The timing of Bloodlust, abilities, and trinkets

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The timing of Bloodlust, abilities, and trinkets

Postby DisRuptive1 » Thu Nov 01, 2012 10:33 pm

I remember reading a thread about the mathematics of Bloodlust where the timing of Bloodlust doesn't affect how long a fight takes compared to other fights where Bloodlust is used at a different point in the fight, even when it is and isn't used during the execute portions of the fight (of course excluding the times when Bloodlust is used when no damage is being done). Despite this, I still see people talk about stacking their extra damaging abilities and trinket activations together.

Here's the part that has me confused. If the timing of Bloodlust doesn't affect how long a fight takes considering that it's used in the first place, can the same be said about trinket activations and abilities which increase damage?

And one more question. Assuming that all trinket activations and abilities which increase damage are used equally fight after fight, does using them together cause the fight to end quicker compared to using them separate from one another?
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Re: The timing of Bloodlust, abilities, and trinkets

Postby lythac » Fri Nov 02, 2012 2:29 am

DisRuptive1 wrote:Despite this, I still see people talk about stacking their extra damaging abilities and trinket activations together.


You want to stack your extra damaging abilities/trinkets/bloodlust and pot together.

Say you have two CDs that increase your damage by 30% and their uptime is 20%. Chaining them gives -

(0.2*1.3) + (0.2*1.3) + (0.6*1.0) = 1.12

A 12% damage increase.

Using them combined gives you

(0.2*1.3*1.3) + (0.8*1.0) = 1.138

A 13.8% damage increase.



The main thing about using Bloodlust at the start is everyones CDs will be available to use, everyone will be alive, you benefit from having the effects of two pots (as you prepot) and maybe a couple of other things that have slipped my mind.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby jere » Fri Nov 02, 2012 7:16 am

Just bear in mind that is not universally true for all specs of all classes. BM hunters (maybe the other specs as well???), for example, experiences a DPS loss by combining all their cooldowns. Due to mechanics of the cooldowns, their passives, and how pets work, they have to chain some of them for maximum dps. Bloodlust/Heroism/Ancient Hysteria/Timewarp is one of those cooldowns they can't combine with all their other cooldowns, only certain ones.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby theothersteve7 » Fri Nov 02, 2012 8:56 am

Ret paladins ideally time Guardian of Ancient Kings, AW, Holy Avenger, a pot and trinkets all to coincide with Bloodlust. The numbers get pretty silly.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Nooska » Fri Nov 02, 2012 12:25 pm

a BM hunte ronly experiences slight dps losses during a combined cooldown. Its the external haste buff dropping CoS to under the GCD, but since we don't really want to use it under BW/RF anyway, its not a significant losss (if at all). The focus gains for the pet especailly though, is a buff, more WH uses during BW, and you don't lose dps by capping focus, unless you would have had better use of the focus regen at another time - and between keeping up SrS, you should have an easy time managing focus without needing the external haste for anything really - ove rthe course of a fight, I very much doubt that you lose more than you gain from staking BW/RF with BL.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby jere » Fri Nov 02, 2012 3:29 pm

A few guides suggest that using RF in combination with Heroism should be avoided. I wanna say icy veins comes to mind, but it's been in a couple others as well. Aside from that, I think you are supposed to avoid casting BW and FF together, which isn't directly related to heroism, but goes along with blowing everything at once mentality (that's assuming you consider FF a cooldown, which some do and some do not).

Granted, I haven't seen any data to back up any of the guides so far (EJ, Icy-veins, etc.).
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Fetzie » Fri Nov 02, 2012 6:26 pm

Back in Cata at least, you avoided stacking RF and BL because the combination of the two would put your cast time for Steady Shot/Cobra Shot under the GCD.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby theckhd » Fri Nov 02, 2012 10:54 pm

DisRuptive1 wrote:I remember reading a thread about the mathematics of Bloodlust where the timing of Bloodlust doesn't affect how long a fight takes compared to other fights where Bloodlust is used at a different point in the fight, even when it is and isn't used during the execute portions of the fight (of course excluding the times when Bloodlust is used when no damage is being done). Despite this, I still see people talk about stacking their extra damaging abilities and trinket activations together.

