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.
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.
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.
Efficiency is not always the most important factor. DPC (per cast) in an infinite resource environment or when there's a small window of opportunity is far more important than DPR (per resource).
As for feel, I haven't been able to get to it yet, but that may need tweaking; just like Bola Shot was tweaked for destructibles.
My impression from beta streams and such is that 2h vs. dual seems to be pretty balanced.
So I will be making the choice just on drops.
If I find a good 2h (go 2h) or a good 1h (go shield) or 2 equally good 1h (go dual).
If they don't differ that much in power I will choose 2h or shield for style over dual.
A flat comparison of DPS is "easy."
For convenience sake, lets use a Monk who uses Hundred Fists unruned and Lashing Kick unruned on single targets to start. Using Monk because he has no non-item/skill Spirit regen.
Given the current ratios of rare weapons at 60 (which presumably scales true at all levels) according to d3db.com, the base damage of a Daibo is 35.93% higher, so I'll use 100 dps fist and 135.9 dps daibo. Fists have a speed of 1.4 APS, and when dual wielding, you have 1.61 after the bonus. Or in other words, you have 115 DPS. Just based on these values, the Daibo is doing 18.2% higher DPS.
You could calculate the damage of each skill or DPS of each skill, however, you have to take into account the Spirit regen, which is:
Fists: 1.61 * 6 = 9.66/s
Daibo: 1.1 * 6 = 6.6/s
In other words, on average after every 30 / [Spirit Regen] seconds, you can perform 1 Lashing Kick.
Fists: 3.11s
Daibo: 4.55s
It will take 1 / APS to actually perform the Ability, so we can add that time to the previous to find the average time of the rotation:
Fists: 3.727s
Daibo: 5.45s
For the end practical dps for Fists, you are doing 3.11s at 140% WD, and 1 instance of 200% for every 3.727s. Add the two damage values and divide by the time to get the overall dps:
Fists: 100 DPS / 1.4 APS = 71.4 Avg Dmg
Daibo: 135.9 DPS / 1.1 APS = 123.5 Avg Dmg
Fists: (3.11 * 115 * 1.4) + (71.4 * 2) = 172.5 DPS
Daibo: (4.55 * 135.9 * 1.4) + (123.5 * 2) = 203.9 DPS
So as a result, Daibo is doing 18.2% more dps, which is exactly what you expect.
The calculations get way more interesting when you add in additional sources of passive spirit regen, multiple targets, skill procs, and rotations beyond 2 skills. But yes, the more important point to be made is that it strongly depends on skill selection. The more passive spirit regen, the better the Daibo will be in using Spenders, while 1H/S and DW will remain the safer option due to requiring less time
This is an awesome point. Using a 2 hander can nullify your need for resource generation under some circumstances because of the higher damage per resource point and lower rate of fire. It's a game changer.
It changes very little... there are still going to be circumstances where you must use your ability N times regardless of the strength of your weapon simply due to the number of targets and how spread out they may be. Also, by using a spender as all attacks, you remove the ability to reserve your resources for more critical moments.
There's an 18% difference in equal level 2h and dual-weilding DPS. DW results in a 15% increased resource regeneration however, which is not immediately quantified in terms of DPS or survivability benefits.
In fairness though, I don't know that it's helpful to consider each skill-rune combination as unique. Most runes don't really change the character of the skill enough to warrant that imho. The realistic difference between two otherwise identical builds with a single rune difference where one does +10% damage and the other does +10% movement debuff is pretty small. Is it fair to consider them entirely separate builds in the context you're talking about? Certainly if one is viable, the other is as well simply because there is about a hair's width of difference between them.
I'm not implying every rune results in a new skill worth completely separate considerations. Many are simply different spreads in where the damage goes (Arcane Missile Split vs Charged Blast), but even those are important, subtle differences worth looking at when comparing a number of measures that are equally subtle in difference such as perfect aoe dps vs target limited aoe dps vs multi-directional aoe dps vs hallway aoe dps. I could also add in close vs long range and the amount of time necessary to move. A channeled line aoe such as Disintegrate has runes that greatly affect the values for each of those situations. The rune choice is further impacted by choosing to have something like Temporal Flux or Critical Mass.
I strongly believe Blizzard has done an exceptional job with runes providing that important personal feel to your play, and theorycrafting should dedicate itself to providing information about each of those skills, particularly with their specific synergies, so that users can make an informed decision after considering their preferences. It isn't reasonable to expect there to be optimal builds for every player. For that reason, I believe most, if not all, runed skills need to be examined carefully for when that rune may be appropriate.
Example of something that doesn't meet those situations: Rend Lacerate and Mutilate. Depending on how Mutilate works, it's either 270% vs 350% or 270% vs 210% over a longer period.
What's the reason in going so far as to avoid knowing it is the better question.
Regardless of the process, which I'm not disagreeing with, it is of interest to know the % of all possible builds that are deemed "viable" as that will indicate Blizzard's success in their implementation, as stated by them. It's also of interest when naysayers claim d3 isn't complex enough in its pure # of builds. It's also of interest when companies claim there are ____ions of ____, to know just how accurate their claims are.
I also disagree with the idea that a single rune change isn't worth investigating. Numerous runes change the functionality of a skill so drastically, that they are separate skills. Disregarding at the skill level is premature.
