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Healing (WoG) and TPS, do we care?

Warning: Theorycraft inside.

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Re: Healing (WoG) and TPS, do we care?

Postby Siral » Sat Jan 08, 2011 7:17 pm

I've done some test when I was killing mobs for daily quest in Tol Barad.

WoG seems to make no threat at all. Instead normal heals does threat as stated in this thread.

I use skada to see threat generation, maybe the addon is bugged?

1 question: seal of insight scales with vengeance (and also mending??). I see bigger numbers when I've a big vengeance buff.
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Re: Healing (WoG) and TPS, do we care?

Postby Fetzie » Sat Jan 08, 2011 8:08 pm

I know that Seal of Insight scales with AP (look at it this way, it wouldn't change the amount healed when your AP changed if it didn't would it?), but I cannot say the same for mending.
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Re: Healing (WoG) and TPS, do we care?

Postby Bept » Sat Jan 08, 2011 8:09 pm

The macro I posted uses the API directly to get the actual Threat value from the server. I'm pretty sure it's accurate. If you're using an adddon to track threat it might not be implemented correctly.

Has it been updated for 4.0?
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Re: Healing (WoG) and TPS, do we care?

Postby 99sitr » Sun Jan 09, 2011 10:25 am

I'm running about the same rotation as the OP. I pull build 3HP then SotR, every single 3HP after that go to WoG on myself or on other raid members unless we are on Chimaeron and I only use 1HP to bump slimed members above the 10k cap. I'm sitting at around 3% hit and only 17EXP with the truth glyph and my threat is still higher than needs to be, I never use Inq because there is no need when that HP can go to saving healer mana. I'm also using the WoG glyph.

I pulled the 2 points from Sacred Duty for this exact reason. Until I see a need for the increased threat I will not be taking SD.

I have attached a link to one of my kill videos if anyone wants to see form my perspective. I know there are things I can improve on.

Remeber to watch in full HD.
http://www.youtube.com/watch?v=auWW8H9TcDo&hd=1
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Re: Healing (WoG) and TPS, do we care?

Postby theckhd » Sun Jan 09, 2011 12:30 pm

99sitr wrote:I pulled the 2 points from Sacred Duty for this exact reason. Until I see a need for the increased threat I will not be taking SD.

You can take all of the prot survival talents and 2/2 Sacred Duty in a 31/10 prot build. The only places you can move those points to are other threat talents - SotP, Hallowed Ground, Reckoning, or Grand Crusader, depending on what your specific build is.

I'd argue that SD is still probably the best place for those points to go, because it provides you a nice bit of burst threat on the pull, which is the only place where threat matters. The rest of those points increase your sustained DPS/TPS, but make little difference on the pull. For DPS burn phases, you can always switch back to SotR on the fly to boost DPS. That gives you higher on-demand DPS, which can be more useful than higher sustained DPS in many cases.
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Re: Healing (WoG) and TPS, do we care?

Postby 99sitr » Sun Jan 09, 2011 2:32 pm

theckhd wrote:
99sitr wrote:I pulled the 2 points from Sacred Duty for this exact reason. Until I see a need for the increased threat I will not be taking SD.

You can take all of the prot survival talents and 2/2 Sacred Duty in a 31/10 prot build. The only places you can move those points to are other threat talents - SotP, Hallowed Ground, Reckoning, or Grand Crusader, depending on what your specific build is.

I'd argue that SD is still probably the best place for those points to go, because it provides you a nice bit of burst threat on the pull, which is the only place where threat matters. The rest of those points increase your sustained DPS/TPS, but make little difference on the pull. For DPS burn phases, you can always switch back to SotR on the fly to boost DPS. That gives you higher on-demand DPS, which can be more useful than higher sustained DPS in many cases.



Theck you are 100% correct and I should have clarified my reasoning behind the 2 point swap. In my situation in our strict 10 we run a hunter and a rogue so between ToT and MD I'm never too worried about the initial threat. I just don't use it enough it seems to justify the 2 talent point cost. I honestly devote all my HP after the first 3 to WoG's and maybe I shouldn't?

At our current stage of the game all of our kills are nowhere near the enrage timer on the encounters that have them so I guess I take the role of small burst healing rather than even smaller dps.

As always Theck, love the work you put in for us all.
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Re: Healing (WoG) and TPS, do we care?

Postby theckhd » Sun Jan 09, 2011 5:07 pm

99sitr wrote:I honestly devote all my HP after the first 3 to WoG's and maybe I shouldn't?


No, I don't see anything wrong with what you're doing. I prefer SD because I use SotR enough to warrant keeping it, either in heroics, while off-tanking, or just to get more burst threat on an add. But it's mostly a flavor choice if you're spending most of your time Wogging, which is true for most of the raiding population.
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Re: Healing (WoG) and TPS, do we care?

