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Heroism timing

Warning: Theorycraft inside.

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Postby Khayne » Wed Mar 04, 2009 7:47 am

rickforking wrote:Forgive me if I'm wrong, but the problem, at least with his statement that number of people alive doesnt matter, is that if X = raid's dps, let's say 30k, and you have 15 dpsers, that's an average of 2k dps per person. If you lose 2 people, then X is now 26k, making X * Z * W smaller.

So losing 2 people makes the new equation for heroism damage X * (13/15) * Z * W.

As for his claim that amount of damage done under the threshold doesn't go up, I'm still looking at it.


Yes, losing 2 people does decrease how much damage you get out of that bloodlust, but that doesn't mean it decreases the time it takes to kill necessarily.

I mean, for this example let's say bloodlust is 100% damage increase. Ridicilous amount, but it's an example here.
Not to mention bloodlust is a % increase in dps, so it shouldn't matter if i use more exaggerated number.

Let's say raid dps is 2, and boss has 240 health

2 raids:

1st one uses bloodlust fast, when boss is at 50% half of their dps dies to something.

Ends up in a 30 secs of bloodlust, which takes them to 50%. half of dps dies, their dps drops to 1, with 120 hp left on boss.

Fight takes 150 secs. 30 sec @ 4 dps+ 120sec @ 1 dps).

2nd one saves bloodlust until 50%, which takes 60 seconds at their 2 dps. Again, the nubs don't move off void zones and dps drops to 1, they pop bloodlust.
Their dps goes back to 2 for 30 secs, they cause 60 damage in this period. Boss still has 60 health left. their dps is now 1 again, so fight takes 60 secs more.

End result is 150 seconds here too
60 sec@2 dps+30sec * 2dps+60 sec@ 1 dps

Using simplified numbers here instead of 200k raid dps and 2,4 million mob hp is irrelevant, as is the % that bloodlust is instead of 100% if i'm not mistaken.

Was written and done fast so feel free to point any silly mistakes i made here :D .
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Postby cordelia » Wed Mar 04, 2009 7:56 am

Here's what is confusing all of you and what is overlooked in the assumptions made in the math model.

If you assume that your dps fluxuates dependent on BOSS HP, the math holds true, and time of heroism will not increase boss kill time.

However, if you assume that your dps fluxuates dependent on TIME INTO ENCOUNTER, heroism will increase boss kill time.

So, for Execute, the math is correct. However, for typical raid deaths, the math is incorrect. People don't day when the boss hits 80%. People die when 2 minutes into the fight, they lose focus and make a mistake.

The VCR example is a perfect example of the former. And Mordinm's explanation is exactly why it holds true for execute.

But most people think of DPS rate increases in the latter situation. They consider that DPS fluxuates dependent on TIME INTO ENCOUNTER. And if that's the case, then heroism matters quite a lot. This is the case for trinkets, for other periodic buffs. This is the case for 90% of raid deaths.

But it's not true for Execute range, and it's not true that popping heroism during Illidan P1 vs. Illidan P2 vs. Illidan P3/4 vs. Illidan P5 would speed up Time to Kill. But it can minimize Time for Mistakes(e.g. P2 or P5).

This is why people pop Heroism when Maexxna enrages. To minimize time for mistakes, to minimize # of web wraps the tank takes. It does not speed up the kill, but it does minimize mistakes.

So when to pop heroism?

(A) to minimize time for mistakes.

(B) Barring (A), then when it gives you the most time-based maximized dps. ie. at the start of the encounter, before deaths, and when trinkets are available.

(C) If your dps is increasing due to a mechanic from boss hp change and not to a timing change, then popping heroism will not increase time to kill, and does nothing.


PS> For those who need to see the math written out, attempt the whole math proof again assuming that the threshold N denotes a static time into the encounter when the dps increases/decreases by value Y. This will show a notable improvement in time to kill when popping heroism during max dps periods.
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Postby Mendin » Wed Mar 04, 2009 8:14 am

(650 000 - 12 000) / 1000 = 638 s
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Postby Mordinm » Wed Mar 04, 2009 8:25 am

Khayne wrote:...
End result is 150 seconds here too
60 sec@2 dps+30sec * 2dps+60 sec@ 1 dps

Using simplified numbers here instead of 200k raid dps and 2,4 million mob hp is irrelevant, as is the % that bloodlust is instead of 100% if i'm not mistaken.

Was written and done fast so feel free to point any silly mistakes i made here :D .


As was pointed out if you assume people die at a given % of boss life the proof works for raid deaths. A more realistic model would be people have a probability of dieing based on time. So the longer a fight goes the more people who die regardless of how much life the boss has. If you make that assumption the proof does not apply to raid deaths

The only big unaddressed point I see is that warriors in particular have very different dps mechanics when it execute range so it seems reasonable that the % dps increase from bloodlust could very well be higher sub 20%.
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Postby trellian » Wed Mar 04, 2009 8:26 am

Mordinm wrote:The only big unaddressed point I see is that warriors in particular have very different dps mechanics when it execute range so it seems reasonable that the % dps increase from bloodlust could very well be higher sub 20%.


