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

[æ]

http://www.frontiernet.net/~gehring/wowcalcs/3.1ptr/ta_perpoint.png
In this graph I have a question; On a non-crusadeweak mob, why is 1/3-crusade not exactly half of 1/5-OHWS? (1% all vs 2% all)

[theckhd]

Parry cap testing indicating 14% cap (56 expertise):

http://elitistjerks.com/f78/t38095-rete ... ons/p3/#73 as well as a couple posts after it with some analysis.

Edit: I can't find any references to exorcism being exempt from crit suppression.

Thanks for the link. I'm busy today but I'll be visiting family all weekend, which means no WoW but lots of time for theorycraft. Expect a flurry of graphs.

@ Echo: The reason your guildy's rotation can't possibly be better than 969 is that he's clumping the 6-second cooldowns, which (as he found out) naturally tends towards a GCD clash that separates them, organically turning into 969. It's very similar to the FCFS analysis linked from the table-of-contents on the first page.

In addition, his ordering is sub-par. He's subbing Exorcism and Avenger's shield in by pushing back Consecration, which is one of our highest-damage moves. While it might make sense to sub Exorcism in for Judgement, it will never make sense to sub it in for Consecration.

Finally, he'd get a much larger threat boost by pulling with AS+Exorcism from range. The way he has it set up, he has to cast Holy Shield while running into melee range of the mob so he can ShoR. If instead he opened with AS+Exorcism, he could then Judge, ShoR, Consecrate, HotR, and then Holy Shield to get a much larger threat lead. In that scenario, you basically get the 969 threat plus a free AS and Exorcism. In his situation, he's giving up some 969 dps to get that AS and Exorcism threat that he could be getting for free on the pull.

[theckhd]

In this graph I have a question; On a non-crusadeweak mob, why is 1/3-crusade not exactly half of 1/5-OHWS? (1% all vs 2% all)

Because that analysis is for 3.1, where OHWS is a 3-point talent giving 4% for the first point and 3% for the next two points. In that analysis I believe I've averaged this to be 3.33% for each talent point, since it's such a good talent that nobody would stop after the first point.

[æ]

I knew it was something obvious
Thanks for the clearification!


Edit: Its alot closer now but im still seeing a 11% (roughly) differance in the graph on a 1pt vs 1pt (1% vs. 3.33%) to all damage done, where 1HWS is doing more than it should per point.

Im assumeing 1HWS is at 286~ on the graph and Crusade is at 76~. 76*3.333=[254~/286]-1=11%~

[Echo]

Thanks Theck

[theckhd]

Edit: Its alot closer now but im still seeing a 11% (roughly) differance in the graph on a 1pt vs 1pt (1% vs. 3.33%) to all damage done, where 1HWS is doing more than it should per point.

Im assumeing 1HWS is at 286~ on the graph and Crusade is at 76~. 76*3.333=[254~/286]-1=11%~

That difference is likely because to calculate each point of crusade, I compared a 5/5 Conviction 3/3 Crusade build with one that had just 5/5 Conviction. Thus, the Crusade talent has the benefit of an extra 5% crit, increasing it's effectiveness.

I could have compared a 0/5 Conviction 3/3 Crusade to 0/5+0/3, but it seems reasonable to include prerequisites, since someone maximizing DPS is likely to take at least 3 in Conviction, if not 5.

[æ]

I re-read the post and I see now that my mind was stuck on this part of it

Now, this test only measures the usefulness of each talent point individually, it's neglecting a lot of the synergistic possibilities that you can create with different specs.

Where I, myself, neglected to read further up in the post more clearly where you state that you’re neglecting "a lot" [not all] synergies. The obvious ones included would be natural additions like 5/5 conv -> Crusade.

It seems like you’re measuring them with only points in one tree. Like for Crusade the spec is http://ptr.wowhead.com/?talent=sZZxf0x while with 1HWS the spec is http://ptr.wowhead.com/?talent=sZA0xA0u rather than a basic for both of http://ptr.wowhead.com/?talent=sZA0xA0uZxf0x where one would think, even with prereqs, each would scale properly being they are of the same mechanic (all damage by %). I saw this because it seems like you’re doing a realistic calculation taking into account what skills people will obviously be getting as prereqs, but I don’t see that following through via both trees, meaning, we are obviously going to be specked into prot down to 1HWS and specked down to Crusade when weighing them against each other.

