[GUIDE] How to properly gear a WD

Witch Doctor
[ WORK IN PROGRESS - please make sure to check in again :)]


INTRODUCTION


“The spirits smile upon me.”

The ability to infect, slow and terrify their enemies gives witch doctors unprecedented control over a battlefield. They can manipulate opposing attacks and movements with debuffs and crowd control spells, rendering enemies easy prey for hungry pets. Witch doctors can also lay down fields of fire and venom that slowly leech life from advancing foes.

The Witch Doctor is a mysterious class - properly gearing one can be overwhelming for new players and those who are not familiar with the class. I frequently encounter questions like:

  • What to reroll on this item?
  • Which stats should I be looking for on my <insert slot here>?
  • Is this <insert item here> any good?
  • What can I improve on my gear?


This guide is meant to help answering those questions. I will go over each item slot and its specialities, discussing what to look out for and which stats to prefer.

TABLE OF CONTENTS


BASICS -- or: where does our damage come from?
http://us.battle.net/d3/en/forum/topic/17346234812#2

TOUGHNESS and HEALING -- or: how do I survive all those affixes?
http://us.battle.net/d3/en/forum/topic/17346234812#3

GEAR -- or: what to look out for?
http://us.battle.net/d3/en/forum/topic/17346234812#4

CDR, RCR, Damage Reduction -- or: the tale of diminishing returns
http://us.battle.net/d3/en/forum/topic/17346234812#5
BASICS -- or: where does our damage come from?


All skills in Diablo 3 are based off WEAPON DAMAGE. For each hit, a number from the damage range on your weapon -- the little white numbers below the big DPS number -- is randomly chosen and further increased by a lot of different multipliers which differ between the numerous builds.

The Witch Doctor has a number of stats to influcence those damage multipliers:

INTELLIGENCE or short INT is our main stat. It directly increases the damage of all abilities and effects.
INT should be on all pieces of gear with the exception of jewellery where other stats can be more beneficial.

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INCREASED ATTACK SPEED or short IAS increases the frequency of your attacks. Damage over time (DoT) skills do not benefit from IAS, pets do. For details see the linked guides.

There are two different kinds of IAS:

  • IAS on WEAPON, which can only roll on weapons and directly increases the attack speed of your weapon
  • and IAS (on GEAR), which can roll on certain gear slots and is further increased by Paragon points, multiplayer and follower buffs and skills.

Multiplying the weapon attack speed with IAS yields your attacks per second (APS):
[APS] = [weapon base APS] * (1 + [weapon IAS%] / 100) * (1 + [IAS%] / 100)

The displayed attack speed on your weapon is rounded and therefore not accurate, which can lead to errors in further calculations - especially when breakpoints are in play. A ceremonial knife with a base APS of 1.4 and 7% IAS has an attack speed of 1.498 but gets displayed as 1.5.

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ELEMENTAL DAMAGE INCREASE is another important multiplier. It increases the damage of all skills that deal the same type of elemental damage. Pet doctors are in a special position since the pet buffs from Mask of Jeram and the legendary gem Enforcer are grouped together in the same multiplier.

This rolls on a limited set of slots and should be targeted whenever possible.
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CRITICAL HIT CHANCE or short CHC is the chance that any attack critically hits. If it does, the CRITICAL HIT DAMAGE, short CHD, is applied on top of the base damage. Certain skills like DoTs do not crit but have an average critical hit multiplier calculated into their weapon damage.

These two stats are amongst the most important ones in Diablo 3 and preferred on as many pieces of gear as possible. There are only a few cases when you want to prefer another stat over CHC/CHD and most have to do with reaching a certain attack speed or CDR breakpoint. Please refer to dedicated threads for more information regarding build mechanics.

Sometimes it becomes neccessary to decide between the two stats - e.g. on rings with mandatory IAS rolls. A simple analysis can help:
Each hit that deals X damage has a CHC% chance to deal additional CHD% damage. The expected damage per hit over a longer period of time is therefore
X + X * [CHC%]/100 * [CHD%]/100

To decide which configuration yields the higher damage output in the long run, we need to look at the last part of that multiplier:
[CHC%] * [CHD%]
and use the configuration that leads to the higher value.


Lets assume we are sitting at 46% CHC and 400% CHD and have to decide if we want to roll 50% CHD or 6% CHC on a ring:
base configuration: 46 * 400 = 18400
add 50% CHD: 46 * 450 = 20700
add 6% CHC: 52 * 400 = 20800

This dismantles the misconception many players believe in that the CHC:CHD ratio should be 1:10. The second configuration which is far from that ratio leads to a higher damage output.

While this ratio would be the optimum in a mathematical optimization where we're trading one stat for a comparable amount of another stat, that's not what we're doing here. On rings, we get up to 6% CHC but only 50% CHD! Other slots are usually not worth considering.
Paragon points are a completely different animal. Here we can distribute a limited amount of points to equally weighted stats. Only getting close to the 1:10 ratio through paragon points is optimal.

TL;DR:

  • Roll your gear for the highest CHC*CHD value, then (and only then!) get as close as possible to the 1:10 ratio through paragon points.
  • If you have enough paragon points to max out both CHC and CHD, do that before considering your gear and ignore the 1:10 myth.


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Balancing DPS stats:
Deciding which stat is better -- INT, IAS, CHC or CHD -- can be quite difficult and must be done on a case to case basis since everyone is special. There are tools out there to help you do that; above all of them thrones this one:
http://www.d3planner.com

I cannot stress this enough. Use it! Simulate gear rerolls to find out the best stats if it's not immediately clear.
TOUGHNESS and HEALING -- or: how do I survive all those affixes?


Short answer: After a certain point, you simply don't. When fishing for the top tier Greater Rifts, everything will one-shot you.

