Among the items to be found in the new Tribal Cache is the Witch Doctor’s weapons, which come with the following effect:
Whenever you hit you have a 33% chance to hex your target and deal additional damage. The damage dealt increases each time this effect is applied, up to a maximum of 5 times, and is guaranteed to trigger on critical hits.
Whenever an enemy affected by a hex is defeated, nearby enemies are dealt damage, based on the number of times the effect has been applied.
Moreover, the Tribal Hex lasts five seconds, refreshes its duration with every new application, persists at maximum strength as long as it is refreshed, and, if it fails to refresh before expiring, all stacks accumulated on a target expire and must be gained anew. This marks the Witch Doctor as a weapon that excels at continuous, sustained damage over time.
How does this compare with previous cache weapons? Let’s go over the math. If we assume your critical hit chance is at 50% and normal hits comprise the remaining 50% of hits, the chance to trigger Tribal Hex is 66.5%:
0.5 + (0.5 * 0.33) = 0.665
Since the chance to gain each stack is equal, we can multiply the maximum number of stacks by the quotient of one second divided by 66.5% to calculate the average time in seconds it takes to reach the greatest damage potential of Tribal Hex:
5 * (1 / 0.665) = 7.519
Each stack of Tribal Hex has a coefficient of 0.15 damage, for up to 0.75 with five stacks. To determine the potential damage per second, we must first calculate the damage per second dealt while the hex is being stacked, which can be done by adding the coefficient of each stack and dividing it by the average time to reach five stacks:
((0.15) + (0.15 * 2) + (0.15 * 3) + (0.15 * 4) + (0.15 * 5)) / 0.7519 = 0.29924
From then on, as long as Tribal Hex is refreshed it will then deal this much damage per second:
0.75 * 0.665 = 0.49875
By how much damage Tribal Hex will deal over time depends on the duration of the encounter and how reliably you can maintain its effect. For example, in order to arrive within 10% of the maximum coefficient of Tribal Hex (0.448875), it’ll take about 69 seconds of combat time:
~0.49875 * (1 - 0.1) = (0.29924 + (0.49875 * (x – 7.519))) / x
x = 69.1902
To evaluate how Witch Doctor compares to other Epic weapons, we must first give an overview of how much damage these weapons are capable of.
Epic Cache Weapons
Anima-Touched: you have a 33% chance to deal 0.85 damage whenever you hit a target. You are healed for 100% of the damage dealt. The damage per second is straightforward:
0.33 * 0.85 = 0.2805
Flame-Wreathed: you have a 15% chance with every hit to deal 0.5 damage to your target every second for five seconds. For instant-cast builds, the damage per second comes to:
0.15 * 0.5 * 5 = 0.375
Plasma-Forged: Whenever you hit, you have a 25% chance to deal 0.563 damage to the target. The damage dealt increases to 1.125 the second time the damage triggers the effect on the same target and 2.813 damage the third time, which then resets the counters to zero. Since you have a 25% chance to gain each counter, it takes an average of four seconds per counter and twelve seconds for three counters. Therefore, the damage per second is determined by dividing the sum of the coefficients by twelve seconds:
(0.563 + 1.125 + 2.813) / 12 = 0.3750833
Frost-Bound: you have a 20% chance to deal 1.5 damage to the target and reduce your incoming damage by 7.5%. 20% of 1.5 is 0.3 damage per second.
Let’s use this formula to calculate approximately how long you must deal damage over time to equal the damage output of these Epic weapons:
x = (0.29924 + (0.49875 * (y - 7.519))) / y
Where x equals the coefficient of an Epic weapon and y equals the anticipated time it takes to match this coefficient. We want to solve for y. Here’s a table of the results:
|Weapon||Time in Seconds|
Witch Doctor will deal more damage per second than other Epic cache weapons when your critical hit chance is 50% and combat time exceeds these values. Its weakness, however, is that it has an up-time and significant ramp-up time that scale with your critical hit chance. A large portion of the Tribal Hex damage may never be realized if your combat encounter is short or has frequent disruptions that would reset your hex counters, like you might experience in the New York raid. The current state of the end game offers few situations that favor sustained DPS once the power of your gear outpaces a given activity’s difficulty level. The Witch Doctor, then, is impracticable to recommend as a long-term solution when burst damage is a dominant end-game force.