I have been looking at a lot of builds and seeing Impale used as the default "single target killing" skill. I wondered...are there any other options? After a very basic look through the skill tree I looked at the following skills for single target damage: Impale, Rapid Fire, Strafe, and Bola Shot. Hungering and elemental are based more on pierce damage than single target, so I ignored those.
For Rapid Fire I'll show attack rates of 1.6 shot per second and 1.84 shots per second (basic dual wield and single wield attack rates).
ST Analysis (basic).......% Damage Done
Impale (obsidian).................495...........220 + 275 over 2 sec
Rapid Fire 1.6s/sec (obsidian).638...........6*speed, small aoe
Rapid Fire 1.6s/sec (obsidian).681...........6*speed, small aoe
Bola Shot (alabaster)............504...........288 + 216 7yd radius (2sec delay)
Strafe (obsidian)..................540...........55% decreased movement speed
Strafe (obsidian + ballistics)...900...........55% decreased movement speed
One assumption about Strafe: It shoots at "random" enemies, so it's inclusion here as a single target damage skill really only applies to boss fights and possibly pvp. But...what else is single target really for other than those applications? Also, 55% increased speed on top of the damage...tough to ignore.
One thing to keep in mind also about the obsidian runed Impale. The fire damage over time means that your return for spamming Impale is greatly diminished.
Obviously, these skills act differently and Impale is the most straight forward direct damage skill. However, if used properly, I think almost any of the other skills will outperform it. If we ignore the big numbers of strafe and rapid fire and look at a simple straight forward comparison between bola shot and impale...it doesn't even stack up to that. It does less direct damage up front (making bola more effective as a spam), less total damage over time, and bola does an AoE...
Golden Runed Hungering Arrow does 2800% weapon damage on average, so it pretty much blows everything out of the water in terms of maximum potential damage, but is effectively a damage over time ability so it's subject to overkill.
Golden Runed Hungering Arrow does 2800% weapon damage on average, so it pretty much blows everything out of the water in terms of maximum potential damage, but is effectively a damage over time ability so it's subject to overkill.
From what I've read, Hungering can only pierce once. So no, nowhere near 2800%
The rune descriptions contradict that.
Obsidian Runestone:
"Each consecutive Pierce increases the damage of the arrow by 140%"
Indigo Runestone:
"If the arrow successfully pierces the first target, it splits into 8 arrows."
"Consecutive pierce" implies multiple pierces, and distinguishing how Indigo rune gets a bonus if it pierces the "first target" implies that it might pierce other targets than the first.
Golden Runed Hungering Arrow does 2800% weapon damage on average, so it pretty much blows everything out of the water in terms of maximum potential damage, but is effectively a damage over time ability so it's subject to overkill.
All damage calculations favoring anything but SP + RF are assuming that you won't be dealing a large amount of magic damage per shot. Assuming a high end bow that does magic damage equal to it's weapon damage on every shot (gemmed radiant star ruby or simmilar maybe?) you would in fact end up doing:
This gets even better when using the Obsidian Rune with the passive Ballistics, giving you an additional 700% weapon damage every second. This brings us up to 1547% weapon damage per second, and we don't have to rely on chaining pierces.
The damage only gets better the higher your proc'ing magic damage is, say 200%.
200% magic damage = 1304% weapon damage
This brings you up to a guaranteed 2199% weapon damage per second. These magic damage numbers shouldn't be hard to hit when you're pushing into inferno level play (which you are if you're using the max level Gold Rune on Hungering Arrow).
Golden Runed Hungering Arrow does 2800% weapon damage on average, so it pretty much blows everything out of the water in terms of maximum potential damage, but is effectively a damage over time ability so it's subject to overkill.
All damage calculations favoring anything but SP + RF are assuming that you won't be dealing a large amount of magic damage per shot. Assuming a high end bow that does magic damage equal to it's weapon damage on every shot (gemmed radiant star ruby or simmilar maybe?) you would in fact end up doing:
This gets even better when using the Obsidian Rune with the passive Ballistics, giving you an additional 700% weapon damage every second. This brings us up to 1547% weapon damage per second, and we don't have to rely on chaining pierces.
The damage only gets better the higher your proc'ing magic damage is, say 200%.
200% magic damage = 1304% weapon damage
This brings you up to a guaranteed 2199% weapon damage per second. These magic damage numbers shouldn't be hard to hit when you're pushing into inferno level play (which you are if you're using the max level Gold Rune on Hungering Arrow).
