Hungering Arrow: Puncturing vs. Devouring

Demon Hunter
Hey folks.
I created a quick spreadsheet of the damage of Hungering Arrow. I factored in the chance of pierce, additional damage from Devouring, and the benefits of higher pierce. I'm interested to hear peoples thoughts, and whether this is accurate. If I'm correct, the Puncturing Arrow nets more damage, though my results don't feel right. I think I've forgotten something. What am I missing?

https://docs.google.com/spreadsheet/ccc?key=0AuxRj3qladjUdHd2WDVfeWZLbE14U2prVVdMNDZ0OEE
I'm on my phone so it's kind of difficult to click links, but puncturing should not give you more damage than devouring. Puncturing averages 230% weapon damage (115/.5) whereas Devouring averages 243% or 294% depending on whether the damage bonus is additive of multiplicative (respectively) since the tooltip is unclear. It would make sense that its additive since the multiplicative bonus is rather overpowering. The math on that is a little more complicated but there are other threads on this forum containing it.

The advantage to puncturing is that more arrows means you hit more targets. This is very useful for clearing large packs of weaker enemies. Devouring concentrates its damage into less arrows that are more powerful which could lead to overkill when fighting mobs that aren't very stout. Puncturing could also proc more on-hit effects because of the extra arrows depending on if there is any sort of penalty for the pierces or if the abilities you're trying to proc have ICDs.
Umm Devouring Arrow is just a rune for Hungering Arrow. I'm confused as to what you're trying to argue here Stone. I'm confused as to if you meant Puncturing Arrow instead.

Either way I'm not sure what you mean by Devouring Arrow being easily disrupted while Puncturing Arrow would be able to find a new target even if you don't have one targetted because Hungering Arrow seeks the same way no matter which rune you put on it.
@wobbuffett
I like the spreadsheet I believe your error is that add. damage should be added after the pierce. so 1.15 for 1 hit
1.15n * .35n + .7n-1

or as for your spreadsheet
add. damage + (% chance to pierce (( #hits x base damage))

I think the problem lies in the .70 additional damage should apply after the %chance to pierce, instead of multiplying it by the % chance to pierce.

I'm sure I'm incorrect but it's something along those lines. I haven't done this type of math in well over a decade.
Sum of an infinite series.

Puncturing:

Sigma n=1 --> infinite: .5^n

= a/1-r = 1/.5 = 2

base dmg is 1.15 so that is 230% total average damage.

Devouring:

Sigma n=1 --> infinite: .35^n*1.7^n Or .595^n

= A/1-r = 1/1-.595 = 2.469

base dmg is 1.15 so 284% total average damage on less targets.
Devouring:

Sigma n=1 --> infinite: .35^n*1.7^n Or .595^n

= A/1-r = 1/1-.595 = 2.469

base dmg is 1.15 so 284% total average damage on less targets.


Applying the math wrong because the 1.7 does not start on the first one. It should only come out to 243 or so.
1.7^0 = 1

Edit: woops change all of those N=1 to N=0
Shatter Shot is better than either of those. 35% chance to split into 3 of the same arrows can basically be modeled as 100% chance to pierce on the first strike. This ends up adding a little over 115% damage to Hungering Arrow on average per cast.

By the way, the base Hungering Arrow (and others permutations that don't do complicated things) can simply be modeled as a sum of infinite series, or:

total damage = (weapon damage)/(1 - (proc chance))

And I just looked at your spreadsheet, you shouldn't be multiplying by the hit number. That's the main reason you're getting such weird values.
from

Shatter Shot is better than either of those. 35% chance to split into 3 of the same arrows can basically be modeled as 100% chance to pierce on the first strike. This ends up adding a little over 115% damage to Hungering Arrow on average per cast.

By the way, the base Hungering Arrow (and others permutations that don't do complicated things) can simply be modeled as a sum of infinite series, or:

total damage = (weapon damage)/(1 - (proc chance))

And I just looked at your spreadsheet, you shouldn't be multiplying by the hit number. That's the main reason you're getting such weird values.

from experience shattered arrows dont behave the way you'd expect them to, they dont repierce, or just 1 repierces, not sure.
Yeah, it seems like only one of the three arrows follow enemies.
from

Shatter Shot is better than either of those. 35% chance to split into 3 of the same arrows can basically be modeled as 100% chance to pierce on the first strike. This ends up adding a little over 115% damage to Hungering Arrow on average per cast.

By the way, the base Hungering Arrow (and others permutations that don't do complicated things) can simply be modeled as a sum of infinite series, or:

total damage = (weapon damage)/(1 - (proc chance))

And I just looked at your spreadsheet, you shouldn't be multiplying by the hit number. That's the main reason you're getting such weird values.

from experience shattered arrows dont behave the way you'd expect them to, they dont repierce, or just 1 repierces, not sure.


That's what I'm seeing too, it hit splits out into a fan of 3 arrows. 1 of them is seeking.
from


from experience shattered arrows dont behave the way you'd expect them to, they dont repierce, or just 1 repierces, not sure.


That's what I'm seeing too, it hit splits out into a fan of 3 arrows. 1 of them is seeking.


Likewise in my experience, the triple proc only has one of them seeking, and as soon as I noticed that, I realized that it isn't as awesome as I thought it was going to be :D

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