You're correct tanis, I typo'd it while converting from 6^6 to see the non runed totals. 5^6 is approximately double 6^5, so it's not too difficult to estimate the correct values from the original, if I also had the typo when using google to calculate.
Nektel, you can dismiss the numbers all you want, but for proper theorycrafting to occur, researching all possible builds is what must be done. You cannot choose skills, or even runes, in a vacuum except when comparing two builds that differ by only those skills, which is an exceptionally small sample space to examine.
There is a difference here. My numbers are not an estimate, they're correct. The OP is bullshit. Your point is completely meaningless in a world of easily swappable skills.
The important point being made here is that there are a significant number of builds to try in the game, and that it's non-trivial to determine the build to use. Compare to d2 where there were significantly *more* builds, but it was obvious what the best were, and your point wasn't meaningless because you *did* need to re-roll for *every minor difference.*
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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.
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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.
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.
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As for feel, I haven't been able to get to it yet, but that may need tweaking; just like Bola Shot was tweaked for destructibles.
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For convenience sake, lets use a Monk who uses Hundred Fists unruned and Lashing Kick unruned on single targets to start. Using Monk because he has no non-item/skill Spirit regen.
Given the current ratios of rare weapons at 60 (which presumably scales true at all levels) according to d3db.com, the base damage of a Daibo is 35.93% higher, so I'll use 100 dps fist and 135.9 dps daibo. Fists have a speed of 1.4 APS, and when dual wielding, you have 1.61 after the bonus. Or in other words, you have 115 DPS. Just based on these values, the Daibo is doing 18.2% higher DPS.
You could calculate the damage of each skill or DPS of each skill, however, you have to take into account the Spirit regen, which is:
Fists: 1.61 * 6 = 9.66/s
Daibo: 1.1 * 6 = 6.6/s
In other words, on average after every 30 / [Spirit Regen] seconds, you can perform 1 Lashing Kick.
Fists: 3.11s
Daibo: 4.55s
It will take 1 / APS to actually perform the Ability, so we can add that time to the previous to find the average time of the rotation:
Fists: 3.727s
Daibo: 5.45s
For the end practical dps for Fists, you are doing 3.11s at 140% WD, and 1 instance of 200% for every 3.727s. Add the two damage values and divide by the time to get the overall dps:
Fists: 100 DPS / 1.4 APS = 71.4 Avg Dmg
Daibo: 135.9 DPS / 1.1 APS = 123.5 Avg Dmg
Fists: (3.11 * 115 * 1.4) + (71.4 * 2) = 172.5 DPS
Daibo: (4.55 * 135.9 * 1.4) + (123.5 * 2) = 203.9 DPS
So as a result, Daibo is doing 18.2% more dps, which is exactly what you expect.
The calculations get way more interesting when you add in additional sources of passive spirit regen, multiple targets, skill procs, and rotations beyond 2 skills. But yes, the more important point to be made is that it strongly depends on skill selection. The more passive spirit regen, the better the Daibo will be in using Spenders, while 1H/S and DW will remain the safer option due to requiring less time
Edit: Corrections made
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http://www.diablofans.com/blizz-tracker/topic/219255-main-hand-damage/
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http://d3db.com/item/i/1867
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I strongly believe Blizzard has done an exceptional job with runes providing that important personal feel to your play, and theorycrafting should dedicate itself to providing information about each of those skills, particularly with their specific synergies, so that users can make an informed decision after considering their preferences. It isn't reasonable to expect there to be optimal builds for every player. For that reason, I believe most, if not all, runed skills need to be examined carefully for when that rune may be appropriate.
Example of something that doesn't meet those situations: Rend Lacerate and Mutilate. Depending on how Mutilate works, it's either 270% vs 350% or 270% vs 210% over a longer period.
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Regardless of the process, which I'm not disagreeing with, it is of interest to know the % of all possible builds that are deemed "viable" as that will indicate Blizzard's success in their implementation, as stated by them. It's also of interest when naysayers claim d3 isn't complex enough in its pure # of builds. It's also of interest when companies claim there are ____ions of ____, to know just how accurate their claims are.
I also disagree with the idea that a single rune change isn't worth investigating. Numerous runes change the functionality of a skill so drastically, that they are separate skills. Disregarding at the skill level is premature.
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Nektel, you can dismiss the numbers all you want, but for proper theorycrafting to occur, researching all possible builds is what must be done. You cannot choose skills, or even runes, in a vacuum except when comparing two builds that differ by only those skills, which is an exceptionally small sample space to examine.
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The important point being made here is that there are a significant number of builds to try in the game, and that it's non-trivial to determine the build to use. Compare to d2 where there were significantly *more* builds, but it was obvious what the best were, and your point wasn't meaningless because you *did* need to re-roll for *every minor difference.*
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([SkillCount] choose 6) * 5^6 * ([PassiveCount] choose 3)
Barb = 22 & 16 = 652,863,750,000
DH = 23 & 15 = 717,670,078,125
Monk = 21 & 13 = 242,492,250,000
WD = 22 & 17 = 792,763,125,000
Wiz = 25 & 15 = 1,259,070,312,500
Edit: Corrected typo and resulting values.