Why would chaining pierces be unreliable? The only disadvantage to Golden Hungering Arrow that I can see is that it's damage over time, so it's prone to overkill once whatever you're attacking dies. That's not an issue for bosses though.
Also, I don't think you can double-rune abilities?
Max HG damage bonus from passives and MfD would be 80%, and since you aren't double-runed you only get a 60% piecing option, which should technically fizzle out piercings alot faster then you'd expect.
80 + 140 + (140xP-1) Assuming 3 piercings with a likely fail rate at 5, your last randomly hit monster will only yield:
500-780% damage on the last mob hit.
The magic bonus bit is somewhat interesting. It will likely be calculated as "if you do 75 weapon damage, add another 75 weapon damage to the total damage amount." and will most likely only stack after the other calculations are done.
Now, the reduced returns effect changes HG quite a bit. Taking the 5 shots, your values add in at 220 + 360 + 560 + 640 + 780 per pierce.
Compare this to multishot: 550 + 550 + 550 + 550 + 550.
HG: 1140-2560
MS: 2750
Then we can add the magic damage bonus... assuming a 75 damage bow.
HG: 75x5(shots) = 375 damage
MS: 75x5(mobs)x5(shots)= 1875 damage(?)
Adding in an actual rune for multishot.. the values change quite a bit. Crimson rune switches MS from 2750 to 6050.
This of course is assuming things don't die so easily end game.
Edited: Made a mistake in the math. Besides.. this only works with multiple targets. This is a single target damage thread...
Why would chaining pierces be unreliable? The only disadvantage to Golden Hungering Arrow that I can see is that it's damage over time, so it's prone to overkill once whatever you're attacking dies. That's not an issue for bosses though.
Your statement of 2800% weapon damage is assuming 20 pierces on a single target (20 * 140%). The chances of achieving 20 pierces in a row at 95% chance to pierce is:
.95^20 = .35 * 100 = 35% chance
35% chance is pretty low when you're looking at a reliable way to deal damage. Will it work? Yes. Will it do lots of damage? Yes. Will it reliably hit 2800% damage per arrow? No, not even close. Also, you're looking at shooting an arrow every 1.5 seconds or so, and having the damage be spread over a long time. Even at .5 seconds per peirce you're looking at a damage of 2800% over 11.5 seconds.
Rapid fire can reliably hit 2100% given high end gear, and it can do it every second. You also don't have to worry about your arrows chasing after adds like you do with HA. The chasing part is a real issue since all bosses now have adds.
It is unclear how the Alabaster rune will be applied. If it is applied before the crit goes into effect it would give you:
(220% + 500%) * 1.5 = 1080% per shot
(220% + 500%) * 2 = 1440% per shot with archery + crossbow.
If it is applied after crit damage, then the alabaster rune becomes terrible:
(220% * 1.5) + 500% = 830% per shot
(220% * 2) + 500% = 940% per shot with archery + crossbow
This also assumes that your crit chance is going to be extremly high. If you're not running a significant amount of crit, then you will be doing a very sub par shot nearly every time. Even if you're critting 100% of the time, Impale still does lower damage than both HA + Gold, or SP + RF + Obsidian.
Also, I don't think you can double-rune abilities?
Max HG damage bonus from passives and MfD would be 80%, and since you aren't double-runed you only get a 60% piecing option, which should technically fizzle out piercings alot faster then you'd expect.
You are mistaken, HA + Gold gives you a 95% chance to pierce. That doesn't require a double rune. Nor is it unthinkable for it to be piercing 20 times at that percentage (35% chance to do that). This would give you the discussed 2800% damage on a single arrow.
Why would chaining pierces be unreliable? The only disadvantage to Golden Hungering Arrow that I can see is that it's damage over time, so it's prone to overkill once whatever you're attacking dies. That's not an issue for bosses though.
Your statement of 2800% weapon damage is assuming 20 pierces on a single target (20 * 140%). The chances of achieving 20 pierces in a row at 95% chance to pierce is:
.95^20 = .35 * 100 = 35% chance
This is not the calculation I used. This is:
SUM( (pierce chance)^n from n=0 to infinity)
= 1/(1 - pierce chance)
= 1/(1-0.95)
= 20
So you have a 100% chance to deal one hit, a 95% chance to deal a second hit, a 95^2 chance to deal a third hit, etc... It comes out to 20 hits on average.
