## n-Depth look at Hungering Arrow

• One is never hurt by being given additional choices, only by taking them away.
A QUADRILLION MAGIC FIND is worthless if you can't kill shit!
• interesting, but i think Cinder and Spray of Teeth still pierce, so shouldn't those be sums as well?

Also, i think the formula for Devouring may not be correct, the damage increase only occurs after a split, so i think it should be .35^n-1 x .7^n

(its been a while since i've taken a math class)
• your part on spray of teeth is lacking...
the total damage done from the explode can vary allot and can sometimes i bet everything else, but also not do it more often

i still like the idea of Shatter shot. makes it an aoe ability

fire 1 arrow, has 35% chance of exploding
of these 3 arrows, everyone got 35% chance of exploding again... and so on.
and its 35% that means its a bit higher then 1 of 3 explode again

but then again, i understand that the +70% damage on pierce is good aswell
Game Designer - Micro Design
• Spray of Teeth is terribly wrong if it's http://d3db.com/skil...hungering-arrow

Scatter is also incorrect, but there's information missing. For example, do the 3 resulting arrows have the same behavior? If not, it's just:

115 + .35 * (3 * 115) = 235.75

If it does... I would need to sit down longer to simplify it. Recursively, it's:
Arrow = 115 + .35 * (3 * Arrow)

Problem with the image is, if it doesn't pierce the first time, it can't pierce a second time.
Also, i think the formula for Devouring may not be correct, the damage increase only occurs after a split, so i think it should be .35^n-1 x .7^n

The Devouring in image is correct, though missing the 'x' to keep it consistent. When n is 0, presumably for 0 targets pierced, it has no effect on the damage.

If Cinder continues to pierce (which it should because Blizzard has stated you should never want the unruned), the results are too timing based to successfully calculate with a simple equation. However, assuming it hits a new target every time (best case), it's simply:

Sum(150 * .35^n) = 230.77

If we assume it takes 1s to hit the same target every time (worst case), it's
Sum((115 + 35/3) * .35^n) = 194.87

194.87 - 230.77, giving it a decent place as the second rune you get.

Spray of Teeth is a little bit more complicated due to the unknowns about its aoe range and the situational unknowns.

For M targets in the aoe, and C for crit chance
SUM((115 * .35^n) + (.35^n * C * ((M * 50) + 57.5)))
.35^n chance to hit the nth target, but each hit is an independent crit check to do 50% WD on M targets. Because you're critting however, you have to add an additional 57.5% for the regular crit damage bonus of 50%.

If we assume M=3, you need a crit chance of ~17% to get 231, beating Puncturing. As M and C increase, it will do much, much more.
• Quote from PantheraOnca

interesting, but i think Cinder and Spray of Teeth still pierce, so shouldn't those be sums as well?

Also, i think the formula for Devouring may not be correct, the damage increase only occurs after a split, so i think it should be .35^n-1 x .7^n

(its been a while since i've taken a math class)

n-1 would have the first number in the series being
0.35^(0-1) = 0.35^(-1)

When they both start at 0, you are just using the initial dmg and there is no piece.

Yah those 2 will likely still pierce, good catch, ill fix it.
One is never hurt by being given additional choices, only by taking them away.
A QUADRILLION MAGIC FIND is worthless if you can't kill shit!
• Now that I look scatter probably pierces the 1st target, and then splits and thats it. I would think those 3 arrows are smart arrows that still seek, but they won't split off again. But they could be dumb arrows as well. It would obviously be stupidly OP if all 3 could continue to piece.
One is never hurt by being given additional choices, only by taking them away.
A QUADRILLION MAGIC FIND is worthless if you can't kill shit!
• Your assumption for Shatter Shot that only one out of the 3 arrows after the split continue to pierce seems odd. I've been assuming that all 3 can pierce, but if that's not the case the second most likely option would seem like none of them can pierce.

I posted a reply to a similar reddit thread earlier today with details on how to calculate these infinite sums as well if anyone is interested: http://www.reddit.co...ungering_arrow/

Quote from Nivius

i still like the idea of Shatter shot. makes it an aoe ability

fire 1 arrow, has 35% chance of exploding
of these 3 arrows, everyone got 35% chance of exploding again... and so on.
and its 35% that means its a bit higher then 1 of 3 explode again

Shatter Shot absolutely will not work like this. If every pierce split and each of the 3 arrows had a chance to pierce causing it to split again, etc, then the expected damage from a single shot would be infinite! (After the first pierce you have 3 chances at 35% to pierce so, on average, you will get 1.05 pierces, which leads to an exponential explosion in damage).
• Shatter Shot absolutely will not work like this. If every pierce split and each of the 3 arrows had a chance to pierce causing it to split again, etc, then the expected damage from a single shot would be infinite! (After the first pierce you have 3 chances at 35% to pierce so, on average, you will get 1.05 pierces, which leads to an exponential explosion in damage).