But we can improve our survivabilty until then by choosing the right rolls on our gear. After all, a dead DPS deals no DPS. Preventing death is sometimes better than dealing a little more damage.

Like all classes we have a number of defensive stats to choose from:

VITALITY and LIFE BONUS increase our health pool, calculated as follows:
HP = [ <base HP> + <life per vit> * Vitality] * [1 + Life% / 100],

which translates to
HP = [ 316 + 100 * Vitality] * [1 + Life% / 100]

in the current patch (2.2). Without any gear at all, the base Vitality is 147.

While stacking Vitality and Life% is often the most effective way to maximize our effective HP, this makes LIFE PER SECOND and LIFE PER HIT less effective because they take longer to refill the pool the bigger it is.

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RESISTANCES reduce the damage taken from elemental attacks before it hits your health pool. Only one elemental resistance can apply per attack. In addition to resistance to all elements (short AR), your items can also roll resistances to a single element as secondary stats.

Resistances work hand in hand with ARMOR, which essentially does the same without distinguishing between different elements.

While Armor gets increased by DEXTERITY and STRENGTH (1 DEX/STR = 1 Armor), Resistances get increased by INTELLIGENCE (1 INT = 0.1 AR). That's why WDs are generally well stacked on Resistances and low on Armor.

Therefore we have to be on the lookout for Armor rolls on our gear.

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Special damage reduction:
Certain slots can roll melee, ranged and elite damage reduction. Those are a separate multiplier in the calculation of damage reduction. An attack is either classified as melee or ranged, so only one of those two stats can be active at any time. Elite damage reduction obviously only applies to attacks from elites.

In combination with elite affixes the mentioned stats are very counter-intuitive and/or bugged.
This thread has a table with all the information you might need:
http://www.diablofans.com/forums/diablo-iii-general-forums/diablo-iii-general-discussion/91166-elite-affixes-types-and-damage-reduction-mechanics


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calculationg your effective HP (eHP):
The raw damage we take gets reduced by the total damage reduction (DR)
[damage taken] = [raw damage] * (1 - [DR])

where the damage reduction gets calculated multiplicatively similar to CDR/RCR
[DR] = 1 - (1 - DR{Armor}) * (1 - DR{Resistance}) * (1 - DR{melee or ranged}) * (1 - DR{elite}) * (1 - DR{other})


In order to kill you, an enemy must deal enough damage that [damage taken] equals your health pool. The [raw damage] neccessary for that is called effective HP:
[eHP] = [HP] / (1 - [DR])


In http://us.battle.net/d3/en/forum/topic/5149150485 TBD has laid out how the single damage reductions are calculated:
DR{Armor} = Armor / (Armor+3500)
DR{Resistance} = Resistance / (Resistance + 350)


This essentially boils down to
[eHP] = [ 316 + 100 * Vitality] * [1 + Life% / 100] * [1 + Armor/3500] * [1 + Resistance/350] * ...

which shows that your effective HP scales linearly with all those 4 stats and there are no diminishing returns. Each additional point of Armor increases your eHP by the same amount as the previous one.
It also shows that in order to maximize our eHP we need to find a balance between Vit, Life%, Armor and AR.

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While Life per Second passively regenerates your health, Life per Hit heals you as long as you are attacking -- since a few patches ago it's essentially Life per Second while attacking.
Fast-attacking builds like pet and Carnevil builds benefit the most from Life per Hit while nuke builds like the old Jade Harvester mainly heal passively (or through skills).

Personally I don't have those two stats anywhere. Paragon points are enough IMO.
GEAR -- or: what to look out for?


Ok, let's get down to business. Here's a list of gear slots and their preferred stats.
The numbers in brackets denote the possible rolls (lvl 70 gear). "L" denotes normal legendaries, "A" their ancient counterparts.

Mandatory stats are bold, the preferred rolls for optional stats italic.
The listed alternative rolls for optional stats, especially toughness related ones should be considered inferior. Generally VIT gives you the most eHP, followed by Life, then Armor and Resistances.
But don't overinflate your health pool, you want to find a balance between raw health and mitigation. OftRepeated put it well:
05/09/2015 01:22 PMPosted by OftRepeated
All else being equal, having a smaller health pool with more mitigation increases the effectiveness of each point of healing compared to a setup with the same effective toughness but a larger health pool.

This balance also depends on the kind of healing you are getting. Fixed values are best paired with a slightly smaller health pool and more mitigation, %-based healing (like Simplicity's Strength or some passives) benefit from a larger health pool.

If you are aiming for a DPS position in group GRifts, prefer high values of mandatory rolls over the "correct" optional stats.

You cannot roll resistance to all elements (primary) and resistance to a single element (secondary) on the same item. If an item has a secondary resistance, it is impossible to enchant all resist on there.

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VOODOO MASK / HELM

One of our build-defining slots. The optimal stats are mostly the same across builds.

1. INTELLIGENCE (L: 626..750 | A: 750..1000)
Must-have!

2. CRITICAL HIT CHANCE (5.0%..6.0%)
Not much to say here. Important damage stat.

3. SOCKET
Be it for the 12.5% CDR from a diamond to lower your cooldowns faster, +23% LIFE from an amethyst or +41% XP for experience GRifts, this roll offers a lot.
Some builds prefer a socket over CHC (e.g. Jade, Tiki/Sac) because they need the CDR to work. So be sure to check out the relevant guides before making a decision.
Possible future builds might not need a socket and favor skill damage or mana regen instead. But for now I'd consider a socket mandatory.

4a. VITALITY (L: 626..750 | A: 750..1000)
preferred roll, alternatives are
4b. LIFE (10%..15%) and to a lesser extent
4c. ARMOR (??..??), ALL RESIST (??..??)
For the upcoming spender builds in patch 2.3,
4d. SKILL DAMAGE (+10..15%)
will become another preferred stat on this slot, although I don't want to give any recommendation yet if it's better to replace VIT or the SOCKET.

