kebess
08-06-2012, 07:58 AM
Hi, guys.
Here's little panic button analysis, extracted from my latest vid : Cooldown Classification and Management Analysis.
http://www.youtube.com/watch?v=BlPSKuy3zRA&feature=plcp
As always, do let me know if I missed something, or would like an in-depth view on any particular section.
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Below 45% life, LS provides more EH than SW
X = life %tage at which LS stops being better than SW as a panic button.
W = total EH amount with only SW (without Armour, or any other DR and life buff)
Z = total EH amount with only LS (without Armour, or any other DR and life buff)
== > W = Z , when life is at x%, since below x% LS provides more EH, and above x% SW provides more EH.
When life is at x% == > Y = W = Z.
EH = Life * [ 100 / (100-DR%tage)] (this is the general EH equation)
== > w = 100x / 60 = y
Since Last Stand gives 30% more life, but 0% DR
== > z = x + 30 = y
== == >> 100x / 60 = x + 30 == > 40x / 60 = 30 == > x = 30 * (60/40) = 45
== > X = 45%
And so below 45% life, and BEFORE its 30% current life increase is consumed, Last Stand is a better panic button than Shield Wall.
Furthermore, since 45% life is much higher than the life we’d have in a ''panicking moment'', we can conclude than in most cases, a life increasing ability or a damage absorption ability (which would be similar to the first), is a better panic button than a damage reduction ability.
Here is a simple equation to calculate X => the life %tage at which a given ''life increasing'' ability (or damage absorption ability) stops being a better panic button than a given DR ability.
X = [ (100/a) - 1 ] * b
a = DR ability's %tage. a > 0.
b = healing (or absorption) amount of the healing ability, expressed in %tage of max HP
For example Rallying Cry (20% HP) stops being a better panic button than Shield Wall (40% DR), at X = ((100/40)-1)*20 = 30% HP.
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Some even more in depth on the LS, SW thing
In the above calculation, I didn't take into account external heal you might be getting from healers in a panicking moment, because here we can't truly count on them to save our life. We can't even be sure we will receive any healing at all during that panicking moment, and not a fraction of a second too late.
Remember a panic button is defined as a life saving ability you simply hit, whenever your life suddenly drop unexpectedly and very dangerously, and you don’t have more than a few seconds to react before the next potential killing blow.
And so the ''panicking moment'' is the time in between the moment your life suddenly drops and the time the potential killing blow hits.
Now, if your healer could heal you during that panicking moment, at least a little bit, because he is very good and can anticipate these sort of things, or is mostly spam healing you, or for whatever other reason;
we could determine whether his healing is enough to bring you above X (45% life) before the potential killing blow, and thus make SW a better panic button than LS, or even remove the need of a panic button all together.
Let's calculate this
(every heal here is expressed in %tage of your max HP)
∆H = average amount of external heal you get in a given time ∆T = to healer's average HPS, solely on you, expressed in ''%tage of max HP / sec''.
∆T = amount of time taken to receive a given amount of heal ∆H.
t = boss attack speed in seconds (can be =/= from boss swing time, if he casts damaging spells between swings and/or has a DoT)
h = average amount of external heal you get in between 2 boss attacks.
The longer t is, the more revealing and scientific will be the final result, because the longer time you'll have to actually receive any heal from your healer. The longer time your healer will have to react and cast a heal.
And so, the shorter ∆T, the more revealing and scientific will be the final result. e.g. fast ticking HoTs are very good here.
During a panicking moment :
=== >> ∆H/∆T = h/t => h = t*(∆H/∆T)
l = life %tage at the panicking moment, right after your HP suddenly drops.
x = life %tage at which a given life increasing ability stops being a better panic button than a given DR ability.
When, x - l = h , LS = SW as a panic button == > x - l = t*(∆H/∆T)
When, x - l < h , LS is a better panic button than SW
When, x - l > h , SW is a better panic button than LS
== > x - l = t*(∆H/∆T) == > [(100/a) - 1]*b = t*(∆H/∆T) + l == > ∆H = {[((100/a) - 1)*b] - l } * (∆T/t)
== >> ∆H' = {[((100/a) - 1)*b] - l } / t
This expression of ∆H represents the amount of HPS (or here, %tage of max HP / sec) your healer needs to do on you, to make a given life increasing CD = to a given DR CD, as a panic button.
If, healer's actual HPS < ∆H' , then the life increasing ability remains a better panic button.
A simple example to illustrate things :
If you have 450K max HP, and boss has a 2 sec attack speed, and you're comparing LS to SW when you drop to 10% HP , your healer will have to do :
∆H' ={[((100/40) - 1)*30] - 10 } * (1/2) = 17.5 % of your max HP as heal every sec, or 78.75K HPS during the whole panicking moment, to make SW a better option. Anything under that makes LS the better choice.
This means that each time SW becomes a better choice when compared to LS, the need of using a panic button simply ''disappears'', since you'd already be above 45% life, and no longer in critical danger.