You say you have a basic spec your working off of (wowhead is bad about their ptr calc btw), but I don’t see how they are scaling so differently unless what I said above is true.

It looks to me like a very difficult thing to weigh properly in a single graph with that many differant talents. I understand that one cant do much more than give a good idea due to changeing trees and weighing one stat means you need to spec tword it up or down a tree and that means another stat will be altered. Oh boy. Ill just shut up and take it as a nice general rule.

[theckhd]

I hadn't noticed that the wowhead link got borked since I posted that - I've updated the link so it should work properly (though it'll probably break if they make any more changes to the talent trees). This is the updated link.

I see that I failed to answer your question properly. You were noticing that 1HWS seemed to be overperforming compared to Crusade, and the answer I gave was the opposite - why I expected Crusade to overperform compared to 1HWS.

Looking at the graph more carefully, I came to the conclusion you did - something was erroneously making 1HWS more potent than it should be. I double-checked the code and found that while the formula worked properly for 1+ points in the talent, it actually gave the wrong value for 0 points (0.97 rather than 1). This was inflating the difference between 3/3 and 0/3 to 13%, rather than 10%. Luckily, since this is the only analysis where 0/3 1HWS ever got used, it should be the only plot that was in error.

I've corrected the formula (and tested it to make sure), and updated the plot. Now 1HWS is roughly 212 TPS per point, to Crusade's 72 TPS per point. This matches my expectation based on the Crusade/Conviction synergy built in to the simulation.


Keep in mind that this is all with the old one-roll code. I'll be re-running this calculation today with the new two-roll code to see if anything changes significantly, though I don't expect it to. In the new version, I may drop down to 3/5 Conviction for the last two configurations so that Crusade doesn't get propped up quite as much by Conviction.

[theckhd]

Parry cap testing indicating 14% cap (56 expertise):

http://elitistjerks.com/f78/t38095-rete ... ons/p3/#73 as well as a couple posts after it with some analysis.

Edit: I can't find any references to exorcism being exempt from crit suppression.

Is that link correct? The post it sends me to is an analysis of whether expertise truncates, and exact determination of the dodge cap. I see no mention of parry anywhere in that thread.

[theckhd]

This link seems to indicate a 14% parry chance for bears.
Tankspot seems to agree.

I wish I could find another EJ reference for this, but for now those two are enough to convince me that 14% is a good value to use for my work. If I get some time maybe I'll do some testing myself on a dummy while I'm messing with simulations today.

[Amaranthea]

Parry cap testing indicating 14% cap (56 expertise):

http://elitistjerks.com/f78/t38095-rete ... ons/p3/#73 as well as a couple posts after it with some analysis.

Edit: I can't find any references to exorcism being exempt from crit suppression.

Is that link correct? The post it sends me to is an analysis of whether expertise truncates, and exact determination of the dodge cap. I see no mention of parry anywhere in that thread.

Heh, oops. That is definitely not the right link.

http://elitistjerks.com/f81/t39944-tank ... es/p5/#104

http://elitistjerks.com/f31/t37032-faq_ ... 0_a/p4/#80

should be more relevant.

[theckhd]

Thanks, that's exactly what I wanted.

Also, I've re-run most of the simulations with the two-roll code, and will be posting the results shortly.

[theckhd]

Before we get into the meat of things, I want to take a step back and make sure the next several posts aren't just a spam of plots with no organization. So let's go over a few basics:

First of all, for people just tuning in at this point in the thread, an explanation of what the terms 'one-roll system' and 'two-roll system' mean can be found here.

If we consider for a second what differences we should expect between a one-roll and a two-roll system, there are a few things that stand out:

• A two-roll system should see a larger benefit from hit and expertise, since misses/dodges/parries reduce your critical strike chance
• A two-roll system should be worse for abilities that can crit, as well as abilities that trigger off of hits (Seal of Blood in particular)
• Abilities that can't crit should see no difference

Based on this, we can make some predictions for what we expect to happen in our case.

