Area Damage (AD) is one of the most valuable primary affixes for increasing one's overall damage output, however, it is also one of the most complicated and confusing affixes within Diablo III. The guide at hand aims to explain the core mechanics to properly understand Area Damage, explains a few misconceptions within the community and showcases a general concept on how to evaluate Area Damage for your character.

As an example, the Aether Walker on the right hand is an item all of us will stumble on eventually. It raises the main question: How should the item be rolled? Intelligence into %Damage or Area Damage? Unfortunately, the question at hand is not answered simply; it's necessary to understand what abilities proc Area Damage, how Area Damage propagates and how monster's positioning can therefore be manipulated to maximize AD.

Napkin Math
Let's take a step back from the two planners and first understand a more simplified scenario. The most common issue is deciding whether to roll 10% Damage or 24% Area Damage on a weapon; assume you were to hit 20 targets with those different weapon rolls. In the first setup you'll hit 20 targets for 110 damage with 150% Area Damage, whereas we denote its total damage as T'. For the second setup you'll hit 20 targets for 100 damage with 174% Area Damage denoting its total damage as T''. In both scenarios each hit on a target will have a 20% chance to proc Area Damage on the 19 nearby standing other targets.

To properly understand how Area Damage propagate—for the sake of maximizing it with playstyle—one needs to understand the four different boxes that define a monster and how to manipulate them.

Center
All of the "within X yards" calculations in Diablo III are defined as a sphere around a center. While Diablo III actually defines any actor's position with three-dimensional coordinates Pmonster = (x,y,z) all "within X yards" calculations internally refer to distances in xy-plane entirely omitting z. One exception to this is the sphere created by Slow Time which, at least for its visual render, constructs an actual three-dimensional sphere; to be clear, there might be more exceptions to this, but this is the most obvious one for most players. Any other "within X yards" -mechanic is therefore simplified in a two-dimensional circle in xy-plane, which thankfully reduces the amount of time I need to put into making the following figures :D We define the center of a monster m as its xy-Position Pxym, which at all times is also the center of its Hit Box.

The above standing table summarizes what we've learned so far. In a perfect world, with an infinite amount of computational power, every Hit Box would exactly be the parallel projection of the Collision Box into the xy-plane. As stated, this is not feasible, which is one of the reasons why some models, Collision Boxes and Hit Boxes are not really aligned for certain monsters.

Death Maiden is a great example on this end; if you've ever played zMonk you'll know the pain of consistently being teleported, even though you could swear you never actually "targeted" her. Death Maiden is a representation of a case where the Collision Box is significantly larger than the model and the Hit Box. Voracity, on the other hand, showcases the except opposite: an over the top large Hit Box with a Collision Box so small that your character can visually stand within the model of Voracity even without wearing Illusory Boots.

Figure 2 showcases one of the surprising results that emerge from Area Damage being a damage instance as a xy-circle around the center of the primary target. Assume a large monster m1 is our primary target that we proc Area Damage on; the resulting Area Damage Instance does not clip m1's (a small monster) Hit Box. In this case there is no secondary target taking extra damage from Area Damage. If we flip the situation however, and we define m2 as our primary target, the resulting Area Damage Instance will clip m1's Hit Box and will damage it as a secondary target.

It's abundantly clear at this point that the density is the most important factor, when it comes to scaling Area Damage. You want for a any primary target, if Area Damage procs on it, to hit as many secondary targets as possible. We learned in the previous section that the size of a Hit Box of a primary target is inconsequential, however, large Hit Boxes on secondary targets will help with the overall damage output, since those secondary targets will provide "more space to be hit with". Unfortunately, we also realized in the previous section, that radius rH of each Hit Box remains a static value and is not scalable with any interaction in the game.

