[VUDU] Pet Damage

Witch Doctor
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Highly Rated
Expanded the topic to include all the WD Pets. This is not a guide. This is a collaborative resource for WDs to understand more about Pet builds.
Updated for Patch 2.3

There is a good simulation website for you to import your gear and build:
www.d3planner.com

Melee Pet Attack Speed not updated (changes to BBV-IAS and perhaps other IAS buffs). Spreadsheet (feel free to download and modify as you wish):
https://docs.google.com/spreadsheets/d/1ZwY2AgfCTYu2sBF4uXM9F-8jfy3BH-w1MzuqV8CEXb4/edit?usp=sharing

Generic Pet Damage Formula:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ APS ] x [ Tooltip ] x [ Pet Buff + %Element ] x [ % Skill ] x [ % Elite ] x [ Character Buff + Monster Debuff ] x [ Bane Trapped ] x [ Zei's Stone ] x [ CoE ] x [ F&R ] x [ Zuni6 ] x [ % MonsterType ] x [ CR passive ]

Where [Weapon Damage] is the sum of all the random "per hit" damage on the weapon, rings, amulet, and mojo. The "per hit" damage range on a weapon is the XXXX-YYYY number just below the huge DPS number. For simplicity, we can take the sum of Averages.

+%damage to Demons, Humans, Beasts, Undead, etc are not grouped with [ %Elite ].
Thanks to Darth for alerting the community. [Elite] and [MonsterTypes] are separate multiplier categories.

Pet Buff includes Mask of Jeram and Enforcer gem.

Topics
1. Pet Concepts & General Pet Mechanics
2. Fetishes - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#2
3. Zombie Dogs - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#3
4. Gargantuan - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#4
5. Effective Gearing, IAS, CHC & CHD Analysis - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#5
6. Known Issues or Unsolved Mysteries - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#6
7. Some Popular Legendary Gems & Items - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#7
-- 7.1 Bane of the Trapped
-- 7.2 Gem of Efficacious Toxin
-- 7.3 Mirinae, Teardrop of the Starweaver
-- 7.4 Wreath of Lightning
-- 7.5 Zei's Stone of Vengeance
-- 7.6 Pain Enhancer
-- 7.7 Strongarm Bracer
-- 7.8 Bastions of Will (Focus & Restraint set rings)
-- 7.9 Convention of Elements
-- 7.10 Broken Promises
8. Everything we know about Pet Attack Speed (by AlCalzone) - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#8

Sample MoJ GR42 video - https://www.youtube.com/watch?v=nch2JoHoFOE
==============================================================
1. Pet Concepts & General Pet Mechanics

If you are new to Pets, welcome to the most versatile path for character builds in the whole game! There are some terms you need to get familiar with:

1) Other than Pain Enhancer gem (Bleed proc), Gem of Efficacious Toxin (Poison proc), and Boon of the Hoarder gem (Gold proc), pets do not proc. Patch 2.2, Pets proc Eul-Jang-Do freeze too, thanks to LordofHatred for alerting the community with a video link. Patch 2.3, Pets can now proc Area Damage.

2) Pets have their own characteristics. Their damage, aura, AI, critical hits, Pet Attack Speed all belong to them. In a good way, WD is safe from reflect damage.

3) Pets can benefit from WD character sheet, and can also benefit from Pet buffs. Do not confuse WD & multi-player buffs with Pet buffs. Some skills and items affect WD only, some affect Pets only, and some affect both WD and Pets.

4) To avoid confusion, I have introduced some new terms such as [ Pet APS ] and [ Pet Buff ]. Tasker & Theo and Mask of Jeram are popular items that affect [ Pet APS ] and [ Pet Buff ]. As we currently understand, [ Pet APS ] affects their hit frequency and not their damage numbers, and [ Pet Buff ] has been grouped together with [ %Element ].

5) Pet damage, and their aura can have normal hits and critical hits. We do not apply their pro-weighted [ CHC&CHD ] into the damage formula because they will either get a normal hit that applies the full damage formula, or a critical hit that multiplies [ 1 + (CHD/100) ] to their damage.

6) Critical hit frequency is essential for Pet builds.

7) Most Pet mechanics follow a similar template. The inconsistencies are recorded in Topic (6).

8) Haunt initial hit or jumps proc and refresh the Zuni6 debuff. Subsequent ticks do not. When going through the whole list of WD skills, the principle to consider is "what counts as a hit".
Video proof for Haunt: http://youtu.be/PQEIK2cVGDw

9) Phantasm, Grasp of the Dead, and Piranhas all interact in a similar mechanic to proc Zuni6 debuff. Phantasm has no cooldown, is cheap to cast, refreshes the debuff just like the other 2 skills, tags mobs even as they walk out of the AOE just like the other 2 skills. Do take note of the line of sight requirement for casting these 3 skills. For details, see the illustrations in the section for "Effective AOE of BBV" below.

Phantasm video proof: https://www.youtube.com/watch?v=HA0senH92Pg

10) Locust bug has been fixed in Patch 2.2.1. Works similar to Haunt, initial cast and "jump" procs or refreshes Zuni6 debuff, subsequent ticks do not.

Effective AOE of BBV

Thanks to Zeturion for alerting the community. The BBV AOE isn't as it seems. Tooltip describes the area of influence and we see the visual on the ground, but we actually need to be able to see the Totem, and windows of full-height walls are not counted.

Baseline damage with BBV = 1.87m damage
http://imgur.com/vnVV1RR

Different sides of full height wall = No effect
http://imgur.com/Nndv7s6

Full height wall with window = No effect
(Set up BBV) - http://imgur.com/4wIgRtW
(Despite clear view of Totem) - http://imgur.com/EMbwqkS

Different sides of high-walled corner = No effect
http://imgur.com/1OClvIu

Opposite sides of pillar = No effect
http://imgur.com/urq85ir

Full height pillar = No effect
http://imgur.com/N9wA13N

Low height pillar stump = Positive effect
http://imgur.com/PfbrBrQ

Different sides of corner of low wall = Positive effect
http://imgur.com/LqrrKYo

Opposite sides of low obstacle or pothole = Positive effect
http://imgur.com/sxan4bV

Full height grill or fence = Positive effect
http://imgur.com/UTqR9QC

Pet Attack Speed and BBV (changed in Patch 2.3)

The 4 Scenarios for WD and Pets when using BBV

1) When WD alone is in BBV - Pets hit with higher damage
2) When WD and Pets are in BBV - Pets no longer hit faster, and with higher damage
3) When Pets are in BBV without the WD - Pets no longer hit faster, no higher damage
4) When WD and Pets are outside BBV - no change in damage or hit frequency.
(Based on Patch notes, not frame counted since Patch 2.3)

AlCalzone has done excellent work on Pet Attack Speed. Details are here:
http://us.battle.net/d3/en/forum/topic/13349475072?page=1#8
(Not updated for frame counting since Patch 2.3)

Skills like SH and GF increase %Intel

Edit: 8 Jun'14. We now have confirmation for SH and GF Intel buffs. The basic equation gets affected. The damage is re-calculated based on the buffed Intel value.

Although classified as buff to character sheet, this %Intel should be stand-alone and not grouped with any other modifiers or categories. We cannot multiply this change in Intel because the root-equation is not [ X Intel ], it is [ 1 + (Intel/100) ].

Special thanks to Rakimallah for helping in the test and providing the health globes.
Video proof - http://youtu.be/etrcTAXKKP8
Base Intel = 7097
So, each 10% Intel buff will add 709.7 Intel to the character sheet.

Video log:
Timer 00:10 -- 1 GF, Intel 7807 or (7097 x 1.1)
Timer 00:16 -- 5 SH, 1 GF, Intel 8516 or (7097 x 1.1) + (7097 x 1.1)
Timer 00:26 -- 1 GF expired, remaining 5 SH, Intel 7807 or (7097 x 1.1)
Timer 00:34 -- 5 SH, 1 GF, Intel 8516
Timer 00:39 -- 5 SH, 2 GF, Intel 9226 or (7097 x 1.1) + (7097 x 1.2)
Timer 00:39 -- 5 SH, 3 GF, Intel 9936 or (7097 x 1.1) + (7097 x 1.3)
Timer 00:40 -- 5 SH, 4 GF, Intel 10646 or (7097 x 1.1) + (7097 x 1.4)
Timer 00:41 -- 5 SH, 5 GF, Intel 11355 or (7097 x 1.1) + (7097 x 1.5)

The stacking of SH & GF is additive. Fully stacked SH & GF, we will get (Intel x 1.6).

The rest of the video just shows the fluctuation of Intel changing dynamically in-game. This is the main reason why the Intel and the BBV-APS needs to be re-worked at the basic equation.

Mask of Jeram - Damage Relationships

The buff from Mask of Jeram is added on to %Element group.
Examples:
1) Sycophants (Physical) - MoJ 80% + 20% Phys on gear = 100% as Physical

2) FA (Head Hunters, Poison) - MoJ 80% + 20% Poison on gear = 100% as Poison

3) FA (Tiki, Fire) - MoJ 80% + 20% Fire on gear = 100% as Fire

4) 8 sycophants & FA (Legion) - MoJ 80% + 40% Physical on gear
= all fetishes get 2.2x multiplier as Physical damage

5) 6 sycophant & FA (Tiki) - MoJ 80% + 40% Fire on gear
= 6 sycophants get 1.8x multiplier as Physical damage,
5 melee FA get 2.2x multiplier as Fire damage,
2 torchers FA get 2.2x multiplier as Fire damage.

Test Set-Up
Video proof FA (Tiki & Head Hunters) - http://youtu.be/fFK96x0QIW0
Video proof FA (Legion) - http://youtu.be/hZBqPF8QyWE

Mask of Jeram config: Weapon 112-120, APS 1.5312, Intel 5472, CHC 39.5%, CHD 208%, Poison 20%, Fire 20%, Physical 0%, FA 27%, PTV.

Non-MoJ config: Weapon 112-120, APS 1.5312, Intel 5483, CHC 38.5%, CHD 208%, Poison 20%, Fire 20%, Physical 0%, FA 27%, PTV.

The difference between the masks has a net change of +11 Intel and -1% CHC.

FA (HH, Poison) ----- Melee Hit - Melee Crit ------- HH Hit --- HH Crit
Non-MoJ -------------- 31k to 33k - 97k to 103k --- 22k to 24k - 71k to 74k
MoJ (80%) ----------- 52k to 56k - 163k to 172k -- 38k to 40k - 117k to 124k

Gear already has 20% Poison. So take non-MoJ result divide by 1.2, then multiply result by 2.

FA (Tiki, Fire) --------- Melee Hit - Melee Crit ------- Tiki Hit --- Tiki Crit
Non-MoJ -------------- 31k to 33k - 97k to 103k --- 15k to 16k - 45k to 48k
MoJ (80%) ----------- 52k to 56k - 163k to 172k -- 24k to 26k - 76k to 81k

Gear already has 20% Fire. So take non-MoJ result divide by 1.2, then multiply result by 2.

FA (Legion, Phys) ---- Melee Hit - Melee Crit
Non-MoJ --------------- 26k to 28k - 81k to 86k
MoJ (80%) ------------ 47k to 50k - 145k to 155k

Gear has 0% Physical (notice the melee damage is lower than other 2 FA runes). Apply MoJ directly, multiply by 1.8.

There is a possibility that other skill runes or multi-player buffs will stack into this [ Pet Buff + %Element ] group.

Character Buffs & Monster De-buffs

Skills like BBV, PTV, and S:PtP buff the character damage. Effect of Harrington belt can be stacked here also. Due to the 2-component nature of BBV, we need to breakdown BBV into its damage-modifier and APS-modifier before we can add the 30% to the damage portion. Even the APS-modifier of BBV, we need to breakdown into the original weapon base APS and the portion of IAS from gear and Paragon points. The BBV-IAS is added to the gear and Paragon point portion.

In line with the SH & GF buff principle, I have re-worked the spreadsheet such that the BBV-IAS loops back to the basic damage equation (concerning APS). This fundamental change is better for calculations, as it allows us to expand the spreadsheet to calculate for other pets or even other skills that may or may not involve APS.

Video proof: http://youtu.be/UB2q1bcIpIk

Sacrifice - Provoke the Pack adds to the damage portion similar to PTV.
Using 3 dogs for 15% damage (no longer applicable since Patch 2.1, 3 dogs now provide 60% buff for a short burst), the game calculates it as
[1 + (0.15 + 0.2 + 0.3)]

In multiplayer games, keep adding the damage portion as shown above. If there is stacking of IAS buff, add it to the gear and Paragon point portion and then multiply to the base Weapon APS. The new stacked-IAS APS affects the basic damage equation.

Edit: Although Sac:PtP rune has been changed, the stacking of buffs is still applicable.

Monster De-buffs
Skills like Piranhas, Hex:Jinx, and MC:Paranoia cause the monsters to take more damage. Simply add the de-buffs if the stacking of effects is successful.

The game calculates as 1 + (0.15 + 0.2 + 0.2) = 1.55

Effect of multi-player Strongarm Bracers and Piranhas can be stacked here also.

Finally, add up all the [ Character Buffs + Monster Debuffs ] in the same multiplier group.

Here is the proof:
Video - http://youtu.be/zDz3s33H8Ak

Config: Weapon = 21 damage, Intel = 5208, Weapon APS = 1.2, IAS (gear & paragon) = 46%, Sheet APS = 1.752, CHC = 31.5%, CHD = 227%, Element = 0%, FA skill = 27%.

Sycophant base damage can be seen at Timer 3:17.
Sycophant ---------------------- Hit ------- Crit --------- Remarks
Unbuffed ---------------------- 3,515 --- 11,495 ----- Calculated Base Damage = 3515.25485
PTV (20%) -------------------- 4,218 --- 13,794 ---- Base x 1.2
add Sac:PtP (15%) --------- 4,746 --- 15,518 ---- Base x 1.35
add Hex:J (20%) ------------ 5,449 --- 17,817 ---- Base x 1.55
add MC:P (20%) ------------ 6,152 --- 20,116 ---- Base x 1.75

The new [ APS ] will affect the whole equation real-time.

Monster Types on Items (updated for Patch 2.2)

+%damage to Demons, Humans, Beasts, Undead, etc are not grouped with [ %Elite ].
Thanks to Darth for alerting the community. [Elite] and [MonsterTypes] are separate multiplier categories. [MonsterTypes] is a standalone multiplier applied on relevant monsters.

Video proof (Patch 2.2) - http://youtu.be/t6QjK9fVfQA
Beast -- 4,546,483 to 5,228,455 (15% increase with BoP gem)
Demon -- 4,326,633 to 4,975,628 (15% increase with BoP gem)

Config: 30% Beast, 10% Demon, 15% Elite (toggled with/without BoP gem)
Sever Weapon 2165.94 and Intel 10570
Pig Sticker Weapon 1866.7 and Intel 10520
Ring & Mojo ave damage = 639.5 (adds to respective weapon per hit)
CHC 5%, CHD 324%, Haunt 45%, PTV 20%, BotT 28.5%, Quetz x2.

Beast Haunt = 2506.2 x 106.2 x [1+(0.05x3.24)] x 1.65 x 1.3 x (40/15) x 1.285 x 2 = 4546482.487
Demon Haunt = 2805.44 x 106.7 x [1+(0.05x3.24)] x 1.65 x 1.1 x (40/15) x 1.285 x 2 = 4326632.591

Confidence Ritual passive (updated for Patch 2.3)

CR with PTV and Pet:
Video - http://youtu.be/wKalU2roJ6E

CR with Hex and Pet:
Video - http://youtu.be/PbSA32qk27A

Just completed 2 tests. Confidence Ritual is not grouped with Buff or Debuff. It appears to be a standalone multiplier currently.

