Wait wait wait... How is reducing max durability a bad thing at all?
The only time you lose durability is if you die. And when you do die you lose 10% of your max durability. So why does it matter if you have 90/100 durability or 9/10 durability? A loss in max durability is meaningless.
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:
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
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.
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'm still skeptical about the piercing a single target, but only gameplay will tell.
I also don't necessarily agree with your conclusion on golden suffering from "massive overkill" because if it CAN pierce a single target, the only time that would matter is on the last handful of shots where the potential bounces are lost, and its not even like a DPS loss would be suffered at the end, just a total damage done per action.
Ok if you want to think of it that way then Hungering Arrow (Golden) suffers from the need to slowly "ramp up" its DPS unlike other options which deal consistent DPS.
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.
Yep. Watch this video at 2:10. Hungering arrow pierces a zombie at the top of the screen then turns around and attacks it again.
Interesting. Although, just to be contrary, all of those re-pierces look like the arrow has acquired a target other than the last pierced enemy and just happens to go through the first getting to the new target.
In other words, it might be that even with 100% pierce and no other targets the shot will only go through the single monster within range once, but could bounce infinitely in between 2 monsters.
If it can loop through a creature that is alone on screen, i would tend to think that indigo would end up with more single target damage than golden, but i would need to do some math and i can't right now.
I've actually done all the math except for Alabaster assuming that it can pierce the same target twice in a row. Here ya go.
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.
Cluster Arrow(Indigo): 120% small AoE + 3960% rockets
Entangling Shot(Crimson): slow + 20% damage boost via Cull the Weak
Hungering Arrow(Golden): 2800% average weapon damage over time.
Shadow Power(Golden): damage boost
Marked for Death (Indigo): More damage boost
Evasive Fire(Golden): Defensive, very cheap.
Ok so Cluster Arrow is for groups, Hungering for single targets. If all the rockets can actually hit a single target, I'll drop Hungering Arrow for either Spike Trap(Golden), Rain of Vengeance (Crimson), or Companion since Cluster Arrow + Rockets does way more damage. In fact, Cluster Arrow + Rockets and Hungering Arrow(Golden) seem to do way way WAY more damage than any of their other runestone combinations, or most any other attack skill at all for that matter. Even AoE skills like Bola Shot (Crimson) would have to hit 30 targets to match Hungering Arrow, or 44 targets to match Cluster Arrow. I'm thinking they might be just a tad bit overpowered with the current damage numbers.
For Entangling Shot I got Crimson Runestone (9 sec duration) rather than Indigo (9 targets hit) because Indigo doesn't give any advantage against single targets, but Crimson still works against mobs.
Shadow Power I could go for the hatred regen, but I suspect I'll have enough from gear to not need it. I could also go for healing, but I'd be getting pretty low on discipline. As it is I'm using 1.5 discipline/sec to keep Marked for Death and Shadow Power up permanently.
I could drop Evasive Fire for Vault, but I'd need more discipline regen. I also don't see why anyone would bother with Vault(Indigo) over Golden. Golden gives you the same 70 yards for only 2 discipline more, and gives you a huge amount of additional flexibility since you can choose to vault a 3rd time, or you can vault in several different directions to get around corners.
Vault indigo and evasive fire alabaster also share the same name , Tumble. I guess they got dry on names at some point.
Still I don't know how deep the discipline pool is and how slow it regens so I can't really tweak it.
Base max discipline is 30, but it can be increased with items. It regens at 1/s. Base max Hatred is 100 and regens at 10/s. You can increase the regen rate with items.
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.
Armor - Reduces physical damage taken only. Appears to be diminish in effectiveness as your character levels. At level 13, my Wiz has 145 armor, with 18.24% physical damage reduction. This translates to each point of armor being worth 0.126~% phys DR; roughly 80 armor = 10% phys DR at level 13.
Defense - Reduces damage taken. Applies to all damage types (physical, elemental) and sources (melee, ranged, dots, etc). Appears to be diminish in effectiveness as your character levels. At level 13, my Wiz has 89 defense, with a 59.38% reduction to all damage. This translates to each point of defense being worth 0.668~% damage reduction; roughly 15 defense = 10% damage reduction at level 13.
It's unreasonable to assume that Armor and Defense provide a flat amount of DR per point as this would constitute extremely strong increasing returns if you measured its effect in terms of survival time. I'd guess that it either has exponential returns, or linear returns with respect to survival time like in World of Warcraft.
Resistances - Reduce damage to the respective element by a percentage. I have found no resist gear yet, so I cannot give any values.
Are you sure about this? I seem to recall someone saying elsewhere that resistance was a flat damage reduction.
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The only time you lose durability is if you die. And when you do die you lose 10% of your max durability. So why does it matter if you have 90/100 durability or 9/10 durability? A loss in max durability is meaningless.
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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
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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
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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.
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http://diablo.incgamers.com/forums/showpost.php?p=8031590&postcount=8
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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.
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Cluster Arrow(Indigo): 120% small AoE + 3960% rockets
Entangling Shot(Crimson): slow + 20% damage boost via Cull the Weak
Hungering Arrow(Golden): 2800% average weapon damage over time.
Shadow Power(Golden): damage boost
Marked for Death (Indigo): More damage boost
Evasive Fire(Golden): Defensive, very cheap.
Ok so Cluster Arrow is for groups, Hungering for single targets. If all the rockets can actually hit a single target, I'll drop Hungering Arrow for either Spike Trap(Golden), Rain of Vengeance (Crimson), or Companion since Cluster Arrow + Rockets does way more damage. In fact, Cluster Arrow + Rockets and Hungering Arrow(Golden) seem to do way way WAY more damage than any of their other runestone combinations, or most any other attack skill at all for that matter. Even AoE skills like Bola Shot (Crimson) would have to hit 30 targets to match Hungering Arrow, or 44 targets to match Cluster Arrow. I'm thinking they might be just a tad bit overpowered with the current damage numbers.
For Entangling Shot I got Crimson Runestone (9 sec duration) rather than Indigo (9 targets hit) because Indigo doesn't give any advantage against single targets, but Crimson still works against mobs.
Shadow Power I could go for the hatred regen, but I suspect I'll have enough from gear to not need it. I could also go for healing, but I'd be getting pretty low on discipline. As it is I'm using 1.5 discipline/sec to keep Marked for Death and Shadow Power up permanently.
I could drop Evasive Fire for Vault, but I'd need more discipline regen. I also don't see why anyone would bother with Vault(Indigo) over Golden. Golden gives you the same 70 yards for only 2 discipline more, and gives you a huge amount of additional flexibility since you can choose to vault a 3rd time, or you can vault in several different directions to get around corners.
Base max discipline is 30, but it can be increased with items. It regens at 1/s. Base max Hatred is 100 and regens at 10/s. You can increase the regen rate with items.
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Are you sure about this? I seem to recall someone saying elsewhere that resistance was a flat damage reduction.