• First of all, we expect that the previous comparison of Seal of Vengeance (SoV) to Seal of Blood (SoB) will be affected. In that post, we noted that SoB can out-threat SoV once we have enough hit or expertise, because SoB was very dependent on the melee swing connecting. In a sense, SoB was already suffering from the two-roll mechanics, because it required a melee hit (first roll) before it made it's single hit/crit roll (second roll).
  
  Now, SoB will be even worse off with low hit, because it will effectively be on a three-roll system - one roll to see if the melee swing hits, another to see if SoB hits, and a third to determine if it crits. Since this seemed extreme, I double-checked it in the latest version of Redcape's ret dps spreadsheet (which has been updated to reflect the two-roll nature of our special attacks), and confirmed that his spreadsheet treats SoB exactly the same way.
  
  We should expect this to widen the gap between SoV and SoB at low hit, and make it much harder for SoB to catch up.
  
  
• We don't expect the talent analysis to change much. Conviction might get a little weaker, because it's benefit will be reduced by our misses/dodges/parries, but none of the other abilities care very much about our crit mechanics.
  
  
• We expect the TPS breakdown in terms of different stats to change, because both Hit and Expertise should give us a larger benefit in the two-roll system.

Given all this, the most logical way to approach presenting the updated plots seems to be the following:

1. Show the updated calculations for SoV, showing how everything works out with standard 969, since this is what most tanks will be using on progression in Ulduar
2. After, revisit the question of whether SoB will still be useful to us as tanks, and try and identify specific situations where that may be the case

[majiben]

Be sure to run Conviction versus SotP again.

[theckhd]

First of all, let's take a look at talents. We'll use Majiben's gear set for this, again with Last Laugh as the weapon. Most of this will be the same methodology as the last comparison, but I'll repeat it here because I want these posts to be a little more independently readable:

The goal of this analysis is to test the relative effectiveness (per talent point) of the following talents (abbreviations used in parentheses):

• Seals of the Pure (SotP or S)
• Touched by the Light (TbtL or T)
• Conviction (Conv or V)
• Crusade (Crus or C)
• One-handed Weapon Specialization (1HWS)
• Reckoning (Reck or R)

Setup:
Rotation: 969
Seals Seal of Vengeance (SoV)
Glyphs: Judgement+Vengeance (JV)
Talents: Various combinations of the talents listed above, in order to isolate each talent's contribution (see below)
Gear: Majiben's T8 Progression set

This will be the basic set of talents we'll start from.
51 points in Prot, with 0/5 Reckoning and 0/3 TbtL
6 in Ret

This leaves 14 points that can be put in other places, 15 if we drop to 1/2 Spiritual Attunement. The 3 points in Divinity could also be put in Reckoning.

We'll try and test the effect of each talent individually, by calculating DPS and TPS for the following builds:
1) 0/3 1HWS (assume 3 more points in non-dps talents lower in prot tree)
2) 3/3 1HWS (base configuration)
3) 5 SotP
4) 3 TbtL
5) 5 Reckoning
6) 3 Conviction
7) 3 Conviction 3 Crusade

And then determine each talent's individual contribution through simple subtraction and division. For example, to find out how much each point of 1HWS contributes, we subtract (1) from (2), and divide the result by 3.

You might note that I've changed the analysis slightly from the last version, in that I'm using a 3/5 Conviction build to calculate the contributions from Conviction and Crusade. This should help lessen the synergistic bonus that Crusade gets from Conviction in the analysis, while still accurately represent the prerequisites that someone might have in a Crusade build.

Code: Select all

Talent  DPS   TPS
1HWS   83.8  209.
TbtL   45.7  127.
Crus   28.2   70.3
Conv   17.5   41.2
SotP   14.3   39.6
Reck   11.2   16.3

As we see, not much has changed. Crusade's synergy with Conviction doesn't seem to be nearly as important as earlier assumed, it's still got a strong lead over Conviction. Also, as expected Conviction got a little bit weaker, but not enough to drop it below SotP.

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

Now, let's look at some realistic talent specs. We'll assume the base spec plus 3 points in TbtL, for 54 points in Prot and 6 in Ret. Since Ulduar is not likely to have many Crusade-friendly bosses, this seems like a reasonable base to work from, since it maxes out our two highest-tps talents.