Unbuffed, Hit = 14617, Crit = 61685
CR only, Hit = 18272, Crit = 77106 (1.25 multiplier)
CR & PTV, Hit = 21926, Crit = 92527 (1.25 x 1.2 = 1.5 multiplier)

CR & Hex, Hit = 23753, Crit = 100238 (1.25 x 1.3 = 1.625 multiplier)

Standalone multipliers are always great, although the 20-yard requirement makes the skill difficult to rely upon. Also, there is no visible debuff on the target, no icon, and nothing on the ground. In the actual game, it will be hard to know if CR is activated.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
2. Fetishes

This is the formula for Sycophant or Fetish Army damage:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ APS ] x [ Fetish Tooltip ] x [ Pet Buff + %Element ] x [ % Skill ] x [ % Elite ] x [ Character Buff + Monster Debuff ] x [ Bane Trapped ] x [ Zei's Stone ] x [ CoE ] x [ F&R ] x [ Zuni6 ] x [ % MonsterType ] x [ CR passive ]

where [ Fetish Tooltip ]
= 180% for Sycophant-Melee (aligns with highest Element on gear)
= 130% for Sycophant-Dart (Poison)
= 180% for FA-Melee (Element follows your choice of rune)
= 85% for FA-Torcher (Fire)
= 130% for FA-HeadHunter (Poison)

+%damage to Demons, Humans, Beasts, Undead, etc are not grouped with [ %Elite ].
Thanks to Darth for alerting the community. [Elite] and [MonsterTypes] are separate multiplier categories.

Pet Buff includes Mask of Jeram and Enforcer gem.

Note: %Fetish Army Skill applies to Fetish Army and Sycophants (Patch 2.3 update). Sycophants are generally weaker in defense also. They look the same, but are different categories of Fetishes. (Not sure if Patch 2.3 changed anything about fetish survival.)

An example to get your "weapon damage".
Your weapon "per hit" (just below the huge DPS number) = 1582-2014
Ring #1 = 60-118
Ring #2 = 76-140
Amulet = 71-133

Your baseline weapon damage = (1582 + 60 + 76 + 71) to (2014 + 118 + 140 + 133)
= 1789 to 2405
You can either put the Min damage into that formula, or the Max damage, or the Average damage. You will get the damage number for each fetish that is actively attacking.

Mask of Jeram and Enforcer pet damage bonus has been grouped together with %Element.

There are also separate factors to the damage output that is not captured in the generic formula above, and that is the hit-frequency (Tasker & Theo). It does not alter the damage numbers you see on screen, but as the hit-frequency changes, so does your eDPS.

We should also note that stacking all into 1 category is not optimal, based on a mathematical function of multiple input factors. A fair distribution of multipliers will be optimal.
(D x 1.1 x 1.1 x 1.1 x 1.8) < (D x 1.3 x 1.3 x 1.3 x 1.2)

Element Alignment - FA Dagger, FA Tiki, FA Head Hunter.

Another stealth change for Patch 2.04 has been tested and proven. Thanks to Brynmor for alerting the community.

Fetish Army (Ambush) - spawn damage and fetish output Cold damage.
Fetish Army (un-runed, Devoted, Legion) - all fetishes output Physical damage.
Fetish Army (Tiki) - all 5 melee and 2 torches output Fire damage.
Fetish Army (Head Hunters) - all 5 melee and 2 head hunters output Poison damage.

Video proof #1 - http://youtu.be/2hhYhV5ntNo
Using FA (Head Hunters)
Config - Intel 5358, APS 1.7712, CHC 34.5%, CHD 145%, %Phys 35%, %FA 12%, PTV.

All fetishes output baseline damage numbers according to their tooltip 180% (4911 damage) for Melee, and 130% (3547 damage) for Dart. None of them benefited from the 35% Physical. Critical hits exactly match character sheet (1 + CHD/100).

Video proof #2 - http://youtu.be/WkiI2O-vg0I
Using FA (Head Hunters)
Config - Intel 5383, APS 1.7712, CHC 34%, CHD 145%, %Phys 20%, %Poison 35%, %FA 12%, PTV. (summary - pushed up %Poison significantly, and some Intel increase due to the gear swap).

New baseline damage due to Intel changes = 4933.75 (melee), and 3563.3 (dart).

All fetishes enjoyed the 35% damage buff from the %Poison. Melee was 6661 damage, and Dart was 4810 damage. Again, the 20% Phys was completely ignored. Critical hits exactly matched expectations.

Video proof #3 - http://youtu.be/gmAhVn6kDMQ
Using FA (Tiki)
Config - same as proof #2
(since %Fire = 0, we expect all damage numbers to fall back to baseline for 5383 Intel).

As expected, none of the fetishes benefited from %Phys or %Poison. Melee was 4934 damage, and Torch was 2330 damage (only 85% tooltip damage for Torch). All the fetishes became aligned to the Fire element. Critical hits exactly matched expectations.

Video proof #4 - http://youtu.be/E9I8EWgbfew
Using FA (Tiki), Carnevil, and capturing the interaction of Carnevil converting Fire Element FA into Poison Element FA, as well as Physical Element Sycophant into Poison Element Sycophant. Also happened to capture %Area Damage proc in action for both normal hits and critical hits of the WD (fetishes do not proc %Area Damage in the past, Patch 2.3 update allows Pets to proc Area Damage).

Config - Intel 5358, APS 1.6872 (1.2 x 1.406), CHC 39%, CHD 145%, 20% Phys, 35% Poison, 12% FA, 38% Area Damage, PTV, Carnevil.

Damage Type ----------------------- Hit ----------- Crit
Sycophant Melee ------------------ 5,013 ----- 12,281 (benefit from %Phys)
Sycophant Dart --------------------- 4,073 ----- 9,978 (benefit from %Poison)
FA (Tiki) Melee --------------------- 4,678 ----- 11,462 (benefit from %Fire)
FA (Tiki) Torcher ------------------- 2,209 ----- 5,413 (benefit from %Fire)
FA (Tiki) Dart Convert ------------ 4,561 ----- 11,175 (benefit from %Poison)

Some interesting points:
1) FA (Tiki) Melee output less damage than Sycophants despite the 12%FA on gear. This is due to all the 5 Melee and 2 Torchers becoming Fire Element on summon, and %Fire on gear is 0.

2) Carnevil converts 5 nearest Fetish into Dart-shooting fetishes with Poison alignment.

3) Sycophants spawn in alignment with the highest Element on gear (Patch 2.2).

4) %Area Damage stat output the exact AOE damage as the damage hit/crit that procs it. The most obvious visual proof for WD normal hit is at timer 1:34, WD hit at 3435 damage, AOE damage at 1305 (exactly 38%). The most obvious visual proof for WD critical hit is at timer 1:27, WD critical hit at 8416 damage, AOE damage at 3198 (exactly 38% also).

5) Fetishes proc %Area Damage since Patch 2.3 update.

Carnevil Mask - Damage Relationships [Updated for Patch 2.3]

Sample videos to learn about:
- Navigating difficult terrain -
GR52 Carnevil and CoE: https://youtu.be/fGZEYCNsQvc
- Using Broken Promises ring -
GR50 Carnevil and BP: https://www.youtube.com/watch?v=-L9vZpi-Q7A
- Techniques for walls and doors -
GR48 Carnevil: https://www.youtube.com/watch?v=NMYdjFMeAEI
- Techniques for corners and pillars -
GR49 Carnevil: https://www.youtube.com/watch?v=2EqK4F-WXG8

*Generally, you need line of sight for a direct hit, but you do not need a direct hit to make your fetishes shoot around corners or shoot at Reflect Damage elites. In those situations, you can "aim-off" for the AOE skills to proc Zuni6, or Spirit Walk up front to cast the AOE and then come back to shoot at the wall or pillar.

Note: Patch 2.3 changed Reflect Damage to adopt the element of the skill damage.

Special thanks to DoubleTwist for doing all the testing in the PTR server, all I needed was to verify the grouping of multipliers in the Live server. His work can be found here:
http://us.battle.net/d3/en/forum/topic/15538335494#16

This is the formula for Sycophant-Dart or FA-Dart damage:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ APS ] x [ Fetish Tooltip ] x [ Pet Buff + %Element ] x [ %FA ] x [ %PD + SS gem ] x [ % Elite ] x [ Character Buff + Monster Debuff ] x [ Bane Trapped ] x [ Zei's Stone ] x [ CoE ] x [ F&R ] x [ Zuni6 ] x [ % MonsterType ] x [ 3.5 (due to Carnevil) ] x [ CR passive ]

Both the sycophants and fetish army will shoot darts when WD shoots darts, at the same APS as the WD. When the fetishes shoot darts, they convert to the Head Hunters rune damage at 130% tooltip damage. You can calculate the APS breakpoints using 58 frames as the base hit interval for Darts. Or you can refer to the Breakpoint Table here:
http://us.battle.net/d3/en/forum/topic/14527433038?page=1#3

When shooting darts, even the FA-Tiki will also shoot darts. Interesting observation - the Tiki are actually 2 fetishes, one sitting on another's shoulders. It is the lower fetish who releases the dart with each stomp of his left foot.

%Poison element affects all the dart fetishes. Carnevil also converts all the various FA runes into Poison Element as long as they are shooting darts.

%Poison Dart skill affects all fetishes when they shoot darts. %Poison Dart and Simplicity Strength belong to the same multiplier group.

Video proof - http://youtu.be/2qngUC6bvwU

Test config - Weapon 21, Intel 7873, CHC 45.5%, CHD 212%, Poison 55%, FA 29%, PoisonDart 30%, PTV 20%, Rank39 SS 44.5%, APS 1.2 x 1.44 = 1.728.

Screen results
WD dart crit without SS gem = 13,360
WD dart crit with SS gem = 17324
FA-Dart without SS gem = 36,604
FA-Dart with SS gem = 49,134

Calculations
For WD Splinter Dart, [%PD + SS + Buffs + Debuffs] are all grouped together, and [APS] is not in the damage formula. [Tooltip] for splinter is 1.1.

WD crit without SS gem = 21 x 79.73 x 3.12 x 1.1 x 1.55 x [1+0.3+0.2] = 13360.147
WD crit with SS gem = 21 x 79.73 x 3.12 x 1.1 x 1.55 x [1+0.3+0.2+0.445] = 17323.657
FA-Dart crit without SS gem = 21 x 79.73 x 1.728 x 3.12 x 1.3 x 1.55 x 1.29 x 1.3 x 1.2 = 36604.011
FA-Dart crit with SS gem = 21 x 79.73 x 1.728 x 3.12 x 1.3 x 1.55 x 1.29 x [1+0.3+0.445] x 1.2 = 49133.848

%FA skill affects both FA-Dart and Sycophant-Dart (Patch 2.3 update).

When WD is not shooting, all the fetishes revert back to their original configuration (Sycophant, Dagger, Tiki, Head Hunter, etc). They will follow their original Element AI and APS as though Carnevil is switched off.

Video proof: http://youtu.be/h593POesvqA

Carnevil is a standalone multiplier (Patch 2.3)

Test config: Weapon 21, Intel 8077, Poison 19%, PD+SS 88%, PTV 20%, APS 1.68, CHD 236%, FA 30%, Tooltip 130%.
video proof - https://youtu.be/wTDtVUQWfDc
Testing for Carnevil standalone x3.5 or grouped with PD+SS.
3.5 x 1.88 = 6.58, or [1.88 + 2.5] = 4.38

Test results prove that Carnevil is a separate multiplier of 3.5.

Hit = 21 x 81.77 x 1.19 x 1.88 x 1.2 x 1.68 x 1.3 x 1.3 x 3.5 = 45810.32
Crit = 45810.32 x 3.36 = 153922.68
Screen Hit = 45,810, Crit = 153,923

Belt of Transcendence does not show on Detail Sheet

Carried out a proof test with the following config:
Intel without Belt 7472
Intel with Belt 7964
APS = 1.2 x 1.33 = 1.598
CHC 34%, CHD 198%, Poison 19%, MoJ 100%, PTV 20%, FA 30%.

Since the FS summoned will be Poison, I used FA:HH rune to be consistent. You can see the difference in damage was due to the Intel difference. After I matched up the Intel towards the end of the video, the FA and FS hit for exactly the same damage.

So, no worries about the Detail sheet not showing "Fetish Sycophants" when you remove the FS passive and equip the Belt of Transcendence.

Video proof - https://youtu.be/ISocHTzQ3_Q

Gidbinn Fetish - Damage Relationships (last updated Patch 2.06)

The Gidbinn fetish is extremely easy to produce. They last (probably, didn't time exactly) 20 seconds. A total of 3 fetishes is the summoning limit. Subsequent production needs to wait for a fetish to die or expire before the next fetish can be summoned.

1) Base Damage = [ weapon damage x (1 + Intel/100) ] x [ CHC x (1 + CHD) + (1 - CHC) ]
This is basically the character sheet damage divided by the APS. Since CHC & CHD is already factored in pro-rated, the fetishes do not have critical hits. There is no damage range for the fetishes.

Video proof at Test 1.

2) Gidbinn fetishes have no Element. Tried Cold, Fire, Poison, Physical. None of them buffed the fetish damage.

Video proof at Test 3.

3) Mask of Jeram boosts Gidbinn damage as a direct multiplier.

4) For MoJ gear swap, the buff to fetish damage changes real-time. For all other gear swap that affects the character sheet (e.g. Intel or CHC or CHD), the fetish properties get snap-shot upon summon for their whole duration until death or expiry.

Video proof at Test 1 & Test 2.

5) Since the Gidbinn fetishes are significantly inferior, there is no point in conducting further tests with character buffs and monster debuffs. We can happily collect a Forgotten Soul whenever we loot a Gidbinn.

Test 1
video - http://youtu.be/Y09k3XU9VzU

Weapon Damage = 1468.5
APS = 1.4 x 1.17 = 1.638
CHD = 161 %
----------------------- MoJ (80%) --- Non-MoJ
Intel ------------------- 3227 ---------- 3238
Sheet Damage -- 112,883 ------ 111,964
CHC ------------------ 25.5% -------- 24.5%
CHC&CHD multi = 1.41055 ------ 1.39445
Weapon & Intel = 48,856.995 --- 49,018.53

From Non-MoJ swap to MoJ (add 1% CHC and minus 11 Intel),
Damage = 68,354 to 123,037 ( x 1.8 immediately upon swap)

From MoJ back to Non-MoJ (add 11 Intel and minus 1% CHC),
Damage = 124,047 to 68,915 ( / 1.8 immediately upon swap)

Note that the numbers are slightly different because the fetish snapshot the character sheet properties upon summon, and the 68k damage numbers correspond exactly to their respective sheet damage divided by APS.

Test 2
video - http://youtu.be/oQHXnPwzBKg

Added a 400 Intel and 6% CHC bracer with 15% Phys.

At first, this test was very confusing because I was expecting the Gidbinn fetish to benefit from the %Phys. It turns out, after a few gear swaps to verify, %Phys does not benefit them at all.

Test 3
video - http://youtu.be/dgou3_VLz2M

This is an easy confirmation test. Changed several pieces of gear to have 0% Phys, 19% Cold, 20% Fire, 15% Poison.
Intel = 3974, CHC = 31%, CHD = 209%, APS = 1.722, Weapon = 1468.5.
Sheet Damage = 169,769

Test results were exactly in line with calculations. Fetishes did not benefit from any of the Elements. Cancelled all further tests due to the obvious weakness of Gidbinn fetishes.

Proof for [ %Skill ] as a Separate Multiplier

Video 1 - http://youtu.be/zDz3s33H8Ak
Config: Weapon = 21 damage, Intel = 5208, Weapon APS = 1.2, IAS (gear & paragon) = 46%, Sheet APS = 1.752, CHC = 31.5%, CHD = 227%, Element = 0%, FA skill = 27%.

Sycophant base damage can be seen at Timer 3:17.
Sycophant ---------------------- Hit ------- Crit --------- Remarks
Unbuffed ---------------------- 3,515 --- 11,495 ----- Calculated Base Damage = 3515.25485
PTV (20%) -------------------- 4,218 --- 13,794 ---- Base x 1.2
add Sac:PtP (15%) --------- 4,746 --- 15,518 ---- Base x 1.35
add Hex:J (20%) ------------ 5,449 --- 17,817 ---- Base x 1.55
add MC:P (20%) ------------ 6,152 --- 20,116 ---- Base x 1.75

Video 2 - http://youtu.be/QgdFo5uMY4Q
Extension from Video 1 (activating PTV, Sac:PtP, Hex:J, MC:P),
Total stacked damage = 6,152 (hit), 20,116 (crit)
27% FA damage = 7,813 (hit), 25,547 (crit)

When applying 27%FA to the stacked buffs and debuffs, the total damage output was multiplied fully by 1.27. This proves that [ % Skill ] is a separate multiplier.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
3. Zombie Dogs

We are still hoping to get Blizzard's clarification for Dog [ Tooltip ], and Burning Dog Aura.

