get 225 haste for a 7th Incinerate while dropping spell dmg/crit?
Want to hear pro Fire Locks on this.
Edit: Actually, I think the math are wrong: incinerate's extra damage from immolate is calculated on time of cast, not when incinerate reaches the target (correct me if im wrong), so the target will be 7 Incinerates in 15 seconds.
Doing the maths again with 7 Incinerate in 14.9 seconds = 125 haste is needed.
"Fitting" incinerates into an immolate is not nearly as important as you'd think. The extra damage to incinerate from immolate is relatively small. You can play around with the sheet to go off of "worse case" immolate uptimes and it will drop your DPS by a handful of points. Add another lock immolating and this loss is nothing.
"Fitting" incinerates into an immolate is not nearly as important as you'd think. The extra damage to incinerate from immolate is relatively small. You can play around with the sheet to go off of "worse case" immolate uptimes and it will drop your DPS by a handful of points. Add another lock immolating and this loss is nothing.
We have 2 fire locks in our guild, I was wondering if some guild use 1 lock to cast immo while the other one only spam Incinerate or "Immolate swapping" between the 2 fire locks is a viable option.
As for haste: (You'll prolly tell me to test in on the spreadsheet) I understand and believe haste is very food for Shadow Bolt spam, but what is your opinion on Incinerate ?
Haste is great for both dps spells. The only difference between the two is SB favors crit more than using Incinerate, both spells love more spell haste.
Millions of words are written annually purporting to tell how to beat the races, whereas the best possible advice on the subject is found in the three monosyllables: 'Do not try.'
Haste also benefits fire locks less than shadow locks, but the difference isn't very large. mainly due to incin being a 2.5 second spell with 10% haste not a 2.25 second spell. (tho there is also the immolate will go below 1.0 second cast during heroism slight penalty)
The ultimate question: Does it worth it to get 225 haste for a 7th Incinerate while dropping spell dmg/crit?
Want to hear pro Fire Locks on this.
Edit: Actually, I think the math are wrong: incinerate's extra damage from immolate is calculated on time of cast, not when incinerate reaches the target (correct me if im wrong), so the target will be 7 Incinerates in 15 seconds.
Doing the maths again with 7 Incinerate in 14.9 seconds = 125 haste is needed.
Also can't the immolate that fills the requirement for the bonus damage be any locks immolate?
The ultimate question: Does it worth it to get 225 haste for a 7th Incinerate while dropping spell dmg/crit?
Want to hear pro Fire Locks on this.
Edit: Actually, I think the math are wrong: incinerate's extra damage from immolate is calculated on time of cast, not when incinerate reaches the target (correct me if im wrong), so the target will be 7 Incinerates in 15 seconds.
Doing the maths again with 7 Incinerate in 14.9 seconds = 125 haste is needed.
It takes a little over 100 haste to get a 7th incinerate in. More haste just resduces the dot gap on immo. 225 haste, as you've calculated it, is the amount of haste needed for 7 Incin + 0 dot gap on Immo.
My question is the real world application of haste when you only have a limited amount of it. Do you really need a good % of haste before you see returns in the 'real world' applications? I know what the spreadsheet says but when you look at movement and slight lag during fights is it worth sacrificing crit for a little bit of spell haste. These are the two gear scenarios i am playing with.
spell hit caped in both
Gear Set A: Dmg-1267 Crit-20.91 Haste-2%(2.43 sec SB)
Gear Set B: Dmg-1277 Crit-22.18 Haste-0
There's some math on Timbal's somewhere in either this thread or the DPS spreadsheet thread (it's actually also in the Wowhead comments for the item). Basically, if you're in a raid as Affliction, it's better than the Icon because the damage of the bolt scales with all the +% shadow damage buffs/debuffs you have going. However, at the same time, it's only better because of these % bonuses so it's worse than the Icon in normal situations.
My question is the real world application of haste when you only have a limited amount of it. Do you really need a good % of haste before you see returns in the 'real world' applications? I know what the spreadsheet says but when you look at movement and slight lag during fights is it worth sacrificing crit for a little bit of spell haste. These are the two gear scenarios i am playing with.
spell hit caped in both
Gear Set A: Dmg-1267 Crit-20.91 Haste-2%(2.43 sec SB)
Gear Set B: Dmg-1277 Crit-22.18 Haste-0
Try the worksheet out with the 2 sets of damage and see what it says. I thought gemming for haste would work well for me but then I started playing with the worksheet and found that 9 times out of 10 choosing a 12 damage gem was better than a 10 haste gem. The only exception seemed to be if the 10 haste gem would meet a socket color requirement that gave me a bonus of at least 4 damage. Anything less and 12 damage won out. I am demo spec however and I am guessing that since the damage scales to my felguard and the haste does not that is what the difference was. Haste still comes out better for me than crit though.
My question is the real world application of haste when you only have a limited amount of it. Do you really need a good % of haste before you see returns in the 'real world' applications? I know what the spreadsheet says but when you look at movement and slight lag during fights is it worth sacrificing crit for a little bit of spell haste. These are the two gear scenarios i am playing with.
spell hit caped in both
Gear Set A: Dmg-1267 Crit-20.91 Haste-2%(2.43 sec SB)
Gear Set B: Dmg-1277 Crit-22.18 Haste-0
In the specific example above the argument being aluded to is that lag or movement would make haste less valuable because you have less time on target. You can just as easily make the argument that haste is more valuable because you have smaller windows than 100% DPS time to throw as much damage up as possible.
The best thing you can hope to maximize from a theory crafting standpoint is the expect value of your DPS. The spreadsheet calculates the average value of your DPS given a set of gear and a fight of infinite length (even if you set the OOM time it is still an average of what the DPS would be given an infinite number of 10 min fights or whatever time it was set to).
Obviously the spreadsheet is going to miss exceptional situations where, in a specific case, X% amount of haste would have resulted in 1 more bolt thrown in a 4' fight and therefor would be better than X% crit or vice versa.
This is largely irrelevent, however, because at the end of the day the specific mechanics of every fight are different and the best thing you can hope to maximize through theorycrafting is still the expected value of your DPS.
04/28/08, 6:03 PM
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