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CHEST ARMOR


1. INTELLIGENCE (L: 416..500 | A: 550..650)

2. VITALITY (L: 416..500 | A: 550..650)
preferred roll, alternatives are
LIFE (10%..15%) and to a lesser extent
ARMOR (??..??), ALL RESIST (??..??)

3. SOCKET (1..3)
Get three and socket Topazes (yellow) in there. Those give you a huge chunk of INT (+840).

4a. SKILL DAMAGE (+10..15%)
All the current cookie cutter builds can get a big boost here. Jade builds choose Haunt, pet builds Fetish Army. Spender builds might not find the correct roll here, go for mitigation instead:
4b. ARMOR (??..??) and ALL RESIST (??..??) and to a lesser extent
4c. LIFE (10%..15%) or
4d. elite damage reduction (10..11%).
Life% will give you the highest toughness, which is not always the best.

5. ATTACK SPEED (5..7%)
The wizard set item http://us.battle.net/d3/en/item/tal-rashas-relentless-pursuit can roll attack speed in this slot. Certain pet builds are flexible enough to take advantage of this additional damage source.

Secondary stats on the Chest Armor include
S1. MELEE DAMAGE REDUCTION (6..7%)
and
S2. RANGED DAMAGE REDUCTION (6..7%),
get those if possible. Rerolling can cost a lot of mats due to the rarity of the affix.

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SHOULDERS


1. INTELLIGENCE (L: 416..500 | A: 550..650)

2. VITALITY (L: 416..500 | A: 550..650)
preferred roll, alternatives are
LIFE (10%..15%) and to a lesser extent
ARMOR (??..??), ALL RESIST (??..??)

For the remaining two slots, we can choose from a list of affixes, very depending on the builds. In general, you want to get skill damage for your used damage dealer if that one is in the list of rolls. Mana heavy builds should target Resource Cost Reduction (RCR), cooldown based builds want Cooldown Reduction (CDR), some builds benefit from a combination of both. If you have room, squeeze in some mitigation here.

3a/4a. SKILL DAMAGE (+10..15%) ← take this if applicable
3b/4b. COOLDOWN REDUCTION (5..8%) ← for cooldown-based builds
3c/4c. RESOURCE COST REDUCTION (5%..8%) ← solid option for Mana heavy builds
3d/4d. ARMOR (??..??) ← highest mitigation (should be preferred over Life)
3e/4e. ALL RESIST (??..??) ← 2nd highest mitigation (should be preferred over Life)
3f/4f. LIFE (10%..15%) ← biggest health pool

For pet builds, the 4th roll is highly controversial. While pet builds certainly don't need cooldown reduction (CDR), this is one of the few slots where we can actually afford it. Higher CDR means we can use Spirit Walk more often and therefore move faster (which is a sore point for WDs) and (more important) avoid more damage. Also we get Big Bad Voodoo off cooldown faster, which translates to more damage in the long run.
I'm a big fan of CDR in this slot, others prefer more mitigation.

Honorable mention: AREA DAMAGE. Pet builds don't benefit from it and Jade has no room for the stat here. Future builds might prefer AD, especially after the planned rework.

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GLOVES

Not exactly build-defining but a very strong slot.
In general, you want to get trifecta gloves, meaning CHC, CHD and a 3rd stat that suits your build.


1. INTELLIGENCE (L: 626..750 | A: 750..1000)

2. CRITICAL HIT CHANCE (8%..10%)
Rolls higher than usual in this slot. Favor this over CHD if you have to choose.

3. CRITICAL HIT DAMAGE (26..50%)

4a. ATTACK SPEED (5%..7%)
for builds that scale with it (e.g. pets) or
4b. COOLDOWN REDUCTION (5%..8%)
if your build needs cooldown reduction (e.g. Jade).
4c. RESOURCE COST REDUCTION (5%..8%)
for Mana-heavy builds (e.g. Helltooth with focus on spenders)

If you can't get trifecta gloves, then
5. VITALITY (L: 626..750 | A: 750..1000)
should be the last stat.
ARMOR (??..??) and ALL RESIST (??..??) are also possible but not recommended.

TASKER and THEO
Those gloves are one of the few things in game that directly increase our pets' attack speed. Most other buffs increase their damage per attack but not the frequency at which they attack.
The affix can roll between 40 and 50% but it does not work like you might expect. Details: http://us.battle.net/d3/en/forum/topic/13349475072?page=1#8
Our pets have a fixed base attack rate which gets increased by T&T, BBV and certain multiplayer buffs. This increased attack rate is then rounded so that the attacks happen at multiples of 6 frame intervals (0.1 second).
Due to this rounding, there is literally no difference between 40% and 50% Taskers for all possible buff configurations (no buff up to 4 stacked voodoos). Only one of the two dog attacks benefits from 45+% Taskers, but since dogs are vastly underperforming, we can ignore that.

TL;DR: 40% and 50% Taskers are the same, choose the ones with better primary stats.

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BRACERS

This slot is highly DPS related. Make no compromises here.

1. INTELLIGENCE (L: 416..500 | A: 550..650)

2. ELEMENTAL DAMAGE (16..20%)
Bracers are one of the few slots where we can roll elemental damage. Get it and get it with the right element. Otherwise your bracers are bad, period.
The exception are bracers for zDPS support builds where you should get a toughness related stat instead.

