Elitist Jerks Moonkin Raiding

07/08/09, 11:32 AM   #1726
Huskar
7 of 9

Tauren Druid

Area 52
 Originally Posted by Arawethion Lunar procs very slightly faster. 3s Starfire vs. 1.5sWrath/60% = 2.5s --> it procs 6/5 faster. It's never been a significant term in the DPS comparison between the two cycles. Though based on the number of people that constantly mention it, it seems to be quite a source of psychological bias; some people really like the "guaranteed" proc of Solar.
This point needs to be shouted! In fact, the time to proc Lunar is even shorter given that NG can play a role on non-procing crits.

As a side note, how did you decide to model pre-lunar-eclipse dps given non-proccing crits and NG and stuff.

07/08/09, 12:00 PM   #1727
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Huskar This point needs to be shouted! In fact, the time to proc Lunar is even shorter given that NG can play a role on non-procing crits. As a side note, how did you decide to model pre-lunar-eclipse dps given non-proccing crits and NG and stuff.
I assumed it was the same as ordinary chaincasting actually. I think that's the correct probability analysis, even though it's counterintuitive since the phase ends when you crit/proc. At the time I start casting any Wrath, the expectation DPS of that Wrath includes the normal probability to crit. The phase only extends longer if you're unlucky and don't crit, but then you can't cycle back around and introduce the assumption that you didn't crit for the purpose of DPS computation.

I bet I could confirm this by expanding out the probability distribution for the number of casts it takes to proc and then re-integrating with a single crit included in each term. I'll try that if I have time.

07/08/09, 12:15 PM   #1728
Happy October 19th!

Night Elf Druid

Dragonblight
 Originally Posted by Arawethion The phase only extends longer if you're unlucky and don't crit, but then you can't cycle back around and introduce the assumption that you didn't crit for the purpose of DPS computation.
Sure you can. Take, for instance, proccing solar Eclipses with 3/3 Eclipse. You're guaranteed to get Eclipse as soon as you crit, so allowing DPS numbers pre-Eclipse to include crit chance inflates them by quite a bit (~ your crit chance). Granted, it's a short period of time, but assume your SF spam DPS is ~2400 without crits, and you have ~40% crit chance. That's about 1k DPS difference between assuming you can crit and assuming you can't (more, factoring in NG). If you're in pre-Eclipse for 5s, that's 125 DPS averaged out, which is non-trivial. It's also not including inflation when counting crit chance for proccing Lunar, which is lower, but I wouldn't be surprised if the total inflation is worth around 200 DPS. That's what the funky math in WC is doing to determine pre-Eclipse DPS. It's finding your chance to crit and not proc Eclipse, then calculating DPS based on that.

07/08/09, 12:40 PM   #1729
Huskar
7 of 9

Tauren Druid

Area 52
 Originally Posted by Adoriele Sure you can. Take, for instance, proccing solar Eclipses with 3/3 Eclipse. You're guaranteed to get Eclipse as soon as you crit, so allowing DPS numbers pre-Eclipse to include crit chance inflates them by quite a bit (~ your crit chance). Granted, it's a short period of time, but assume your SF spam DPS is ~2400 without crits, and you have ~40% crit chance. That's about 1k DPS difference between assuming you can crit and assuming you can't (more, factoring in NG). If you're in pre-Eclipse for 5s, that's 125 DPS averaged out, which is non-trivial. It's also not including inflation when counting crit chance for proccing Lunar, which is lower, but I wouldn't be surprised if the total inflation is worth around 200 DPS. That's what the funky math in WC is doing to determine pre-Eclipse DPS. It's finding your chance to crit and not proc Eclipse, then calculating DPS based on that.
No, I think Hamlet is right here. Because the amount of time you spend in the pre-eclipse phase depends on when you crit, the average dps wont be effected by the phase ending on the first crit. Think of it this way: if you crit on your first spell, your dps is very high for the period, but if you crit on the 10th starfire, it is very low. You should still "expect" to crit after 1/[crit%] spells, which would give "expected" dps equal to non-eclipse spam (including crit). I think if you summed up the chances of critting on spell #1, #2, #3.. etc. you'd get the same result.

07/08/09, 1:28 PM   #1730
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Adoriele Sure you can. Take, for instance, proccing solar Eclipses with 3/3 Eclipse. You're guaranteed to get Eclipse as soon as you crit, so allowing DPS numbers pre-Eclipse to include crit chance inflates them by quite a bit (~ your crit chance). Granted, it's a short period of time, but assume your SF spam DPS is ~2400 without crits, and you have ~40% crit chance. That's about 1k DPS difference between assuming you can crit and assuming you can't (more, factoring in NG). If you're in pre-Eclipse for 5s, that's 125 DPS averaged out, which is non-trivial. It's also not including inflation when counting crit chance for proccing Lunar, which is lower, but I wouldn't be surprised if the total inflation is worth around 200 DPS. That's what the funky math in WC is doing to determine pre-Eclipse DPS. It's finding your chance to crit and not proc Eclipse, then calculating DPS based on that.
I know the argument; I think I actually recommended the change in WC a while back where you modify the crit chance of the pre-Eclipse Wraths. I'm just not so sure of it at the moment.

