What rune makes Hungering Arrow do the most damage on average?

I have a Demon Hunter alt, and I was interested in comparing Hungering Arrow runes. Specifically, which rune should make it do the most damage on average? I saw on average because it can pierce and thus get you multiple hits in. Even if you're firing at one target it can pierce, turn around, and hit them again!

So which of the runes is best?

• Base: 115% damage, 35% pierce
• Puncturing Arrow: 115% damage, 50% pierce
• Cinder Arrow: 150% damage, 35% pierce
• Shatter Shot: 115% damage, 35% pierce, pierce means splitting into 3 arrows (that can all pierce too?)
• Devouring Arrow: 115% damage, 35% pierce, each pierce means +70% damage
• Spray of Teeth: This one depends on your crit percentage and doesn't help with single mobs, so I'll ignore it

My gut says that Puncturing Arrow or Cinder Arrow are best on average, doing 150% damage up-front, or doing 115% more often do to 50% pierce. But I'm not good enough at statistics to back this up... maybe Devouring Arrow is better mathematically over time.

Plus, I haven't unlocked Devouring Arrow yet, so I don't know if all 3 arrows can continue to pierce. For example, if there's one enemy and it pierces, do all 3 sub-arrows hit the mob again?

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Shatter Shot has the best overall output.

The expected average damage outputs per use (calculated up to the 10th piercing) are:

• 177% for Hungering Arrow (base)
• 230% for Puncturing Arrow
• 231% for Cinder Arrow rune
• 301% for Shatter Shot rune
• 283% for Devouring Arrow rune (assuming each piercing does 170% damage of the previous one), or
• 235% for Devouring Arrow rune (assuming each piercing does an additional cumulative 70% base weapon damage)

You could see the breakdown on this document.

Note: The dual interpretation on the Devouring Arrow rune (multiplicative, i.e. the damage on the 3rd pierce is 1.7*1.7*BASE, or additive which would be (1.7+0.7)*BASE) comes from this other answer. The answer states that the additive interpretation is the correct one.

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Nice doc! I'm not sure if the math for Devouring Arrow is right (based on how the 70% is added), but assuming all 3 Scatter Shot sub-arrows can continue to pierce, it looks like a clear winner. – Wikwocket May 31 '12 at 14:42
Mmm... that's a good point. Does Devouring Arrow increase by 70% of it previous value after each pierce, or does it increase by 70% of its original value after each pierce? Seems to deserves another question. – Erik Burigo May 31 '12 at 14:49
– Wikwocket May 31 '12 at 15:13
I'm pretty sure devouring arrow boosts each consecutive pierce by another 70%. Just last night I critted a pony for over 250k on inferno off of a twice pierced arrow. Having said that, for most general (non crit) builds, shatter shot is probably better. – l I Jun 8 '12 at 13:01
I have to say after trying out shatter shot, its very underwhelming. Even though on paper it does the most DPS, the three split shots rarely bend back to strike a second time, thus making it pretty useless when you are fighting just a single enemy. I switched back to devouring arrow personally due to the stacking of 70% per pierce. – l I Jun 19 '12 at 10:56

Spray of teeth is currently gimped. I've been running HA runed with SoT for a while, and the bone spray actually hits mobs with large hitboxes. This means that if assuming i'm fighting Azmodan, and Hungering arrow crits, i'll have dealt the initial HA damage crit + 50% bone Spray (which also crits) to him because his hitbox is so huge.

Furthermore, you're forgetting that Hungering arrow itself always have a 35% chance to pierce regardless of rune, so theoretically it's possible to crit with HA (triggering bone spray), and at the same time have it pierce the mob and come back round for a second possible crit (triggering another bone spray)

These are just based on my observations using that particular rune.

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Does gimped mean good or bad? – Coomie May 31 '12 at 3:03
@Coomie Coming from a wow background, gimped (broken) usually means bad. – deutschZuid Jun 1 '12 at 8:46

With an base damage of 100 (non fluctuating), counting the average puncturing chance with theoretically infinite possible punctures you would get the following numbers per shot:

Base: 176.9230769 dmg Puncturing: 230.0000000 dmg Cinder: 230.7692308 dmg Shatter: 300.7692308 dmg Hungering (each pierce is 170% dmg of the previous): 283.9506173 dmg Hungering (each pierce adds 70% of base weapon dmg): 261.9135802 dmg

So the definitive highest overall damage output is with Shattering shot, but since these numbers are purely statistical, and Shattering shot is highly situational (depends on number of enemies on screen), your best bet for single target is devouring arrow.

Did the math with the limit function.

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