3. CRITICAL HIT CHANCE (5%..6%)

4a. VITALITY (L: 416..500 | A: 550..650)
or
4b. ATTACK SPEED (5..7%)
This can roll on http://us.battle.net/d3/en/item/steady-strikers instead of Vitality and on http://us.battle.net/d3/en/item/lacuni-prowlers

5. MOVEMENT SPEED (10%..12%)
This is a fixed roll on Lacuni Prowlers. Depending on the other rolls (which can be quite bad), you can either choose to keep it for more DPS (each % of MS translates to 10 INT in Paragon) or reroll it to VIT for more toughness.

Secondary stats on Bracers include
S1. MELEE DAMAGE REDUCTION (6..7%)
and
S2. RANGED DAMAGE REDUCTION (6..7%),
get those if possible. Rerolling can cost a lot of mats due to the rarity of the affix.
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BELT

This slot can either be DPS "{D}" oriented or toughness "{T}" oriented, the rolls differ vastly between those two choices.

1. INTELLIGENCE (L: 416..500 | A: 550..650)

2 {D}. VITALITY (L: 416..500 | A: 550..650)
if you are gearing for toughness or didn't get a http://us.battle.net/d3/en/item/the-witching-hour with skill damage. Alternatively LIFE (10%..15%) or if you got really unlucky, ARMOR (??..??).
The DPS choice for the second roll would be
2 {T}. PRIMARY SKILL DAMAGE (10..15%)
Must-have for Carnevil (Poison Dart). Otherwise, primary skills are so bad, it's usually not worth gearing for. Spirit of Arachyr could make some use of it, but the set is still undergoing iterations.

3 {D}. ATTACK SPEED (5..7%)
which can roll on http://us.battle.net/d3/en/item/the-witching-hour, http://us.battle.net/d3/en/item/hellcat-waistguard after patch 2.2 and the craftable (!) http://us.battle.net/d3/en/artisan/blacksmith/recipe/fleeting-strap.
3 {T}. LIFE (10%..15%)
is your alternative when gearing for toughness, other toughness stats to a lesser extent.

4a {D}. CRITICAL HIT DAMAGE (26..50%)
only rolls on the Witching Hour, other DPS belts should have
4b {D}. VITALITY (L: 416..500 | A: 550..650)
When gearing for toughness,
4c {T}. ARMOR (??..??)
is your best bet.

Other choices for a 4th stat include
4d. COOLDOWN REDUCTION (5%..8%) from http://us.battle.net/d3/en/item/vigilante-belt
4e. RESOURCE COST REDUCTION (5%..8%) from http://us.battle.net/d3/en/item/saffron-wrap, could be interesting for spender builds, but sadly we seem to be forced into http://us.battle.net/d3/en/item/belt-of-transcendence for those.

Bets can roll certain interesting secondary affixes:
S1. Chance to Freeze on Hit (1.0%..5.1%) which is great for Crowd Control (CC) but hard/expensive to get (also heavily nerfed in patch 2.3)
and
S2. MELEE DAMAGE REDUCTION (25..30%). Those exceptionally high values are found on http://us.battle.net/d3/en/item/string-of-ears

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PANTS

Pretty boring slot, not much to choose from

1. INTELLIGENCE (L: 416..500 | A: 550..650)

2. VITALITY (L: 416..500 | A: 550..650)
preferred roll, alternatives are (to a lesser extent)
ARMOR (??..??), ALL RESIST (??..??)

3. SOCKET (1..2)
Get two and socket Topazes (yellow) in there. Those give you another huge chunk of INT (+560).

4a. ARMOR (??..??)
preferred roll for most builds.
4b. ALL RESIST (??..??) and
4c. Life per Second (??..??)
are ok as well.
4d. PRIMARY SKILL DAMAGE (10..15%)
Same as for the belt slot: Carnevil prefers Poison Dart damage, all other builds should not roll primary skill damage, unless stated in a specific build guide.

http://us.battle.net/d3/en/item/swamp-land-waders can roll
4e. POISON ELEMENTAL DAMAGE (15..20%)
However not many builds currently benefit from that. The roll also takes up a primary affix, therefore conflicts with a toughness stat.

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BOOTS


1. INTELLIGENCE (L: 416..500 | A: 550..650)

2. VITALITY (L: 416..500 | A: 550..650)
preferred roll, alternatives are (to a lesser extent)
ARMOR (??..??), ALL RESIST (??..??)

3a. ARMOR (??..??)
preferred roll for most builds.
3b. ALL RESIST (??..??) and
3c. Life per Second (??..??)
are ok as well.

4a. MOVEMENT SPEED (10..12%)
Each % of MS here lets you invest another 10 INT through paragon points. So either take this roll for more DPS or choose an additional affix from 3a..c.
For the upcoming spender builds in patch 2.3,
4b. SKILL DAMAGE (+10..15%)
will become another preferred stat on this slot. Boots can roll the same skill damage as Voodoo Masks and Helms.
You could replace the mitigation/healing affixes with skill damage and keep Movement Speed for slightly more DPS.

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WEAPON

Probably the most important slot in our arsenal. The base for all damage calculations and often a build-defining item.

The best rolls on the weapon vastly depend on the build they are used in and cannot be generalized like the other slots.

1. WEAPON DAMAGE
The rolls vastly differ between the type of weapon used. In general you want the range to be as high as possible and as narrow as possible -- the average should be as high as possible.
For example, +1250..1440 (average 1345) is better than +1200..1480 (average 1340).

The type of elemental damage on here mostly does not matter. It was supposed to have an effect on crit but that has been dropped during development of D3.
Does anyone have a link the the source, cannot find it right now...

There are however two types that still have an effect in combination with certain legendaries:


All skills take the element of your chosen skill runes and are not influenced by the element on your weapon.

