Heroism timing

Hey guys,

This isn't explicitly a Tankadin problem but it's a theorycrafting problem that has come to my attention and is bugging me to no end. It started with the following blog post:

http://blessingofkings.blogspot.com/2009/03/bloodlust-timing.html

In short, the author is putting forth the idea that popping heroism in execute range actually does nothing to speed up boss kills. I was fairly skeptical of the result, but one of my guildmates gave the following proof that the result is correct

I read BoK often, however haven't read this post (will immediately after this posting lol). I see the theory, but it just seems the more people and more +dmg modifying you can stack would give the most benefit. Assuming everyone lives and people blow trinkets at start, then save them for Heroism/BL (post 35%).

Ok after reading it, I see what he's getting at, and generally that's how we handle it. Maexxna enrage, stuff like that. Or usually after about 10 seconds for me to establish myself.
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I didn't look over the math in this thread, but I've seen the math before. Bloodlust doesn't matter dps when you use it, so the following should be what you base bloodlust time on:

-Boss enrages
-Phases you want to last as short as possible (last 2 phases of KJ for example is when my guild often bloodlusted)
-When DPS can get maximum DPS time during the bloodlust
-When as many people in your raid are alive as possible


Another important thing about bloodlusts is you want to tell your DPS when you plan to bloodlust. This allows DPS to save and stack cooldowns with bloodlust for maximum DPS as almost all cooldowns scale with bloodlust.

While I can't find any error with his math it doesn't make any sense and usually when math doesn't make any sense there's some silly hard to find logical error.
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Someone made a good analogy in the comments :

This simple matlab program gets different results for when you use bloodlust but I might have coded it wrong : P

I just thought of one thing the math doesn't account for, the use of flat damage increses below threshhold such as trinkets. They're a bitch to model though

Also it doesn't take into account things like warriors in execute range, they need the bloodlust to get rage to execute.
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Let's use a very simplified example with only one DPS, who gets an obvious damage increase sub-35%.

Say a fire mage does an average of 3k DPS without the use of any cooldowns in normal conditions.

Sub-35%, due to 12% extra damage from Molten Fury, he does 3.36k DPS.

Say an imaginary boss has 1 million hp.


With no bloodlust:

The first 650k HP is burned in 216.67 seconds @ 3k DPS
The second 350k HP is burned in 104.17 seconds @ 3.36k DPS

Total kill time is 320.83 seconds


Bloodlust means 30% more casts in the same period of time, or a 30% increase in DPS.


With bloodlust at the start:

The first 40 seconds of the fight is at 3.9k DPS. In this time, the boss will lose 156k hp, leaving (650 - 156) = 494k HP until 35%.

This 494k HP will be burnt @ 3k DPS, in 164.67 seconds.

The last 350k HP will be burnt @ 3.36k DPS, in 104.17 seconds.

The total kill time is 40 + 164.67 + 104.17 = 308.8 seconds.


With bloodlust just after the boss goes below 35%:

The first 650k HP is burned in 216.67 seconds @ 3k DPS

For 40 seconds after the boss drops below 35%, DPS = 3.36 * 1.3 = 4.368k DPS.

In this time the boss loses 40 * 4.386 = 174.72k HP.

This leaves him with (350 - 174.72) = 175.28k HP left to burn @ 3.36k DPS.

This will take 52.167 seconds.

Total kill time = 216.67 + 40 + 52.167 = 308.8 seconds.


Counter-intuitive indeed, I expected the example not to agree. Interesting!
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After reading the post, and doing the math with the same numbers myself, I came to the same result, however when I checked how much dmg you would gain from using bloodlust something was a bit odd.

The whole fight with with no heroism would be
650 000 / 1000 = 650 s

350 000 / 1200 = 291.666...

total: 941.666... sec


After that I calculated how much dmg a bloodlust would at at the different percentages.

100% - 35%
Bloodlust:
40 sec * 1000 dps * 1.3 = 52 000 dmg

Normally:
40 sec * 1000 dps = 40 000 dmg

Dmg gained from bloodlust:
52 000 - 40 000 = 12 000 dmg

35% - 0%
Bloodlust:
40 sec * 1200 dps * 1.3 = 62 400 dmg
Normally:
40 sec * 1200 dps = 48000 dmg

Dmg gained from bloodlust:
62 400 - 48 000 = 14 400 dmg

That would make the the amount of damage one would need to do out of bloodlust be reduced by 12 000 dmg or 14 400 dmg depending on when you use it.

Bloodlust at 100%

(650 000 - 12 000) / 1000 = 648,8 s

350 000 / 1200 = 291.666...

total: 940,4666... sec


Bloodlust at 35%

650 000 / 1000 = 650 s

(350 000 - 14 400) / 1200 = 279,666...

total: 929,666... sec


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I think I might be doing some obvious mistake though, the numbers don't seem quite right
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