This is the generic damage formula for Zombie Dogs:
[ Weapon ] x [ 1 + (Intel/100) ] x [ APS ] x [ Tooltip ] x [ Pet Buff + Element ] x [ Buffs + Debuffs ] x [ %Skill ] x [ %Elite ] x [ TMF ] x [ CoE or F&R ] x [ Midnight Feast ] x [ Bane Trapped ] x [ Zei's Stone ] x [ Zuni6 or HT6 ] x [ % MonsterType ] x [ CR passive ]

[ Tooltip ] is not steady at 30%, there is a variable that makes the damage fluctuate around 27.9% to 33%, according to past test observations.

+%damage to Demons, Humans, Beasts, Undead, etc are not grouped with [ %Elite ].
Thanks to Darth for alerting the community. [Elite] and [MonsterTypes] are separate multiplier categories.

Pet Buff includes Mask of Jeram and Enforcer gem.

[ Midnight Feast ] is a stand-alone multiplier because it is not a generic "Pet Buff".

[ TMF ] multiplier changes with the number of Dog passives used -
Thanks to Wachati for providing the simplified formula
[ TMF ] = 4n + 1, where n is the number of dogs.

TMF3 = (4x3) + 1 = 13
TMF4 = (4x4) + 1 = 17
TMF5 = (4x5) + 1 = 21
TMF6 = (4x6) + 1 = 25

From AlCalzone's work in Topic (8), there are 4 combat situations that can be observed:
1. Bite attack -> Bite attack: 54 frames
2. Bite attack -> Claw attack: 62 frames
3. Claw attack -> Claw attack: 60 frames
4. Claw attack -> Bite attack: 52 frames
*see illustration - http://imgur.com/HjIXxPZ

Burning Dog Aura

Damage formula:
[ Weapon ] x [ 1 + (Intel/100) ] x [ APS ] x [ Tooltip ] x [ Pet Buff + Element ] x [ Buffs + Debuffs ] x [ %Skill ] x [ %Elite ] x [ TMF ] x [ CoE or F&R ] x [ Midnight Feast ] x [ Bane Trapped ] x [ Zei's Stone ] x [ Zuni6 or HT6 ] x [ % MonsterType ] x [ CR passive ]

Note 1 - Tooltip says 20% damage, but it is actually 10%. Bug has been reported.
Note 2 - Aura damage scales with [ APS ], but always ticks 2 times per second.
Note 3 - [ Tooltip ] = 0.1 x (30/60) = 0.05
Note 3 - Aura is Fire Element, and can have critical ticks.
Note 4 - %Skill is Summon Zombie Dogs skill.

Video proof - http://youtu.be/ldw7Pc64HLc

Test config - Intel 6746, CHD 276%, MoJ 85%, Fire 0%, PTV 20%, Skill 30%, APS 1.2 x 1.46 = 1.752

Calculations
Tick = [21] x [68.46] x [1.752] x [0.1] x [1.85] x [1.2] x [1.3] / 2 = 363.46
Critical Tick = 363.46 x 3.76 = 1366.61

Calculations match screen results exactly.

Proof for Tall Man's Finger and Midnight Feast

Before we proof MF we first need to proof TMF, so that the logical evidence can tie up nicely. Since [ Tooltip ] for Dog attack is a variable, we will use Burning Dog aura to provide the necessary evidence.

Video - http://youtu.be/b1IyZoqbN5o

Test config - Weapon 21, Intel 5789, CHC 27.3%, CHD 219%, IAS 37%, APS = 1.2 x 1.37 = 1.644, Poison 40%, ZD Skill 30%, PTV 20%.

Test Results

Single Dog Aura = 159 (aura), 506 (aura crit)
Calculation: 21 x 58.89 x 0.05 x 1.644 x 1.2 x 1.3 = 158.58
Aura Crit = 158.58 x 3.19 = 505.87

When TMF is added - Intel 6288, CHC 32.8%, CHD 263%.

TMF3 Aura = 2,236 (aura), 8,118 (aura crit)
Calculation: 21 x 63.88 x 0.05 x 1.644 x 1.2 x 1.3 x [13] = 2,236.2685
Aura Crit = 2236.2685 x 3.63 = 8117.6546

TMF4 (Zombie Handler) Aura = 2,924 (aura), 10,615 (aura crit)
Calculation: 21 x 63.88 x 0.05 x 1.644 x 1.2 x 1.3 x [17] = 2,924.3512
Aura Crit = 2924.3515 x 3.63 = 10,615.39

TMF4 (Midnight Feast) Aura = 4,387 (aura), 15,923 (aura crit)
Calculation: 21 x 63.88 x 0.05 x 1.644 x 1.2 x 1.3 x [17] x [1.5] = 4,386.5268
Aura Crit = 4386.5268 x 3.63 = 15,923.092

TMF5 (MF + ZH) Aura = 5,419 (aura), 19,670 (aura crit)
Calculation: 21 x 63.88 x 0.05 x 1.644 x 1.2 x 1.3 x [21] x [1.5] = 5,418.6507
Aura Crit = 5418.6507 x 3.63 = 19,669.702

TMF6 (MF + ZH + FL) Aura = 6,451 (aura), 23,416 (aura crit)
Calculation: 21 x 63.88 x 0.05 x 1.644 x 1.2 x 1.3 x [25] x [1.5] = 6,450.7794
Aura Crit = 6450.7794 x 3.63 = 23,416.329

Midnight Feast

Added in MoJ to the TMF test config. New Intel = 6917. Used MF + FL passives for TMF5 Dog. MoJ = 85%.

Video - http://youtu.be/20Y_kq680P4

If Midnight Feast is a "Pet Buff", then it will be grouped together with MoJ. If Midnight Feast is not a generic "Pet Buff", it will be a stand-alone multiplier since it cannot fit into any of the group multipliers.

Test result = 11,012 (aura), 39,972 (aura crit)
Aura = 21 x 70.17 x 0.05 x 1.644 x 1.2 x 1.3 x 21 x [1.85] x [1.5] = 11,011.575
Aura Crit (at 263% CHD) = 11011.575 x 3.63 = 39,972.017

Rabid Dog

Patch 2.1.2 has brought about somewhat stable test results for us to identify some parts of the Rabid Dog mechanics.

1) For each melee hit from the dog, the series of DoTs will either be normal or critical ticks. The first tick determines the rest of the ticks. There is no co-relation for the DoT to follow the melee normal/critical hit. The melee hit can be normal, and the subsequent series of DoTs can be critical, or vice versa, or they can all be normal or critical.

2) The series of critical ticks are also white numbers. There are no yellow numbers for Rabid ticks.

3) The series of DoT ticks can stack. If the dog hits fast enough, and the series of DoTs have not fully played out, they will stack and you can sometimes see the white numbers greater than the yellow numbers if you can buff the dog to hit fast enough to stack a few ticks.

4) The sum of each series of DoTs will be the same as each melee normal/critical hit. Due to the [Tooltip] being a range instead of the fixed 30%, the sum of DoTs do not exactly add up to be the same number as the melee normal/critical hit. However, by the time all the ticks play out, you can be assured that Rabid rune does double the damage of the unruned dog.

5) There are either 4 ticks or 5 ticks in each series. This is most probably due to the synchronization of the visual tick, in the same context of sub-ticks and DoT mechanics. After adjustment of first-last visual tick, we can roughly identify all the series of ticks to be:
3 ticks to total 80% of the total DoT (around 26.7% each tick)
1 tick at around 20% of the total DoT

With enough Pet APS buffs, we can have moments where we stack 4 attacks within any rolling 3 sec period, and that's when you will see the Rabid dot doing similar damage or greater than a critical melee hit.

The more obvious method is to use several small dogs to hit and let their Rabid stack. (Timer 0:50 and 1:56 of the video proof).

Test Config
Weapon 21, Intel 4760, CHC 14%, CHD 82%, IAS 26%, APS = 1.2 x 1.26 = 1.512.
If applicable, weighted CHC&CHD = [1 + (0.14 x 0.82)] = 1.1148

Calculated normal hit, 21 x 48.6 x 0.3 x 1.512 = 462.94
Calculated critical hit, 1.82 x 462.94 = 842.558
If critical ticks were disabled, weighted CHC&CHD will lead to 1.1148 x 462.94 = 516.09 total DoT damage

Video - http://youtu.be/60BewFgN7jA

There were some critical melee hits (Timer 0:51 and 1:53), but they are not relevant to this test.
Claw hit #1 -- 446 (normal hit)
Rabid dots -- 123, 123, 123, 93. (normal DoT, total - 462)

Claw hit #2 -- 467 (normal hit)
Rabid dots -- 139, 247, 247, 216, 77
(adjust to fit pattern) -- 185, 247, 247, 247 (critical DoT, total - 926)

Claw hit #3 -- 434 (normal hit)
Rabid dots -- 139, 247, 247, 216, 62
(adjust to fit pattern) -- 170, 247, 247, 247 (critical DoT, total - 911)

Claw hit #4 -- 457
Rabid dots -- 225, 225, 225, 169 (critical DoT, total - 844)

From the results of the DoT ticks, it is clear the whole series of DoTs will either be normal ticks or critical ticks. The weighted CHC&CHD multiplier is not involved in the damage formula.

Overall, we can expect to get the 30% immediate damage + 30% decay damage to total about 60% Tooltip, and if we allow the Dog to keep attacking, we should be getting steady 2x damage versus un-runed Dog.

This section will be updated if someone can provide more accurate results.

Chilled to the Bone

Similar to all the dog runes, the [Tooltip] is not a fixed number. This section will be updated if there is clarification from Blizzard or other players with accurate test results.

Patch 2.2 introduced this new rune, as Cold element. The cold dogs apply 15% debuff to their targets, which is grouped together with the [Buff + Debuff] multiplier.
Video proof - http://youtu.be/c6RiDaGwGYc

Fetish crit with PTV = 32,490
==> Fetish crit is (32,490 / 1.2)
Fetish crit with PTV and Cold Dog 15% debuff = (32490/1.2) x 1.35 = 36551
as shown on screen.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
4. Gargantuan

Patch 2.3, anything regarding BBV and Pet Attack Speed is outdated. According to Patch notes, the Pets no longer hit faster when inside BBV.

Before I begin, much of the work has been done by Nubtro more than a year ago:
http://us.battle.net/d3/en/forum/topic/9245624978#8

This is the generic damage formula for Gargantuan:
[ Weapon ] x [ 1 + (Intel/100) ] x [ APS ] x [ Tooltip ] x [ Pet Buff + Element ] x [ Buffs + Debuffs ] x [ %Skill ] x [ %Elite ] x [ Midnight Feast ] x [ Bane Trapped ] x [ Zei's Stone ] x [ SMF ] x [ CoE or F&R ] x [ Zuni6 or HT6 ] x [ % MonsterType ] x [ CR passive ]

+%damage to Demons, Humans, Beasts, Undead, etc are not grouped with [ %Elite ].
Thanks to Darth for alerting the community. [Elite] and [MonsterTypes] are separate multiplier categories.

Pet Buff includes Mask of Jeram and Enforcer gem.

[ Midnight Feast ] is a stand-alone multiplier because it is not a generic "Pet Buff".

[ SMF ] splits Gargantuan into 3 small Gargantuans, each x1.5 standalone damage. If all 3 are fighting, we get x4.5 multiplier.

Gargantuan has a base attack speed of (1/1.4 secs), or 84 frames interval. Buffs to Pet Attack Speed such as T&T glove or BBV are added up, and then divided from the base attack speed.

Example, 47% T&T and BBV.
Garg will attack at 84 / (1.47 + 0.2) = 50.3 frames interval

Big Stinker

This rune is straightforward.

The [ Tooltip ] for
Garg melee (Poison element) = 100% or x1
Stinker cloud (Poison element) = 45% or x0.45

Stinker cloud ticks once every second.

Good news is that Garg and Stinker cloud can both get critical hits.

Video proof - http://youtu.be/o_67q-ICrMk
Test config - Weapon 21, Intel 7442, CHC 47.4%, CHD 274%, PTV 20%, APS = 1.2 x 1.43 = 1.716.

Garg hit = 21 x 75.42 x 1.716 x 1 x 1.2 = 3,261.4021
Garg crit = 3261.4021 x 3.74 = 12,197.643

Stinker cloud = 21 x 75.42 x 1.716 x 0.45 x 1.2 = 1467.6308
Stinker crit = 1467.6308 x 3.74 = 5,488.9391

Calculations match screen damage exactly.

Wrathful Protector

Patch 2.1 has "fixed" Garg: Wrathful Protector damage formula.

The Gargantuan: Wrathful Protector damage formula:
[ Weapon ] x [ 1 + Intel/100 ] x [ APS-Snapshot ] x [ Tooltip ] x [ Pet Buff + Element ] x [ Buff + Debuff ] x [ %Skill ] x [ %Elite ] x [ Midnight Feast ] x [ Bane Trapped ] x [ Zei's Stone ] x [ SMF ] x [ CoE or F&R ] x [ Zuni6 or HT6 ] x [ % MonsterType] x [ CR passive ]

where [ Tooltip ] = 575% as Fire element.

Edit: Looks like I got my expectations wrong! The inconsistency in the coding is rather disappointing. Patch 2.1 removed the [ APS ] multiplier instead of the [ APS-Snapshot ] multiplier. This means, at the moment you summon your Garg:WP, the [ APS-Snapshot ] is fixed as a multiplier for the whole duration of its fight. All the other Pets (including other Garg runes) and the WD react real-time to APS changes!

3 videos as proof:
Video 1 - http://youtu.be/sy7wVnqVb8c
Testing if Garg:WP is still considered an "Ally" when he is inside the BBV buff. The scenario where both WD and Garg were inside the BBV AOE was the tell-tale sign that the [ APS ] got snapshot.

WP is a "Pet" as well as an "Ally". BBV specifically buffs all allies within the AOE. That means, WD receives the BBV damage buff and Garg also receives the BBV damage buff, if both of them are within the BBV AOE. If Garg alone is in the BBV AOE, add 0.3 to [ Buff + Debuff ] multiplier. If WD alone is in the BBV AOE, add 0.3 to [ Buff + Debuff ] multiplier. If both are in the AOE, add 0.6 to the [ Buff + Debuff ] multiplier. If both are outside the AOE, add nothing to the [ Buff + Debuff ] multiplier.

Test config - Weapon 21, APS = 1.2 x 1.334 = 1.6008, Intel 7495, CHD 244%, PTV 20%, MoJ 92%, Enforcer 24% (rank 30).

BBV-APS = 1.2 x 1.534 = 1.8408

Screen results -
Normal Hit = 38,043, Crit = 130,867
Both WD and Garg inside BBV, Hit = 57,064, Crit = 196,301
Garg only inside BBV, Hit = 47,554, Crit = 163,584

Calculations -
No BBV Hit = 21 x 75.93 x 1.6008 x 5.75 x 2.16 x 1.2 = 38042.81 (Crit = 130867.26)
Both inside BBV, Hit = 21 x 75.93 x 1.6008 x 5.75 x 2.16 x 1.8 = 57064.21 (Crit = 196300.89)
Garg only in BBV, Hit = 21 x 75.93 x 1.6008 x 5.75 x 2.16 x 1.5 = 47553.51 (Crit = 163584.08)

Video 2 - http://youtu.be/OR7Kn7xBl-8
Confirmation test on Garg:WP with snapshot APS upon summon. Higher damage due to buffed APS conditions upon summon even after WD walked out of the BBV AOE. When Garg alone was inside the BBV and WD walked out, he was hitting for 54,683 when summoned under BBV-APS compared to 47,554 when summoned without BBV in Video 1. That difference is exactly accounted for in the 20% IAS buff provided by BBV at the time of summon.

Calculations -
Both inside BBV, Hit = 21 x 75.93 x 1.8408 x 5.75 x 2.16 x 1.8 = 65619.57 (Crit = 225731.32)
Garg only in BBV, Hit = 21 x 75.93 x 1.8408 x 5.75 x 2.16 x 1.5 = 54682.97 (Crit = 188109.43)

Video 3 - http://youtu.be/CaAK49opciM
Confirmation that Fetish damage still react to WD [ APS ] dynamically, in contrast to Garg:WP [ APS-snapshot ].