Postby wrathblood » Mon Jan 10, 2011 6:43 am

GASP!

Theorycrafting on WoG/healing threat for paladin tanks! How have I missed this? (Actually, I had a stomach bug for a few days which is probably why). Regardless, I'm beside myself with excitement. Time to go run tests.
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Re: Healing (WoG) and TPS, do we care?

Postby theckhd » Mon Jan 10, 2011 8:51 am

We've added WoG to the MATLAB model, though there's still some testing to be done to determine the exact interplay between different modifiers (glyphs, talents, etc). The plan is to try and add full support for WoG in the 4.0.6 version of the code.

Nonetheless, here's a quick estimate based on what we have at the moment.

In the T11 raid gear set (2.8% hit, 16.7 expertise), SotR does around 23k on average before crits or misses are accounted for, which works out to around 3.5k DPS after SD crits and misses are included. This is assuming 80% Vengeance to account for the current cap mechanics, which aren't yet reflected in the code. You also get a seal proc worth about 100 DPS. So in sum, you get about 10.8k TPS from SotR.

Word of Glory heals for about 25k (non-crit) under these circumstances, or 28k on average once crits are included, which is 42k threat. If we ignore Eternal Glory, that's 3.1k HPS and 4.67k TPS.

To include EG, we need to do some modeling. It's got a 15-second ICD, which means that at most, we can get one every other WoG cast. In addition, it's not guaranteed to proc, so we have to account for streaks (EG-0-0-EG). If this looks familiar, it's because it's very similar to the Grand Crusader problem. Luckily, this one is easier, because it converges.

Let p be the EG proc chance (30% if fully talented). The proc chance P(N) for cast N is always p*[1-P(N-1)], or

Code: Select all
p*(chance previous cast did not result in EG proc).


Let's work this out starting from the first cast (N=1).
On the first cast, you have a probability p of getting a proc, and q=1-p of not getting a proc.
On the second cast, you can only get a proc if the previous cast was not a proc (due to the ICD). So you have a p chance to proc [1-p] % of the time, or a net proc chance of p-p^2.
On the third cast, you have a p chance [1 - (p - p^2)] % of the time, for a net chance of p - p^2 + p^3.

You can already see the pattern here. This clearly works out to

Code: Select all
P(N) = sum_1^N (-1)^(N-1)*p^N = p - p^2 + p^3 - p^3 + p^4 - ...


This is a standard form of geometric series, and converges to p/(1+p) as N goes to infinity.

Thus, on average we cast 1+p/(1+p) = 1.23 WoGs every cycle. The average cycle is also slightly longer than 9 seconds because of these extra WoGs. This can be expressed as an "extra" GCD cost:

G = 1.5*p/(1+p)

So that the cycle is actually 9+G seconds, which works out to 9.3462 seconds.

Now that we have Eternal Glory properly modeled, we can make a more accurate assessment of WoG's healing and threat potential. We cast 1.23 WoGs every 9.3462 seconds, for a net HPS of 3.68 HPS and 5.52 TPS.

In other words, WoG puts out a little over half of the threat that SotR does under these conditions (low hit/exp, full Vengeance).

Quick summary of values
SotR DPS: 3.6k
SotR TPS: 10.8k
WoG HPS: 3.68
WoG TPS: 5.52k

<edit>
Interesting observations:
-EG is worth about 580 HPS (290 HPS per point). It's also worth 850 TPS (425/point).
-That's 2-3x better than Seals of the Pure even under the best conditions, provided you're using WoG as a Holy Power sink.
-Divinity is worth ~600 HPS (200/point) just from WoG alone, or 900 TPS (300/point). Also 2-3x better than SotP for threat, and we haven't even considered SoI. External healing will make Divinity much stronger than EG for total HPS, of course.
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Re: Healing (WoG) and TPS, do we care?

Postby PsiVen » Mon Jan 10, 2011 9:43 am

99sitr wrote:
theckhd wrote:
99sitr wrote:I pulled the 2 points from Sacred Duty for this exact reason. Until I see a need for the increased threat I will not be taking SD.

You can take all of the prot survival talents and 2/2 Sacred Duty in a 31/10 prot build. The only places you can move those points to are other threat talents - SotP, Hallowed Ground, Reckoning, or Grand Crusader, depending on what your specific build is.

I'd argue that SD is still probably the best place for those points to go, because it provides you a nice bit of burst threat on the pull, which is the only place where threat matters. The rest of those points increase your sustained DPS/TPS, but make little difference on the pull. For DPS burn phases, you can always switch back to SotR on the fly to boost DPS. That gives you higher on-demand DPS, which can be more useful than higher sustained DPS in many cases.



