Theck's MATLAB TPS analysis - WotLK/3.x

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Postby Dorvan » Sun Mar 15, 2009 12:59 pm

Laz wrote:Do the Broken Promise calculations account for the fact that it is too slow to use up all 4 charges of Reckoning? The maximum weapon speed that can use all 4 charges is 2.0 (8 sec duration / 4 charges).

For every proc Last Laugh gets 4 extra attacks and Broken Promise only gets 3.


This is a very old question....the number of procs you use doesn't matter, because each proc hits harder the slower your weapon. The only thing that matters for maximizing Reckoning damage is that your swing speed is 2.0 or slower. That's only a very rough outline of the proof, you can probably find som more detail by looking at some of the really early posts on reckoning here.
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Postby Laz » Sun Mar 15, 2009 1:26 pm

Dorvan wrote:This is a very old question....the number of procs you use doesn't matter, because each proc hits harder the slower your weapon. The only thing that matters for maximizing Reckoning damage is that your swing speed is 2.0 or slower.

Isn't your statement contradictory? The underlined portion agrees with what I said. Broken Promise has an attack speed of 2.5. Although, now that I think about raid buffs, it will be much closer to 2.0.

Intuitively, though, using the unbuffed attack speed you only get 3 extra swings where Last Laugh gets 4. In order for those 3 extra swings to out perform 4 wouldn't they need to do be doing 4/3 as much damage per swing? Is this the case? I could be way out in left field here. I don't remember ever seeing the proof, but I've only been lurking since mid-TBC.
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Postby majiben » Sun Mar 15, 2009 1:32 pm

Shouldn't the speed be 2.4 or greater given the large amount of haste from windfurry and ret aura?
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Postby Laz » Sun Mar 15, 2009 1:54 pm

I think this is the post Dorvan is referring to:

http://maintankadin.failsafedesign.com/viewtopic.php?t=785&postdays=0&postorder=asc&start=0

The conclusion here is that Reckoning provides a 100% increase in DPS over an 8 second window, regardless of how many charges are used up. The problem that I have with this statement is that in spite of that conclusion, they found that a 2.2 weapon speed maximized the benefit of Reckoning. If the dps increase due to a Reckoning proc does not depend on the number of charges used, how can it be affected by weapon speed?

Someone help me out here, maybe I'm thinking one-dimensionally.
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Postby Dorvan » Sun Mar 15, 2009 3:58 pm

Laz wrote:In order for those 3 extra swings to out perform 4 wouldn't they need to do be doing 4/3 as much damage per swing?


Yes, that is correct, and that's exactly how the math works out (if the weapons have the same stats/DPS).

Shouldn't the speed be 2.4 or greater given the large amount of haste from windfurry and ret aura?


I said swing speed 2.0 or slower than than base weapon speed 2.0 or slower for exactly that reason. I'm not sure offhand what 2.0 comes out to pre-buffs.

they found that a 2.2 weapon speed maximized the benefit of Reckoning


Basically, the 2.2 number came from an estimate of the effective speed up due to parries...the key is that your actual weapon speed needs to be 2.0 or slower, not your base weapon speed, and at the time some back-of-the-envelope math indicated that a 2.2 base speed corresponded to 2.0 effective speed. I don't remember the parry math being formalized that well, but I haven't looked at it in a long time.
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Postby theckhd » Mon Mar 16, 2009 9:00 am

Adanel asked for some analysis of weapon speeds a few pages back. It can be found over in the SoV vs. SoR thread for anyone interested.
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Postby Laz » Mon Mar 16, 2009 9:25 am

The previous conclusion that Reckoning provides the same benefit regardless of weapon speed was clearly not correct. Weapon speed does matter, but slower is better (which is opposite of my initial intuition). I think theckhd's graphs posted above clearly illustrate that weapon speed has a significant effect on the benefit of reckoning.
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Postby theckhd » Mon Mar 16, 2009 9:34 am

Laz wrote:The previous conclusion that Reckoning provides the same benefit regardless of weapon speed was clearly not correct. Weapon speed does matter, but slower is better (which is opposite of my initial intuition). I think theckhd's graphs posted above clearly illustrate that weapon speed has a significant effect on the benefit of reckoning.