Even if you were to limit it to a maximum of 50 pierces total, it would still come out to 18.5 hits on average. There's a 7.7% chance for it to pierce 50 targets in a row as well, so from what I see, that 20 hit estimate is not unreasonable.
35% chance is pretty low when you're looking at a reliable way to deal damage. Will it work? Yes. Will it do lots of damage? Yes. Will it reliably hit 2800% damage per arrow? No, not even close. Also, you're looking at shooting an arrow every 1.5 seconds or so, and having the damage be spread over a long time. Even at .5 seconds per peirce you're looking at a damage of 2800% over 11.5 seconds.
Why is it unrelaible? It only costs 15 hatred and I'm sure you can fire at LEAST 1 per second. As for it being a damage over time skill, that disadvantage is actually negligable. Against large groups, it will use up its pierces much faster, and against bosses, the boss should have enough HP that overkill is not that big of a problem.
Rapid fire can reliably hit 2100% given high end gear, and it can do it every second. You also don't have to worry about your arrows chasing after adds like you do with HA. The chasing part is a real issue since all bosses now have adds.
Why is it a problem that they chase after adds? Golden Hungering Arrow is actually on par with most AoE attacks. Here, I calculated how many targets each of these AoE attacks would need to hit to match Golden Hungering Arrow.
Bola Shot (Crimson): 31 targets to match Golden Hungering Arrow
Multishot (Crimson): 12 targets to match Golden Hungering Arrow
Impale (Crimson): 12 targets to match Golden Hungering Arrow
If you consider that golden costs less than any of these, it's really quite convenient.
I hate to say it, but I think hungering arrow is being overestimated. Look at D2 for example, the skills pierce was nerfed hardcore to a skill that guided, but did not pierce often or at all. Not to mention here that its counter intuitive to think that a near free skill has the highest DPS. Math or not I would need to see it tested in game.
What do you want tested? The pierce chance is built directly into Hungering Arrow as per the tooltip. If the pierce chance is different that's a tooltip bug.
SUM( (pierce chance)^n from n=0 to infinity)
= 1/(1 - pierce chance)
= 1/(1-0.95)
= 20
I am honestly not 100% sure how to calculate that acurately by hand. So I wrote a program to do it. To run it while in Chrome press F12, click console, paste in the code and hit enter.
var arrows = 1;
var totalArrows = 0;
function HA () {
function pierce () {
return Math.random() < .95;
}
while (pierce()) {
arrows = arrows + 1;
}
totalArrows = totalArrows + arrows;
arrows = 1;
}
for (var x = 0; x < 10000; x = x + 1) {
HA();
}
console.log('Average pierces per arrow: ' + (totalArrows / 10000));
This code runs a simulation on 10,000 HA's and totals the number of pierces per arrow. According to the simulation, the average number of pierces is 20. Unless someone can find something wrong with my code, this is the most accurate HA pierce data there is right now.
This means that unless HA is nerfed hard, once you hit inferno level Gold Runes, HA is the most effective multi target and single target attack in the game.
This means that unless HA is nerfed hard, once you hit inferno level Gold Runes, HA is the most effective multi target and single target attack in the game.
There is a kind of symmetry in your first skill being the last one you'll need. Too bad I can't take up 2 ability slots for an extra rune and get gold and obsidian runes for it!
SUM( (pierce chance)^n from n=0 to infinity)
= 1/(1 - pierce chance)
= 1/(1-0.95)
= 20
I am honestly not 100% sure how to calculate that acurately by hand. So I wrote a program to do it. To run it while in Chrome press F12, click console, paste in the code and hit enter.
var arrows = 1;
var totalArrows = 0;
function HA () {
function pierce () {
return Math.random() < .95;
}
while (pierce()) {
arrows = arrows + 1;
}
totalArrows = totalArrows + arrows;
arrows = 1;
}
for (var x = 0; x < 10000; x = x + 1) {
HA();
}
console.log('Average pierces per arrow: ' + (totalArrows / 10000));
This code runs a simulation on 10,000 HA's and totals the number of pierces per arrow. According to the simulation, the average number of pierces is 20. Unless someone can find something wrong with my code, this is the most accurate HA pierce data there is right now.
This means that unless HA is nerfed hard, once you hit inferno level Gold Runes, HA is the most effective multi target and single target attack in the game.
Hahahahaha aah I applaud your effort but this is what we have calculus for.
This means that unless HA is nerfed hard, once you hit inferno level Gold Runes, HA is the most effective multi target and single target attack in the game.