Most likely, but without testing or word from Blizzard...

Even without that though, it's in a good place as far as the runes go, doing a little bit more than Puncturing. Right now, Cindering is easily the weakest, but I forget if DH's get any kind of synergy with burning targets.
• Quote from chippydip

Your assumption for Shatter Shot that only one out of the 3 arrows after the split continue to pierce seems odd. I've been assuming that all 3 can pierce, but if that's not the case the second most likely option would seem like none of them can pierce.

I posted a reply to a similar reddit thread earlier today with details on how to calculate these infinite sums as well if anyone is interested: http://www.reddit.co...ungering_arrow/

Quote from Nivius

i still like the idea of Shatter shot. makes it an aoe ability

fire 1 arrow, has 35% chance of exploding
of these 3 arrows, everyone got 35% chance of exploding again... and so on.
and its 35% that means its a bit higher then 1 of 3 explode again

Shatter Shot absolutely will not work like this. If every pierce split and each of the 3 arrows had a chance to pierce causing it to split again, etc, then the expected damage from a single shot would be infinite! (After the first pierce you have 3 chances at 35% to pierce so, on average, you will get 1.05 pierces, which leads to an exponential explosion in damage).

Shatter most certainly can't have all 3 new arrows smart pierce as the potential dmg output would be outrageous. The dmg output would be about 708% wpn dmg per shot.

Do you guys know if the pierced arrow prioritizes other mobs in the vicinity or the mob it hit?
One is never hurt by being given additional choices, only by taking them away.
A QUADRILLION MAGIC FIND is worthless if you can't kill shit!
• I believe the arrow homing prioritizes the closest to the arrow itself.

• Quote from jaclashflash

Shatter most certainly can't have all 3 new arrows smart pierce as the potential dmg output would be outrageous. The dmg output would be about 708% wpn dmg per shot.

I think you did something wrong in your calculations. If all 3 pierce after the split then the average damage is about 300%, making it the best rune, but not wildly better than Devouring.

The damage formula is:

115 + 0.35 * 3 * SUM(0, inf, 115 * 0.35^n)
(initial hit plus 35% chance to get 3 arrows that are effectively each a non-runed version)

= 115 * (1 + 3 * 0.35 * SUM(0, inf, 0.35^n)
= 115 * (1 + 3 * 0.35 + 3 * 0.35^2 + 3 * 0.35^3 + ...)
= 115 * (1.7 / 0.65)

~= 301%
• I think you did something wrong in your calculations. If all 3 pierce after the split then the average damage is about 300%, making it the best rune, but not wildly better than Devouring.

You are assuming the behavior of the skill by stating that the 3 spawned act as normal non-runed hungering arrows, just as he assumed the behavior that the 3 spawned act as runed Shatter Arrows, though his number should really be infinite.
• Quote from chippydip

Quote from jaclashflash

Shatter most certainly can't have all 3 new arrows smart pierce as the potential dmg output would be outrageous. The dmg output would be about 708% wpn dmg per shot.

I think you did something wrong in your calculations. If all 3 pierce after the split then the average damage is about 300%, making it the best rune, but not wildly better than Devouring.

The damage formula is:

115 + 0.35 * 3 * SUM(0, inf, 115 * 0.35^n)
(initial hit plus 35% chance to get 3 arrows that are effectively each a non-runed version)

= 115 * (1 + 3 * 0.35 * SUM(0, inf, 0.35^n)
= 115 * (1 + 3 * 0.35 + 3 * 0.35^2 + 3 * 0.35^3 + ...)
= 115 * (1.7 / 0.65)

~= 301%
Yah my bad, forgot to take the 35% chance into account, and forgot the initial arrow split into 3. That # is certainly plausible then.

There I think I have it fixed about as good as it can get anyways.
One is never hurt by being given additional choices, only by taking them away.
A QUADRILLION MAGIC FIND is worthless if you can't kill shit!
• Actually now that I look at it, they recently just nerfed puncturing arrow from 55% to 50% didnt they? That means they nerfed the dmg from 255% to the 230%.

