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.
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.
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)
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/
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).
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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.
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.
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 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/
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).