Although the Tooltip does not describe, Wrathful Protector has the Cleave ability to hit surrounding mobs in the same swipe.

Video proof - http://youtu.be/JrAdGQrPgwg

Restless Giant

When activated, this rune has 2 impacts on Garg damage:

The "Gain 200% damage" changes the [ Tooltip ] to 300%.
The "Gain 35% attack speed" adds 35% to the same group as T&T glove and BBV for Pet Attack Speed calculations. Example using 47% T&T glove and no BBV,
Garg hit interval = 84 / (1.47+0.35) = 46.2 frames

Test config - Weapon 21, Intel 6922, CHD 263%, IAS 37%, APS = 1.2 x 1.37 = 1.644, PTV 20%, MoJ 85%

Video (from timer 1:20) - http://youtu.be/JrAdGQrPgwg

Test Results
Rune activated = 24,219 (hit), 87,913 (crit)
Rune not activated = 8,073 (hit), 29,304 (crit)

[Tooltip] = 1 without rune activation, [Tooltip] = 3 with rune activated.
21 x 70.22 x 1.644 x 3 x 1.85 x 1.2 x 1.5 = 24,218.507
21 x 70.22 x 1.644 x 1 x 1.85 x 1.2 x 1.5 = 8,072.8356

Bruiser

There was some confusion due to the text in the Bruiser's Tooltip. The Tooltip box shows overall Fire Element, but the text within describes the Garg's usual hit as Physical, while the Bruiser hit as Fire.

Both the regular hit and the Bruiser hit are Fire element. Bruiser does double damage.

To prove this, I needed to swap bracers during the fight to toggle between Physical-Fire elements.

Test config - Weapon 21, APS = 1.2 x 1.334 = 1.6008, Intel 7495 (for 20% Fire bracer), Intel 7493 (for 20% Physical bracer), CHD 244%, PTV 20%, MoJ 92%, Enforcer 24% (rank 30).

BBV-APS = 1.2 x 1.534 = 1.8408

Video - http://youtu.be/03PELe28Jpg

Screen results -
Fire bracer,
Normal Hit = 7,231, Crit = 24,873
Bruiser Hit = 14,461, Crit = 49,747
Physical bracer,
Normal Hit = 6,616, Crit = 22,760
Bruiser Hit = 13,232, Crit = 45,519
Garg and WD in BBV, Hit = 9,510, Crit = 32,715
Garg only in BBV, Hit = 6,616, Crit = 22,760
(Video timer 2:10 to 2:20 prove the real-time APS affecting the damage per hit)

Calculations -
Fire bracer,
Normal Hit = 21 x 75.95 x 1.6008 x 1.00 x 2.36 x 1.2 = 7230.65 (Crit = 24873.44)
Physical bracer,
Normal Hit = 21 x 75.93 x 1.6008 x 1.00 x 2.16 x 1.2 = 6616.14 (Crit = 22759.53)
Garg and WD in BBV, Hit = 21 x 75.93 x 1.8408 x 1.00 x 2.16 x 1.5 = 9510.08 (Crit = 32714.69)
Garg only in BBV, Hit = 21 x 75.93 x 1.6008 x 1.00 x 2.16 x 1.2 = 6616.14 (Crit = 22759.53)

Conclusion - The Tooltip Header aligns the overall element of the skill and rune.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1 [b][/b]
5. Effective Gearing, IAS, CHC & CHD Analysis

The most "value" for each gear slot will probably depend on the slot.

1) Amulet is the only place to get 100% CHD.

2) Glove, Mojo, Amulet can get 10% CHC, while others cap at 6%

3) If CHC is not in your build (>50% sheet CHC recommended), then don't bother thinking about CHD. Amulet + Weapon + sheet default provides 280% CHD already. If you have 50% CHC, you get 0.5D + 1.9D = 2.4D on average. It's a high "value" multiplier with only 2 pieces of CHD.

4) MOJ alone is worth nearly 100% Element (grouping remains unchanged as at Patch 2.1.1). Use 90% as example.

5) Amulet, Bracer and SOJ can provide 20% Element each.

If we follow the balanced recommendations from Point 1 to 5 (mostly dual factors only, most players will be able to attain such gear). We actually have a few gear slots to take care of Toughness needs.

In terms of gearing, it is very much individual preference, and there is no "best" method for gearing. I do, however, have some analysis and insights to share.

[ % CHC&CHD Multiplier ] - Analysis and Gearing Impact

Using the pro-rated formula per hit, [ CHC x (1 + CHD) ] + [ 1 - CHC ], we can simplify the formula to [ 1 + (CHC/100 x CHD/100) ].

We do not use this formula in estimating our eDPS because Pets do not go for "long-run averaging", Pets go for high crit-frequency, kill and move on. We use it to evaluate for Mystic re-roll purposes only.

Here is a list of typical gearing configuration and corresponding multiplier:

CHC --- CHD --- Pro-rated Multiplier
41 ------ 400 ----- 2.64
42 ------ 400 ----- 2.68
45 ------ 400 ----- 2.8
50 ------ 400 ----- 3.0
55 ------ 400 ----- 3.2

CHC --- CHD --- Pro-rated Multiplier
46 ------ 350 ----- 2.61
48 ------ 350 ----- 2.68
52 ------ 350 ----- 2.82
58 ------ 350 ----- 3.03

From the typical variations, I have identified the multipliers as -
2.52 to 2.68 = easy to gear, most players can casually achieve this set up
2.8 to 3.0 = requires some effort to gear
>3 = hard to gear, requires a lot of DPS stats

What is the significance of this analysis?

It shows that the 2.8 multiplier is only 4.5% higher damage than the easy gearing path.
It shows that the >3 multiplier is only 7.1% higher damage than the configuration that only requires reasonable effort to gear.
The >3 multiplier is only 12% higher damage than the easy gearing multiplier of 2.68.

When we have a multiplier of say 3 vs 2.68, we feel as though the 2.68 is much weaker because the character sheet says so. Is that really true?

Now we recall the overall fetish damage formula,
[ Weapon damage ] x [ 1+(Intel/100) ] x [ APS ] x [ Fetish Tooltip ] x [ %MoJ+%Element ] x [ % Skill ] x [ % Elite ] x [ Character Buff + Monster De-buff ] x [ Bane Trapped ] x [ Zei's Stone ]

In the game, we get a %CHC chance to critical hit at Damage x [ 1 + (CHD/100) ].
Otherwise, for the (1 - %CHC) chance we hit at normal Damage.

The [ %CHC&CHD ] is only one of the many components. If there is any "untouched" multiplier on the gear set-up ( multiplier = 1 ), a simple introduction of one piece of gear stat is more than enough to make up for that damage difference. Perhaps 12% vs Elite damage, or 12% Fetish Army.

Even if the group multiplier already has some value, say 90% MoJ + 20% Phys = 110% Element. If we just add another %15 Element from one gear stat, we get 2.25/2.1 = 7.15% increase, which makes the easy gearing path (2.68 multiplier) out-perform the higher CHC&CHD gearing (2.8 multiplier) category.

Another example contributed by Vaynard,
So adding another 15% to this would give you 2.25/2.1 = 7.15% increase.
Let's say you want to decide between 6% CHC and 15% additional Element damage and currently have a 2.68 crit multiplier with 42% CHC and 400% CHD. Adding 6% CHC would increase your damage by 9% which is better than the 7.15% from additional Element damage. With +20% Element providing 9.5% increased damage, it would be a little better than CHC in this example.

Conclusion

When we analyse objectively and look beyond the sheet e-peen, we begin to identify the best "value" per slot and "value' per gear stat. If we do not need so much CHC or CHD, then the stat could provide the important Vit or AR or %Life needed for us to survive higher difficulty levels. Previously not stated in Points 1-5 above, glove, helm, mojo, amulet, weapon can roll 750 Vit, whereas chest, shoulder, boots, pants, rings, bracers can only roll 500 Vit. With careful gear planning, dual-factor DPS gear can possibly provide the same damage output with far superior Toughness for survival.

Example 1: Cindercoat and Amulet. Let go of the 500 Vit on the chest and let the amulet have 750 Vit. Let go of the %Fire on the amulet because the chest provides it. You can have the same %Fire, the same damage output, and extra 250 Vit just from this 2-piece optimization.

Example 2: Chest and Pants can get >550 Armor while other slots are limited to <400 Armor. In terms of gear "value", the overall configuration can be optimized when we allocate certain stats to specific gear slots.

Fallacy of the CHC&CHD 1:10 Ratio

This section is added on 13 June 2014 to debunk the stupidity and flawed logic spreading in the WD forums.

There is no doubt that CHC & CHD work as a pair, but the sequence in which we gear for the multiplier makes a very big difference.

We begin our analysis from the basic Character Sheet and Paragon Points:
--------------- CHC ----- CHD
Base --------- 5% ------ 50%
Paragon ----- 5% ------ 50%
==> Add most valuable core items
Weapon ----- 0% ------ 130%
Mojo -------- 10% ------- 0%
Amulet ----- 10% ----- 100%
Glove ------- 10% ------ 50%
==> Multiplier is now at [ 1 + (0.4 x 3.8) ] = 2.52

This value should be easily within reach of all the casual players when they combine all their gear stats. So casual players can still enjoy the game with good distribution of multipliers.

Each piece hereafter is adding 6% CHC and/or 50% CHD (2 Rings, Bracer, Helm, Belt).

1st addition,
Add 6% CHC ----- 1 + (0.46 x 3.8) = 2.748
Add 50% CHD --- 1 + (0.4 x 4.3) = 2.72
CHC wins. Optimum config becomes 46% CHC and 380% CHD (9.05% damage increase).

2nd addition,
Add 6% CHC ----- 1 + (0.52 x 3.8) = 2.976
Add 50% CHD --- 1 + (0.46 x 4.3) = 2.978
CHD wins. Optimum config becomes 46% CHC and 430% CHD (8.37% damage increase).

If the above 2 additions were contributed by just 1 piece of Ring, the multiplier is almost 3 and the WD can focus on %Element, %Elite, or Mitigation.

3rd addition,
Add 6% CHC ----- 1 + (0.52 x 4.3) = 3.236
Add 50% CHD --- 1 + (0.46 x 4.8) = 3.208
CHC wins. Optimum config becomes 52% CHC and 430% CHD (8.67% damage increase).

4th addition,
Add 6% CHC ----- 1 + (0.58 x 4.3) = 3.494
Add 50% CHD --- 1 + (0.52 x 4.8) = 3.496
CHD wins. Optimum config becomes 52% CHC and 480% CHD (8.03% damage increase).

Used up both Rings for CHD. Only 1 item (WH Belt) can increase CHD further.

5th addition,
Add 6% CHC ----- 1 + (0.58 x 4.8) = 3.784
Add 50% CHD --- 1 + (0.52 x 5.3) = 3.756
CHC wins. Optimum config becomes 58% CHC and 480% CHD (8.24% damage increase).

6th addition,
Add 6% CHC ----- 1 + (0.64 x 4.8) = 4.072
Add 50% CHD --- 1 + (0.58 x 5.3) = 4.074
CHD wins. Optimum config becomes 58% CHC and 530% CHD (7.66% damage increase).

7th addition,
Add 6% CHC ----- 1 + (0.64 x 5.3) = 4.392 (no more CHD slot available)
Max config at 64% CHC and 530% CHD increases damage further by 7.81%.

Note #1: Weapons with in-built CHC or CHD will have some minor impact. Need to re-calculate.

Note #2: Looking at the step increments, %CHC and %CHD will always be better than %IAS, except for Oculus ring with 9% IAS. For Paragon points, always max out IAS first.

Note #3: The MoJ+Element above 140% or 150% is probably the cross-over point where CHC or CHD is better. Below 140%, adding 20% Element where possible is always the best stat (benefit >8.33% damage).

Conclusion

The way to build this multiplier is always pushing up CHC first (leading stat), then push CHD (lagging stat). Even with a lower multiplier, I will advise to push CHC above 50% first, not to mention that the multiplier difference is only 0.002.

Like tossing a coin for each hit on single targets, it is essential to have high critical hit frequency. Not to ignore that TMF burning dog aura and Garg Stinker aura can crit also, as at Patch 2.06.

Considering the exact same multiplier, in a scenario where 7 hits are needed to kill a mob, chances are >50% CHC will kill the mob faster, or at the same rate as the <50% CHC player. In a scenario where 8 hits are needed to kill a mob, the >50% CHC WD will definitely clear the whole rift faster. The <50% CHC WD will probably need 1 extra hit all along the journey. For fast moving mobs, we may not even get the chance for the next hit, so every hit counts.

For Pet path, we do not go for the long-run averaging and pro-weighted multiplier concept. The multiplier is only for Mystic re-roll consideration. Crit frequency is essential for Pet WDs, regardless of low-end gearing or top-tier gearing.

Last but not least, in the whole item by item analysis above, never was there a configuration where 1CHC:10CHD provided good results. Hope this proof can stop the rubbish from spreading and misleading people. When you look at your various gear slots, you'll find the possible rolls are usually in favour of CHC. That's just the way item stats roll. Worst-case comparison is 6 CHC against 50 CHD (unfair advantage to CHC). Other slots provide a whopping 10 CHC. There are two slots that provide the majority of the CHD and that's amulet and weapon socket. You will need to have a significant disproportionate ratio for 50 CHD to be better than 6 CHC.

In a previous reply to help a Jade player, I wrote:
----------
In your case of 40 CHC and 360 CHD.
CHC -- CHD -- Multiplier
40 ----- 360 ----- 2.440
40 ----- 410 ----- 2.640 (you thought getting closer to 1:10 is better?)
46 ----- 360 ----- 2.656 (6 CHC is better than 50 CHD)
----------
I've thought of another way to explain to you ratio troopers. Hopefully you all will finally get it.

The CHC&CHD function, getting to the ratio balancing point is a minima, among many sets of minima curves. It is the worst-case-scenario for damage output. In economic and engineering, it is the point of greatest efficiency, using the smallest combination of resources or input. Minima in maths has its purpose, but not for D3 damage output. On either side of the minima point, whether you push CHC or CHD up, you are going to get better results. A more appropriate application for minima can be the Armor/AR gearing efficiency, although the overall mitigation is still "the more the merrier".

The CoB APS function for wasted damage is a maxima, among many sets of maxima curves. It is the best-case-scenario for damage output. In economics and engineering, this method is used to maximise profits or output of technical purposes. On either side of the maxima point, whether you increase or decrease APS, you are going to get worse results.

Details of CoB Mechanics (Part 1) Wasted Damage can be found here:
http://us.battle.net/d3/en/forum/topic/9377379828

The two types of turning points are actually opposite.

Here are 2 videos to illustrate the usefulness of CHC for Pet builds:

CHC26 video - http://youtu.be/-IUEGmRvup0
Counted the 1st 100 hits, got 26 crits.

CHC51 video - http://youtu.be/FB0TeM0XIzs
Counted the 1st 100 hits, got 53 crits.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
6. Known Issues or Unsolved Mysteries
Updated for Patch 2.1.1.

1. Burning Dog aura is at 10% Tooltip damage, not the listed 20%.

2. Zombie Dogs have 2 types of attack animation, with different hit intervals.

3. Zombie Dogs have in-built damage range. We do not get exactly 30% Tooltip damage.

4. Zombie Dogs have short paws. Even the big TMF Dog cannot hit from behind a fetish (whereas the Garg can). This causes the dog to just stand around.

5. Pet Attack Speed items and skills affect the various Pets differently.

(see Topic 8).

6. Gargantuan Wrathful Protector is an "ally" that benefits from the 30% Damage BBV buff. Instead of getting grouped with [ Pet Buff (%MoJ) + %Element ], it is grouped with [ Character Buff + Monster Debuff ], which is rather strange. Since when is the Garg regarded as another player or the WD himself?

7. Instead of removing [ APS-Snapshot ] in the Gargantuan:Wrathful Protector formula, Patch 2.1 removed the [ APS ] multiplier. Now Garg:WP is the only Pet that snapshots APS upon summon. All the other Garg runes, other Pets, and the WD, react to real-time APS changes.