Here's little panic button analysis, extracted from my latest vid : Cooldown Classification and Management Analysis.
http://www.youtube.com/watch?v=BlPSKuy3zRA&feature=plcp
As always, do let me know if I missed something, or would like an in-depth view on any particular section.
------------------------------------------------------------------------------------
Below 45% life, LS provides more EH than SW
X = life %tage at which LS stops being better than SW as a panic button.
W = total EH amount with only SW (without Armour, or any other DR and life buff)
Z = total EH amount with only LS (without Armour, or any other DR and life buff)
== > W = Z , when life is at x%, since below x% LS provides more EH, and above x% SW provides more EH.
When life is at x% == > Y = W = Z.
EH = Life * [ 100 / (100-DR%tage)] (this is the general EH equation)
== > w = 100x / 60 = y
Since Last Stand gives 30% more life, but 0% DR
== > z = x + 30 = y
== == >> 100x / 60 = x + 30 == > 40x / 60 = 30 == > x = 30 * (60/40) = 45
== > X = 45%
And so below 45% life, and BEFORE its 30% current life increase is consumed, Last Stand is a better panic button than Shield Wall.
Furthermore, since 45% life is much higher than the life we’d have in a ''panicking moment'', we can conclude than in most cases, a life increasing ability or a damage absorption ability (which would be similar to the first), is a better panic button than a damage reduction ability.
Here is a simple equation to calculate X => the life %tage at which a given ''life increasing'' ability (or damage absorption ability) stops being a better panic button than a given DR ability.
X = [ (100/a) - 1 ] * b
a = DR ability's %tage. a > 0.
b = healing (or absorption) amount of the healing ability, expressed in %tage of max HP
For example Rallying Cry (20% HP) stops being a better panic button than Shield Wall (40% DR), at X = ((100/40)-1)*20 = 30% HP.
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Some even more in depth on the LS, SW thing
In the above calculation, I didn't take into account external heal you might be getting from healers in a panicking moment, because here we can't truly count on them to save our life. We can't even be sure we will receive any healing at all during that panicking moment, and not a fraction of a second too late.
Remember a panic button is defined as a life saving ability you simply hit, whenever your life suddenly drop unexpectedly and very dangerously, and you don’t have more than a few seconds to react before the next potential killing blow.
And so the ''panicking moment'' is the time in between the moment your life suddenly drops and the time the potential killing blow hits.
Now, if your healer could heal you during that panicking moment, at least a little bit, because he is very good and can anticipate these sort of things, or is mostly spam healing you, or for whatever other reason;
we could determine whether his healing is enough to bring you above X (45% life) before the potential killing blow, and thus make SW a better panic button than LS, or even remove the need of a panic button all together.
Let's calculate this
(every heal here is expressed in %tage of your max HP)
∆H = average amount of external heal you get in a given time ∆T = to healer's average HPS, solely on you, expressed in ''%tage of max HP / sec''.
∆T = amount of time taken to receive a given amount of heal ∆H.
t = boss attack speed in seconds (can be =/= from boss swing time, if he casts damaging spells between swings and/or has a DoT)
h = average amount of external heal you get in between 2 boss attacks.
The longer t is, the more revealing and scientific will be the final result, because the longer time you'll have to actually receive any heal from your healer. The longer time your healer will have to react and cast a heal.
And so, the shorter ∆T, the more revealing and scientific will be the final result. e.g. fast ticking HoTs are very good here.
During a panicking moment :
=== >> ∆H/∆T = h/t => h = t*(∆H/∆T)
l = life %tage at the panicking moment, right after your HP suddenly drops.
x = life %tage at which a given life increasing ability stops being a better panic button than a given DR ability.
When, x - l = h , LS = SW as a panic button == > x - l = t*(∆H/∆T)
When, x - l < h , LS is a better panic button than SW
When, x - l > h , SW is a better panic button than LS
== > x - l = t*(∆H/∆T) == > [(100/a) - 1]*b = t*(∆H/∆T) + l == > ∆H = {[((100/a) - 1)*b] - l } * (∆T/t)
== >> ∆H' = {[((100/a) - 1)*b] - l } / t
This expression of ∆H represents the amount of HPS (or here, %tage of max HP / sec) your healer needs to do on you, to make a given life increasing CD = to a given DR CD, as a panic button.
If, healer's actual HPS < ∆H' , then the life increasing ability remains a better panic button.
A simple example to illustrate things :
If you have 450K max HP, and boss has a 2 sec attack speed, and you're comparing LS to SW when you drop to 10% HP , your healer will have to do :
∆H' ={[((100/40) - 1)*30] - 10 } * (1/2) = 17.5 % of your max HP as heal every sec, or 78.75K HPS during the whole panicking moment, to make SW a better option. Anything under that makes LS the better choice.
This means that each time SW becomes a better choice when compared to LS, the need of using a panic button simply ''disappears'', since you'd already be above 45% life, and no longer in critical danger.