2. INTELLIGENCE (L: 626..750 [1 hander], 946..1125 [2 hander] | A: 750..1000 [1 hander], 1125..1465 [2 hander])

3. SOCKET
Putting a Flawless Royal Emerald in there gives you +130% CHD. The biggest gain of CHD in a single slot, absolutely mandatory!

For the remaining rolls, please look in the dedicated build threads, e.g.
Jade Harvester - http://us.battle.net/d3/en/forum/topic/13138914261 (reached post limit, seems dead, any better ones?)
Carnevil - http://us.battle.net/d3/en/forum/topic/14527433038
Helltooth - CDR/RCR could be useful, depending on the build. No guides yet.

Generic pet builds favor +10% damage over +7% IAS (get both if possible).

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MOJO

The Witch Doctor's handbag with about as many affixes as you might expect in there. Too heavy to carry together with a 2-handed weapon.

1. DAMAGE RANGE (L: 340..450 | A: 450..600)
Like on the weapon the average should be as high as possible.

2. INTELLIGENCE (L: 626..750 | A: 750..1000)

3. VITALITY (L: 626..750 | A: 750..1000)
A major slot to stack Vitality, too good to pass up.

4. CRITICAL HIT CHANCE (8.0%..10.0%)
CHC rolls as high as on gloves here!

5. SKILL DAMAGE (+10..15%)
Our 3rd slot for relevant skill damage, very important damage boost. After patch 2.2,
http://us.battle.net/d3/en/item/zunimassas-string-of-skulls rolls 20-25% Fetish Army damage,
http://us.battle.net/d3/en/item/homunculus 20-25% Sacrifice damage (another stat can be rerolled for up to 40% Sac damage total).

Additional stats (might replace one of the aforementioned ones) include
6a. COOLDOWN REDUCTION (5..8%)
6b. ELITE DAMAGE (5..8%) ← one of our few sources of elite damage after patch 2.2 in certain builds. Get it if you can do so without sacrificing other stats!
6c. MANA REGENERATION (12..14) ← might be viable in spender builds. No recommendations yet.

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AMULET


1. SOCKET
Since the introduction of legendary gems, each WD build uses 3 of them. This makes a socket in amulets mandatory.

2. CRITICAL HIT CHANCE (8.0%..10.0%)
Our last major slot for up to 10% CHC.

3. CRITICAL HIT DAMAGE (51%..100%)
2nd best slot for CHD after the weapon. Rolls up to 100%!

4a. ELEMENTAL DAMAGE (16..20%)
Getting this on top of CHC and CHD is the dream. But since not all amulets are perfect, we often have to deal with
4b. INTELLIGENCE (L: 626..750 | A: 750..1000)
which is not bad either.

The http://us.battle.net/d3/en/item/eye-of-etlich has a very interesting secondary stat:
S1. RANGED DAMAGE REDUCTION (27.7–32.9%),
allowing you to stack damage and toughness in a single slot.

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RINGS

1. SOCKET
Just like on the amulet. Get a socket in each ring!

The next two rolls will heavily depend on the build. Deciding between rolls on rings can be very tricky. For really well geared Carnevil docs, IAS/CHC/CHD/Socket rings are best in slot (BiS). This is not neccessarily true for other builds. Sometimes IAS is better than a mediocre CHD roll and so on. Some builds prefer completely different stats.
2a/3a. CRITICAL HIT CHANCE (5.0%..6.0%)
2b/3b. CRITICAL HIT DAMAGE (26%..50%)
Balance those two stats by maximizing CHC*CHD if you have to decide between them, otherwise get both. You usually want at least one of those two. Other options are
2c/3c. ATTACK SPEED (5.0%..7.0%)
Must-have for Carnevil builds.
2d/3d. COOLDOWN REDUCTION (6.0%..8.0%)
Interesting stat for some builds, especially Jade
2e/3e. RESOURCE COST REDUCTION (6.0%..8.0%)
Rolls on http://us.battle.net/d3/en/item/obsidian-ring-of-the-zodiac and mostly used by hybrid cooldown/spender builds. No real use for WD yet, but might come to glory after the next patch.

4. INTELLIGENCE (L: 416..500 | A: 550..650)
Not exactly preferred on the best rings out there, but many will have it. Decent boost on ancient rings.

The http://us.battle.net/d3/en/item/stone-of-jordan used to be BiS for many builds until patch 2.2 hit. It rolls elite damage and elemental damage. Rolling off either stat results in a ruined ring. Don't do that!

http://us.battle.net/d3/en/item/unity rolls elite damage. The best ones have Socket/CHC/CHD/Elite affixes.
CDR, RCR, Damage Reduction -- or: the tale of diminishing returns

Statements like those can be read everywhere:

  • "CDR has diminishing returns"
  • "Armor gets worse the more you have"
  • I even saw "Crit Chance has diminishing returns" once...

But in fact, they are all far from the truth.

So, what are DIMINISHING RETURNS?
Oversimplified, there are 3 types of mathematical relationships between inputs and outputs:

  • 1. Adding a fixed amount to the input leads to an absolute gain on the output that becomes less and less the more you add to the input. The output becomes saturated, this is what we call DIMINISHING RETURNS. A prime example are monster CC resistances - the more you CC a monster with hard crowd control effects, the less effective subsequent CCs will become, until they stop working almost completely.
  • 2. A linear relationship like gas mileage (thanks PaulNG for the example): If my car can drive 100km with 6l of fuel, adding another 6l will allow it to drive another 100km on top. Adding a fixed amount to the input always yields the same absolute gain on the output. The relative growth becomes less and less - but in contrast to these are not diminishing returns, because we always gain the exact same amount!
  • 3. Exponential growth: Adding a fixed amount to the input always yields the same relative gain, no matter how high the input is. This is the strongest type of relationship between stats!