There is a kind of symmetry in your first skill being the last one you'll need. Too bad I can't take up 2 ability slots for an extra rune and get gold and obsidian runes for it!
MWAHAHAHAHHAHAHAHA...
Interestingly, Wolfram Alpha says combining Obsidian and Gold runes would cause Hungering Arrow to do infinite damage on average. http://www.wolframalpha.com/input/?i=sum of (.95)^(n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+infinity%29
Interestingly, Wolfram Alpha says combining Obsidian and Gold runes would cause Hungering Arrow to do infinite damage on average. http://www.wolframalpha.com/input/?i=sum of (.95)^(n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+infinity%29
mind... hurtin:exploding watermelon:
Now, to get something more head-wrap-around-able, lets assume that the average case is what happens. Would this be correct for the damage done after 20 pierces:
Interestingly, Wolfram Alpha says combining Obsidian and Gold runes would cause Hungering Arrow to do infinite damage on average. http://www.wolframalpha.com/input/?i=sum of (.95)^(n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+infinity%29
mind... hurtin:exploding watermelon:
Hey cool that kind of infinite series and its head-exploding nature also has a wikipedia article.
Now, to get something more head-wrap-around-able, lets assume that the average case is what happens. Would this be correct for the damage done after 20 pierces:
But no, I see no problem with your code. I'll have to remember that Chrome has a javascript console more often.
Lol, I haven't done calculus in 7 years. Nice job on the math side of it. I am a coder, so that's how I solve problems quickly ^_- That's a cool site though, never seen it before.
Interestingly, Wolfram Alpha says combining Obsidian and Gold runes would cause Hungering Arrow to do infinite damage on average. http://www.wolframalpha.com/input/?i=sum of (.95)^(n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+infinity%29
If we could combine runes, we'd get some sick effects.
20 Pierces is great theoretical DPS, but please keep in mind that the arrows don't turn around and retarget instantly - they fly a certain distance before turning back. If they hit any walls or other terrain features, the arrow is lost and your wonderful '20 pierces' goes out the window.
I wish we knew stats of lower level runes. Calcultaing for lvl 7 rune is still valid, but how many people will get lvl 7 runes to all skills (remember they will be random)
If it's a new effect, see what numbers divide by 7 neatly.
If its an improved effect, subtract the base then divide by 7.
(i'm guessing, but that seems a really nice way to do it)
For instance, the yellow run on hungering arrow probably adds 5% pierce chance per level.
sigh... if you are looking at hitting 20 different targets then it is 20 x140% over 20 targets for... surprise, surprise... a stunning single-target shot of 140% percent.
multishot begins at 110% damage unruned. Give it the damage modifier and it's at 242%
Besides, this doesn't matter anymore... they apparently already updated the new demon hunter skills.
New stats for HA is 115% with a 60% chance to pierce targets when unruned and now generates 5 hatred.
For Rapid Fire I'll show attack rates of 1.6 shot per second and 1.84 shots per second (basic dual wield and single wield attack rates).
ST Analysis (basic).......% Damage Done
Impale (obsidian).................495...........220 + 275 over 2 sec
Rapid Fire 1.6s/sec (obsidian).638...........6*speed, small aoe
Rapid Fire 1.6s/sec (obsidian).681...........6*speed, small aoe
Bola Shot (alabaster)............504...........288 + 216 7yd radius (2sec delay)
Strafe (obsidian)..................540...........55% decreased movement speed
Strafe (obsidian + ballistics)...900...........55% decreased movement speed
One assumption about Strafe: It shoots at "random" enemies, so it's inclusion here as a single target damage skill really only applies to boss fights and possibly pvp. But...what else is single target really for other than those applications? Also, 55% increased speed on top of the damage...tough to ignore.
One thing to keep in mind also about the obsidian runed Impale. The fire damage over time means that your return for spamming Impale is greatly diminished.
Obviously, these skills act differently and Impale is the most straight forward direct damage skill. However, if used properly, I think almost any of the other skills will outperform it. If we ignore the big numbers of strafe and rapid fire and look at a simple straight forward comparison between bola shot and impale...it doesn't even stack up to that. It does less direct damage up front (making bola more effective as a spam), less total damage over time, and bola does an AoE...
Obsidian Runestone:
"Each consecutive Pierce increases the damage of the arrow by 140%"
Indigo Runestone:
"If the arrow successfully pierces the first target, it splits into 8 arrows."
"Consecutive pierce" implies multiple pierces, and distinguishing how Indigo rune gets a bonus if it pierces the "first target" implies that it might pierce other targets than the first.