8. BBV effective area is not as described. We see the visual on the ground, but we actually need to be able to see the Totem to benefit from BBV, and windows from full height walls are not counted.

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
7. Some Popular Legendary Gems & Items

-- 7.1 Bane of the Trapped
-- 7.2 Gem of Efficacious Toxin
-- 7.3 Mirinae, Teardrop of the Starweaver
-- 7.4 Wreath of Lightning
-- 7.5 Zei's Stone of Vengeance
-- 7.6 Pain Enhancer
-- 7.7 Strongarm Bracer
-- 7.8 Bastions of Will (Focus & Restraint)
-- 7.9 Convention of Elements
-- 7.10 Broken Promises

7.1 Bane of the Trapped (updated for Patch 2.1.2)

Confirmation tests concluded that
1) BotT is a standalone multiplier -

Bane of the Trapped is a standalone multiplier. I redid the proof test with a logical flow that is much neater, and easier to observe visually.

Test config: Weapon 21, Intel 6923, CHD 99%, Poison Dart 14%, Poison Element 55%, Piranhas 15%, PTV 20%, APS = 1.2 x 1.32 = 1.584.

The whole idea is to see the grouping of the various multipliers, and test the damage formula for nukes and general skills.

For skills that separate normal hits from critical hits,
[Weapon] x [Intel] x [Tooltip] x [Element] x [Skill + Buff + Debuff] x [BoT] x [Zei's Stone]

For skills that cannot crit, they include the pro-weighted CHC&CHD multiplier,
[Weapon] x [Intel] x [CHC&CHD] x [Tooltip] x [Element] x [Skill + Buff + Debuff] x [BoT] x [Zei's Stone]

All the nukes don't benefit from [APS].

Video proof - http://youtu.be/RaiqW124Py4

Screen Results
----------------------------------------- Hit ----- Crit
Splinter Darts (110%) ---------- 2867 --- 5705
with PTV --------------------------- 3370 --- 6705
with PTV & Piranhas ----------- 3747 --- 7456
with PTV & Piranhas & BoT -- 4590 --- 9134

Calculations
[Weapon] x [Intel] x [Tooltip] x [Element] x [Skill + Buff + Debuff] x [BoT] x [Zei's Stone]

Splinter Darts only,
21 x 70.23 x 1.1 x 1.55 x 1.14 = 2866.627, Crit = 5704.59
with PTV,
21 x 70.23 x 1.1 x 1.55 x 1.34 = 3369.54, Crit = 6705.39
with PTV & Piranhas,
21 x 70.23 x 1.1 x 1.55 x 1.49 = 3746.73, Crit = 7455.995
with PTV & Piranhas & BoT,
21 x 70.23 x 1.1 x 1.55 x 1.49 x 1.225 = 4589.75, Crit = 9133.59

2) BotT works with the following effects -
- Immobilize (shown as Rooted) - video - http://youtu.be/SL3lalD9kYk
- Chill (shown as Slowed) - video - http://youtu.be/Qw1TQMwbVyQ
(Haunt & Phantasm both have in-built slow effect,
Phantasm video proof - http://youtu.be/brPK9pJhSJ8)
- Cord of Sherma (due to Slow effect) - video - http://youtu.be/s8j8DXaBzdg
- Hwoj Wrap (due to Slow effect) - video - http://youtu.be/RV8ZVy01aZE
- Stun (shown as Stunned) - video - http://youtu.be/Tj-Lm15oFxQ
- Freeze (shown as Frozen) - video - http://youtu.be/VqcijnZ6vOo
(*Ignore the Freeze video, Patch 2.1.1 allows BoT to be proc by Freeze*)
- Fear (shown as Feared with skull symbol) - video - http://youtu.be/MsmyRrlhSi4
(can be used with or without Tiklandian Visage)
- Hex (chicken or pig) - video - http://youtu.be/AZxgcPwt_eE
- SH:Languish (due to Slow) - video - http://youtu.be/0az-O1Kjiow
- Sac:Black Blood (due to Stun) - video - http://youtu.be/Jef0Nz-Peqo

As announced by Patch notes 2.1.2,
BotT gets activated by Blind and Charmed (including Addling Toad's confused).
Video - http://youtu.be/1NAJ10pIDHg

3) BotT does not work with the following effects -
- Cold elemental roll on weapon - video - http://youtu.be/ZBz5WyGoX1I
- WoZ:Wrecking Crew (shown as Taunted) - video - http://youtu.be/7WKvC93b6UA
- Knock or "jump uncontrollably" (Halcyon) - http://youtu.be/YAOd94mTSm4
(All forms of Knocks do not proc BotT, which includes Vortex, Knock up, Knock back, and "jumps uncontrollably". Ess of Johan has a slow component, so that slow component provides the BotT proc.)
- Piranhado - http://youtu.be/6cW6ruflBvY
(There is the "stunned" text on screen, but it is not the stun effect. There is no extra damage other than the 15% due to Piranhas. In my video proof, I had PTV also, which makes the extra damage (1.35/1.2) x damage of normal/crit hit. Piranhado property is "knock" effect depending on situation, see Strongarm Bracer.)

Changes in Patch 2.1.2 has made this section invalid.
- Blind (shown as Blinded) - video - http://youtu.be/a6y4Jrh0zXc
- Addling Toads Confused (shown as Charmed) -

Addling Toads do not proc Bane of the Trapped. Confusion is not classified as a control impairing effect.

Video proof (timer 2:10) - http://youtu.be/po-TZxcc_0Q

Since Addling Toads proc shows up as "Charmed", I did an additional test with the Overwhelming Desire amulet.

Results -- The Confusion by Addling Toads showing up as "Charmed" is a wrong screen display. The mob is not Charmed. The actual Charm-proc from the amulet shows up occasionally with the higher damage numbers in the video. The unwritten proc chance of the Overwhelming Desire amulet is underwhelming low. With my usual gear, I can probably kill the whole elite pack before I succeed to Charm 1 mob.

Video proof (timer 1:20 to 1:30) - http://youtu.be/oguKebYfjQk

Off topic discussion - the wrong tagging of Confusion as Charmed may be the reason why our Pets are not attacking. Perhaps they think the mob is our ally or follower.

Feel free to submit a bug report.

4) Tested BotT with a clan mate. BotT only benefits the player using the gem, other players do not benefit from the "debuff".
Video proof - http://youtu.be/3jpl64y-Oyc

5) How far is 15-Yards? It's about the radius of the waypoint circle.
Video proof - http://youtu.be/As9qQ2g8exM

6) BotT updates real-time and does not snap-shot for Locust and Haunt.
Video proof - http://youtu.be/yzd-P86bm0s

7) BotT benefits any player equipped with the gem, as long as the target mob is under control impairing effect. Doesn't matter which player provided the control.

Here's the proof. Thanks to AgroAnt for helping out with the test. He is not equipped with any item that provides control impairing effects, so the Horrify was the only control when he moved in.
Video - http://youtu.be/_RUhYR-P3sY

BotT gem at Rank 25 = 22.5%
Crit hit with my BotT slow proc = 30762
Crit hit without any proc = 25112
Crit hit with his Horrify = 30762

7.2 Gem of Efficacious Toxin (updated for Patch 2.2.1)

1) There is a total of 12.5 ticks, or 12 ticks with the 13th tick being half damage.

2) DoT mechanics apply. For further reading on DoT mechanics (DoT snap-shot, DoT refresh, 1st tick and final tick adjustments, sub-ticks, visual tick damage adjustments due to lag, etc), read here:
http://us.battle.net/d3/en/forum/topic/12943834736#1

3) At Rank 25, the gem does 3250% weapon damage over 10 secs. This tooltip description is wrong, or there is a stealth buff to shorten the DoT interval as we upgrade the gem. In all my counts, the DoT interval is around 29-31 frames. Before 7 secs, the full tooltip damage has been executed. There is another possibility where higher APS may have caused the tick interval to shorten. Need to investigate on a slow 2H weapon with minimal IAS on gear.

4) Hits from Pets do proc Toxin gem (official Patch notes).

5) Toxin damage does not crit. We can regard this as a regular nuke skill that cannot crit.

The Toxin (Poison) formula is:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ Tooltip ] x [ %Element ] x [ % Elite ] x [ 1 + (CHC/100 x CHD/100) ] x [ Buff + De-buff ] x [ Bane Trapped ] x [ Zei's Stone ] x [ CoE or F&R ] x [ % MonsterType ]

where [ Tooltip ] = (%number / 100) / 12.5

Video 1 - http://youtu.be/bnNAFfAw4K8
Test config - Rank25 Toxin @3250%, Intel 8031, CHC 44%, CHD 282%, Weapon 21, Tooltip = 32.5/12.5 = 2.6, PTV 20%.

Calculations:
Tick damage = 21 x 81.31 x 2.6 x (1 + 0.44x2.82) x 1.2 = 11937.71
13th tick (half damage) = 5968.85

As we test further details, we discover more complications.

6) Toxin proc @R25 does not apply De-buff to itself. The De-buff only applies to subsequent hits or skills. Even if we "refresh" the poison, or trigger the proc again after applying other skills, the Toxin DoT itself cannot enjoy the R25 10% De-buff.

7) Jade SH consumes all remaining Toxin DoT ticks, but Creeping Death does not extend the duration of Toxin DoT. That means, whether you use Jade set or not, you will output the same total Toxin damage. We take less than 7 secs to fully output all 12.5 ticks, even if the Jade nuke cycles faster than 7 secs, the amount of remaining Toxin DoT is negligible after setting up the sequence for snap-shot and giving priority to Haunt. Therefore, do not consider Toxin Poison in the Jade nuke, just consider Toxin as another separate damage like Mirinae, Wreath, Zombie Bears, Acid Cloud, etc.

I tested without using the Quetzacoatl mask. Using that mask, in theory, will output all Toxin damage in just over 3 secs.

8) Uncovered some bugs where Toxin damage appears "wrong". There is some "memory" effect from Soul Harvest. Possibly GF passive too, but didn't test GF.

Video 2 - http://youtu.be/_BfMX6oI9lA

Calculations (no buffs):
Tick damage = 21 x 81.31 x 2.6 x (1 + 0.44x2.82) = 9948.09
1st Jade nuke = 124,351 ( = remaining 12.5 ticks consumed)
2nd Jade nuke = 54,714 ( = remaining 5.5 ticks consumed)
3rd Jade nuke = 34,818 ( = remaining 3.5 ticks consumed)
4th Jade nuke = 74,611 ( = remaining 7.5 ticks consumed)

If we take a typical Jade set up, casting Piranhado to begin the sequence, the Piranhado damage will trigger the Toxin to start ticking. By the time Haunt is applied to a few mobs, and moving in for the nuke, there may not be many Toxin ticks remaining.

Further in Video 2, the Jade nukes started to throw the numbers off. The Intel buff from the Soul Harvest didn't quite match up.

Calculations (PTV & Hex):
Tick damage = 21 x 81.31 x 2.6 x (1 + 0.44x2.82) x 1.4 = 13927.325
To get the screen damage of 14,202, the Intel needs to be (8031 x 1.02) = 8191.62, which leads to the suspicion about SH Intel buff having some "memory" effect.

The calculations for the last part of Video 2 showed a similar problem, where Intel needs to have 1 stack of Soul Harvest buff.

Proof for SH Intel bug (memory effect)

Pumped some paragon points so the config has changed slightly-
Intel 8041, CHC 44%, CHD 282%, Weapon 21, Tooltip 2.6, PTV 20%.
1-stack SH Intel = 8041 x 1.02 = 8201.82
2-stacks SH Intel = 8041 x 1.04 = 8362.64
3-stacks SH Intel = 8041 x 1.06 = 8523.46
4-stacks SH Intel = 8041 x 1.08 = 8684.28
5-stacks SH Intel = 8041 x 1.1 = 8845.1

Calculations for:
1-stack SH, Tick damage = 21 x 83.0182 x 2.6 x 2.2408 x 1.2 = 12188.5
2-stacks SH, Tick damage = 21 x 84.6264 x 2.6 x 2.2408 x 1.2 = 12424.6
3-stacks SH, Tick damage = 21 x 86.2346 x 2.6 x 2.2408 x 1.2 = 12660.7
4-stacks SH, Tick damage = 21 x 87.8428 x 2.6 x 2.2408 x 1.2 = 12896.8
5-stacks SH, Tick damage = 21 x 89.451 x 2.6 x 2.2408 x 1.2 = 13132.9

Video 3 - http://youtu.be/R-XHMedm8gw
Timer 0:13 - 11,952 (0-stack SH, baseline damage)
Timer 1:14 - 13,133 (5-stacks SH)
Timer 1:32 - 13,133 (0-stack SH, memory as 5-stacks)
Timer 2:04 - return to town to reset
Timer 2:12 - 11,952 (0-stack SH, baseline damage)
Timer 3:12 - 13,133 (5-stacks SH)
Timer 3:22 - 11,952 (after killing another mob, memory effect went off. Could be due to distance reset, or weapon swap)
Timer 3:45 - 11,952 (1-stack SH, memory as 0-stack)
Timer 4:10 - 12,897 (4-stacks SH, correct application, why no memory as 1-stack?)
Timer 4:37 - 12,879 (1-stack SH, memory as 4-stacks)
Timer 4:57 - 12,189 (4-stack SH, memory as 1-stack)
Timer 5:11 - 12,897 (4-stack SH, correct application)
Timer 5:25 - 12,897 (0-stack SH, memory as 4-stacks)
Timer 5:39 - 11,952 (3-stacks SH, memory as 0-stack)
Timer 5:53 - 12,661 (3-stacks SH, correct application)
Timer 6:14 - 12,661 (2-stacks SH, memory as 3-stacks)

Conclusion:
The bug could be Creeping Death, and/or Jade Set, and/or Toxin gem, and/or Soul Harvest itself. Not bothered to isolate each of the parameters for further testing. The best approach is to get Blizzard to fix the bug.


Proof for Multiplier Grouping & Snap-shot

9) This section will prove that the Rank 25 10% De-buff is added to [ Buff + De-buff ] group, and the sequence for casting. By the sequence proof, we also prove that the Toxin DoT itself does not get buffed by its own Rank 25 ability, no matter what sequence we use to proc it.

Config - Intel 8041, CHC 44%, CHD 282%, Weapon 21, Toxin Tooltip 2.6, PTV 20%, Cold 40%, Haunt 29%.

Video 4 - http://youtu.be/ZHcBMAZZNbI
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ Tooltip ] x [ %Element ] x [ % Elite ] x [ 1 + (CHC/100 x CHD/100) ] x [ Damage-modifier (character buff + monster de-buff + %Skill) ] x [ Quetzalcoatl ] x [ Bane Trapped ] x [ Zei's Stone ]

Direct Haunt
Screen results -
PTV & Haunt & Toxin = 33,262
PTV & Haunt (Toxin expired) = 21,310
==> Toxin DoT was 11,952 (confirmed in Video 3 testing)

Haunt tick = 21 x 81.41 x (40/15) x 1.40 x 2.2408 x 1.49 = 21309.99

Melee (proc Toxin Rank 25), then Haunt
Screen results -
PTV & Toxin = 11,952
PTV & Toxin & Haunt = 34,693 (visibly higher damage than direct Haunt)
PTV & Haunt (Toxin expired) = 22,740

Haunt tick = 21 x 81.41 x (40/15) x 1.40 x 2.2408 x 1.59 = 22740.19

Hex, then Haunt
Screen results -
PTV & Hex & Haunt & Toxin = 38,115
PTV & Haunt (Hex & Toxin expired) = 24,170
==> Toxin DoT = 13,945

Toxin tick = 21 x 81.41 x 2.6 x 2.2408 x 1.4 (due to PTV & Hex) = 13944.454
Haunt tick = 21 x 81.41 x (40/15) x 1.4 x 2.2408 x 1.69 = 24170.386
Check total tick damage = 38114.84, matches screen result.

Hex does not provide damage, and we did not proc Toxin Rank 25. Haunt and Toxin Poison both benefited from Hex, but Haunt could not benefit from the Toxin Rank 25. Piranhas will probably be the best tool to proc Toxin Rank 25 due to the AOE and low damage.

Melee to proc Toxin Rank 25, then Haunt, then Jade SH nuke
Haunt tick = 21 x 81.41 x (40/15) x 1.40 x 2.2408 x 1.59 = 22740.19
Jade nuke = 38.5 x 22740.19 = 875497.31

Exactly matches screen results.

