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

[Thalastor82]

well, I wasn't expecting this...

so I guess that, taking in account the avoidances + treath bonus of expertise, the expertise/stam gem would be preferable to the agi/stam gem if below the soft cap.

But since expertise is present in many new items and everybody uses the V glyphe, I think that very few people will be in this situation and that some agi/stam will be still sitting somewhere in our equipment

[Saiph]

Well, for one, expertise/stam gems are purple, and have nothing to do with yellow sockets.

Yup, that is just me mixing up the color of expertise with hit.

[danceswithchihuahuas]

Do these calculations take into account using alternate rotations? I.E. under 15% health, using HoW every other Judgment, or AS instead of Judgment when on cd?

I understand that HoW TPS is less than that of JoV, but I am hesitant, particularly since it hits harder than a judgment, to take it out of a potential maximum TPS rotation. Same with Holy Wrath. Substituting these for every other Judgment, after all, still allows for the JotJ/JoL/JoW debuffs to remain present on the target (assuming hit cap).

As a matter of fact, after seeing this information I feel only more justified in keeping them in my max TPS rotations. TPS doesn't matter when your ability hits twice as hard and has twice the cooldown, when you are substituting it for a half damage half cooldown ability every other rotation.

edit: I am also feeling justified in taking the SoV glyph again, once I dip below soft cap. Woo 40+ expertise! X_X

[Phonic]

Been reading through pages of the latest updates since Theck posted in my other thread If only I read this beforehand!!

The answer might be buried in there, but can someone explain to me in a very simple and easy way why slower DPS weapons are now better?

And if so, by the graph a few pages back, for threat, Broken Promise out-TPSs my Shiver? Should I switch to that for threat and trash tanking?

[danceswithchihuahuas]

Been reading through pages of the latest updates since Theck posted in my other thread If only I read this beforehand!!

The answer might be buried in there, but can someone explain to me in a very simple and easy way why slower DPS weapons are now better?

And if so, by the graph a few pages back, for threat, Broken Promise out-TPSs my Shiver? Should I switch to that for threat and trash tanking?

I would say that depends on whether or not you're hitting expertise soft cap without Broken Promise. Otherwise Shiver seems to pull slightly ahead. Also note that Shiver boasts more stamina and defensive statistics, which would tell me that unless you're having threat problems, or you're trying to get a big enough threat lead to use Hand of Barkskin effectively, Shiver is a better choice.

As to your other question, I'll just steal directly from Theck here:

* Slow weapons are good for us, because SoV 5-stack proc rewards weapon speed, at roughly 28 TPS per 0.1 weapon speed.
* The only spec-related choice that can change the outcome is Reckoning. Each point in Reckoning will add 24-28 TPS for a 1.5-1.6 speed weapon, while it will add 40-45 TPS for a 2.5-2.6 speed weapon.

[Phonic]

Hmm interesting... Thanks for the info. I don't think I'll "roll back" to Broken Promise, just curious. I ditched Hand of Sac glyph a while back since I'm in a guild where I can almost never afford to lose that 20% (stupid threat-capped locks).

Just always trying to find ways to work on threat! Need to keep my reputation solid! haha

[theckhd]

Do these calculations take into account using alternate rotations? I.E. under 15% health, using HoW every other Judgment, or AS instead of Judgment when on cd?

Yes.

I understand that HoW TPS is less than that of JoV, but I am hesitant, particularly since it hits harder than a judgment, to take it out of a potential maximum TPS rotation. Same with Holy Wrath. Substituting these for every other Judgment, after all, still allows for the JotJ/JoL/JoW debuffs to remain present on the target (assuming hit cap).

Hammer of Wrath does only slightly more damage than Judgement, but less than Judgement+SoV proc. So the damage of a single Judgement cast is greater than the damage of a single HoW cast. HoW also has a shorter cooldown than Judgement, not longer.

Maybe you meant AS? But even that is a DPS loss if it's unglyphed.

As a matter of fact, after seeing this information I feel only more justified in keeping them in my max TPS rotations. TPS doesn't matter when your ability hits twice as hard and has twice the cooldown, when you are substituting it for a half damage half cooldown ability every other rotation.