All damage calculations favoring anything but SP + RF are assuming that you won't be dealing a large amount of magic damage per shot. Assuming a high end bow that does magic damage equal to it's weapon damage on every shot (gemmed radiant star ruby or simmilar maybe?) you would in fact end up doing:
12x 1.84 Attack Speed = 6.5 shots per second
30% weapon damage = 195% weapon damage
100% magic damage = 652% weapon damage
847% weapon damage per second.
This gets even better when using the Obsidian Rune with the passive Ballistics, giving you an additional 700% weapon damage every second. This brings us up to 1547% weapon damage per second, and we don't have to rely on chaining pierces.
The damage only gets better the higher your proc'ing magic damage is, say 200%.
200% magic damage = 1304% weapon damage
This brings you up to a guaranteed 2199% weapon damage per second. These magic damage numbers shouldn't be hard to hit when you're pushing into inferno level play (which you are if you're using the max level Gold Rune on Hungering Arrow).
HG is not a rocket.
Also, I don't think you can double-rune abilities?
Max HG damage bonus from passives and MfD would be 80%, and since you aren't double-runed you only get a 60% piecing option, which should technically fizzle out piercings alot faster then you'd expect.
80 + 140 + (140xP-1) Assuming 3 piercings with a likely fail rate at 5, your last randomly hit monster will only yield:
500-780% damage on the last mob hit.
The magic bonus bit is somewhat interesting. It will likely be calculated as "if you do 75 weapon damage, add another 75 weapon damage to the total damage amount." and will most likely only stack after the other calculations are done.
Now, the reduced returns effect changes HG quite a bit. Taking the 5 shots, your values add in at 220 + 360 + 560 + 640 + 780 per pierce.
Compare this to multishot: 550 + 550 + 550 + 550 + 550.
HG: 1140-2560
MS: 2750
Then we can add the magic damage bonus... assuming a 75 damage bow.
HG: 75x5(shots) = 375 damage
MS: 75x5(mobs)x5(shots)= 1875 damage(?)
Adding in an actual rune for multishot.. the values change quite a bit. Crimson rune switches MS from 2750 to 6050.
This of course is assuming things don't die so easily end game.
Edited: Made a mistake in the math. Besides.. this only works with multiple targets. This is a single target damage thread...
Your statement of 2800% weapon damage is assuming 20 pierces on a single target (20 * 140%). The chances of achieving 20 pierces in a row at 95% chance to pierce is:
.95^20 = .35 * 100 = 35% chance
35% chance is pretty low when you're looking at a reliable way to deal damage. Will it work? Yes. Will it do lots of damage? Yes. Will it reliably hit 2800% damage per arrow? No, not even close. Also, you're looking at shooting an arrow every 1.5 seconds or so, and having the damage be spread over a long time. Even at .5 seconds per peirce you're looking at a damage of 2800% over 11.5 seconds.
Rapid fire can reliably hit 2100% given high end gear, and it can do it every second. You also don't have to worry about your arrows chasing after adds like you do with HA. The chasing part is a real issue since all bosses now have adds.
It is unclear how the Alabaster rune will be applied. If it is applied before the crit goes into effect it would give you:
(220% + 500%) * 1.5 = 1080% per shot
(220% + 500%) * 2 = 1440% per shot with archery + crossbow.
If it is applied after crit damage, then the alabaster rune becomes terrible:
(220% * 1.5) + 500% = 830% per shot
(220% * 2) + 500% = 940% per shot with archery + crossbow
This also assumes that your crit chance is going to be extremly high. If you're not running a significant amount of crit, then you will be doing a very sub par shot nearly every time. Even if you're critting 100% of the time, Impale still does lower damage than both HA + Gold, or SP + RF + Obsidian.
You are mistaken, HA + Gold gives you a 95% chance to pierce. That doesn't require a double rune. Nor is it unthinkable for it to be piercing 20 times at that percentage (35% chance to do that). This would give you the discussed 2800% damage on a single arrow.
SUM( (pierce chance)^n from n=0 to infinity)
= 1/(1 - pierce chance)
= 1/(1-0.95)
= 20
So you have a 100% chance to deal one hit, a 95% chance to deal a second hit, a 95^2 chance to deal a third hit, etc... It comes out to 20 hits on average.
Even if you were to limit it to a maximum of 50 pierces total, it would still come out to 18.5 hits on average. There's a 7.7% chance for it to pierce 50 targets in a row as well, so from what I see, that 20 hit estimate is not unreasonable.