Proof for Multi-player Stacking of Debuffs

Special thanks to ButteryNugs for helping out with the multi-player tests.

10) In multi-player mode, each player can proc their own Toxin gem and see their own DoT damage. When they attack the mob, they stack up the 10% Debuff for subsequent hits/casts.

Video 5 - http://youtu.be/1e3Nt-uHYhg

Base Locust damage = 813
Single player punch-proc, then Locust = 894
Two player punch-proc, then Locust = 976

11) If you cast Haunt, double application can benefit from the 10% debuff, and subsequent Haunts can also proc or refresh the Toxin DoT. This is the logical way we expect the gem to work based on the description. Probably, the Blizzard testing team only tried out with Haunt and did not test with Locust.

Video 6 (timer 2:30) - http://youtu.be/6gyv-0ViaEw

Haunt base damage = 3336
Single player proc, then Haunt = 3669
Double player proc, then Haunt = 4003

The following section may no longer be valid from Patch 2.2.1. Locust recast bug now refreshes the DoT properly. However, the "Poisoned" status only applies the Toxin to subsequent casts and not the 1st application. Meaning, Pestilence does not benefit from the Toxin 10% debuff, we need to cast Locust (any rune) 2 times for Locust to benefit from the 10% debuff.
Video proof - https://youtu.be/SlqRIgE3w3c
Locust + Toxin = Lots of Bugs & Bad News

Special thanks to ButteryNugs for helping out with the multi-player tests.

12) If you cast Locust, double application does not benefit from the 10% debuff, subsequent Locust cast cannot even proc the Toxin DoT, until you reset the whole DoT (go to town or go very far away, or have mobs with teleporter/illusionist). Once the "memory effect" sets in, even melee hits cannot reset the Locust DoT to proc the 10% debuff casting sequence. Toxin gem is bugged for Locust (all runes).

Video proof - http://youtu.be/rZ2pr2gz4xo
Video proof (timer 2:13) - http://youtu.be/Y7KqVCFhi98

13) Sometimes, the Toxin debuff doesn't get proc'ed by melee hits after the 1st Locust has been applied. There's some "memory effect" going on again.

Video proof (timer 0:46) - http://youtu.be/6gyv-0ViaEw

14) Sometimes, the Toxin debuff doesn't stack properly.

Video proof (timer 2:43) - http://youtu.be/1OMUA9eKLAE

Locust base damage = 1301
Single player debuff, then Locust = 1431
Double player debuff, then Locust = 1431 (should have been 1561)

15) Horrify procs Toxin gem.

Video proof - https://www.youtube.com/watch?v=DsdC6Ccbicg

16) Toxin gem activates Bad Medicine passive.

Video - https://www.youtube.com/watch?v=7jk0fMsJf6I

Although this proof is not conclusive, we compare the highest highs and compare the lowest lows for in-coming damage, and the Bad Medicine passive activated by the Toxin gem does seem to provide the 20% damage reduction.

7.3 Mirinae, Teardrop of the Starweaver (updated for Patch 2.1.1)

Luckily, this gem is straightforward to test. We don't have %Holy and %Smite gear. Due to the ability to have critical hits, this gem can probably come close to the damage of a Pestilence Jade nuke when fighting single targets. When in a crowd, hopefully the Area Damage gets proc'ed.

For Mirinae and Wreath of Lightning, beware of Reflect Damage affix.

The Mirinae (Holy) formula is:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ Tooltip ] x [ %Element ] x [ % Elite ] x [ Buff + De-buff ] x [ Bane Trapped ] x [ Zei's Stone ]

For critical hits, we multiply the damage by [ 1 + (CHD/100) ].

Test config - Rank32 Mirinae @3280%, Intel 8031, CHC 44%, CHD 282%, Weapon 21, Tooltip = 32.8.

Video proof - http://youtu.be/2P5JBKTTk2I
Screen results:
Melee = 1,708 (hit), 6,523 (crit)
Mirinae = 56,006 (hit), 213,944 (crit)
Mirinae & PTV & Hex = 78,409 (hit), 299,522 (crit)
Mirinae & PTV = 67,208 (hit), 256,733 (crit)

Calculations:
Melee = 21 x 81.31 x 1 = 1707.51
Mirinae = 21 x 81.31 x 32.8 = 56006.33
Mirinae & PTV & Hex = 21 x 81.31 x 32.8 x 1.4 = 78408.86
Mirinae & PTV = 21 x 81.31 x 32.8 x 1.2 = 67207.59

7.4 Wreath of Lightning (updated for Patch 2.1.1)

This gem has rather interesting mechanics.
For Mirinae and Wreath of Lightning, beware of Reflect Damage affix.

1) Each proc of the gem gives 15 lightning tick. To be more precise, it is 3 groups of 5 lightning ticks.

2) Due to the group of 5 lightning ticks, the [ Tooltip ] is divided by 5. If there are 2-4 mobs within range, some of them will receive more than 1 tick. If there is only 1 mob within range, that mob will receive all 5 ticks per group, total (Tooltip x 3) damage when all the ticks are executed.

3) At Rank 37, the gem does 970% weapon damage each sec, for 3 secs. This tooltip description is wrong, or there is a stealth buff to shorten the tick interval as we upgrade the gem. In all my counts, the tick interval is around 6-7 frames. In about 2 secs, all 15 ticks were executed. There is another possibility where higher APS may have caused the tick interval to shorten. Need to investigate on a slow 2H weapon with minimal IAS on gear.

4) If the gem procs, the 1st lightning tick will be on the same frame that proc'ed the gem. Each subsequent tick will come after 6-7 frames.

The Wreath of Lightning (Lightning) formula is:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ Tooltip / 5 ] x [ %Element ] x [ % Elite ] x [ Buff + De-buff ] x [ Bane Trapped ] x [ Zei's Stone ]

For critical hits, we multiply the damage by [ 1 + (CHD/100) ].

Test config - Rank37 Wreath @970%, Intel 8031, CHC 44%, CHD 282%, Weapon 21, Tooltip = 32.8.

Video 1 - http://youtu.be/oQKNLpFxB4Q
Screen results:
Melee = 1,708 (hit), 6,523 (crit)
Wreath = 3,313 (hit), 12,654 (crit)
Wreath & PTV & Hex = 4,638 (hit), 17,716 (crit)
Wreath & PTV = 3,975 (hit), 15,185 (crit)

Calculations:
Melee = 21 x 81.31 x 1 = 1707.51
Wreath = 21 x 81.31 x (9.7/5) = 3312.56
Wreath & PTV & Hex = 21 x 81.31 x (9.7/5) x 1.4 = 4637.60
Wreath & PTV = 21 x 81.31 x (9.7/5) x 1.2 = 3975.08

Timer 1:33 - Proof that Wreath reacts real-time to buff changes, even during the 15 ticks within a proc.

Video 2 - http://youtu.be/E1kGjqI73CA

If there are many targets, mobs are randomly selected. If there is only 1 target, all 15 ticks go to that target. The scanning range is quite limited, guessing 30-40 yards. Those further away will not be targeted. Therefore this gem needs to be proc'ed from close-range to mid-range.

Timer 1:02 - Area Damage procs.

7.5 Zei's Stone of Vengeance (updated for Patch 2.1.1)

Initial testing for Zei's Stone @5.25%. Zei's Stone at Rank 25 can stun on hit, on initial cast, and on jump, but not on tick. Pet's don't proc the stun.

Zei's Stone melee video - http://youtu.be/bGkIeu4ur3A
Zei's Stone dart video - http://youtu.be/nBdGtm_5qyg

Test config - Intel 7626, APS = 1.2 x 1.32 = 1.584, CHD 182%, Weapon damage = 21.
Calculated critical hit = 13,045.20

Without Zei's Stone,
Critical hit = 13,045
Crit with MC:P = 15,654
Crit with PTV = 15,654
Crit with MC & PTV = 18,263

Confirms pre 2.1 grouping of [ Character buff + Monster debuff ].

With Zei's Stone @5.25%,
Crit with PTV = 16,157 (about 3.2%)
Crit with MC & PTV = 18,821 (about 3%)

Walking around with PTV so that the fetish and mob distance gets adjusted,
Crit with PTV
16,153 ------------------- 23.823%
16,144 ------------------- 23.754%
16,149 ------------------- 23.793%
16,129 ------------------- 23.364%
16,164 ------------------- 23.908%
16,532 ------------------- 26.729%
16,357 ------------------- 25.387%
16,240 ------------------- 24.490%
15,918 ------------------- 22.022%

This proves that Zei's Stone is not calculated per 10 yards, not even per yard. It is probably calculated within fractions of each yard.

Further testing in Video 2 using FA:HH (focus on the dart fetish), and walking around to vary the distance between the mob and the darter,

Crit with PTV
17,940
19,086
19,728
20,055
20,430
19,253
18,500
18,372
17,524

You only see steady numbers (same damage number) when the mob and fetish settle down and fight each other without moving. In Melee combat, we do not even get the listed 5.25% stated on the Gem.

Since the effect is calculated on fractional yard (even smaller than 0.5 yard increments), the above is not sufficient to confirm that Zei's Stone is a separate multiplier.

Zei's Stone as a standalone multiplier

This time I used 1 FA to tank as the decoy, then I used the WD with Splinter Darts (no residual ticks in that rune) and began shooting from across the screen, until the damage number could not go higher.

My gear had 55% Poison, and then I had PTV and Hex:Jinx to use. Zei's Stone @26.25% max range.

Looking at critical hits only,
Baseline crit without Gem = 6735
Crit with Zei's Stone = 8503
That's exactly 26.25% increase, which establishes the baseline effect of the Gem.

With PTV (character buff)
Crit with Zei's Stone = 10204 (or 1.51507 times baseline crit)

With PTV & Hex:Jinx (monster debuff)
Crit with Zei's Stone = 11905 (or 1.76763 times baseline crit)

If we consider Zei's Stone as a standalone multiplier,
For PTV, we expect the baseline crit to increase to 6735 x 1.2 x 1.2625 = 10203.525
For PTV and Hex, we expect the baseline crit to increase to 6735 x 1.4 x 1.2625 = 11904.11

There could be some rounding taking the baseline crit value without calculating all the component details. At least, this verifies the [Tooltip] description at maximum distance, that Zei's Stone is not grouped up with [%Element] or [Character buff + Monster debuff].

There were 2 other factors I did not test, [%Elites] and [%Skill (I used Poison Darts)]. For the time being, I'll just go along with Zei's Stone being a standalone multiplier, until someone else bothers to test and prove its independence or grouping with some multiplier.

Zei's Stone effect is real-time and dynamic

Video 3 - http://youtu.be/JDVWQhxv7ZA

Timer 0:13 - Establish baseline Haunt damage at 42,458. We know about Haunt snap-shot mechanics and this baseline is established with the ring socket empty.

Timer 0:20 - Insert Zei's Stone into socket. Damage changes real-time.

Timer 0:33 - 50,473 damage (18.9% higher damage from a Rank 0 gem!)

Timer 0:47 - 44,142 is the last visual tick before the Jade nuke

Timer 0:48 - 1,686,176 Jade nuke, reverse calculating to a tick at 43,797. This proves that Zei's Stone works at sub-yard distances and sub-tick damage updating.

Timer 0:48 - 43,811 immediate visual tick just after the Jade nuke. Again, the sub-yard distance and real-time changes.

7.6 Pain Enhancer (updated for Patch 2.2)

1) There is a total of 3.75 ticks, or 3 ticks with the 4th tick being 0.75 damage.

2) DoT mechanics apply. For further reading on DoT mechanics (DoT snap-shot, DoT refresh, 1st tick and final tick adjustments, sub-ticks, visual tick damage adjustments due to lag, etc), read here:
http://us.battle.net/d3/en/forum/topic/12943834736#1

3) At Rank 36, the gem does 2280% weapon damage over 3 secs. This tooltip description is wrong, or there is a stealth buff to shorten the DoT interval as we upgrade the gem. In all my counts, the DoT interval is around 22-30 frames. Before 3 secs (about 2 secs), the full tooltip damage has been executed. There is another possibility where higher APS may have caused the tick interval to shorten. Need to investigate on a slow 2H weapon with minimal IAS on gear.

The DoT interval should be steady, but I am unable to test accurately. We'll just take it as all damage output in 2 secs for the time being, until someone else provides accurate frame count measurements.

4) Critical hits from Pets do proc Pain Enhancer gem.

5) Pain Enhancer damage does not crit. We can regard this as a regular nuke skill that cannot crit.

6) The rank 25 buff only triggers for Bleeding mobs within the 20-yard range from the WD. Each 3% IAS is added to the (gear + paragon + multi-player buff) portion.

The Pain Enhancer (Physical) formula is:
[ Weapon Damage ] x [ 1 + (Intel/100) ] x [ Tooltip ] x [ %Element ] x [ % Elite ] x [ 1 + (CHC/100 x CHD/100) ] x [ Buff + De-buff ] x [ Bane Trapped ] x [ Zei's Stone ]

where [ Tooltip ] = (%number / 100) / 3.75

Video 1 - https://www.youtube.com/watch?v=oZkI2SE4pcg
Test config - Rank36 PE @2280%, Intel 7860, CHC 45.5%, CHD 212%, Weapon 21, Tooltip = 22.8/3.75 = 6.08, PTV 20%, FA 29%, APS = 1.2 x 1.44 = 1.728.

All the hit/crit Fetish damages were checked with the respective elements. Calculations exactly match screen results.

Timer <0:30
Screen result - 1st tick 23,960, 2nd tick 23,960, 3rd tick 23,960, 4th tick 17,970
[Weapon Damage] x [1 + (Intel/100)] x [Tooltip] x [1 + (CHC/100 x CHD/100)] x [Buff + De-buff]
Tick damage = [21] x [79.6] x [6.08] x [1.9646] x [1.2] = 23960.248
75% of 1 Tick damage = 0.75 x 23960.248 = 17970.186

Timer 0:30 to 1:00
Dart has residual DoT, not good for testing.

Timer 1:00 to 1:30
Various positioning to observe the IAS buff and procs.
0 mob Bleeding, APS = 1.2 x 1.44 = 1.728
1 mob Bleeding, APS = 1.2 x 1.47 = 1.764
2 mobs Bleeding, APS = 1.2 1.5 = 1.800

Timer 1:19 to 1:21
Checking fetish non-crit damage against the changing APS conditions.
Screen result @1.73 APS = 8049
Screen result @1.76 APS = 8216
Screen result @1.80 APS = 8384

Calculations for fetishes,
@1.73 APS -- [21] x [79.6] x [1.728] x [1.8] x [1.29] x [1.2] = 8048.5852
@1.76 APS -- [21] x [79.6] x [1.764] x [1.8] x [1.29] x [1.2] = 8216.2642
@1.80 APS -- [21] x [79.6] x [1.800] x [1.8] x [1.29] x [1.2] = 8383.9431

Video 2 - http://youtu.be/tqBIBGdA6uY
Test config - swapped Bracer with 20% Physical that has higher Intel, total Intel = 7872.

Screen result - 1st tick 28,796, 2nd tick 28,796, 3rd tick 28,796, 4th tick 21,597
Calculations,
[Weapon Damage] x [1 + (Intel/100)] x [Tooltip] x [%Element] x [1 + (CHC/100 x CHD/100)] x [Buff + De-buff]
Tick damage = [21] x [79.72] x [6.08] x [1.2] x [1.9646] x [1.2] = 28795.64
75% of 1 Tick damage = 0.75 x 28795.64 = 21596.73

Pain Enhancer and Broken Promises (Patch 2.2)

There is good synergy between PE gem and BP ring. To work the ring well, sheet CHC is kept at the minimum 5%. Once the BP ring procs, the CHC shoots up to 100%, and the multiplier increases significantly.

Video proof - http://youtu.be/FYIz2I5GJSY
PE DoT increased from 90,852 to 326,376.
At 5%CHC, multiplier = [1 + (0.05 x 3.16)] = 1.158
At 100%CHC, multiplier = [1 + (1 x 3.16)] = 4.16
*BP ring when proc'ed increases PE and all DoTs by 3.59. (snap-shot rules apply).