Keep in mind that this includes all the contributions, including SoR procs (which scale with weapon speed). Since this somewhat obscures the issue, here's a plot of just the melee dps contribution for different weapon speeds:
Image
Which seems to confirm your suspicion.
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Postby Dorvan » Mon Mar 16, 2009 9:37 am

theckhd's graph is in line with the earlier conclusion....that Reckoning is maximized for any effective swing speed of 2.0 or slower. The finding that that corresponds to a base weapon speed of 2.4 is largely due to how Windfury works now I believe. The additional slope you see on the SoR graph is due to the effect of HotR, which gives you an additional seal proc every 6 seconds regardless of weapon speed, and therefore does more damage the slower your weapon is.
Last edited by Dorvan on Mon Mar 16, 2009 9:58 am, edited 1 time in total.
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Postby theckhd » Mon Mar 16, 2009 9:52 am

Also, since PsiVen asked for an analysis with boss swing speed, here's something I threw together quickly: HS_contribution

It plots Holy Shield DPS, as well as the % of your total DPS due to Holy Shield, as a function of "Incoming attack speed." In other words, the mean time between incoming blockable attacks. This should make it valid for normal and dual-wield bosses.

Also, I've modified the rotation_969 file a little bit to treat Holy Shield more accurately for fast-attacking bosses. The previous version used
Code: Select all
((1-player_avoid)./boss_swing_speed).*Holy_Shield

to calculate Holy Shield DPS. Clearly, this is only true as long as
((1-player_avoid)./boss_swing_speed) < 8 / (recast time), or 8/9 for 969.
Now, for player_avoid=0.55, and boss_swing_speed=2.4, we're in no danger of that limit. But when I started these calculations, it got into the range where it would matter.

As a result, I've added a variable to the rotation file that calculates the average HS procs per second:
Code: Select all
avg_HS_pps=min([8/9.*ones(size(boss_swing_speed)); ((1-player_avoid)./boss_swing_speed)]);


The 8/9 is specific to that rotation, and would need to be changed for other ones - I should have the Exorcism rotation file updated shortly.

This simplifies the Holy Shield DPS contribution as such:
Code: Select all
avg_HS_pps.*Holy_Shield



Anyway, on to the graphs. Keep in mind that I'm using a fixed 55% for player avoidance, since I haven't started calculating avoidance from gear properly yet. Thus, there's a fixed 45% chance to block - Obviously changing this value will move the speed at which HS DPS caps out around somewhat.

<edit>I forgot to include that this simulation assumes 0/5 Reckoning.

In this simulation, Holy Shield hits like a 747.. er.. for 747 damage each charge. So in a 969 rotation, it should cap out at 8*747/9 = 664 DPS:
Image
And it does so for a boss swing speed of 0.50 for this block %.

As for HS's relative contribution:
Image
It caps out at 18.3%.

For comparison, here's the DPS contribution for all skills, with a 2.4 swing speed:
Code: Select all
    'HS'       [140.1183]
    'ShoR'     [831.2658]
    'JoV'      [282.3018]
    'DoT'      [333.3194]
    'HotR'     [540.9153]
    'Cons'     [355.3900]
    'Melee'    [623.9290]

None of the others should change significantly with boss swing speed, since we're not modeling parry-haste at all yet.
Last edited by theckhd on Mon Mar 16, 2009 10:58 am, edited 1 time in total.
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Postby Dorvan » Mon Mar 16, 2009 9:56 am

theckhd wrote:None of the others should change significantly with boss swing speed, since we're not modeling parry-haste at all yet.