Here's the part that has me confused. If the timing of Bloodlust doesn't affect how long a fight takes considering that it's used in the first place, can the same be said about trinket activations and abilities which increase damage?

And one more question. Assuming that all trinket activations and abilities which increase damage are used equally fight after fight, does using them together cause the fight to end quicker compared to using them separate from one another?


Your memory is correct. There was a thread that contained a proof of the fact that the timing of Bloodlust doesn't affect the length of an encounter. However, that proof was limited in scope by the one major assumptions: It assumed that your DPS scaled linearly with haste, inside and outside of execute range.

If you adhere to that assumption, the proof was completely valid. If you do X DPS above execute range and Y DPS below it, and you do 1.3*X DPS and 1.3*Y DPS above and below execute range during Bloodlust, respectively, then the timing of Bloodlust is completely irrelevant. The fight will take the same amount of time no matter when you use it.

However, this assumption is not correct, generally speaking. In particular, the use of trinket procs and DPS cooldowns tends to have a strong nonlinear interaction with haste (and crit). That's why people plan around lining them up together to maximize DPS. Mathematically you could say that in practice, X and Y aren't static and don't scale the same way with haste. So you might get 1.3*X DPS during bBloodlust above execute, but 1.35*Y DPS during Bloodlust below the Execute threshold, which breaks the proof.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Nooska » Sat Nov 03, 2012 6:18 am

jere wrote:A few guides suggest that using RF in combination with Heroism should be avoided. I wanna say icy veins comes to mind, but it's been in a couple others as well. Aside from that, I think you are supposed to avoid casting BW and FF together, which isn't directly related to heroism, but goes along with blowing everything at once mentality (that's assuming you consider FF a cooldown, which some do and some do not).

Granted, I haven't seen any data to back up any of the guides so far (EJ, Icy-veins, etc.).

As far as BM on EJ, thats me ;-)

FF is on CD a slong as our pets are focus starved, regardless of BW or not - an extra special is more damage than the 1-2 extra autoattack(s) from the pet in the 10 second BM period, the only time you shouldn't use FF is if the pet is focus capped - which should not be an issue in regards to having a 5stack of frenzy and a focus capped pet - not realistic.

In regards to RF and BL, as said, the increased focus regen (for our pet as well) means more basic attacks in the duration, thanks to WH it won't result in pet focuscapping, and as the hunter, you may focus cap, but as long as you pop off KC on CD, there is no time constraints on our focus to damage, so you can pump out extra AS and just use CoS to keep up SrS.

On cooldown usage, the current best solution is use everything on CD as much as you can (stacking BW and RF every 3rd BW (excluding readiness))
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Weebey » Sat Nov 03, 2012 12:57 pm

theckhd wrote:
DisRuptive1 wrote:
However, this assumption is not correct, generally speaking. In particular, the use of trinket procs and DPS cooldowns tends to have a strong nonlinear interaction with haste (and crit). That's why people plan around lining them up together to maximize DPS. Mathematically you could say that in practice, X and Y aren't static and don't scale the same way with haste. So you might get 1.3*X DPS during bBloodlust above execute, but 1.35*Y DPS during Bloodlust below the Execute threshold, which breaks the proof.


I'm actually not sure this explanation is quite correct; or at the very least, I think there is something interesting going on here. To a first approximation, a character's dps is a multilinear function a function of one's attack/spell power, haste, crit, mastery for dps specs, and "damage % bonus"(*). The wikipedia entry has a reasonable definition of a multilinear function: http://en.wikipedia.org/wiki/Multilinear_map

If you think simply of e.g. a mage spamming fireball, this is almost exactly correct. For example, if the mage's spellpower increases by 10%, while everything else stays the same, his fireballs will hit almost 10% harder (actually slightly less than that, since spells have a base damage component, but in this, and many other, cases the base component is very small, on the order of 2% of the damage of the spell.) Similarly, increasing his crit chance by 10% (multiplicatively) causes about 10% more of his fireballs to do double damage, so a 10% dps increase. Similarly, a 10% increase in haste is 10% more fireballs is 10% more dps.