At typical 55% CHC, multiplier = [1 + (0.55 x 3.16)] = 2.738
*Compared to typical builds at 55% CHC, BP ring when proc'ed increases PE and all DoTs by 1.52.

7.7 Strongarm Bracer (updated for Patch 2.1.1)

Carried out detailed testing on this popular item because there is often some confusion in the forums and among players on the mechanics and proc stacking.

1) Strongarm Bracer cannot be proc'ed by Pets. Garg:WP does not proc Strongarm.

2) For multiplayer stacking, each "knock" animation must be completed from start to end, otherwise the "knock" will not count for the subsequent player(s). Each player has to "knock" the target to trigger their debuff effect. For example, player #1 casts Wave of Mutilation to "knock" the target. While the animation is in process, player #2 casts Wave of Mutilation and has no visual effect because the "knock" animation from player #1 in still on-going. The group will only enjoy the Strongarm proc from player #1 and not from player #2. To successfully stack both players Strongarm proc, player #2 must wait for the target to land on the ground, then cast the skill to "knock" the target. In other words, for 2 players, the target must bounce 2 times, and each player must cause their own "knock".

Sidenote: the same Piranhas rune does not stack, just as the same BBV rune does not stack.

3) Halcyon "jumps uncontrollably" is considered as a knock and will proc Strongarm Bracer.

4) Piranhado is situational. It needs to "pull in" the target to proc Strongarm. If the target does not move from its original location, there will be no proc. The completion of the "push/pull" animation is extremely important to qualify as a "knock".
Piranhado video proof - http://youtu.be/9Yc8k7UBunQ

5) In general, all forms of "push", "pull", "jumps", "knockback", "knock-up", etc., will trigger Strongarm as long as the target is moved from its original location. This includes WoZ:Offensive Line.

Test Set-up
Weapon 21, Intel 7679, CHD 145%, Fire Element 20%, PTV 20%, APS 1.2x1.32 = 1.584, Strongarm 29%, BotT 22.5%, Midnight Feast 50%.

Video - http://youtu.be/aBaz74tRlkY
Observing critical hits only,
Timer < 2:30 (Piranhado)
13,694 (PTV only)
16,775 (PTV & BotT)
18,872 (PTV & BotT & Piranhas)
22,925 (PTV & BotT & Piranhas & SA)
*Note the different situations where Piranhado can or cannot trigger Strongarm.
Timer 2:30 to 3:40 (Wave of Mutilation)
18,715 (PTV & Piranhas & SA)
15,405 (PTV & Piranhas, SA expired)
Timer 4:00 (to confirm shorter Piranhado duration)
18,715 (PTV & Piranhas & SA)
17,003 (PTV & SA, Piranhas expired before SA expires)
Timer 5:20 onwards (Garg:WP)
78,738 (PTV only, didn't proc SA)

Calculations (critical hits only)
Fetish: 21 x 77.79 x 1.8 x 1.584 x 2.45 = 11411.344
for PTV (x1.2) = 13693.61
for PTV & BotT (x1.2 x1.225) = 16774.67
for PTV & BotT & Piranhas (x1.35 x1.225) = 18871.51
for PTV & BotT & Piranhas & SA (x1.64 x1.225) = 22925.39

Garg: 21 x 77.79 x 5.75 x 1.584 x 2.45 x 1.2 (fire) x 1.5 (midnight feast) = 65615.229
for PTV (x1.2) = 78738.27
for PTV & SA (x1.49) = 97766.69 [this was not the case]

Calculations match screen results exactly. Garg:WP did not proc Strongarm.

Multi-player Stacking (same test config)
Special thanks to Crwth for helping out with the multi-player tests.

Video - https://www.youtube.com/watch?v=UEN3uOnqQu4
Observing critical hits only,
Timer < 0:39
13,694 (PTV only)
18,715 (PTV & myPiranhas & mySA)
17,802 (PTV & hisPiranhas & hisSA)
*From here, I can deduce that his Strongarm is 21%.
Timer 0:39 to 0:51
21,111 (PTV & hisPiranhas & bothSA)
18,715 (PTV & myPiranhas & mySA, his expired)
15,405 (PTV & myPiranhas, my Strongarm expired)
13,694 (PTV only)
Timer 1:20 to 1:35
18,715 (PTV & myPiranhas & mySA)
21,111 (PTV & myPiranhas & bothSA)
17,802 (PTV & hisPiranhas & hisSA, mine expired)
15,405 (PTV & hisPiranhas, his Strongarm expired)
13,694 (PTV only)

Calculations (critical hits only)
Fetish: 21 x 77.79 x 1.8 x 1.584 x 2.45 = 11411.344
for PTV (x1.2) = 13693.61
for PTV & Piranhas & 29%SA (x1.64) = 18714.60
for PTV & Piranhas & 21%SA (x1.56) = 17801.70
for PTV & Piranhas & 29%SA & 21%SA (x1.85) = 21110.99
for PTV & Piranhas (x1.35) = 15405.31

Calculations match screen results exactly.

Separate Test for Halcyon

Video proof - https://www.youtube.com/watch?v=bABYtsBM9Ic

Proof for WoZ:Offensive Line

Video proof - http://youtu.be/mbkIZVuog5w

7.8 Bastions of Will (updated for Patch 2.2)

Special thanks to DoubleTwist for the detailed testing when Patch 2.2 went Live.
I used a level one weapon, amulet with plus minimum damage, Focus and Restraint. This allowed me to see a constant hit number and a larger constant crit number.

I used fetish army as my baseline, as it is neither a primary nor a spender.

Fetish Army Damage with no spender and no primary cast
Hit=8444
Crit=28371
Fetish Army Damage with spender cast
Hit=12665
Crit=42556
Fetish Army Damage with primary cast
Hit=12665
Crit=42556
Fetish Army Damage with spender and primary cast
Hit=18998
Crit=63834

Casting a Primary will activate the 50% buff ( x1.5 standalone multiplier).
Casting a Spender will activate the 50% buff ( x1.5 standalone multiplier).
Using a Primary and Spender combo in quick succession will lead to (1.5 x 1.5) = 2.25 multiplier.

Separately, I did a quick test video to verify his test results:
Video - http://youtu.be/khTxVd24P38

7.9 Convention of Elements (updated for Patch 2.2)

This ring rotates the 4 elements for the WD class - Cold, Fire, Physical, Poison.
It is a standalone multiplier when applicable. [1 + (%Buff / 100)] as the multiplier. CoE does not affect the spawn element of the Fetish Sycophants.

Overall, we will net higher DPS compared to other single rings.
.... x1 .... x1 ..... x3 ..... x1 will average out to 1.5
or 50% net gain to total DPS.

Videos
CoE and Jade2 and Jade6 - https://youtu.be/4XZTeh632pA
CoE and DoT - https://youtu.be/yg2yF9-y2oQ

For Jade2 or Jade6 nuke, you need to wait for 1 full visual tick after the Element rotation arrives.

Example
I chose Cold in my test video. When the CoE rotates to Cold, and I Jade2 or Jade6 immediately, it is not counted (still regarded as Poison in that rotation). I need to wait to somewhere around 1/4 to 1/2 of the buff icon rotation, then I cast Jade2 or Jade6 for the full benefit (Proof: Timer 2:04 & 3:24).

When Cold rotates out to Fire, if I Jade2 or Jade6 immediately, I can still benefit from the CoE fully (Proof: Timer 1:44). So we are not short-changed, there is just a phase-difference in the timing and application of the CoE buff due to the ticks and the sub-ticks mechanics.

Test Config
Weapon 21, Intel 7097, Cold 38%, Haunt 29%, CHC 45.5%, CHD 238%, CoE 173%.

Haunt tick = 21 x 71.97 x 1.38 x 1.29 x [1 + (0.455 x 2.38)] x (40/15) = 14944.339
Haunt tick (Cold) = 14944.339 x 2.73 = 40798.045

Jade6 (non-Cold) = 14944.339 x 51 = 762161.28 (Timer 3:12)
Jade6 (Cold) = 40798.045 x 51 = 2080700.2 (Timer 3:01)

Jade2 (normal, non-Cold) = 21 x 71.97 x 1.38 x 1.29 x (40/15) x 12.5 = 89684.686
Jade2 (normal, Cold) = 89684.686 x 2.73 = 244839.19
Jade2 (crit, non-Cold) = 89684.686 x 3.38 = 303134.23
Jade2 (crit, Cold) = 244839.19 x 3.38 = 827556.46

7.10 Broken Promises (updated for Patch 2.2)

This ring allows a whole new way of gearing. Previously trash gear can actually become useful. There are 7 slots of items where the CHC stat can be replaced by some utility stat or defensive stat or IAS/Element/Ave Damage.

The pre-requisite, is to keep the sheet CHC at 5%. That means, do not assign paragon points into CHC. The chosen skill/rune has significant impact on maintaining the "up-time" of the proc.

The best methods to proc BP ring, while being compatible with various popular builds, are:
Grasp of the Dead, Phantasm, Haunt (without Jade2), & Piranhas. None of them can crit.

Edit: The above statement is wrong. Piranhas, Spirit Barrage, Grasp of the Dead -- all runes can crit, even if they only show up as white numbers. The damage number is clearly multiplied by the CHD factor.

I tested with 45% CHC on character sheet, which made it very difficult to proc the BP ring. Rule of thumb is to maintain the sheet CHC at the minimum of 5%. Next factor to consider is how fast you can unleash the 5 hits.
GotD video - https://youtu.be/uyyqFmnjSoo
Piranhas video - https://youtu.be/5VfPlQmy6X8
SB video - https://youtu.be/zK-ESi2BWrI

For the 3 ground AOE I tested above (Phantasm for SB), each tick is considered as a hit, regardless of how many enemies are inside the AOE. So if you spread out the AOEs, chances are you get to proc the BP ring as fast as a channel skill. If you only have 1 target on screen like RG battle, the BP ring will proc on the 5th tick if there was no "crit". If fighting the RG and you're not on a Carnevil build, you'd probably be spamming Poison Haunt and Piranhas whenever available. That will proc-cycle the BP ring, will not have full up-time, but will be on-par or better than the typical 55% CHC build.

Similar mechanics for GotD, Phantasm, Piranhas:
1) The AOE is counted as 1 hit, regardless of the number of targets within.
2) Each tick is considered as 1 hit. If you only have 1 target, after about 4 secs inside the AOE, BP ring will proc.
3) Each tick refreshes the Zuni6 debuff.
4) In addition, if target is "Slowed", BotT gem will get proc'ed.

*Note: Phantasm has no cooldown, and we can cast 3 at any time. Subsequent casts cancel the earlier casts, but the targets remain tagged for Zuni6 with the timer counting down.

Differences between Haunt and the 3 AOEs:
1) Haunt tags the targets wherever they go, the 3 AOEs are stationary ground effects
2) When the target leaves the ground AOE, the Zuni6 timer counts down, and the "Slowed" expires. While the target remains "Haunted", it remains "Slowed" also.
3) Haunt is considered a hit only for the initial cast and the "jump". Ticks are not considered as hits. For this reason, Zuni6 timer counts down the moment the Haunt hits.

Each Haunt cast is 1 hit, regardless of the number of targets, or double-haunt or triple-haunt.
BP and Haunt proof - http://youtu.be/fYOaUYjT05M

BP ring and DoT snap-shot
At 5%CHC, multiplier = [1 + (0.05 x 3.16)] = 1.158
At 100%CHC, multiplier = [1 + (1 x 3.16)] = 4.16
*BP ring when proc'ed increases all DoTs by 3.59. (snap-shot rules apply).

Proof for DoT snap-shot - http://youtu.be/H4sQ-K9HRqQ
Huge difference whether you apply the DoT before or after BP ring procs.

BP and Jade2 - https://www.youtube.com/watch?v=wt2RdiVcO8E
BP and Frozen Piranhas - https://www.youtube.com/watch?v=h4IidRmz0es
BP and Phantasm - https://www.youtube.com/watch?v=KEIlpsCeuWw
BP and PE gem - https://www.youtube.com/watch?v=FYIz2I5GJSY
Sample GR42 run - http://youtu.be/FvealeCDmK0
Sample GR43 run - http://youtu.be/hF-yLuU2rHo

BP ring and Darts
Splinters rune is an excellent method to proc BP ring. SttF rune has residual DoT which messes up the 5-hit counter and has lower "up-time" compared to Splinters. Using Splinter rune, sometimes the ring will proc in 2 casts, usually in 3 casts.

Sample GR49 run - https://www.youtube.com/watch?v=eaiH3lJXUDA

Sample GR50 run - https://youtu.be/-L9vZpi-Q7A
sheet damage - 837k goes up to 4m when ring activates
sheet toughness - 34.6m with 23 fetishes

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
8. Everything we know about Pet Attack Speed

This section is dedicated to the research and detailed testing works of AlCalzone. Without him, our community would still be in the dark days of wondering how our Pets fight. My comments (if any) are in the quoted frames.

Comments/Summary from Paul
This is the list of base frames per attack (FPA) for various Pets:
Melee Fetish = 48 FPA [from (1 / 0.8) = 1.25 APS]
Head Hunter = 48 FPA [from (1 / 0.8) = 1.25 APS]
Tiki Torcher = 42 FPA [from (1 / 0.7) APS]
Gargantuan = 84 FPA [from (1 / 1.4) APS]
Zombie Dog
1. Bite attack -> Bite attack: 54 frames (bite retreat 26 + bite 28)
2. Bite attack -> Claw attack: 62 frames (bite retreat 26 + claw 36)
3. Claw attack -> Claw attack: 60 frames (claw retreat 24+ claw 36)
4. Claw attack -> Bite attack: 52 frames (claw retreat 24+ bite 28)
*see illustration - http://imgur.com/HjIXxPZ

Melee Fetish & Head Hunter (uses Additive Formula),
FPA = 60 / [ Base APS + (sum of Pet Attack Speed buffs) ]
Rounded to the nearest multiple of 6 (32.9 rounds down to 30, 33 rounds up to 36)

Tiki Torcher & Zombie Dogs (uses Multiplicative Formula),
FPA = Base FPA / [ 1+ (sum of Pet Attack Speed buffs) ]
Rounded to the nearest multiple of 6 (32.9 rounds down to 30, 33 rounds up to 36)

Gargantuan (uses Multiplicative Formula),
FPA = Base FPA / [ 1 + (sum of Pet Attack Speed buffs) ]
Rounded Up to the nearest multiple of 6 (30.1 rounds up to 36)

Multi-player BBV (different runes), Crusader Laws of Valor, Monk Mantra of Retribution are all added to the (sum of Pet Attack Speed buffs).

For Zombie Dog, the claw and bite animation are affected by T&T and BBV also. See AlCalzone's test details. Depending on what type of animation is used, piece together the total frames like a jigsaw puzzle. His spreadsheet can be downloaded here:
https://docs.google.com/spreadsheets/d/1GGhths70vTMGjCpsGAKPDJNd3653JLaLfHo0tSSMpes/

Results include 42%, 44%, 48% and 49% Taskers.

