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Old 09/20/06, 3:31 PM   #1
Friedrich
his surgical quality
 
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Tauren Warrior
 
Maelstrom
Hi all,

sorry to make yet another ignite thread, but I think this is interesting, and I haven't seen it yet around here.

(Note: a LaTeX'd .pdf of this text is available here: http://astro.physics.upenn.edu/~hsta...e_halflife.pdf, which should be more readable.

Inspired by the interest in rolling ignites, I decided to calculate the expected duration of an ignite, assuming your mages are all spamming scorch once the initial stack is set up.

Let P(crit) be the chance to score a crit on a single scorch. Let P(hit) = 1 - P(crit). Let there be N mages each with the same %crit chance. I will use ** to denote exponentiation and ! to denote factorial.

In a given 4-second interval, a mage will either land 2 or 3 scorch spells: two thirds of the time, there will be 3 scorches, one third of the time, the mage will land 2. Let's assume then, that due to lag etc. the offsets are random and that, for a given mage, her contribution will be
P(2s) = 1/3
P(3s) = 2/3

The number of ways to land M scorches in 4 seconds with N mages is [N choose (M-2N)]

[top] N!/((3N-M)!(M-2N)!).
You can verify this by considering the first few cases with N


1,2,3,4. (It makes a Pascal's triangle).

So, in a 4-sec interval, the probability that M scorches will land is:
P(M scorches) = {[N choose (M-2N)] * P(3s)**(M-2N) * P(2s)**(3N-M)} if 2N<=M<=3N

[top] 0 otherwise

So, the probability that with you do not crit in 4 secs is:
P(no crit given M scorches)


P(M scorches) * P(hit)**(M)

P(no crit in 4sec given n mages) = Sum_i P(i scorches)*P(hit)**i, for 2N<=i<=3N

[top] P(fall)


1-P(stay).

So then the length of the ignite should follow a [a href="http://en.wikipedia.org/wiki/Geometric_distribution"]geometric distribution[/a]: the expectation value for the number of 4sec intervals that the ignite lasts is
<T_ignite> = P(stay)/P(fall).
The probability that it lasts exactly n intervals is
P(ignite lasts 4n seconds) = P(stay)**n * P(fall).

A perl program (ignite_time.pl) to calculate these quantities is available at
http://astro.physics.upenn.edu/~hstabena/

Some numbers:

N_mages critrate P(fall) <T_ignite> (sec)

3 0.15 0.27 10.5
3 0.2 0.17 19.4
3 0.25 0.10 34.8
4 0.15 0.18 18.4
4 0.2 0.095 38.3
4 0.25 0.048 78.9
5 0.15 0.12 30.4
5 0.2 0.052 72.2
5 0.25 0.023 173.

I would be interested to see if anyone can check these results in a real raid. There are several factors I haven't taken into account, of course: lag is the most notable I think.
 
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Old 09/20/06, 6:54 PM   #2
 Arawethion
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Tauren Druid
 
Mal'Ganis
Here are my first attempts at it (bottom of first page):

http://forums.elitistjerks.com/viewt...hp?id=7742&p=1

Answers to Moonkin questions:
0) Read the TTT/use the spreadsheet: http://elitistjerks.com/f47/t66856-moonkin_pve_dps/
1) Maintain high DoT uptime. Use WiseEclipse.
2) Nothing beats 2T8.
3) Yes, sometimes you cast many Wraths and no Eclipse procs. Deal with it.
 
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Old 09/20/06, 7:54 PM   #3
Boevis
Bald Bull
 
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Tauren Druid
 
Lightbringer
I'm not too bad at math, but I'm a bit confused what C and i are, since you make no mention of what they represent ...
 
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Old 09/20/06, 10:15 PM   #4
Moleva
Von Kaiser
 
Human Warrior
 
Durotan
C looks like short hand for Choose and i is a dummy variable for the sum that he does.
 
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Old 09/20/06, 11:09 PM   #5
Friedrich
his surgical quality
 
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Tauren Warrior
 
Maelstrom
Originally Posted by Moleva
C looks like short hand for Choose and i is a dummy variable for the sum that he does.
yes, sorry - I'll edit my post to make that shorthand explicit
 
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Old 09/21/06, 6:59 AM   #6
zepi
Miekkamies
 
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Human Mage
 
Darksorrow (EU)
Great, too bad that I can't run perl :/

One thing to note: 2.66666 scorches inside the 4s timer is only possible for those mages who don't refresh the timer. The one who refreshes, can never get more than 2 scorches.

Reason should be fairly obvious, as your own scorch timer starts from the worst possible point after crit.
 
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Old 09/21/06, 10:26 AM   #7
Friedrich
his surgical quality
 
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Tauren Warrior
 
Maelstrom
hey zepi: if you want to run perl on your windows machine, a good option is Cygwin, which emulates a UNIX environment under windows. It is quite easy to install the perl package and then you are all set. Either that, or you can get a native windows perl here: http://www.perl.com/download.csp#win32

Alternatively, someone could incorporate this into a spreadsheet, but I don't have access to excel atm so not me.

It is true that one of the mages will definitely only get 2 scorches, rather than 2 or 3 with some probability. However, if the casting times between the mages are uncorrelated, what I've done should hopefully still be an OK approach.

I also stuck a LaTeX .pdf version of the above math text into the same web directory, which should make it a little more readable.
 
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Old 09/21/06, 12:17 PM   #8
Quantuvis
Von Kaiser
 
Murloc Mage
 
Magtheridon (EU)
Nice theory crafting for sure, but with only 16 debuff slots, Ignite just gets pushed off too often to really test your findings.

 
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Old 09/25/06, 7:47 PM   #9
Evice
Glass Joe
 
Undead Mage
 
Illidan
If everyone is spamming scorch it is really really low probability that it will be dropped.
 
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