Now in practice, of course, secondary stats can have more complicated effects (primary stat scaling, however, is as far as I know always linear in WoW.) For instance, a fire mage with more crit actually sees a change in his rotation in that he casts a higher percentage of pyroblasts; a balance druid with more haste spends a higher percentage of time under eclipse; some abilities don't scale with haste at all, etc. Even in these cases, I'm not sure the multilinearity model fails--these look to be situations where your dps is still multilinear, but with a slope that is different from the "naive" assumption. So I'm actually not convinced that Bloodlust doesn't take you from X to roughly 1.3X in non-execute, and Y to 1.3Y in execute.

But if dps is a multilinear function, then why do people (correctly) state things like e.g. crit scales "non-linearly" with haste? Here I think language misleads a little bit if you aren't careful: a multilinear function is separately linear in each variable, but that does not imply that if you scale each variable by a fixed number you scale the result by the same.

In symbols, suppose f(x,y,z) is multilinear (you can assume e.g. x is spellpower, y is crit, z is haste. Now suppose that you increase x, y, and z by 20%; how much does f increase by? NOT 20%, or 60%; in fact, f(1.2x,1.2y,1.2z)=(1.2)^3f(x,y,z)=1.728f(x,y,z), a 73% dps increase.

Let's go back the "paradoxical" result that an execute bloodlust does not shorten the fight. Naively, even taking the multilinearity into account, this seems wrong. Why? Well, think about a non-execute lust: for 40 seconds, you do 1.3X damage instead of X damage, so your total "bonus" lust damage is 40*(1.3X-X)=12X. Similarly, for an execute lust you do 12Y extra damage. Since 12Y>12X (execute dps is higher than non-execute dps), it looks like you have gained more extra damage with the execute lust. So what's going on?

The intuition for the why you don't actually benefit from an execute lust is that, by lusting during execute, you shorten the amount of time you are in execute, while lusting pre-execute only shortens your non-execute phase. But execute phase is obviously higher dps than non-execute, so by shortening execute phase you see a dps loss relative to the second scenario. This indirect dps loss precisely cancels the dps gain from the previous paragraph.

However, this does not apply to lining up cooldowns with lust, rather than execute. It is not as if the length of Avenging Wrath is shortened if you happen to use it during lust. So in this case, you get the damage gain, without the countervailing loss of time in an elevated damage phase.

So I'm inclined to believe that, roughly speaking, lusting during execute may not in actual fact be an overall damage increase, but lusting during cds/trinket procs etc certainly is. This isn't, of course, to say that one should never lust during execute, since quite often that is the most challenging stage of the fight to survive (e.g. Elegon) and shortening that phase will increase your chances of success more then a shortening of the fight as a whole.

(*) Slight mathematical subtlety: your dps is a linear function of haste, but is actually an affine function of your haste rating, since haste itself is an affine function of haste rating. If dps were a linear function of haste rating (in the linear algebra sense of "linear"), that would imply that your dps would be zero at zero haste rating, which is obviously false.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby theckhd » Sat Nov 03, 2012 8:20 pm

Weebey wrote:
theckhd wrote:However, this assumption is not correct, generally speaking. In particular, the use of trinket procs and DPS cooldowns tends to have a strong nonlinear interaction with haste (and crit). That's why people plan around lining them up together to maximize DPS. Mathematically you could say that in practice, X and Y aren't static and don't scale the same way with haste. So you might get 1.3*X DPS during bBloodlust above execute, but 1.35*Y DPS during Bloodlust below the Execute threshold, which breaks the proof.

I'm actually not sure this explanation is quite correct; or at the very least, I think there is something interesting going on here. To a first approximation, a character's dps is a multilinear function a function of one's attack/spell power, haste, crit, mastery for dps specs, and "damage % bonus"(*). The wikipedia entry has a reasonable definition of a multilinear function: http://en.wikipedia.org/wiki/Multilinear_map

To a first approximation, yes. However, it's not multilinear if you're rigorous, because of a variety of mechanics. Haste break points are an obvious one - a prime example is Cataclysm Ret, whose rotation changed significantly when they can reach a 3-second Crusader Strike. Similar mechanics for other classes cause nonlinear scaling with crit or mastery (ex: things that proc on crits can change your spell usage breakdown, which is an nonlinear DPS change).

