Hi there! It’s time for another informative math post explaining why increasing monster density greatly increases the damage dealt by Devouring Arrow.
With the new release of the Gears of Dreadlands set alongside a major buff to the Ninth Cirri Satchel, many players are now using a Devouring Arrow Strafe build. Specifically, the important aspect to focus on is the guaranteed pierce chance of Hungering Arrow.
To start, let us assume the Hungering Arrow is fired from a distance where it hits a single target exactly 5 times and there are no walls or other obstructions that prevent the arrow from doing so. With a missile dampening elite, many more pierces are possible, but for this analysis we will assume such an enemy is not present.
Next, assume there are n targets stacked up on top of each other, this is somewhat possible with a “pixel-pull” like Barbarian’s Ground Stomp - Wrenching Smash.
So now the question is:
How does the total damage of a single Devouring Arrow scale with the number of targets n with some fixed amount of area damage a%?
To answer this question, we need a couple facts:
- Devouring Arrow’s damage is multiplied by (1 + 0.7*pierce_count). So that the first hit does normal damage, the second does 1.7 times, third 2.4 times, etc.
- Area damage is applied to all other targets per hit. We will assume a fixed amount of a% area damage at a 20% proc chance, we can simplify this to 0.2*a area damage at a 100% proc chance for the expected value over a large number of trials.
So now let’s simulate the entire process where the base damage of the Devouring Arrow is 1. On the first hit on the first target, the damage dealt is 1 and all other n-1 targets take 0.2*a damage.
Now the arrow hits the second target for 1.7 times the damage and 0.2*a of that amount to the other n-1 targets:
Following this pattern to the kth target, we obtain:
Now, how many hits do we get? Well since we assumed the arrow would hit an isolated target exactly 5 times, the arrow would hit n times (piercing the stack of targets), turn around and hit n more times, etc. for a total of 5n hits. Now we can sum the formula above for k = 1 to 5n:
Note that this reveals that Devouring Arrow scales cubically with the number of targets since the highest order term of n in the equation is n^3. The coefficient of that term involves the area damage total “a” which means area damage is extremely important for this build!
To summarize, Devouring Arrow’s potential depends heavily on the number of targets present in a close proximity. While area damage scales very strongly with density, so do the number of pierces. This interaction leads Devouring Arrow to have cubic order scaling with the number of stacked targets in very high density.
TL;DR: Get as much area damage as you can for Devouring Arrow and try to stack things at tight as possible with Ess of Johan, Leonine-enhanced Bolas, or a supporting player (e.g. Barbarian). Also, Missile Dampening allows for many more pierces to occur!
Thanks for reading another of my math posts!
I’m currently trying a build which seems to be working quite well and is based on max AD, no CD on any items, with Zodiac in the cube to give the CD for permavengeance.