Well, warlocks now also have an execute (drain soul) and their damage scales very nicely with haste. Their spell priority actually changes quite a bit when in execute range and I would think it would matter for them aswell. Though not by much.

Khayne wrote:Yes, losing 2 people does decrease how much damage you get out of that bloodlust, but that doesn't mean it decreases the time it takes to kill necessarily.


It will if one of those two is the shammy ;)

(sorry, couldn't resist)



I think it's safe to say that if people don't change their 'rotation' when in execute range, it wouldn't matter when you'd hit heroism. However when in execute (and drain soul execute) range, players' rotation changes. Assuming said person is not haste 'capped', it will change boss kill time when used in the last 20%.
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Postby Mordinm » Wed Mar 04, 2009 8:58 am

trellian wrote:Well, warlocks now also have an execute (drain soul) and their damage scales very nicely with haste. Their spell priority actually changes quite a bit when in execute range and I would think it would matter for them aswell. Though not by much.


What I mean is that warriors switch from a cool down based rotation to a rotation not constrained by cool downs. Above 20% a warrior's main specials are WW and BT and you don't get any more dps out of those from lust. So above 20% a warrior get a white damage boost but must spend the additional rage in increasingly inefficient ways.

Sub 20% a warrior can execute on every white swing so lust might provide a 20% dps increase at 100% and a 30% dps increase at 15%. Mages and warlocks both stay in dps cycles limited almost entirely by cast time and procs no matter what percentage the boss is at. So it seems to me the dps increase % would be the same for casters classes any time you pop lust.
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Postby Jonesy » Wed Mar 04, 2009 8:59 am

trellian wrote:However when in execute (and drain soul execute) range, players' rotation changes. Assuming said person is not haste 'capped', it will change boss kill time when used in the last 20%.


It's not necessarily about rotation change - Ret rotation changes < 20% too, but Bloodlust won't shorten a fight length if you have just Ret paladins DPSing. The important question to ask is, does the efficiency of converting 1% haste into damage change sub-execute? If it does, Bloodlust in execute range is an overall DPS increase (or decrease!). If it doesn't, no change.
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Postby MomysLidlMonsta » Wed Mar 04, 2009 9:17 am

I think i've found the error in his math:

Potera wrote:Important point is that: Time = Health / (Damage/sec). In other words, Time = Health * Sec/Dmg

which gets used throughout his calculations. But Time = sec and Damage = Health, so he actually says Time = Health/(Health/Time) which simplyfies to Time = Time which doesn't mean anything.

And in his calculations (and folowing his principle you in yours) he effectively doesn't multiply the damage done in this time by X but divides the time by X and 40/X =40/X independent on the DPS.
The only one who got it right was agnara.
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Postby Rehlachs- » Wed Mar 04, 2009 9:37 am

MomysLidlMonsta wrote:which gets used throughout his calculations. But Time = sec and Damage = Health, so he actually says Time = Health/(Health/Time) which simplyfies to Time = Time which doesn't mean anything.


I .. what?!
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Postby Rhiannon » Wed Mar 04, 2009 9:54 am

MomysLidlMonsta wrote:I think i've found the error in his math:

Potera wrote:Important point is that: Time = Health / (Damage/sec). In other words, Time = Health * Sec/Dmg

which gets used throughout his calculations. But Time = sec and Damage = Health, so he actually says Time = Health/(Health/Time) which simplyfies to Time = Time which doesn't mean anything.

And in his calculations (and folowing his principle you in yours) he effectively doesn't multiply the damage done in this time by X but divides the time by X and 40/X =40/X independent on the DPS.
The only one who got it right was agnara.


...

Time to kill boss = (total boss health) / (the damage being done to it per second)

That's all that first bit is saying, which is quite obviously true.

Just like distance travelled = speed * time

distance = distance per time * time

distance = (distance / time) * time

distance = distance

Which is quite obviously true. I'd be more worried if it didn't simplify to have two sides of the equation being equal.
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Postby trellian » Wed Mar 04, 2009 10:08 am

Mordinm wrote:Sub 20% a warrior can execute on every white swing so lust might provide a 20% dps increase at 100% and a 30% dps increase at 15%. Mages and warlocks both stay in dps cycles limited almost entirely by cast time and procs no matter what percentage the boss is at. So it seems to me the dps increase % would be the same for casters classes any time you pop lust.


Sub 25% (affliction) warlocks will drop shadowbolt and immolate from their rotation and start using drain soul in its place. Drain soul (since it's channeled) increases in DPS with haste. Hence a locks' DPS will increase below 25%, the haste buff from heroism will increase it even more. The hast will also make the GCD and cast time go down more, so dot casts go faster and thus they can spend more time in drain soul. Which in turn means more DPS.