@Huskar, yeah, that's what I meant. Let me see if the infinite summation looks hard.

 07/08/09, 1:39 PM #1731 • Adoriele Happy October 19th!     Adoriele Night Elf Druid   Dragonblight Hmm. I think I get what you're working at. Pre-Eclipse DPS value in WC doesn't take into account the single crit that procs Eclipse. Perhaps by pulling out a single cast and forcing it to be a crit from that value, we could count that DPS while still allowing the pre-Eclipse conditions?
07/08/09, 1:41 PM   #1732
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Adoriele Hmm. I think I get what you're working at. Pre-Eclipse DPS value in WC doesn't take into account the single crit that procs Eclipse. Perhaps by pulling out a single cast and forcing it to be a crit from that value, we could count that DPS while still allowing the pre-Eclipse conditions?
The result should be the same, mathematically. That's what I've been commenting on trying to prove above.

07/08/09, 2:17 PM   #1733
Quewatoka
Von Kaiser

Quewatanka
Tauren Warrior

No WoW Account
 Originally Posted by Altiris Can we let Balance of Power die? ... There's no reason for them to buff it to 6%. Not only would it make gearing awkward, it would not be in line with any other caster's hit talent. It's just a miswording because they changed the second part of the tooltip text without realizing how that affected the way the first part was worded.
Don't write it off just yet. The awkward gearing would push moonkins into more leather. Making 52 points of hit rating useless would nerf hit cloth pieces and make spirit leather relatively more attractive. Some pieces (e.g. [Leggings of the Enslaved Idol]) would become very difficult to work into a set. Do I hear clothies rejoicing?

It's not problematic for us to have better hit talents than clothies. They have plenty of non-tier hit pieces in their armor class while we have zero. If Blizzard wants us to pew pew wearing healing leather then the balance tree needs to compensate for the non-optimal gear like the feral tree compensates for bears wearing DPS leather. The balance tree doesn't need to work as hard as the feral tree, but it's obviously not there yet.

07/08/09, 2:59 PM   #1734
Altiris
Von Kaiser

Tauren Druid

Zul'Jin
 Originally Posted by Quewatoka Don't write it off just yet. The awkward gearing would push moonkins into more leather. Making 52 points of hit rating useless would nerf hit cloth pieces and make spirit leather relatively more attractive. Some pieces (e.g. [Leggings of the Enslaved Idol]) would become very difficult to work into a set. Do I hear clothies rejoicing? It's not problematic for us to have better hit talents than clothies. They have plenty of non-tier hit pieces in their armor class while we have zero. If Blizzard wants us to pew pew wearing healing leather then the balance tree needs to compensate for the non-optimal gear like the feral tree compensates for bears wearing DPS leather. The balance tree doesn't need to work as hard as the feral tree, but it's obviously not there yet.
I don't think that's what Blizzard intends, and you seem to be ignoring the fact that it's almost definitely just an oversight. If all the talent was was 4% hit and they changed the tooltip to say 6% hit, then I might be inclined to believe they were changing it. But it's not, it's obviously just an oversight, please let it drop. It's been at least two PTR builds now... don't you think they would have changed the value from a 4 to a 6 by now? Do you really think they want alliance druids to be over the hit cap wearing just T9 hat and pants?

Last edited by Altiris : 07/08/09 at 3:04 PM.

07/08/09, 4:15 PM   #1735
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Arawethion The result should be the same, mathematically. That's what I've been commenting on trying to prove above.
Here it is. Let's imagine a Solar proc (simpler to work with due to 100% rate, concept is the same). Crit chance C. A non-crit does D damage and a crit does D_c.

The probability of a proc on the nth cast is
$P(n)=(1-C)^{n-1}C$

The expected number of casts before a proc is
$\sum_{n=1}^{\inf}nP(n)$
$\sum_{n=1}^{\inf}nC(1-C)^{n-1}$
$\frac{C}{1-C}\sum_{n=1}^{\inf}n(1-C)^n$
$\frac{C}{1-C}\frac{1-C}{(1-(1-C))^2}$ *
$\frac{1}{C}$

(kind of a sanity check since it should be clear that it takes 1/C casts to proc anyway)

My DPS computation simply multiples that by the ordinary mean damage per cast of $(D_CC+D(1-C))$

Total damage done:
$\frac{1}{C}(D_CC+D(1-C))$
$D_C+D\frac{1-C}{C}$

-----------

Actual total damage done in each scenario = $D_C+(n-1)D$

Mean total damage done:

$\sum_{n=1}^{\inf}(D_C+(n-1)D)P(n)$
$D_C\sum_{n=1}^{\inf}P(n)+D\sum_{n=1}^{\inf}(n-1)P(n)$
$D_C\cdot 1+DC\sum_{n=1}^{\inf}(n-1)(1-C)^{n-1}$
$D_C+DC\sum_{n=0}^{\inf}n(1-C)^n$
$D_C+DC\frac{1-C}{C^2}$ *
$D_C+D\frac{1-C}{C}$

QED

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

*The summation used in both these lines is:

$\sum_{n=0}^{\inf}nx^n=\frac{x}{(1-x)^2}$

e: fixed typos noted below.