I've also made some revisions to the particular combinations we'll consider. For one, I've changed the Conviction/Reckoning build from 5V+2R to 5V+3R. This is probably a minor thing, but people looking to maximize their TPS could consider spending all 3 of their "discretionary" prot points in Reckoning. By choosing this particular spec, we can compare it more fairly to 5V+3C since both take 8 points in "dps" talents.

I've also added a 3V+3C spec to the list to simulate a PoJ+Crusade "mobility" spec, so we have more accurate data on exactly how this mobility spec stacks up to the 5V+3C version.

Finally, I've removed the 5V+3C-1T (dropping one from TbtL) spec from the list. It always under-performed compared to 5V+2C on regular mobs, and we're not likely to see much in Ulduar that gets the double-benefit from Crusade. In addition, with the changes to our trees, it seems much more likely that people will drop a point out of Spiritual Attunement to get the 3rd point in Crusade rather than dropping TbtL. As such, I didn't see much point in trying to squeeze it into the graph.

Setup:
Rotation: 969
Seals (Glyphs) SoV (JV), SoB (JE), SoR (JR)
Glyphs: Judgement+Vengeance (JV) for SoV, Judgement+Exorcism (JE) for SoB, Judgement+Righteousness (JR) for SoR
Talents: Various combinations of Seals of the Pure (S), Reckoning (R), Conviction (V), Crusade (C)
Gear: Majiben's T8 Progression set


dps plot

I've included SoB and SoR on this plot to serve as a teaser of what's to come in the SoB analysis, so I'll comment on it briefly here. SoB sees a significant reduction in performance with the move to a two-roll system, and takes another hit from our updated 2-piece T8 set bonus (which only affects SoV and SoR). It's now back down with SoR, which we have already concluded was "not a tanking seal." We'll come back to this in a later post to see whether there's anything we can do to salvage SoB.

For now, let's just concentrate on the blue curve (SoV) and see what we can infer from it. First of all, looking at the 5S and 5V data points, we see that SotP is slightly ahead of Conviction for threat, despite trailing it for DPS. At first, this seems counter-intuitive; the point-by-point breakdown showed Conviction slightly ahead for both DPS and TPS. The resolution of this is simply synergy with TbtL, which wasn't present point-by-point analysis - SotP boosts SoV, which scales with spellpower but doesn't crit (and thus sees no benefit from Conviction). Presumably this will change as we increase our chance to hit, which will increase the benefit our abilities see from Conviction.

Another interesting thing to note is that 5S+5R is very close to the 3V+3C "mobility" build (only 4 TPS behind, in fact: 3047 for 3V+3C and 3043 for 5S+5R). So those who are worried about giving up utility talents to push deep ret need not worry too much, since SotP and Reckoning can provide a competitive level of threat without needing to waste points in T2 of Ret to get there.

3V+3C is also pretty competitive with 5V+2C, trailing it by only 7 TPS. And of course, the 5V+3C deep ret build is the best, at 87 TPS ahead of 3V+3C. So those folks who prefer PoJ now know exactly how much TPS they're giving up for their mobility.


TLDR Summary:

• To maximize threat, fill these talents in the following order: 1HWS > TbtL > Crusade > Conviction > SotP > Reckoning. If you're fighting Crusade-friendly mobs only, you can prioritize Crusade above TbtL.
• Spec-wise, anything with Crusade beats anything with SotP, point for point. However, 3V+3C is very close to 5S+5R, for those looking for a way to keep competitive TPS while still picking up utility goodies in Holy or Prot.
• Conviction is slightly worse than SotP for threat at low hit/expertise values, but should pass it as we accumulate more hit. Conviction is strictly superior for DPS, though.
• Reckoning, as weak as it is, is not as terrible as many make it out to be. It's still our weakest option, but since it's already in Protection, it doesn't require us to waste any points in filler to get to. In fact, since it's one of the eligible talents for the 3 points of filler we need to get to the deeper Prot talents, 3/5 Reckoning is a viable alternative to 3/3 Divinity. 2/5 if you want Divine Sacrifice.

In the next post, we'll re-visit the stat breakdown analysis, and see how that's changed.