I'm not sure what you're basing this decision on, but it's not math. You're right that TPS is irrelevant for substitutions, raw damage per cast is what matters. But both HoW and unglyphed AS do less raw damage per cast than Judgement, not 2x more.

edit: I am also feeling justified in taking the SoV glyph again, once I dip below soft cap. Woo 40+ expertise! X_X

SoV was already our highest TPS glyph in 3.2. Nothing's changed about that.

[danceswithchihuahuas]

Ah, I see; I hadn't taken into account the additional SoV proc vis a vis melee strike. Makes sense now. Is this based on Judgment proccing a melee swing, Judgment proccing a SoV (which, the more I think about it, the more likely it seems to be the case), or HoW resetting the swing timer? (I'm sure the information is in there... I just can't seem to find it). If it's the latter, then theoretically by watching my swing timer I can sometimes squeeze a HoW in there to maximize TPS assuming perfect timing if it happens to be the next button on my rotation right as my swing timer resets to 0.

Far as the glyph goes, I was referring to the expertise loss on gear in 3.3, not necessarily any new information presented... Sorry XD!

Thanks for the clarification

[Zibey]

As Theck pointed out long ago - SoV glyph was best tps glyph even if it was all above soft cap.

Also - Judgement, HotR, and ShoR all proc SoV, just as melee attacks do. Hence whenever you hit with them, you also hit with 1/3 of your white attacks damage.
You cant squeeze HoW into rotation instead of Judgement and have more TPS, because HoW dmg < Judge dmg + SoV tick dmg.

[theckhd]

Ah, I see; I hadn't taken into account the additional SoV proc vis a vis melee strike. Makes sense now. Is this based on Judgment proccing a melee swing, Judgment proccing a SoV (which, the more I think about it, the more likely it seems to be the case), or HoW resetting the swing timer? (I'm sure the information is in there... I just can't seem to find it). If it's the latter, then theoretically by watching my swing timer I can sometimes squeeze a HoW in there to maximize TPS assuming perfect timing if it happens to be the next button on my rotation right as my swing timer resets to 0.

Zibey already answered this, but the discussion is at the end of the Ability Damage post. There's even a pretty graph showing the net damage per ability cast.

Also, as far as I'm aware, instant-cast spells don't reset the swing timer, so that's not an issue.

[Eredor]

.... the value of each point in Redoubt will decrease exactly the same way block value does in the region of diminishing returns, and will drop to 0 once you're above the ShoR block value cap. Keep in mind that dropping the talent might bring you back into the DR region again though.

The BV break points at which the points in Redoubt actually become useless for threat should be easily calculated. The cap is 3161 BV, so if you let B be the base block value break point when 1.2*B=3161, then the break point with 3/3 Redoubt is 1.3*B=1.3(3161/1.2). Thus:
If you have over 3434 block value with 3/3 Redoubt, you'll see no difference in threat between 2/3 and 3/3 Redoubt
If you have over 3448 block vlaue with 2/3 Redoubt (3736 with 3/3), you'll see no difference in threat between 1/3 and 2/3 Redoubt
If you have over 3477 block vlaue with 1/3 Redoubt (4109 with 3/3), you'll see no difference in threat between 0/3 and 1/3 Redoubt

Where do I find the equations to calculate block value?

Summing all block value on my armory I have 829.
Rawr tells me I have 2273.
The block value you mention are way way bigger than mine.

Thanks,
Eredor

[theckhd]

3.3 Seal Comparison

Since this is probably the most anticipated result of this patch, I'll skip ahead to this and save the other, less significant calculations for later.

The code for this sim has undergone a considerable overhaul, which is part of the reason it's taken me so long. When I wrote the old version, I did so in probably the least transparent way possible, which made it very difficult to go back and edit it. In the end, I decided to re-write the whole thing to make it simpler to debug.

The results haven't changed that much. The only real change is that Shield of Righteousness now procs all seals, including Seal of Cleave, turning ShoR into "Shield of Seal of Righteous Cleaving" or ShSoRC. Because we really needed another acronym.