Last edited by Hamlet : 07/08/09 at 8:23 PM.

 07/08/09, 5:23 PM #1736 Xerophyte King Hippo     Awnh Tauren Warrior   No WoW Account (EU) It's probably worth keeping in mind that real pre-eclipse phases don't actually end on a crit thanks to travel time, the spell queue and player reactions all conspiring to ensure that we'll keep going with the wrong spell for at least a single cast. For Wraths at max distance I'd expect 2-3 extra casts after the proccing cast before you swap, at least going by my own logs. We're also going to have some fun if not very significant distance-to-mob related effects at the end of our Solar Eclipses in 3.2. If we're at a distance then the last couple of Wraths we cast in Solar will be able to proc Lunar by the time they hit, which is good for Lunar's time to proc. If the last casts in Solar fail to proc Lunar then our time to proc following the dot refresh is increased by the current Wrath travel time, which is bad for time to proc. Specifically assuming a 50% crit chance and a 2.5 second travel time causing the 2 last Wraths in Solar hitting late enough to proc Lunar gives: Early Lunar (average TTP = 0s after dot refresh): 51% of the time Late Lunar (average TTP = 1/.3 +2.5 $\approx$ ~5.8s after dot refresh): 49% of the time. Average TTP: ~2.9s. Assuming no Wrath travel time and no Wraths from Solar hitting late enough to proc Lunar -- melee range, in effect -- gives a TTP of ~3.3 seconds in the same scenario. It's not a very significant difference, but it might be worth taking into account when designing a model.
07/08/09, 5:25 PM   #1737
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Xerophyte real
shhh theoretical math major don't want to hear it

But if you look my spreadsheet models for both 3.1 and 3.2, I did adjust the start/end times of the Eclipse phases to try to account for the dangling half-casts at each transition.

 We're also going to have some fun if not very significant distance-to-mob related effects at the end of our Solar Eclipses in 3.2. If we're at a distance then the last couple of Wraths we cast in Solar will be able to proc Lunar by the time they hit, which is good for Lunar's time to proc. If the last casts in Solar fail to proc Lunar then our time to proc following the dot refresh is increased by the current Wrath travel time, which is bad for time to proc. Specifically assuming a 50% crit chance and a 2.5 second travel time causing the 2 last Wraths in Solar hitting late enough to proc Lunar gives: Early Lunar (average TTP = 0s after dot refresh): 51% of the time Late Lunar (average TTP = 1/.3 +2.5 $\approx$ ~5.8s after dot refresh): 49% of the time. Average TTPr: ~2.9s. Assuming no Wrath travel time and no Wraths from Solar hitting late enough to proc Lunar -- melee range, in effect -- gives a TTP of ~3.3 seconds in the same scenario. It's not a very significant difference, but it might be worth taking into account when designing a model.
Yeah, I'd included a Wrath travel time factor in my 3.1 model, but forgot that it would work this way in 3.2 as well. I think I have to add that back in.

07/08/09, 5:38 PM   #1738
Huskar
7 of 9

Tauren Druid

Area 52
 Originally Posted by Arawethion $D_CC+D\frac{1-C}{C}$ QED
/Applause

Woot!

07/08/09, 5:47 PM   #1739
Happy October 19th!

Night Elf Druid

Dragonblight
 Originally Posted by Huskar /Applause Woot!
Quite agreed, good work. Should make life less complex now.

07/08/09, 6:37 PM   #1740
ehakam
Glass Joe

Draenei Shaman

Aerie Peak
Your math is solid, but I believe you have some typo's. Here's what I'm seeing (high-lighting typo's with <-).
Intuitively, this makes sense, as total damage done should be your crit $D_C$ + mean damage of your non-crits $D\frac{1-C}{C}$

 Originally Posted by Arawethion The expected number of casts before a proc is $\frac{1}{C}$ My DPS computation simply multiples that by the ordinary mean damage per cast of $(D_CC+D(1-C))$ <- Total damage done: $\frac{1}{C}(D_CC+D(1-C))$ <- $D_C+D\frac{1-C}{C}$ <- ----------- Actual total damage done in each scenario = $D_C+(n-1)D$ Mean total damage done: $D_C+DC\frac{1-C}{C^2}$ $D_C+D\frac{1-C}{C}$ <- ------------

 Elitist Jerks Moonkin Raiding