Theck you are 100% correct and I should have clarified my reasoning behind the 2 point swap. In my situation in our strict 10 we run a hunter and a rogue so between ToT and MD I'm never too worried about the initial threat. I just don't use it enough it seems to justify the 2 talent point cost. I honestly devote all my HP after the first 3 to WoG's and maybe I shouldn't?

At our current stage of the game all of our kills are nowhere near the enrage timer on the encounters that have them so I guess I take the role of small burst healing rather than even smaller dps.

As always Theck, love the work you put in for us all.


I often do this as well, but don't forget that DPS matters sometimes too, even when threat doesn't. Tank DPS with Vengeance can easily account for a 4k DPS difference if you stop using WoG spam, which can be a significant amount of RDPS in a 10-man. Berserk timers are not the only failure modes; fights like Al'akir P2 and Cho'gall are strongly time sensitive. For these reasons I would never drop the extremely high potential of Sacred Duty, even if it does frequently get wasted by parries.
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Re: Healing (WoG) and TPS, do we care?

Postby Dapperdann » Mon Jan 10, 2011 10:24 am

I don't even use SotR anymore I am build around Word of Glory and healers love me because of it.
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Re: Healing (WoG) and TPS, do we care?

Postby wrathblood » Mon Jan 10, 2011 2:19 pm

Theck, nice work on modeling EG.

In answer to your earlier question, no, sadly I never repeated my work in 4.0.3a or later. I would LOVE to know when the 0.25 to 0.50 threat healing change-over actually happened (I believe the announced change actually was implemented when they said it was on Beta, but was reverted within 24 hours. After it was announced, I spent like 5 minutes checking that it at least appeared to be 0.50 (was hardly comprehensive about it, though), did a bunch of analysis and put up a bunch of posts, then came back the next day for "real" testing and it was 0.25 which was aggravating. Adding insult to injury, Zarko's big thread on the old forums is gone, afaik, taking a lot of my stuff with it), just for posterity.

As I'm sure you're aware, leaving out crits and misses on ShoR is going to severely skew things in favor of WoG, and I don't think one can blythely assume that no one is speccing into SD. I mean, SD, by itself, generates roughly as much threat as WoG (sans EG).

I found the really fun work to be around the individual talents and glyphs. If you're going heavily with WoG, then expertise is certainly less important, so why not run with SoI, glyph it and then glyph WoG instead of ShoR? Obviously, threat is essentially binary. If you have enough to not threat cap your dps (which, with all the kiting, add pick-up and target switching required in this these fights makes threat rather less trivial to maintain than it would be on Patch, especially if you're in a hunter and rogue-less 10-man) then the excess doesn't matter, but the question of "How much is enough?" will vary dramatically from person to person depending on their situation.

As a result, the important part is to look at the trade-offs in a more granular/functional fashion. What is the trade-off for the various abilities? Which give the best return in survivability for the threat loss? If, as a tank, you've got a 5k tps lead over your top dpser, what's the best way to "spend" that?

Edit - A few thoughts. First, overhealing. Back in Beta, we tended to assume overhealing would be in the neighborhood of 50% for something passive like SoI and built that into analysis. SoI overhealing generates nothing, while WoG overhealing generates a shield that (worked out by someone here, who's name escapes me) generates a flat 12 or so threat. Against Magmaw the other day I had ~29% overheal from SoI and ~35% overheal from Mending (SoL is giving me a busy signal on every other fight, oddly enough), which is a good bit better than I had been assuming, but still enough to take a bite out of those threat numbers.

Second, Vengeance or Threat Sufficiency. As a side note, did y'all already know about Vengeance being Stam + 10% of base health? Probably so, but I sure didn't until it was announced today. Guess I was just off-the-ball on that. Regardless, even on a tank n' spank, I find that fights definitely have two phases. Pre-Vengeance stacking and post-Vengeance stacking. Especially on fights with a lot of movement or other trickiness, I typically throw at least my first 2 or even 3 3-HoPo accumulations into ShoR's for threat, and then if there are switches I often throw my first 3-HoPo into a ShoR onto my target just to be safe. The rest go into WoGs, but that's still a lot of lost WoG opportunities. How feasible is it to reflect something like that?

Finally, something that I'm curious about: I found giving up SoT (even including the OP glyph) for SoI (glyphed) to be a much more attractive trade-off than giving up ShoR (glyphed) for WoG (glyphed), though this was back when ShoR scaling was, ahem, different. Even so, SoI puts out a startlingly large amount of healing and I'm curious how it turns out for you.
Last edited by wrathblood on Mon Jan 10, 2011 2:52 pm, edited 1 time in total.
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Re: Healing (WoG) and TPS, do we care?