Now if heroism was used before 25%, the lock would still not change his rotation and have only a static increase in DPS (only cast time changes, no channeled spell is used). Below 25% heroism will have an exponential increase in DPS.

FYI http://www.wowhead.com/?spell=47855 is what i'm talking about.

Edit: so yes, for affliction locks heroism after 25% is more beneficial then heroism before 25% boss hp. This is only because Drain Soul is channeled and scales so nicely with haste.
Last edited by trellian on Wed Mar 04, 2009 10:23 am, edited 4 times in total.
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Postby Dorvan » Wed Mar 04, 2009 10:17 am

cordelia wrote:Here's what is confusing all of you and what is overlooked in the assumptions made in the math model.

If you assume that your dps fluxuates dependent on BOSS HP, the math holds true, and time of heroism will not increase boss kill time.

However, if you assume that your dps fluxuates dependent on TIME INTO ENCOUNTER, heroism will increase boss kill time.

... snip ...



Yeah, I was wondering if that might be the case myself. Of course, for many fights players deaths *are* pegged to boss health rather than time, because they're related to phases or phases transitions. The simplest example would be Magtheridon, where for a starting guild that couldn't get their raid topped off, you'd see a DPS drop consistently at 30% of Mag's health. It really depends on the fight.
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Postby Mordinm » Wed Mar 04, 2009 10:22 am

trellian wrote:
Mordinm wrote:Sub 20% a warrior can execute on every white swing so lust might provide a 20% dps increase at 100% and a 30% dps increase at 15%. Mages and warlocks both stay in dps cycles limited almost entirely by cast time and procs no matter what percentage the boss is at. So it seems to me the dps increase % would be the same for casters classes any time you pop lust.


Sub 25% warlocks will drop shadowbolt and immolate from their rotation and start using drain soul in its place. Drain soul (since it's channeled) increases in DPS with haste. Hence a locks' DPS will increase below 25%, the haste buff from heroism will increase it even more. The hast will also make the GCD and cast time go down more, so dot casts go faster and thus they can spend more time in drain soul. Which in turn means more DPS.

Now if heroism was used before 25%, the lock would still not change his rotation and have only a static increase in DPS (only cast time changes, no channeled spell is used). Below 25% heroism will have an exponential increase in DPS.

FYI http://www.wowhead.com/?spell=47855 is what i'm talking about.


I really don't think exponential means what you think it means.

Shadow bolts increase in dps just like drain soul. A 30% haste buff will increases shadow bolt dps by the same factor as it will increase drain soul dps. Channeled spells do not gain more from haste then spells with cast times.

That said DoTs have an effective cool down of their duration so the value of haste to a caster might change based on boss health if the rotation caused you to drop DoTs in favor of cast or channeled spells. Though if locks are just dropping immolate I doubt the effect would be all that large.
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Postby Elsie » Wed Mar 04, 2009 10:26 am

If your DPS above a certain percentage health (N%) is X, and below is X * Y, and heroism boosts your DPS by Z for W seconds, and the total boss health is H:

I don't like this assumption. If X is personal DPS, then X*Y is bears no significance for every X unless Y is equally variable. If you think of X as raid DPS, then X is a summation of x1, x2, ..., xn. So you're trying to multiply a summation by a constant Y. This means the affect of bloodlust is evenly distributed among all x when we know this not to be true.

Bloodlust only affects time-to-kill if you have a class whose damage increase is based on a "haste affected" change. For example, ret paladins don't gain anything from sub-n% lust since Hammer of Wrath is not affected by haste. Locks with a channeled drain soul do gain a net DPS increase. At any rate, once we state a significant juncture in HP, we are no longer looking at one fight. We are looking at two fights. To put it in an economics perspective, it's like considering an ARM teaser period. What you really have is a ~2 year loan and then a 28 year loan. This should make it clearer for you if you study finance and economics.

So, to sum this rambling: He's trying to use static values of time in a time series, and he's oversimplifying some equations.
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Postby Dorvan » Wed Mar 04, 2009 10:36 am

Elsie wrote:
If your DPS above a certain percentage health (N%) is X, and below is X * Y, and heroism boosts your DPS by Z for W seconds, and the total boss health is H:

I don't like this assumption. If X is personal DPS, then X*Y is bears no significance for every X unless Y is equally variable. If you think of X as raid DPS, then X is a summation of x1, x2, ..., xn. So you're trying to multiply a summation by a constant Y. This means the affect of bloodlust is evenly distributed among all x when we know this not to be true.

So, to sum this rambling: He's trying to use static values of time in a time series, and he's oversimplifying some equations.


The fact that heroism doesn't affect all players equally doesn't affect the math at all. If Q is raid DPS during heroism, Q = X*Y doesn't imply q1 = x1*Y, q2 = x2*Y, etc., but that's not important anyway. The only thing that matter is raid DPS during heroism and raid DPS outside of heroism, whether the raid is 1 person or 25.

There are some important caveats to interpreting the result, but this isn't one of them.
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