Why is it unrelaible? It only costs 15 hatred and I'm sure you can fire at LEAST 1 per second. As for it being a damage over time skill, that disadvantage is actually negligable. Against large groups, it will use up its pierces much faster, and against bosses, the boss should have enough HP that overkill is not that big of a problem.
Why is it a problem that they chase after adds? Golden Hungering Arrow is actually on par with most AoE attacks. Here, I calculated how many targets each of these AoE attacks would need to hit to match Golden Hungering Arrow.
Bola Shot (Crimson): 31 targets to match Golden Hungering Arrow
Multishot (Crimson): 12 targets to match Golden Hungering Arrow
Impale (Crimson): 12 targets to match Golden Hungering Arrow
If you consider that golden costs less than any of these, it's really quite convenient.
I am honestly not 100% sure how to calculate that acurately by hand. So I wrote a program to do it. To run it while in Chrome press F12, click console, paste in the code and hit enter.
This code runs a simulation on 10,000 HA's and totals the number of pierces per arrow. According to the simulation, the average number of pierces is 20. Unless someone can find something wrong with my code, this is the most accurate HA pierce data there is right now.
This means that unless HA is nerfed hard, once you hit inferno level Gold Runes, HA is the most effective multi target and single target attack in the game.
There is a kind of symmetry in your first skill being the last one you'll need. Too bad I can't take up 2 ability slots for an extra rune and get gold and obsidian runes for it!
MWAHAHAHAHHAHAHAHA...
The wikipedia article on that particular class of infinite series:
http://en.wikipedia.org/wiki/Geometric_series
Wolfram Alpha's answer:
http://www.wolframalpha.com/input/?i=SUM( (x)^n from n=0 to infinity)
But no, I see no problem with your code. I'll have to remember that Chrome has a javascript console more often.
Interestingly, Wolfram Alpha says combining Obsidian and Gold runes would cause Hungering Arrow to do infinite damage on average.
http://www.wolframalpha.com/input/?i=sum of (.95)^(n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+infinity%29
Also, I've done the calculations for all the other Hungering Arrow runes if you'd like to check them out:
http://diablo.incgamers.com/forums/showpost.php?p=8031590&postcount=8
mind... hurtin:exploding watermelon:
Now, to get something more head-wrap-around-able, lets assume that the average case is what happens. Would this be correct for the damage done after 20 pierces:
http://www.wolframalpha.com/input/?i=sum of (n) *+%281.40%29^%28n%2B1%29+from+n%3D0+to+n%3D20%29
Which it appears (based on the approximate form on that page) is a little less than 71758% WD?
Well, that explains why you can't use 2 slots now doesn't it!
P.S. I should really go back to college and take some refresher math classes, i remember so little from way back then (get off ma lawn!).
P.P.S. There is a strong likelyhood I in-put the calculation incorrectly.
Edit: Also, what about an ever-splitting Indigo? In other words, the split arrows can repeatedly split.
http://en.wikipedia.org/wiki/St._Petersburg_paradox
The formula should be:
sum of (0.95^n) * (1.40)^(n+1) from n=0 to n=20
It would only be n * (1.40)^(n+1) from n=0 to n=20 if the pierce chance is 100%.
If you evaluate it for the first 50 pierces, you get about 900 million percent weapon damage.
It says only the first pierce splits, so I assumed the 8 split arrows can't split again.
My calculations for each rune:
http://diablo.incgamers.com/forums/showpost.php?p=8031590&postcount=8
Stated another way: "When the arrow pierces 20 times, how much damage would it do, including the effect from an obsidian rune?"
Lol, I haven't done calculus in 7 years. Nice job on the math side of it. I am a coder, so that's how I solve problems quickly ^_- That's a cool site though, never seen it before.
If we could combine runes, we'd get some sick effects.
If it's a new effect, see what numbers divide by 7 neatly.
If its an improved effect, subtract the base then divide by 7.
(i'm guessing, but that seems a really nice way to do it)
For instance, the yellow run on hungering arrow probably adds 5% pierce chance per level.
lvl 7 gold rune: 95
Base skill chance: 60
difference: 35
divided by 7 levels: 5% increase per level
multishot begins at 110% damage unruned. Give it the damage modifier and it's at 242%
Besides, this doesn't matter anymore... they apparently already updated the new demon hunter skills.
New stats for HA is 115% with a 60% chance to pierce targets when unruned and now generates 5 hatred.