Fetishes:

Baseline:
expected 48 fpa = 1,25 aps
measured 48,0 fpa = 1,25 aps

only BBV:
expected 41,4 fpa = 1,25+0,2 = 1,45 aps
measured 42,0 ± 0,00 fpa = 1,429 ± 0,000
frames: 42, 42, 42... all the time

42% Taskers, no BBV:
expected 35,9 fpa = 1,25+0,42 = 1,67 aps
measured 36,0 ± 0,00 fpa = 1,667 ± 0,000 aps
frames: 36, 36, 36... all the time

42% Taskers + BBV:
expected 32,1 fpa = 1,25+0,42+0,2 = 1,87 aps
measured 30,0 ± 0,32 fpa = 2,000 ± 0,022 aps
frames: 30, 30, 30, 30, 30, 30, 30, 30, 31, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 29

44% Taskers, no BBV:
expected 35,5 fpa = 1,25 + 0,44 = 1,69 aps
measured 36,0 ± 0,00 fpa = 1,667 ± 0,000 aps
frames: 36, 36, 36... all the time

44% Taskers + BBV:
expected 31,7 fpa = 1,25 + 0,44 + 0,2 = 1,89 aps
measured 30,0 ± 0,00 fpa = 2,000 ± 0,000 aps
frames: 30, 30, 30... all the time

48% Taskers, no BBV:
expected 34,7 fpa = 1,25 + 0,48 = 1,73 aps
measured 36,0 ± 0,00 fpa = 1,667 ± 0,000 aps
frames: 36, 36, 36... all the time

48% Taskers + BBV:
expected 31,1 fpa = 1,25 + 0,48 + 0,2 = 1,93 aps
measured 30,0 ± 0,38 fpa = 2,000 ± 0,026 aps
frames: 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 29, 30, 30

49% Taskers, no BBV:
expected 34,7 fpa = 1,25 + 0,49 = 1,74 aps
measured 36,0 ± 0,00 fpa = 1,667 ± 0,000 aps
frames: 36, 36, 36... all the time

49% Taskers + BBV:
expected 31,1 fpa = 1,25 + 0,49 + 0,2 = 1,94 aps
measured 30,0 ± 0,00 fpa = 2,000 ± 0,000 aps
frames: 30, 30, 30... all the time

The fetish results indicate that there is really a frame bracketing / breakpoints going on. It is however unclear which formula is indeed correct. As it stands, there are still two possibilities:

•1. additive formula (Base APS + T&T + BBV), as currently assumed. FPA would have to be rounded to the nearest multiple of 6 (32,999 -> 30; 33 -> 36)•2. multiplicative formula (Base FPA / [1 + T&T + BBV]), as currently used for the Gargantuan. FPA would always be rounded up to the nearest multiple of 6 (30,001 -> 36).
Both formulas fit the data, the latter one is closer to how DH sentries currently work. You gain nothing until you reach the next breakpoint. I simulated both in Excel with T&T ranging from 40-50% with and without BBV. Both yield exactly the same results.

There are however two data points at which there is a difference between the two formulas. At 98% and 99% pet APS buff (e.g. 48/49% T&T, 20% BBV, 30% something else), #1 results in 24 FPA while #2 outputs 30 FPA. I'm not sure if that state can even be reached.

Tiki Torchers:
The animation has a duration of 42 frames.
FPA also seems to be 42, but sometimes no numbers are displayed. Enemy HP is still going down, so most likely a display error.
42% Taskers: 30 frames
42% Taskers + BBV: 24 frames

Head Hunters:
FPA is 48, noticed one attack without a number, enemy HP is still going down.
42% Taskers: 36 frames
42% Taskers + BBV: 30 frames

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

Gargantuan:
he had some jitter in his frame count, mostly one attack that came 1 frame too late and the next one was back on the earlier rhythm.

Baseline:
expected 84 fpa
measured 84,0 ± 0,73 fpa
frames: 84, 84, 85, 83, 84, 85, 83, 84, 84, 84, 84, 84, 85, 83, 85, 83

only BBV:
expected 84 / (1 + 0,2) = 70 fpa
measured 72,1 ± 0,70 fpa
frames: 73, 72, 71, 72, 72, 72, 72, 72, 73, 71, 72, 72, 73, 71, 73

42% Taskers, no BBV:
expected 84 / (1 + 0,42) = 59,2 fpa
measured 60,0 ± 0,79 fpa
frames: 59, 60, 60, 61, 59, 60, 60, 61, 59, 60, 61, 59, 61, 59, 60, 61, 60, 60, 59, 61

42% Taskers + BBV:
expected 84 / (1 + 0,42 + 0,2) = 51,9 fpa
measured 53,9 ± 0,47 fpa
frames: 54, 54, 54, 54, 54, 54, 53, 55, 54, 54, 54, 54, 54, 53

44% Taskers, no BBV:
expected 84 / (1 + 0,44) = 58,3 fpa
measured 60,0 ± 0,00 fpa
frames: 60, 60, 60... all the time

44% Taskers + BBV:
expected 84 / (1 + 0,44 + 0,2) = 51,2 fpa
measured 54,0 ± 0,00 fpa
frames: 54, 54, 54... all the time

48% Taskers, no BBV:
expected 84 / (1 + 0,48) = 56,8 fpa
measured 60,0 ± 0,00 fpa
frames: 60, 60, 60... all the time

48% Taskers + BBV:
expected 84 / (1 + 0,48 + 0,2) = 50,0 fpa
measured 54,0 ± 0,00 fpa
frames: 54, 54, 54... all the time

49% Taskers, no BBV:
expected 84 / (1 + 0,49) = 56,4 fpa
measured 60,0 ± 0,00 fpa
frames: 60, 60, 60... all the time

49% Taskers + BBV:
expected 84 / (1 + 0,49 + 0,2) = 49,7 fpa
measured 54,0 ± 0,00 fpa
frames: 54, 54, 54... all the time

The Gargantuan also has noticeable breakpoints/frame bracketing. As with the fetish formula #2, it seems that FPA is always rounded up to the next multiple of 6.

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

If the rounding/breakpointing is indeed correct, it seems there is no difference between 40% and 50% T&T. While that is correct for almost all pets/attacks, the combination of BBV and (probably) 45+% Taskers lets the dog bite faster.

In this case there are 4 distinct attack speeds for fetishes and garg:
Fetishes: 48 frames (base), 42 frames (BBV), 36 frames (T&T), 30 frames (T&T + BBV)
Gargantuan: 84 frames (base), 72 frames (BBV), 60 frames (T&T), 54 frames (T&T + BBV)
Edited by AlCalzone#2424 on 11/29/2014 2:32 AM PST

----------------------------
I think I solved the mystery of the Dogs' attack speed. Using perma-Horrify I was able to remove any variation from the enemies hitting back and got very consistent results.

There are 4 combat situations that can be observed:
1. Bite attack -> Bite attack: 54 frames
2. Bite attack -> Claw attack: 62 frames
3. Claw attack -> Claw attack: 60 frames
4. Claw attack -> Bite attack: 52 frames

The difference between two identical attacks, where you can observe a complete animation cycle, confirms the 1/0.9 APS (bite) and 1 APS (leap). The 52 and 62 frames however are odd, because they are not 6-frame-aligned. That's because the damage numbers are displayed in the "middle" of each attack. While the attack animations themselves are 6-frame-aligned, in this case, the damage display is not.

The animations can be broken down like this:
Claw:
animation start
attack: 35 frames [*]
damage number displayed
retreat: 25 frames
animation end

Bite:
animation start
attack: 27 frames
damage number displayed
retreat: 27 frames
animation end

or in a more graphical way: http://imgur.com/HjIXxPZ

[*] is estimated, the remaining numbers can be calculated afterwards.

This way, the transition from claw to bite can be explained by adding the claw-retreat (25 frames) and the bite-attack (27 frames), resulting in 52 frames.
The transition from bite to leap equals bite-retreat (27 frames) plus claw-attack (35 frames), resulting in 62 frames.

I started looking into the Dog attack puzzle pieces. Abbreviations: bite attack = BA, bite retreat = BR, claw attack = CA, claw retreat = CR.

Unbuffed:
either BA=28, BR=26, CA=36, CR=24
or BA=29, BR=25, CA=37, CR=23

only BBV:
either BA=21, BR=27, CA=28, CR=20
or BA=22, BR=26, CA=29, CR=19

The damage display and the animation are frequently offset by 1 frame. On a skeleton, the damage number is sometimes displayed when the dogs head is still above the skeleton, sometimes when his head is at the same height as the skeleton's head.

See http://i.imgur.com/ojB2TOq.jpg
Both screenshots are from the moment the damage is registered but from different animation cycles.

---------------------
Buffed attack speeds:
With BBV:
1. Bite attack -> Bite attack: 48 frames
2. Bite attack -> Claw attack: 55 frames
3. Claw attack -> Claw attack: 48 frames
4. Claw attack -> Bite attack: 41 frames
The animation parts would be: Claw 28 + 20 frames, Bite 21 + 27 frames

With 42% T&T, no BBV:
1. Bite attack -> Bite attack: 36 frames
2. Bite attack -> Claw attack: 41 frames
3. Claw attack -> Claw attack: 42 frames
4. Claw attack -> Bite attack: 37 frames
The animation parts would be: Claw 23 + 19 frames, Bite 18 + 18 frames

With 42% T&T + BBV:
1. Bite attack -> Bite attack: 36 frames
2. Bite attack -> Claw attack: 40 frames
3. Claw attack -> Claw attack: 36 frames
4. Claw attack -> Bite attack: 32 frames
The animation parts would be: Claw 20 + 16 frames, Bite 16 + 20 frames
Edited by AlCalzone#2424 on 11/29/2014 8:13 AM PST

I went through the remaining dog videos and counted the attack and transition durations I started yesterday, since those are easy and consistent to observe.

Unbuffed:
Bite attack -> Bite attack: 54 frames
Bite attack -> Claw attack: 62 frames
Claw attack -> Claw attack: 60 frames
Claw attack -> Bite attack: 52 frames

BBV:
Bite attack -> Bite attack: 48 frames
Bite attack -> Claw attack: 55 frames
Claw attack -> Claw attack: 48 frames
Claw attack -> Bite attack: 41 frames

42% T&T:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 41 frames
Claw attack -> Claw attack: 42 frames
Claw attack -> Bite attack: 37 frames

42% T&T + BBV:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 40 frames
Claw attack -> Claw attack: 36 frames
Claw attack -> Bite attack: 32 frames

44% T&T:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 37 frames
Claw attack -> Claw attack: 42 frames
Claw attack -> Bite attack: 41 frames

44% T&T + BBV:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 41 frames
Claw attack -> Claw attack: 36 frames
Claw attack -> Bite attack: 31 frames

48% T&T:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 37 frames
Claw attack -> Claw attack: 42 frames
Claw attack -> Bite attack: 41 frames

48% T&T + BBV:
Bite attack -> Bite attack: 30 frames
Bite attack -> Claw attack: 35 frames
Claw attack -> Claw attack: 36 frames
Claw attack -> Bite attack: 31 frames

49% T&T:
Bite attack -> Bite attack: 36 frames
Bite attack -> Claw attack: 37 frames
Claw attack -> Claw attack: 42 frames
Claw attack -> Bite attack: 41 frames

49% T&T + BBV:
Bite attack -> Bite attack: 30 frames
Bite attack -> Claw attack: 35 frames
Claw attack -> Claw attack: 36 frames
Claw attack -> Bite attack: 31 frames

Multi-player Pet Attack Speed Buffs

I tested the effect of 2x BBV:
Used a TMF Zombie Dog and counted the frames of the Claw -> Bite transition. With 49% T&T on all tests:
no BBV: 37 frames
1x BBV: 31 frames
2x BBV (same rune): 31 frames (no effect)
2x BBV (different runes): 26 frames

=> BBV with different runes stacks the attack speed buff.

I tested the effect of Mantra of Retribution - Transgression (+10% AS).
Again, I used a TMF zombie dog. This time without any further buffs.
Claw attack unbuffed: 60 frames
Claw attack with Mantra: 54 frames
Bite attack unbuffed: 54 frames
Bite attack with Mantra: 48 frames

I tested the effect of Laws of Valor (1x unruned):
This has a passive 8% buff and goes up to 15% when activated.

Melee fetishes and Head Hunters:
LoV passive (8%): 48 FPA
LoV active (15%): 42 FPA

=> So LoV has an influence. Without other buffs, the results are consistent with both formulas (additive and multiplicative).

Now it gets interesting.
With 44% Taskers and 8% LoV passive (total 52% buff), I would expect the following:
additive formula: 33.9 FPA, rounded to 36 FPA
multiplicative formula: 31.58 FPA rounded up to 36 FPA
Frame counting confirms this. 52% buff = 36 FPA.

With 44% taskers and 15% LoV active (total 59% buff), I would expect this:
additive formula: 32.61 FPA, rounded to 30 FPA
multiplicative formula: 30.19 FPA rounded up to 36 FPA
Frame counting results in 59% buff = 30 FPA

=> This disproves the multiplicative formula for melee fetishes/head hunters.

Edited by AlCalzone#2424 on 11/29/2014 3:09 PM PST

Back to Opening Post - http://us.battle.net/d3/en/forum/topic/13349475072?page=1#1
Wow, what a read.

I got a new computer and I'll give you T&T numbers when I have some time to figure out how to record video to disk and experiment properly.
I think there's enough of the population doing pet builds, and from what I've heard from PTR pet builds will also possibly/probably? be better in greater rifts too...

so this may in fact be worth stickying...

I know this isn't as important as Reaper's thread... but it's damn near close

the fastest way of accomplishing this is getting as many people as possible to do these three things:

02/04/2013 01:26 PMPosted by Nameless
please help in the campaign to get this thread stickied! Three things I want to ask you guys to do to help:

(1) "like" this thread - and get this thread to "highly rated status"
(2) click "request sticky"
(3) email forum@blizzard.com and
give them your name (battletag too, perhaps), title of thread, link to thread, and request for sticky. Dunno if they need a short reason, but it probably wouldn't hurt - and do this regularly (like once a week until it's stickied).

(FWIW, I just sent my 3rd weekly email with my request).

Let's do it!
07/07/2014 01:45 PMPosted by MCP
Wow, what a read.

I got a new computer and I'll give you T&T numbers when I have some time to figure out how to record video to disk and experiment properly.


Thanks for helping. There's also Garg:Restless Giant rune with Pet APS buff.

Currently we expect the Pet APS to be added for melee fetish and dogs because their basic Pet APS is 1.0 or higher.
We get Pet APS = 1.25 + (T&T + BBV + any other multi-player IAS buff)
Then to get frame interval, we take 60/(Pet APS) for the frames.

Currently, we expect the Pet APS to be divided for Garg because its basic Pet APS is (1/1.4 secs).
We get Garg frame interval = 84 / (1 + T&T + BBV + Restless + any other multi-player IAS buff)

Currently, Tiki Torchers and Head Hunters do not conform to either of the 2 scenarios above.

Another topic, see if you can breakdown the Rabid Dog mechanic for the residual poison effect.

To record, high-end Nvidia graphics card come with Shadowplay support. Otherwise, Bandicam allows up to 10 minutes per recording session (more than enough for our purposes). Frame by frame replay can be done using the default windows media player or the common free downloads such as VLC.
Awesome work paul.

Much appreciated

Got my answer on the damage roll on rings.

Ias/crit/crit damage rolls still outperform damage roll on a ring.
I think zombie dog AI was intended for tanking and thus wonder off to new trash adds despite already attacking am elite or RG.

I wonder how pet doctors are performing in Greater Rifts

GARG WP does enough cleave damage for me to live with it sitting around doing nothing half of the time
TY Paul!

...now my head hurts :)

and why dont we have an MVP yet?
07/07/2014 04:43 PMPosted by SpeedWeed
GARG WP does enough cleave damage for me to live with it sitting around doing nothing half of the time


Does Garg WP have cleave ability? I thought it was single target, according to the tooltip?
07/07/2014 07:20 PMPosted by PaulNg
07/07/2014 04:43 PMPosted by SpeedWeed
GARG WP does enough cleave damage for me to live with it sitting around doing nothing half of the time


Does Garg WP have cleave ability? I thought it was single target, according to the tooltip?


It does indeed have a cleave type swing.
07/07/2014 07:20 PMPosted by PaulNg
07/07/2014 04:43 PMPosted by SpeedWeed
GARG WP does enough cleave damage for me to live with it sitting around doing nothing half of the time


Does Garg WP have cleave ability? I thought it was single target, according to the tooltip?

His attack is AoE. This is clearly seen if you cast him, and then use piranhado to suck a bunch of trash to him. He will decimate it all at once.
07/07/2014 07:23 PMPosted by TristinRowe
It does indeed have a cleave type swing.


07/07/2014 09:35 PMPosted by vishnu
His attack is AoE. This is clearly seen if you cast him, and then use piranhado to suck a bunch of trash to him. He will decimate it all at once.


Thanks guys. I did a quick check for WP on the same video proof that tested Restless Giant. Captured good evidence on WP's Cleave characteristic there.
Thanks for all of this number crunching. I had decided a while back to run my pets on physical elemental dmg due to the attack speed differences after seeing a post hinting at just this... (I'm using SMK with no Zuni). Seems like a huge oversight on Blizz's part.
07/08/2014 08:27 AMPosted by d3tox
I had decided a while back to run my pets on physical elemental dmg due to the attack speed differences after seeing a post hinting at just this

can you post the link to where you saw this por favor?

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