"But CDR has diminishing returns! If I add 10% here and 10% there, I don't get 20%!"
Stop right there. CDR, RCR and Damage Reduction (DR) are calculated multiplicatively, not additively because that would allow the numbers to go over 100%, which makes no sense. The individual sources of those stats are multiplied with each other in this fashion (same for RCR and DR):
CDR = 1 - (1 - CDR1) * (1 - CDR2) * ... * (1 - CDRn)
The reason many people think that leads to diminishing returns is because they are looking at the wrong output. The percentages may grow less and less, but we don't stack CDR sources to get a high CDR value.

"Wait, what?!?"
Yeah, I meant that.

Let's say we're heavily relying on a skill that has a 10s cooldown, deals 1000 damage and has a 1s duration.
With 0% CDR, we can cast this skill 6 times per minute and have 10% uptime and deal average 100 DPS.
Adding one (hypothetical) CDR source that gives us 50% CDR reduces the cooldown to 5s, we can now cast 12 times per minute, have 20% uptime and deal average 200 DPS ‒ a 100% relative gain in DPS and uptime!
Adding another 50% CDR source puts us at 75% sheet CDR and 2.5s cooldown. Although our sheet CDR has only increased by 25% absolute (or 50% relative), we can cast our skill 24 times per minute now, have 40% uptime and deal 400 DPS ‒ another 100% relative gain in DPS and uptime!

  • A CDR source always contributes the same relative gain to uptime and DPS, no matter how much CDR we have already stacked.
  • Bigger CDR sources result in a higher relative gain per %CDR than smaller CDR sources, see the spreadsheet I linked at the bottom of this post.


Back to my statement: We don't stack CDR sources to get a high CDR value. We stack CDR sources to cast our skills more often. And in doing so, CDR always gives you the same relative gain, no matter how much you already have!

"So what about RCR?"
To evaluate RCR, we need to look at our skills in a different way: Mana consumption.
Assuming we have a Mana pool of 1000 and a skill that deals 10 damage and costs 100 Mana. Let's ignore Mana Regen for now.

Without any RCR, we can cast the skill 10 times, dealing a total 1000 damage.
Adding a 50% RCR source (for example a specialized weapon) reduces the skill's cost to 50. We can now cast it 20 times before running out of Mana and deal 2000 damage total ‒ a 100% relative gain in damage!
Another 50% RCR source puts the skill's cost at 25. Which means we can cast it 40 times for a total of 4000 damage ‒ another 100% relative gain in damage.

RCR works just like CDR in that fashion. No matter how much RCR we already have, a RCR source always gives us the same relative gain in damage per mana. Like with CDR, bigger sources contribute a larger gain per %RCR than smaller sources.

To sum it up: We don't stack RCR sources to get a high RCR value. We stack RCR sources to cast our spenders more often with a limited Mana pool.
And in doing so, RCR always gives you the same relative gain, no matter how much you already have!

tl;dr:

CDR and RCR are not subject to diminishing returns. In fact they are not even linear, because they always give the same relative gain, no matter how much we've already stacked. Which means they grow in effectiveness as we stack those stats.

CDR and RCR scaling spreadsheet:
https://docs.google.com/spreadsheets/d/14e_hZi9TwbmEhBFFstunUsUzkPXfinXRm3SCJ5MXik0/edit?usp=sharing


"But Armor/Damage Reduction has diminishing returns!"
Nope, still not true. We shall not be looking at Damage reduction from Armor in our character sheet, these are not the numbers we are looking for. What really matters is how much damage we can take before dying, this is called EFFECTIVE HP (eHP). As I've shown in Post #3, eHP essentially boils down to
[eHP] = [ 316 + 100 * Vitality] * [1 + Life% / 100] * [1 + Armor/3500] * [1 + Resistance/350] * ...

For simplicity's sake we keep all the multipliers at 1 except the Armor one.

With 0 Armor, our eHP becomes 1 * 1 * (1 + 0) * 1 = 1, so we can take 1 damage before dying.
Adding 3500 Armor, that becomes 1 * 1 * (1 + 1) * 1 = 2, we can now take 2 damage, that is 1 damage more than before (+100%).
Add another 3500 Armor, and our eHP becomes 1 * 1 * (1 + 2) * 1 = 3, we can now take 3 damage, that is 1 damage more than before (+50%).

Armor is a prime example of a linear relationship. We always gain the same absolute amount of eHP for a fixed amount of Armor. Although the relative growth becomes less and less, these are not diminishing returns!
Because VIT, LIFE%, AR and Armor are all multipliers to eHP, another effect happens here. As we stack Armor, all those other multipliers increase in effectiveness. This is why it is not recommended to only stack Armor ‒ not because Armor becomes worse the more you have, but because the other stats become better!

In contrast to Armor, Damage reduction scales just like CDR and RCR, which makes DR scaling an exponential relationship - the opposite of diminishing returns.
(you guessed it... this one is reserved too)
(this one too)
(just one more...)
05/08/2015 05:15 AMPosted by AlCalzone
This dismantles the general concensus that the CHC:CHD ratio should be 1:10.


There was no concensus ever. It was a fallacy and I've provided the counter-proof many months ago.

05/08/2015 05:16 AMPosted by AlCalzone
which shows that your effective HP scales linearly with all those 4 stats and there are no diminishing returns.


This is a wrong concept. The definition of diminishing returns compares the input vs the output.
If you think 1% increase in Armor mitigation leads to 1% increase in effective HP, that is correct. However, 1% increase in Armor is not the input in the game.
At low Armor, you get 1% increase in mitigation by say 500 Armor. At high Armor, you get a further 1% increase in mitigation by perhaps 1500 Armor. On that account, diminishing returns are evident for Armor.

Same goes for all other forms of mitigation, or damage calculations, or cooldown calculations.