The new code is almost certainly correct, but it's still new code, so I encourage those interested to double-check it for me to make sure. I'll go into some detail about how I coded it to help those willing to double-check my math.

Setup:
Rotation: 969
Seals: SoV, SoC, SoR
Glyphs: V (for SoV), no glyphs (for SoCom)
Talents: 1V+3C
Gear: T10 progression set
File: calc_seals.m

First of all, I'm not even bothering with Seal of Righteousness. A quick check of the default 969 simulation shows it's 500 DPS and 1200 TPS behind Seal of Vengeance on a single mob, so there's really not much point in bothering with it. SoR is a leveling seal, and might have niche uses for tanking in cases where you can't DoT or Cleave the mobs, but that's about it.

To aid in the debugging, I'm going to describe the process flow of the code somewhat. If you're not interested in the "under the hood" details, skip down to the pretty graphs.

<MASSIVE NERDERY>

This version of the simulation calculates the damage of each ability for three gear/glyph configurations: standard gear with no glyphs, standard gear with Glyph of Seal of Vengeance (V glyph), and standard gear + V glyph + Libram of Valiance. The results are in the table below:

Code: Select all

Abil    none    V   V+LoV
ShoR    3621  3833  4074
HotR    4309  4561  4828
Cons    4197  4197  4460
JoV     3023  3326  3604
JoC     1495  1645  1773
JoR     2895  3184  3451
AS      2750  2750  2826
HoW     3739  3739  3900
SoV      590   590   624
SoC      549   582   616
SoR      480   480   520
HV      5914  5914  6410
HS      1131  1131  1199
Exor    3071  3071  3210
Melee    909   953  1008

To calculate overall damage, we need two variables: HV stack size (h), and number of mobs (N). So I make a two-dimensional mesh with the meshgrid() command:

Code: Select all

[h,N]=meshgrid(0:5,1:10);

which gives me variables that look like this:

Code: Select all

h =  0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5
     0     1     2     3     4     5

N =  1     1     1     1     1     1
     2     2     2     2     2     2
     3     3     3     3     3     3
     4     4     4     4     4     4
     5     5     5     5     5     5
     6     6     6     6     6     6
     7     7     7     7     7     7
     8     8     8     8     8     8
     9     9     9     9     9     9
    10    10    10    10    10    10

I then calculate the damage of each seal combination for all 60 possible situations:

Code: Select all

sov_dps_nolib = [dmg_arr(1,2)./t_shor + ...                 %shor
                dmg_arr(2,2).*hotr_hits./t_hotr + ...       %hotr
                dmg_arr(3,2).*N./t_cons + ...               %cons
                dmg_arr(4,2).*(1+h./10)./1.5./t_jud + ...   %jud
                dmg_arr(12,2).*h.*N./5./15 + ...               %HV
                dmg_arr(13,2).*avg_HS_pps + ...             %HS
                dmg_arr(15,2)./player_swing + ...           %melee
                dmg_arr(9,2).*h./5.*( ...              %SoV procs
                    1./player_swing + ...              %melees
                    hotr_hits./t_hotr + ...            %hotrs
                    1./t_jud + ...                     %jud
                    1./t_shor) ...                     %shor
                ]./N;  %convert to DPS per target
               
sov_dps_lib   = [dmg_arr(1,3)./t_shor + ...                 %shor
                dmg_arr(2,3).*hotr_hits./t_hotr + ...       %hotr
                dmg_arr(3,3).*N./t_cons + ...               %cons
                dmg_arr(4,3).*(1+h./10)./1.5./t_jud + ...   %jud
                dmg_arr(12,3).*h.*N./5./15 + ...               %HV
                dmg_arr(13,3).*avg_HS_pps + ...             %HS
                dmg_arr(15,3)./player_swing + ...           %melee
                dmg_arr(9,3).*h./5.*( ...              %SoV procs
                    1./player_swing + ...              %melees
                    hotr_hits./t_hotr + ...            %hotrs
                    1./t_jud + ...                     %jud
                    1./t_shor) ...                     %shor
                ]./N;  %convert to DPS per target

