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Heroism timing

Warning: Theorycraft inside.

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Postby Varmin » Thu Mar 05, 2009 3:13 pm

Elsie wrote:
Dorvan wrote: The reason popping heroism during execute doesn't shorten the fight length (assuming fixed Z, which may not be the case) is that doing so also shortens the duration of the "execute" buff.

Well, after about 3 minutes of research before my next class, here's my synopsis:
    Haste stacks multiplicatively. This means that it is beneficial to stack multiple haste effects. For instance, stacking Slice and Dice with Blade Flurry gives a total of 68% haste (140% * 120% = 168% of the base attack speed). (Source: Wowwiki)
Given Atk Spd*Haste confers some x% dps increase and Atk Spd*Other-Haste {e.g., lust} is also some y% dps increase, then Atk Spd*Haste*lust confers some x*y% dps increase which, with order of application being a non-issue, does not change Z.

The only issue now is sub-35% spells.


^This, Haste stacks multiplicatively. Arguing basic DPS mechanics is getting pretty tiring.

The concept of saving all Cooldowns for bloodlust is a myth, only haste needs to be timed with it. The only 'exception' to this rule, is if as a caster, bloodlust puts you below the GCD anyway, popping a haste cooldown will provide no DPS increase.
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Postby Dorvan » Thu Mar 05, 2009 3:20 pm

Varmin wrote:^This, Haste stacks multiplicatively. Arguing basic DPS mechanics is getting pretty tiring.

The concept of saving all Cooldowns for bloodlust is a myth, only haste needs to be timed with it. The only 'exception' to this rule, is if as a caster, bloodlust puts you below the GCD anyway, popping a haste cooldown will provide no DPS increase.


Suppose that you've got a spellpower buff that comes out to 200 damage per fireball that you cast. If you use it when you can get 4 fireballs off, you increased your damage by 800. If you use it when you can get 5 fireballs off, you've increased your damage by 1000. The duration of your cooldown is unaffected by when you use it (unlike with the execute/heroism interaction). Damage is maximized by stacking cooldowns with heroism/bloodlust, whether the difference is "significant" depends on the exact numbers you put in. Now if you "save" your cooldowns for heroism, and as a result get one fewer cooldown use then you otherwise would, that's different, but that wasn't how the problem was stated.
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Postby Mordinm » Thu Mar 05, 2009 3:33 pm

Varmin wrote:^This, Haste stacks multiplicatively. Arguing basic DPS mechanics is getting pretty tiring.

The concept of saving all Cooldowns for bloodlust is a myth, only haste needs to be timed with it. The only 'exception' to this rule, is if as a caster, bloodlust puts you below the GCD anyway, popping a haste cooldown will provide no DPS increase.


You haven't argued a damn thing. Making an argument involves supporting what you say with reasons (sometimes called arguments for your position.) You simply pop in every once in a while and tell other people they are wrong with out providing any evidence or reasons why they are wrong. DPS stats have always stacked in a multiplicative way with other dps stats. For example the higher your crit is the more dps you will get from each point of AP you have.

It's been pointed out several times why you are wrong and explained in several different contexts.
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Postby Elsie » Thu Mar 05, 2009 5:54 pm

Varmin wrote:
Elsie wrote:
Dorvan wrote: The reason popping heroism during execute doesn't shorten the fight length (assuming fixed Z, which may not be the case) is that doing so also shortens the duration of the "execute" buff.

Well, after about 3 minutes of research before my next class, here's my synopsis:
    Haste stacks multiplicatively. This means that it is beneficial to stack multiple haste effects. For instance, stacking Slice and Dice with Blade Flurry gives a total of 68% haste (140% * 120% = 168% of the base attack speed). (Source: Wowwiki)
Given Atk Spd*Haste confers some x% dps increase and Atk Spd*Other-Haste {e.g., lust} is also some y% dps increase, then Atk Spd*Haste*lust confers some x*y% dps increase which, with order of application being a non-issue, does not change Z.

The only issue now is sub-35% spells.


^This, Haste stacks multiplicatively. Arguing basic DPS mechanics is getting pretty tiring.

The concept of saving all Cooldowns for bloodlust is a myth, only haste needs to be timed with it. The only 'exception' to this rule, is if as a caster, bloodlust puts you below the GCD anyway, popping a haste cooldown will provide no DPS increase.

I'm not sure why you quoted me when my statement doesn't support your argument. You are aware that all buffs stack multiplicatively if stated as such, right?

Being "below the GCD minimum" doesn't matter if you're a caster who is casting something over 1s cast or channel time. Furthermore, stacking cooldowns is, in principle, the same as compound interest.

You do X base DPS. If you use Avenging Wrath, you deal X(1+0.2). Say you get 5% DPS out of bloodlust, then you're dealing X(1+0.2)(1+0.05). Note 1.2 > 1.05, thus the previous equation is greater than X(1+0.05)(1+0.05) = X(1+0.05^2... repeat and you see that your modified DPS value > X(1+r)^n where n is the number of buffs you use, and r is the lowest gain rate of all said CDs.
Last edited by Elsie on Thu Mar 05, 2009 5:59 pm, edited 1 time in total.
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Postby theckhd » Thu Mar 05, 2009 5:59 pm

Laz wrote:Good work, Theck. May I ask what you do by trade? Your mathematical analyses are very thorough.