Postby theckhd » Mon Jan 10, 2011 2:28 pm

wrathblood wrote:As I'm sure you're aware, leaving out crits and misses on ShoR is going to severely skew things in favor of WoG, and I don't think one can blythely assume that no one is speccing into SD. I mean, SD, by itself, generates roughly as much threat as WoG (sans EG).


I didn't ignore either crits or misses.

theckhd wrote:In the T11 raid gear set (2.8% hit, 16.7 expertise), SotR does around 23k on average before crits or misses are accounted for, which works out to around 3.5k DPS after SD crits and misses are included. This is assuming 80% Vengeance to account for the current cap mechanics, which aren't yet reflected in the code.


In other words, a non-crit SotR is 23k, which would only be roughly 2.6k TPS. SD crits and misses both modify that value, but in non-trivial ways that I didn't want to explain in detail (since it's all in the post I linked for the Grand Crusader derivation). After applying those modifications, you get 3.5k DPS out of SotR.

This calculation was with SoT/SotR glyphs however, so things will get slightly better with SoI/WoG glyphed. But again, this was a quick hand-calculation rather than an exhaustive analysis.
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Re: Healing (WoG) and TPS, do we care?

Postby wrathblood » Mon Jan 10, 2011 2:54 pm

theckhd wrote:
wrathblood wrote:As I'm sure you're aware, leaving out crits and misses on ShoR is going to severely skew things in favor of WoG, and I don't think one can blythely assume that no one is speccing into SD. I mean, SD, by itself, generates roughly as much threat as WoG (sans EG).


I didn't ignore either crits or misses.

theckhd wrote:In the T11 raid gear set (2.8% hit, 16.7 expertise), SotR does around 23k on average before crits or misses are accounted for, which works out to around 3.5k DPS after SD crits and misses are included. This is assuming 80% Vengeance to account for the current cap mechanics, which aren't yet reflected in the code.


In other words, a non-crit SotR is 23k, which would only be roughly 2.6k TPS. SD crits and misses both modify that value, but in non-trivial ways that I didn't want to explain in detail (since it's all in the post I linked for the Grand Crusader derivation). After applying those modifications, you get 3.5k DPS out of SotR.

This calculation was with SoT/SotR glyphs however, so things will get slightly better with SoI/WoG glyphed. But again, this was a quick hand-calculation rather than an exhaustive analysis.


Doh! My bad. Saw the initial "... before crits or misses are accounted for..." and missed the "...after SD crits and misses are included."

My bad. :(
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Re: Healing (WoG) and TPS, do we care?

Postby theckhd » Mon Jan 10, 2011 3:43 pm

wrathblood wrote:My bad. :(


No problem. In response to your edits:

- This assumes no overhealing. So that will obviously reduce the healing and threat output of WoG. The MATLAB code can handle that properly though, it's just a matter of putting in the average expected overheal %. The bubble threat is very low, so just multiplying by (1-overheal%) is a very good approximation.

- I heard about the Vengeance clarification a few days ago. The code isn't updated to reflect that yet, but it will be for 4.0.6. That's the reason I've used 80% in this calculation, since that's an estimated ceiling on the amount of Vengeance AP in the current model.

- We could certainly model the initial ramp-up period, but it's complicated. The threat ramp-up period is only about 30 seconds. During that time, you're rapidly gaining Vengeance, applying debuffs, and may have external cooldowns. In addition, this may happen several times during a fight due to tank swaps or phase transitions. All in all, it's a very difficult system to accurately model, simply because there are so many parameters that vary significantly between encounters or raid compositions.

I think that it's easier to stick with steady-state solutions. A 939 steady-state model gives you a rough approximation of what you're doing during a DPS/Burn phase. A 939-WoG model gives you a good estimate of a survival phase. You switch between them based on the situation as appropriate, knowing that you're trading ~X DPS for ~Y HPS, and so forth. If we have to, we can approximate an entire fight by using weighted averages of those two.

-I don't have numbers for SoI at the moment, but that's another one of the things I'd like to investigate. I'm running SoI/WoG glyphs right now myself, and I know I'm not the only one. Knowing what the DPS->HPS trade-in value of the SoT/SoI and SotR/WoG glyphs are would be very useful. Similarly, knowing what the DPS->HPS trade for tanking with SoI instead of SoT is would be nice so we can compare against these numbers for SotR->WoG. But that will have to wait until we have time to implement all of that stuff in the MATLAB code, unless someone beats me to it.
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