soc_dps       = [dmg_arr(1,1)./t_shor + ...                 %shor
                dmg_arr(2,1).*hotr_hits./t_hotr + ...       %hotr
                dmg_arr(3,1).*N./t_cons + ...               %cons
                dmg_arr(4,1)./t_jud + ...                 %jud
                dmg_arr(13,1).*avg_HS_pps + ...             %HS
                dmg_arr(15,1)./player_swing + ...           %melee
                dmg_arr(9,1).*( ...                         %SoC procs
                    soc_procs./player_swing + ...              %melees
                    hotr_hits./t_hotr + ...                    %hotrs
                    soc_procs./t_jud + ...                     %jud
                    soc_procs./t_shor) ...                     %shor
                ]./N;  %convert to DPS per target

This gives me three 10x6 matrices that contain "DPS per mob" values for the three gear/glyph configurations. Note that I'm using the "no glyphs" version for SoC (because it doesn't gain the 10 expertise bonus).

So if sov_dps_nolib(4,4) < soc_dps(4,4), that means that for N=4 mobs and h=3 stacks per mob on average, SoV will do less dps than SoC even without the libram. If you look at the code, soc_procs is limited to min([3 N]) and hotr_hits is limited to min([Htars N]), where Htars can be set to 3 or 4 depending on whether you want the glyph or not. I'm not going to bother showing data for Htars=4, because the difference turns out to be very small and doesn't change the TLDR any.

Also note that this gear set is below the expertise soft cap, so the benefit of that 10 expertise is twice as large as it will be if you're soft-capped without the glyph. This means that this simulation will always give the "worst-case scenario" for SoCommand, and it will only get better with gear.

For the line plots, I can just plot sov_dps_nolib(:,h+1)-soc_dps(:,h+1) to see which seal does more damage as the number of mobs increases for h stacks.

For the mesh plots, I just make a surface plot of sov_dps_nolib-soc_dps and sov_dps_lib-soc_dps. Nothing fancy there.

</MASSIVE NERDERY>

Welcome back. Now that we've gotten our nerd on, let's look at the results.

First, I'll do a simple line plot showing the difference in DPS for a 5-stack and a 3-stack of Holy Vengeance:

The vertical axis is the difference between SoV DPS and SoCom DPS, so a positive number means that SoV does more damage, and a negative number means SoCom does more damage.

The plot is pretty clear, but it's also misleading. If you can maintain a 5-stack on every mob, then in the many-mob limit SoV is bound to win since SoC is limited to 3 procs. In that sense, the plot seems to reflect things accurately. As you drop to 3 stacks of HV, SoCom gains enough ground that it's a better choice for 2-4 mobs.

What makes the graph misleading is that it ignores ramp time. It takes a few seconds to build a 5-stack on a mob, but it takes over 10 times as long to build and maintain a 5-stack on 10 mobs. For ballpark figures, if it takes 5 seconds to build your single-mob stack, it takes nearly a minute to build a 5-stack on 10 mobs with tab targeting. So if the mob pack dies before that minute is up, SoV's value drops thanks to ramp-up effects. It also ignores fall-off, which is a distinct worry for large packs of 6 or more.

What we really want is the average stack size per mob, which goes as 1/N. In other words, if you have just enough time to build a 5-stack on two mobs, then that's roughly the same amount of time it will take to build a 1-stack on ten mobs.

To more accurately see this, we move to a mesh plot that shows how DPS varies with both variables:

The colormap here shows us which seal wins - if it's green, yellow, or red SoV does more sustained DPS, while any blue color indicates that SoCom does more. The black lines are the curves 5/N, 10/N, and 15/N or the average stack size for N mobs over about 10 seconds, 20 seconds, and 30 seconds respectively.

The third line shows that if the mobs live for less than 20 seconds, you're better off using Seal of Command for 3+ mobs. Even at 30 seconds, SoCom is roughly even for 3 mobs, and slightly better for 4 or more. However, for packs that live longer than 30 seconds, you should feasibly be able to spread enough HV stacks around for SoV to win out. Again, that's assuming you're properly tab-targeting - if you're lazy, just use SoCom for 3 or more mobs. And if you're tanking enough mobs that you're going to have trouble maintaining the 5-stack on all of them (say 6 or more), then Seal of Command is the better choice.

