Heroism timing

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Heroism timing

Postby Dorvan » Tue Mar 03, 2009 11:58 pm

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/200 ... iming.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

Potera wrote:Nothing wrong with the math listed. The math listed could mis-represent the DPS increase of >35% and <35% (that is, that it's a percentage increase and not an additive increase).

However, assuming that the numbers are semi-accurate representations, the math is fine.

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:

H * (1 - N) = hit points above the "low health" threshold
H * (1 - N) / X = Time to get boss to the threshold
H * N = hit points below the threshold
H * N / (X * Y) = Time to get boss from threshold to dead

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

X * Z * W = Hit points of damage done while Heroism active, if above threshold
X * Y * Z * W = Hit points of damage done while Heroism active, if below threshold

Case 1: Heroism at 35%
Time to reach threshold = H * (1 - N) / X (Same as above)

Time to do damage while affected by Heroism: W
Damage done: X*Y*Z*W
Remaining HP: H*N - X*Y*Z*W
Time to finish off boss from that point: (H*N - X*Y*Z*W) / (X*Y)

Total time: H * (1 - N) / X + W + (H*N - X*Y*Z*W) / (X*Y)
= H/X - HN/X + W + HN/XY - XYZW/XY
= H/X - HN/X + W + HN/XY - ZW

Case 2: Heroism at 100%
Time to do damage while affected by Heroism: W
Damage done: X*Z*W
Remaining HP to Threshold: H * (1 - N) - X*Z*W
Time to get boss to threshold from that point: (H * (1 - N) - X*Z*W) / X

Time to get boss from threshold to 0: H * N / (X * Y)

Total Time: W + (H * (1 - N) - X*Z*W) / X + H * N / (X * Y)
= W + ( H - HN - XZW ) / X + HN / XY
= W + H/X - HN/X - XZW/X + HN/XY
= W + H/X - HN/X - ZW + HN/XY
= H/X - HN/X + W + HN/XY - ZW

Notice that the formula for total time to boss death yields the same equation in both cases.

Again, this is reliant on Z and Y being percentage increases, but does not dictate WHAT percents they are. They could be anything. This also means that the Heroism doesn't have to correlate into an exact 40% increase for this to work. The percent can also vary amongst classes, when you consider that the raid-wide DPS will increase by a certain amount with heroism up vs. without it.

Basically, it boils down to Heroism rocks, use it at the time when you can best stack it with trinkets and cooldowns, generally the start of a fight, unless there's a specific phase which benefits from being burned through (Maexxna enrage, Thane kill on 4H, etc).


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.
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Postby Morpheren » Wed Mar 04, 2009 12:22 am

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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Postby Varmin » Wed Mar 04, 2009 1:49 am

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.
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Postby Dorvan » Wed Mar 04, 2009 2:35 am

Varmin wrote: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.


The weird thing about the math though, is that your last bullet point and final remark don't appear to be true. That is, stacking Heroism with other gains doesn't actually shorten kill time, nor even does using it when more people are alive. It's damn unintuitive, but that appears to be the result. I've got a bit of an inkling of where the wrinkle is, but I'm not quite sure about it yet.
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Postby Zironic » Wed Mar 04, 2009 3:21 am

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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Postby culhag » Wed Mar 04, 2009 3:36 am

Someone made a good analogy in the comments :

Moxy wrote:I think a way to make it more intuitive is to think of a boss kill on a videotape. Heroism is the fast forward button. You get to hold down fast forward for exactly 40 seconds at any point in the tape you like. Obviously you can't make the tape finish any faster no matter when you push it.
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Postby Zironic » Wed Mar 04, 2009 3:45 am

This simple matlab program gets different results for when you use bloodlust but I might have coded it wrong : P
Code: Select all
function [ kek ] = heroism(toggle)
treshhold=0.35;
heroismd=45;
heroismboost=1.3;
treshholdboost=1.3;
health=1000;
dps=1;

if toggle==1
    kek=(health*(1-treshhold)/dps)+((health*treshhold-heroismd*heroismboost*treshholdboost*dps)/dps*treshholdboost)
else
    kek=((health*(1-treshhold)-heroismd*heroismboost*dps)/dps)+(health*treshhold/dps*treshholdboost)
end
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Postby rickforking » Wed Mar 04, 2009 3:53 am

Dorvan wrote:
Varmin wrote: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.


The weird thing about the math though, is that your last bullet point and final remark don't appear to be true. That is, stacking Heroism with other gains doesn't actually shorten kill time, nor even does using it when more people are alive. It's damn unintuitive, but that appears to be the result. I've got a bit of an inkling of where the wrinkle is, but I'm not quite sure about it yet.
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.
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Postby Zironic » Wed Mar 04, 2009 4:06 am

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 :P

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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Postby Varmin » Wed Mar 04, 2009 4:53 am

Dorvan wrote:
The weird thing about the math though, is that your last bullet point and final remark don't appear to be true. That is, stacking Heroism with other gains doesn't actually shorten kill time, nor even does using it when more people are alive. It's damn unintuitive, but that appears to be the result. I've got a bit of an inkling of where the wrinkle is, but I'm not quite sure about it yet.


Any class with a haste cooldown will benefit from combining it with Bloodlust as all haste affects are multiplicative rather than additive. No current execute talents scale with bloodlust.

Example, mages:

No matter whether the boss is below 35% or above 35%, a mage will gain 30% more haste for 40s from a bloodlust.

If that mage uses Icy veins for example during the bloodlust. He will gain 26% haste from the Icy veins. Where when he uses it outside bloodlust, he will only gain 20% haste.
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Postby Jonesy » Wed Mar 04, 2009 6:29 am

Zironic wrote:I just thought of one thing the math doesn't account for, the use of flat damage increses below threshhold such as trinkets.


The second proof of the assertion does in fact account for that.

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


The maths is sound. If you want an intuitive answer, you spend 65% of the boss's health doing low DPS and 35% of the boss's health doing high DPS. If you use bloodlust early, you minimize the amount of *time* spent doing low DPS. If you use bloodlust late, you maximise the height of DPS that you do, at the expense of having the boss alive less time in the high DPS phase.

Does it make more sense that way?
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Postby Mordinm » Wed Mar 04, 2009 7:09 am

Dorvan wrote:
The weird thing about the math though, is that your last bullet point and final remark don't appear to be true. That is, stacking Heroism with other gains doesn't actually shorten kill time, nor even does using it when more people are alive. It's damn unintuitive, but that appears to be the result. I've got a bit of an inkling of where the wrinkle is, but I'm not quite sure about it yet.


You're reading too much into the proof. What this shows is that the damage lost by blowing lust at 100% is exactly the same as the damage gained by spending longer in the sub 35% or 20% high damage zone. Stacking heroism with trinkets and what not will still increase dps in general. This math does not generalize into it trinkets and deaths not mattering for lust.
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Postby Mendin » Wed Mar 04, 2009 7:27 am

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


In fact the math proves that losing ppl does not matter for heroism IF the lost of ppl is dependent of the boss HP. In this case you can consider the (13/15) the Y in the original formula.

*removed example from Heigan as it was incorrect.
Last edited by Mendin on Wed Mar 04, 2009 7:59 am, edited 2 times in total.
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Postby Rhiannon » Wed Mar 04, 2009 7:32 am

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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Postby agnara » Wed Mar 04, 2009 7:45 am

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


---------------

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