Numerical illustration. At 56% mitigation to 57% mitigation, say you need 500 Armor. 100 in-coming damage reduced from 44 to 43. At 80% mitigation, adding 500 Armor does not lead to 81% mitigation. So that 100 incoming damage does not get reduced from 20 to 19. That is also proof of diminishing returns.

A linear relationship is like 1L of petrol running 20km for a car. Adding 1L will run another 20km, adding 2L will run another 40km. No diminishing returns. If you add 5L and the car runs only 97km, then it experienced diminishing returns based on the petrol as input vs the distance as output.
05/09/2015 05:02 AMPosted by PaulNg
There was no concensus ever. It was a fallacy and I've provided the counter-proof many months ago.

Let me reword it, "concensus" might not have been the best choice of words. However, many people still religiously believe it, which is why I absolutely want to show it here again.
Do you have a link to your post, I'll gladly reference it.

This is a wrong concept. The definition of diminishing returns compares the input vs the output. [...] On that account, diminishing returns are evident for Armor.

I disagree.

We have to be careful what we apply the diminishing returns to. Of course adding 500 Armor increases the %mitigation less and less the more armor we have. The damage we take does not get reduced linearly. Hoever, I wasn't talking about damage taken, but the total damage we can take before dying.

Because of the way eHP is calculated (dividing base HP through the mitigation), each % we add here gets more and more powerful. If each point of Armor would add the same amount of mitigation, our eHP would increase more for each point of Armor the more we already have.

Quin69 has made a good video about this concept regarding CDR and RCR, showing that those two stats get even powerful/efficient the more you already have: https://www.youtube.com/watch?v=G26OM19vR8g

Above I've shown that eHP scales linearly with all the toughness:
[eHP] = [ 316 + 100 * Vitality] * [1 + Life% / 100] * [1 + Armor/3500] * [1 + Resistance/350]

Lets assume for a simplified calculation that all multipliers except the one with Armor are 1. We start with 0 Armor and add 3500 a few times after that (this is the input we have, fixed armor numbers):
eHP (0 Armor) = 1 * 1 * (1 + 0) * 1 = 2
eHP (3500 Armor) = 1 * 1 * (1 + 1) * 1 = 2
eHP (7000 Armor) = 1 * 1 * (1 + 2) * 1 = 3
eHP (10500 Armor) = 1 * 1 * (1 + 3) * 1 = 4

Each 3500 Armor we add increase our eHP by exactly the same amount, 1 in this case. Just like your gas mileage example. Add 1 liter, increase total distance by 20km.

The fact that incoming damage in a GR setting scales exponentially and therefore quickly overtakes the amount of toughness we can stack is a different animal.
05/09/2015 05:28 AMPosted by AlCalzone
Each 3500 Armor we add increase our eHP by exactly the same amount, 1 in this case. Just like your gas mileage example. Add 1 liter, increase total distance by 20km.


I see what you mean now, thanks for the clarification. The delta Mit diminishes, but the delta eHP still increases linearly with the input Armor.

I prefer your short summary on the CHC&CHD argument. Mine was too long-winded written at a time against the growing misconception to provide a counter-proof.

Good work so far! What will be your thread title?
Al,

Nice post. I especially like the section you did on toughness, because way too many people think you have to be a glass cannon to succeed in GR's. Every day I see people asking why they can't survive GR 45 affixes, and when I look at their profile I see a bunch on non ancient armor with lousy +vit rolls.

The truth is there are only 3-5 slots that you DON"T want a good vitality roll in, and maximizing DPS doesn't help if you can't survive long enough to make use of it. Especially when you're gambling I think it's a good idea to spend some time getting a good set of ancient armor before you start spending everything trying to get any weapon. Maybe it's just me, but I'd prefer to fail with no deaths because I still need to upgrade my jewelry/weapons than to fail because I keep getting one shot by T-storms or charging anarchs.
Just a minor point.
Generally, life% provides more toughness than armor or all resists, if you have to choose between the three.

However everyone is special and a tool such as d3planner.com will show you the best toughness stat, if you have a choice.
05/09/2015 10:25 AMPosted by MCP
Generally, life% provides more toughness than armor or all resists, if you have to choose between the three.

I've written that at the beginning of post #3
While stacking Vitality and Life% is often the most effective way to maximize our effective HP...

but I'll make sure to mention it again where it becomes relevant -- for the alternative affixes.

The holy grail D3Planner will be linked to and recommended, that's for sure.

05/09/2015 06:14 AMPosted by PaulNg
Good work so far! What will be your thread title?

Thanks! I was thinking "[GUIDE] How to properly gear a Witch Doctor", but I'm open to suggestions.

05/09/2015 08:03 AMPosted by EdGreyfox
maximizing DPS doesn't help if you can't survive long enough to make use of it. Especially when you're gambling I think it's a good idea to spend some time getting a good set of ancient armor before you start spending everything trying to get any weapon.

Very good points! I'll make sure to include your thoughts.

Do you guys have content ideas for the reserved posts? After the discussion with PaulNG, I was thinking of dedicating one of those to diminishing returns. Maybe there are some other topics that fit into the whole gearing theme and are worth discussing.
A short Math. proof for optimum ratio of CC : CD = 1:10.

Assuming 1 CC = 10 CD
Let x = CC, y = CD

Without loss of generosity, for each character you have

10x + y = K where K is some constant depending your gear
From the damage formula, we know that the damage is proportional to a factor z where

z= xy

Now from above equations, we have
z = xy
= (K- y) • y / 10
= ky/ 10 - y^2/10

By differentiation,
dz/dy = k/10 - 2y/10
Setting dz/dy =0
We have
dz/dy = k/10 -2y/10= 0
So z is at maximum when y = K/2

Since 10x +y = K
We have
x = (K-y)/10 = (K- K/2)/10 = K/20

So max z when y=K/2, x=K/20
CC:CD = y: x = K/2 : K/20 = 10:1

QED
PS
The proof in previous post in general should apply to most common build cases when we can choose between CC and CD

Note that we should always max out the constant K whenever possible to get max damage; therefore get CC CD whenever possible. (this agree to PaulNG's comment).