Physicist. I like taking complicated systems apart to see how they work. Mathematically or otherwise. :)
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Postby Elsie » Thu Mar 05, 2009 6:00 pm

theckhd wrote:
Laz wrote:Good work, Theck. May I ask what you do by trade? Your mathematical analyses are very thorough.

Physicist. I like taking complicated systems apart to see how they work. Mathematically or otherwise. :)

My urge to link xkcd is so strong right now.
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Postby theckhd » Thu Mar 05, 2009 6:25 pm

Also, in case anyone else was curious - redoing the Time-based analysis with this method goes as follows - Keep in mind that B and A refer to "below" T (i.e. after T) and "above" T (i.e. before T), so the subscripts are a little trickier:

Hero Early:
Damage before time T: WDHA + (T-W)D0A, taking time T
Damage after time T: H-WDHA - (T-W)D0A, taking time [H-WDHA - (T-W)D0A]/D0B

Total Time: T + H/D0B - (D0A/D0B)T - (DHA/D0B)W + (D0A/D0B)W

Hero Late:
Damage before time T: TD0A, taking time T
Damage after time T: WDHB, taking time W, as well as:
H-TD0A-WDHB, taking time [H-TD0A-WDHB]/D0B

Total Time: T + W + H/D0B - (D0A/D0B)T - (DHB/D0B)W

Subtracting the two gives
=- (DHA/D0B)W + (D0A/D0B)W - W + (DHB/D0B)W

= -(W/D0B)[(D0B - D0A) - (DHB - DHA)]

Which makes pretty much sense - the net benefit is basically the difference in the DPS without heroism minus the difference in DPS with heroism.

Plugging in X, XY, XZ,and XYZ as in my previous version gives
= -(W/XY)[(XY-X) - (XYZ - XZ)] = -(W/Y)(Y-1)(1-Z)
= (W/Y)(Y-1)(Z-1), which agrees with my last calculation.
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Postby majiben » Thu Mar 05, 2009 6:28 pm

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Just a physicist eh? Mwahaha
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Postby Selgar » Thu Mar 05, 2009 6:47 pm

HAH I love it Majiben !
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Postby Dorvan » Thu Mar 05, 2009 6:52 pm

I actually looked up that exact comic when xkcd was mentioned here >.>

In other news, Machine Learning > all.

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Ok, sorry for the interruption, back to our regularly scheduled heroism theorycrafting.
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Postby Joanadark » Fri Mar 06, 2009 8:06 am

The thing is, the proof looks correct to me, and not only that, it leads to some weird corollaries: for example, having 20% of your raid die when the boss is at 50% is the same as plugging N=50 and Y=.8 into the above, so even popping Heroism before vs. after raid members start dying has no effect on the total boss kill time.

Any of the other math folks here have some insight on this? I find the results bizarre and completely counter-intuitive.


Still working my way through the thread, but this statement is NOT true.

The assumption being made which is incorrect is that you assume that 5 people are going to die regardless when the boss hits 50%, as opposed to say, 3 minutes into the encounter.
When you recognize that having people alive before hand would mean that the boss would be LOWER than 50% at the 3 minute mark when they die, you see where the flaw is.
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Postby Kelaan » Fri Mar 06, 2009 10:13 am

Dorvan wrote:I actually looked up that exact comic when xkcd was mentioned here >.>
In other news, Machine Learning > all.


I admit that I love XKCD's semi-frequent nods at Lisp. This is, of course, because I am now somewhat spoiled by Lisp. ;) XKCD is the kind of nerdy humor that rocks my world.
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Postby cordelia » Sat Mar 07, 2009 8:42 am

Majiben wrote:Image

Just a physicist eh? Mwahaha



Where is mathematical psychology?
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Postby majiben » Sat Mar 07, 2009 8:46 am

On another axis
Amirya wrote:some bizarre lovechild of Hawking, Einstein, and Theck
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Postby Elsie » Sat Mar 07, 2009 4:03 pm

Joanadark wrote:
The thing is, the proof looks correct to me, and not only that, it leads to some weird corollaries: for example, having 20% of your raid die when the boss is at 50% is the same as plugging N=50 and Y=.8 into the above, so even popping Heroism before vs. after raid members start dying has no effect on the total boss kill time.

Any of the other math folks here have some insight on this? I find the results bizarre and completely counter-intuitive.


Still working my way through the thread, but this statement is NOT true.

The assumption being made which is incorrect is that you assume that 5 people are going to die regardless when the boss hits 50%, as opposed to say, 3 minutes into the encounter.
When you recognize that having people alive before hand would mean that the boss would be LOWER than 50% at the 3 minute mark when they die, you see where the flaw is.

Joanadark is correct in that people dying does change the result.
On another axis

Or plane, or possibly dimension if you angle it right.
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