Well, any builds involving reckoning should have melee DPS and SoR (when that seal's being used) damage depend significantly on boss swing speed.
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Postby theckhd » Mon Mar 16, 2009 10:56 am

Dorvan wrote:Well, any builds involving reckoning should have melee DPS and SoR (when that seal's being used) damage depend significantly on boss swing speed.

Very true, which is why the build tested did not have Reckoning. :)

However, Reckoning won't change HS DPS (if we ignore parry-hasted boss swings), it'll just change it's relative contribution to total DPS by a few percent.
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Postby Dorvan » Mon Mar 16, 2009 11:10 am

theckhd wrote:However, Reckoning won't change HS DPS (if we ignore parry-hasted boss swings), it'll just change it's relative contribution to total DPS by a few percent.


Yep, however I think what the HS question is ultimately getting at is "what happens to our threat as boss swing speed increases?", and particularly as we're trying to evaluate circumstances in which SoR can surpass SoV this seems an important source of variation.
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Postby theckhd » Mon Mar 16, 2009 11:22 am

Dorvan wrote:Yep, however I think what the HS question is ultimately getting at is "what happens to our threat as boss swing speed increases?", and particularly as we're trying to evaluate circumstances in which SoR can surpass SoV this seems an important source of variation.

You're probably right, it's just not what I had in my head when I wrote the m-file. I was mostly curious at what % the HS contribution maxed out - and the answer seems to be roughly 20%. It would be higher than the 18% in this simulation for a weaker gear or raid-buff setup, since HS scales more slowly with our stats than our 6-second cooldowns do.

By the way, I've updated the post to mention that it uses 0/5 Reckoning, since I forgot to the first time.
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Postby theckhd » Wed Mar 18, 2009 11:59 am

Trying to get through the backlog of things to simulate, but it's slow going due to other time commitments. However, I had time to test out cordelia's seal swapping rotations.

The calculation file is here: SealSwap_rotation_testing.m

The analysis assumes 5/5 Reckoning and the default gear set. I've only bothered to consider two-glyph combinations for this simulation.

First, let's look at how the rotations fare with Last Laugh:
Image
The first two sets of bars are for 969 and Holy Shield Substitution (HSS) with Exorcism using SoV, the next two sets of bars are for 969 and HSS using SoR, and the rest of the plots are for the seal swapping rotations suggested in cordelia's post. MaxOL is the maximum Overlap rotation, HSsub(ss) is the HS substitution seal-swapping variant, HSJ-sub is the HS-J substitution, and HSC is the HS-C substitution.

The 969 with SoV beats out 969 with SoR , and similarly with the HS substitution, as we expect from previous results with Last Laugh. The seal-swapping rotations fail to consistently beat out the standard 969 in this case, despite giving up 100% HS uptime. However, we aren't really surprised by this for Last Laugh, since SoR tends to perform worse with it in general, and the gain of SoR damage is offset by losing or substituting for other, higher-dps abilities.

Comparing the variation with spec, and only looking two seal-swappers that require the Consecration glyph (you'll see why in a minute):
Image
It's clear here that the seal-swappers scale roughly like 969, but never catch up to the Exorcism HSS rotation. Also note that SotP makes a pretty noticeable difference here, because it helps SoR more than Conviction. Crusade is still excellent, however.

Next, let's look at how Broken Promise changes things:
Image
As expected, SoR shines with a slower weapon, and the seal-swapping rotations benefit a bit. However, the Exorcism HSS still holds the lead. The two highest are now the ones that use the Consecration glyph, which is why I chose to use those in the last spec plot. It doesn't matter much though, they all scale very similarly with spec. Unfortunately the legend cut off the last bar - it has a value of 3210ish, about 10 higher than the MaxOL (RC) rotation.

Not surprisingly, this doesn't change with spec very much:
Image

So, it seems that seal-weaving isn't going to make a comeback in 3.1 unless things drastically change between now and then.

TLDR version: If you're willing to give up Holy Shield uptime, you get far better returns by replacing Holy Shield with Exorcism than you do by trying to use seal-weaving to take advantage of the SoR glyph.
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