Also, other exceptions may apply
For examples, breakpoint fulfillment, double dip attack speed, etc...

Different builds have different requirements and player should refer to the individual build guide for the best build result.
Luffy, you have just proven that getting a 1:10 ratio through paragon points, where your assumption
05/09/2015 11:02 AMPosted by Luffy
10x + y = K where K is some constant

holds, is optimal. Here, x and y denote the amount of paragon points we spend on CHC and CHD, which are naturally limited (for Paragon <400), meaning we have to trade between those two. This is what mathematical optimization is all about.

This does not work for rerolling gear slots for two reasons:
1. You either add 6% CHC or 50% CHD or reroll one of two existing crit stats to the maximum, essentially adding more of this stat. You don't trade between those two stats, as in removing 10% CHD to add 1% CHC.
2. The interesting slots (rings) don't follow the 1:10=5:50 ratio. The rolls here are 6:50, heavily favoring CHC.

05/09/2015 11:22 AMPosted by Luffy
other exceptions may apply
For examples, breakpoint fulfillment, double dip attack speed, etc...

Different builds have different requirements and player should refer to the individual build guide for the best build result.

Good points, I'll mention those.
05/09/2015 12:12 PMPosted by AlCalzone
This does not work for rerolling gear slots for two reasons:1. You either add 6% CHC or 50% CHD or reroll one of two existing crit stats to the maximum, essentially adding more of this stat. You don't trade between those two stats, as in removing 10% CHD to add 1% CHC.2. The interesting slots (rings) don't follow the 1:10=5:50 ratio. The rolls here are 6:50, heavily favoring CHC.


yea, you bet I knew the 6cc/50cd tradeoff on rings before I put the math up there.

the purpose of posting the proof is
1. to show the missing piece of where the rumor of cc:cd = 1:10 is from.
2. as a guideline in general.

it's, by no means, a flawless one.
as what I put in P.S., you always want to max out the K.
that means u almost always wanna put both CC and CD on ring... and CC is better than CD as you can get a high K in general, if u have to choose one out of the two.
05/09/2015 11:02 AMPosted by Luffy
Assuming 1 CC = 10 CD


No Luffy, you didn't prove anything. All you did was make an assumption, and then manipulate equations in one circle and come back to your same assumption.

If we assume 1.2 CHC : 10 CHD, we going to end up one circle with your maths and come back to the same result 1.2:10. What does that prove? Nothing.

In fact, due to the way the items roll of CHC and/or CHD on many of the slots (mask, bracer, rings, glove, belt), the "ratio" 1.2:10 is a closer approximate, but ratios are meaningless because the higher output is what we seek.

The gearing for 1:10 ratio is always the minimum point or worst-case-scenario for gearing. Any extra CHC or CHD is going to yield better output from that point.

When we look at a function z = x.y
obviously the more x or y the merrier, there is no maximum point at all, they are all minimum points. I don't even need to go into calculus or derivatives to understand this simple multiplication.

In mathematics, a maximum turning point means that if you increase x or y further, the output will decrease, or if you decrease x or y further, the output will also decrease. That is not the case here.

Neither are APS breakpoints maximum points, they are just efficient breakpoints for gearing. If you keep increasing APS, you keep entering the next higher bracket (DPS).

The only application for maximum point in this game so far, is the legacy Cloud of Bats, where you have "wasted damage" as part of the mechanics, where the final incomplete tick is discarded. In that situation, APS 1.99 is lower DPS than APS 2.01, APS 2.04 is lower DPS than APS 2.01 also.

Taken from July2013,
CoB Mechanics (Part 1): Wasted Damage
*Special thanks to sssc, Nubtro, Wachati for the research collaboration:http://us.battle.net/d3/en/forum/topic/9661246127?page=1

CoB begins channel at 500.5% damage and rises every tick until 1001% damage. This is a multiplier of 10.01 at maximum efficiency. However, we seldom get maximum efficiency and we always encounter some "wasted" damage.

The game calculates the
Tick Incremental Damage = [ (Half Melee Damage x 5.005) / (APS x 10) ]

The missing portion of the CoB multiplier comes from the way the Tick Incremental Damage is calculated. In my test, I had an APS of 1.45, which means I can expect 14.5 ticks over 5 seconds. I only enjoyed 14 increments instead of 14.5 increments. The final 50% of the tick increment value fizzled off, because in the game, we either get a tick or no-tick. The decimal point is discarded.

If my APS is 1.49, 90% of the final tick increment value will fizzle off.
If my APS is 1.41, 10% of the final tick increment value will fizzle off, getting closest to the 10x multiplier.

It seems strange that slower sheet APS and lower sheet DPS can actually produce higher CoB DPS in-game, but it is true (accurate as at Patch 1.08).
05/09/2015 08:03 AMPosted by EdGreyfox
way too many people think you have to be a glass cannon to succeed in GR's

Well, the unfortunate truth is that at the very highest levels this is still the case, when you're really pushing the capabilities of your gear. Not to say that you're wrong - there's a swath of difficulty below the absolute fishing-peak where you do benefit from increased toughness. This is a lot more fun, too.

Also, I'll make a plug for armor/AR over %life in gearing for toughness. All else being equal, having a smaller health pool with more mitigation increases the effectiveness of each point of healing compared to a setup with the same effective toughness but a larger health pool.

Great work, Al! I'm sure we'll be sending people here regularly.

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