Now, if shatter arrow doesn't allow piercing its at 230% range with the other 3. Then that would only leave devouring as an outlier. However, seeing as it drastically increases in dmg per pierce it has a high chance to overkill, thus lowering the overall effective dmg.

Therefore, I think its safe to assume that shatter arrow's won't be allowed to pierce. However, if that is not the case then shatter becomes the only choice, as it will be the best in pretty much any situation.
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• This is where gaming goes too far. I am meant to blow stuff up after work not have a headache looking at some nerds forum post
• Quote from Casanova

... looking at some nerds any forum post

there we go.
• Quote from jaclashflash

There I think I have it fixed about as good as it can get anyways.

If you want to include a closed-form version of Spray of Teeth it would be:

SUM(0, inf, (115 + 50CM) * 0.35^n)

= (115 + 50CM) * SUM(0, inf, 0.35^n)
= (115 + 50CM) * (1 / 0.65)
= (115 + 50CM) / 0.65

At CM = 1.6 the total damage is 300%, making it equal to Shatter Shot with piercing arrows. This requires hitting at least 3 mobs at a ~53% crit rate, 4 at a 40% crit rate, 5 at a 32% crit rate, etc.

Quote from Mysticjbyrd

Now, if shatter arrow doesn't allow piercing its at 230% range with the other 3. Then that would only leave devouring as an outlier. However, seeing as it drastically increases in dmg per pierce it has a high chance to overkill, thus lowering the overall effective dmg.

Therefore, I think its safe to assume that shatter arrow's won't be allowed to pierce. However, if that is not the case then shatter becomes the only choice, as it will be the best in pretty much any situation.

If Shatter doesn't pierce then I wonder if it would lose its homing ability as well? If there are 4+ monsters around it wouldn't really matter, but against a boss it would be worse than the non-runed version if it split and never turned around to come back and actually hit the boss.

You also bring up a good point with Devouring Arrow. It's important not just to look at average damage, but also the probability distribution of that damage. With a 35% chance to pierce, ~96% of all attacks will hit 3 times or fewer. With the normal un-runed version, the first 3 hits account for~ 96% of the overall damage as well. With Devouring Arrow on the other hand, those first 3 hits which happen ~96% of the time only account for ~79% of overall damage. This leaves ~21% of the average damage is coming from that ~4% chance of getting 4 or more hits.

Here's a comparison of roughly 95th-percentile damage:

No Rune: ~169% (at 3 hits max ~= 96th percentile)
Puncturing Arrow: ~216% (at 4 hits max ~= 94th percentile)
Puncturing Arrow: ~223% (at 5 hits max ~= 97th percentile)
Devouring Arrow: ~224% (at 3 hits max ~= 96th percentile)
Shatter Arrow: ~235% (at 4 hits max ~= 65th percentile--assuming no piercing after the first, this is max damage)

This means that, even without additional piercing, Shatter Arrow will do more damage than the other rune options most of the time. It also hits slightly more times on average than Puncturing Arrow (2.05 vs 2.00) if you are fishing for procs. Looking at it this way, it definitely looks like it would be most balanced if the arrows retained their homing ability, but not their piercing ability after the split.
• Quote from Kyrenin

If Cinder continues to pierce (which it should because Blizzard has stated you should never want the unruned),

Not a Sound Assumption. The reason you don't want this unruned is because there are runes that make it operate better with the same principals. This could remove the seeking portion and add the fire damage and other runes would be taken if you want it to operate identically but better (Puncturing arrow comes to mind)
If that made sense to you, Bravo! I think I even confused myself...
• Quote from Raptorbonz42

Quote from Kyrenin

If Cinder continues to pierce (which it should because Blizzard has stated you should never want the unruned),

Not a Sound Assumption. The reason you don't want this unruned is because there are runes that make it operate better with the same principals. This could remove the seeking portion and add the fire damage and other runes would be taken if you want it to operate identically but better (Puncturing arrow comes to mind)

If you remove the pierce & seek from this ability, then it would operate worse than the unruned version, far worse.
% wpn dmg: 150

The DoT likely doesn't stack, which is why there is a minimum and maximum dmg range for that ability.

@Chippydip Yah I see Shatter maintaining the homing ability, but not pierce. Of course, it could definitely go another way too.
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