That's where the proof breaks down. It rests on the assumption that when you use hero, you get a flat 30% increase to whatever DPS you'd be doing otherwise, which isn't strictly true.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Weebey » Sun Nov 04, 2012 10:45 am

Yes, obviously haste breakpoints are values where your dps fails to be a multilinear function--indeed, it isn't even continuous. As I said in the follow-up paragraph to the one quoted, I'm not sure that I believe that things like e.g. pyroblast procs challenge linearity; it seems rather like a case where the "slope" of the linear function is steeper than one would naively expect, rather than a case where the second derivative is positive. Even if the slope is changing, it is unlikely to be doing so very quickly, and in any case not in a way that would change the scale factor w.r.t. being in execute vs not being in execute.

So I actually think, even if it isn't perfect, the assumption that lust provides a similar % boost whether in execute or not is probably reasonably close to the truth.

The original question, however, was about whether this argument also showed that it is not advantageous to stack cooldowns with lust. And for me the key point is that, even if you believe that argument that lusting during execute provides no benefit, it is still case that lining up cooldowns with lust provides a large benefit.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby theckhd » Sun Nov 04, 2012 5:37 pm

Weebey wrote:Yes, obviously haste breakpoints are values where your dps fails to be a multilinear function--indeed, it isn't even continuous. As I said in the follow-up paragraph to the one quoted, I'm not sure that I believe that things like e.g. pyroblast procs challenge linearity; it seems rather like a case where the "slope" of the linear function is steeper than one would naively expect, rather than a case where the second derivative is positive. Even if the slope is changing, it is unlikely to be doing so very quickly, and in any case not in a way that would change the scale factor w.r.t. being in execute vs not being in execute.


I disagree. Discreteness starts to dictate that you break nonlinearity in a lot of those cases. If your rotation with 0% haste is roughly Fb-Fb-Pb-Fb-Fb-Pb (or one Pyro for every 2 Fireballs), but with 30% haste gets condensed down to Fb-Pb-Fb-Pb, that's a significantly different distribution in spell composition, and will be a very nonlinear (and as you said, potentially discontinuous) function. You're not casting 33% pyro and 66% fireball, you're casting 50% pyro and 50% fireball, which may be a significantly better DPS increase than just a flat 30% (assuming Pyro is much higher DPCT than Fireball here, obviously).

Weebey wrote:So I actually think, even if it isn't perfect, the assumption that lust provides a similar % boost whether in execute or not is probably reasonably close to the truth.

I don't actually know for sure how large the magnitude of these effects are, to be honest. Easiest way to test would be to check it for a few classes in Simcraft - basically model a 45-second fight with and without Heroism, and see what the DPS difference is. I suspect it varies a lot from class to class.

Weebey wrote:The original question, however, was about whether this argument also showed that it is not advantageous to stack cooldowns with lust. And for me the key point is that, even if you believe that argument that lusting during execute provides no benefit, it is still case that lining up cooldowns with lust provides a large benefit.

Yup, that part I completely agree with.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Nooska » Mon Nov 05, 2012 2:55 am

There is one thing that I think is missing in the "doesn't matter when tol Lust" thinking.
If BL cuts down the fight by a specific amount, which part of the fight to cut down matters greatly. If like Gara'jal the execute phase is also a phase of increased damage output, that makes it more benefiial to shorten that phase of the fight, rather than simply looking at "we have to lust at some point to shave off X seconds of total fight time".

The same reality argument applies to stacking CDs with Lust, if you use your CDs X number of times during the fight, they will shave off Y seconds (across the raid). Where you want to shave off the seconds may matter, and if there is a phase you want to take down asap, then making sure your CDs and Lust is available in that phase will make it end faster.
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Re: The timing of Bloodlust, abilities, and trinkets

Postby Worldie » Mon Nov 05, 2012 6:03 am

Usually the "doesnt matter when you lust" discussion applies to Patchwerk fights when the fight is essentially the same from start to end.
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