Also note that for snap threat, you can look at the 10-second line, where Seal of Command wins for everything but a single mob.

This plot was without using Libram of Valiance; let's see what happens when you equip the libram:

We see that we're now breaking even after about 20-25 seconds thanks to the buff. A lot of this is due to Consecration, which scales with STR and doesn't have a damage cap.

Now, for some example situations:

• Heroics - trash dies in 10-15 seconds, so Seal of Command will easily be the winner. This is how we get 5k+ damage parses on recount for trash packs. Switch back to SoV for bosses though.
• Onyxia whelps - If done properly, these things die quickly, and with many whelps snap aggro is important. Seal of Cleave all the way.
• ICC trash - The trash packs of 4 skeletons would seem like a good place for SoCom, and it's certainly the better choice for snap aggro. But those mobs have a lot of hit points, and can easily live for 30+ seconds. If your group's DPS takes less than 30-40 seconds to kill the pack, then go with SoCom, otherwise use SoV and tab target. If you group up all 8 mobs and AoE them down, just use SoCom.
• Gunship adds - SoCom, even with a 5-stack SoV is only barely ahead, and snap aggro matters here.
• Deathwhisper adds - Again I'd use Seal of Command, as they die quickly and snap aggro is important

TLDR Summary:
Rule of thumb for choosing seals:

• SoV for 1-2 Mobs and bosses
• SoV for AoE tanking things that live for 40+ seconds and that you can reasonably maintain a 5-stack on (so ~6 or fewer mobs at most)
• SoCom for 3+ mobs that die in 30 seconds or less, and basically anything else

Alternatively, if you're lazy and don't feel like tab-targetting, you can simplify this to:

• SoV for 1-2 mobs/bosses
• SoCom for 3+

Also: hooray for the new Shield of Seal of Righteous Cleaving.

[Thalastor82]

Where do I find the equations to calculate block value?

Summing all block value on my armory I have 829.
Rawr tells me I have 2273.
The block value you mention are way way bigger than mine.

Thanks,
Eredor

the block value of your items is only part of the total.

part comes from strenght (1 block value per 2 force), plus you have Redoubt (+30%) and possibly the metagem (+5%) that increase the total.

In the block value set I use for instancing, I have around ~1k block value coming from items, the same coming from strenght (~2k force, full red gemmed) and after kings, meta, redoubt and buffs I come to ~3k blocking. In raid it would be even bigger, but in raid I usually don't use the blocking set (with few exceptions).

If you want to increase the block value gem force and put the meta. A greath trinket for this is the noble deck, it gives 390 force (195 block value) during uptime. Also, you can make use of low lvl items that are perfectly ok for instance even if already unused in new raids. Many drop from ulduar25, for instance.

In any case, the DR mentioned in the previous posts concerns only the treath contribution of the blocking value. In effect, the SotR has diminishing returns, probably to avoid huges slams in pvp. The effectivenes of the blocking value against white non-bleeding attacks is not affected by diminishing returns and, the more you have, the more you block

[theckhd]

Where do I find the equations to calculate block value?

Summing all block value on my armory I have 829.
Rawr tells me I have 2273.
The block value you mention are way way bigger than mine.

Thanks,
Eredor

Rawr should be correct, or if you want an in-game source, Tankadin2 will calculate it for you. It's not surprising that the values I gave are large, since they're near the levels of the ShoR damage cap, which most people don't reach in regular gear.

If you sum your BV from gear, the formula is

Code: Select all

block_value=floor((floor(STR.*0.5) - 10 + Gear_BV + T84pc).*(Redoubt + BV_Meta));

Assuming 3/3 Redoubt:
STR is character sheet strength * 1.1 for kings, plus 291 for raid buffs
Gear_BV is whatever you summed it to be
T84pc = 225 if you have 4-piece T8 equipped
Redoubt = 1.3 (or 1.2 for 2/3, 1.1 for 1/3, etc)
BV_Meta = 0 if you don't have it gemmed, 0.05 if you do

[rocket]

theckd-

about time you started the contour plots .

next i want to see 4d plots : 3d contours with color.