This means the only thing left for us to manipulate is the positioning of monster in relation to each other; the denser the centers of all targets are, the higher our Area Damage output will be. This inherently means that our limiting factor is the Collision Box of each target. We already know that a few monsters have the capability to disable their Collision Box temporarily, mostly for the sake of a moving ability (Winged Assassins, Executioners, Punishers, etc.). Fortunately, we have a few abilities in the game that allow us to disable a monster's Collision Box at our own will, allowing us to reposition them as densely as we want:

The picture above (use the slider) showcases a—so called—Pixelpull. In this example Energy Twister with Ranslors Folly are utilized to pull nearly the entirety of the screen into a single pull. With these spicy pulls Area Damage simply skyrockets 8-) Not all displacement abilities are, however, capable of creating pixel density; as an example Cyclone Strike does displace multiple monsters, however, the Collision Box of each displaced target is not temporarily disabled. Overall the following skills and item combinations are capable of pixelpulling:

Press F for our fellow dexterity classes; Monk and Demon Hunter do not have any pixelpulls in their repertoire. Properly executed pixelpulls carry most of the 4-Man Push METAs; they are quintessential for the highest of Greater Rifts, especially from a competitive perspective. Keep in mind that displacing monsters increases their Crowd Control Resistance, meaning at some point they'll eventually become immune to displacement; you can not indefinitely re-pixel a pixelpull.

Damage Calculation
If we want to check out how Area Damage scales, we'll need to take a closer look at the the total damage calculation. Let's assume you'd hit t-many targets in a pull with an Area of Effect (AoE) ability, such as Energy Twister. We have y Area Damage equipped and our Energy Twister ticks exactly for s damage. All targets are within 10 yards of each other, meaning we are damaging a perfect pixelpull. Per hit we'll have a 20% chance per target to receive an Area Damage proc resulting in t ⋅ 0.2 = t ÷ 5 many AD procs. Each AD proc will hit t-1 many targets for its damage value y ⋅ s. Overall this yields:

The interesting part is now to look at certain trade-offs, as described in the Introduction with LoD Hydra. We are comparing two Serpent's Sparker with each other in the exact same build. In the first setup, the increased damage one, we'll equipp a 300% Sparker with 10% Damage while sitting at 150% Area Damage. The second setup will use a 275% Sparker with additional 24% Area Damage. The most common misconception within the community at this point is that there is a number of targets at which the AD Sparker always outperforms the Damage Sparker at all times. This is incorrect. The breakpoint of target, at which the second Sparker outperforms the first one, does not always exist. We have two look at two different cases:

In this very example, let's denote our currently equipped Area Damage as d with 150% and our additional Area Damage granted as y with 24%. Lastly, we must estimate how much better the first Sparker is with its primary target hits than the second one x = (4 ÷ 3.75) ⋅ 1.1 ≈ 1.1733. All we need to do to figure out whether we are in the above standing case (1) or (2), is to check whether (x ⋅ d) ÷ (d + y) is larger or smaller than 1. If you are further interested in why this is the case, you are welcome to read through the generic derivation and proof in the Appendix (Limit Proof).

The takeaway here is that the first Sparker, with 10% Damage and a 300% affix, will always outperform the second one with at least 1.1% more damage, regardless of the amount of targets hit. But what if we end up in the (2) case? If and only if (x ⋅ d) ÷ (d + y) ≨ 1, then there is a t0 ∈ ℕ such that the AD-item starts outperforming the DPS-item, when you start hitting more than t0 targets in a pixelpull. Let's take a look at our Hydra scenario once again and alternate it slightly. Let's assume the second Serpent's Sparker for the Area Damage setup has an Affix of 295% with 24% Area Damage, which yields x = (4 ÷ 3.95) ⋅ 1.1 ≈ 1.1139. Let's plug it in and see if we end up in (2).

Indeed we do; this means there is a number of targets t0 ∈ ℕ at which the AD-item starts outperforming the DPS-item. We can calculate said t0 with a simple formula; feel free to look up its derivation in Appendix (Target Proof):

This simply means that starting from 10 targets the Area Damage Sparker beats out the %Damage one. One a single target, however, for instance on certain Rift Guardians the %Damage Sparker will deal x ≈ 1.1139 more damage; whether or not you want to make that specific trade-off is entirely up to you. Usually, if your build scales well with Area Damage, you are comfortable making this specific trade-off, since the Rift itself is the hard part, while the extra time on the Rift Guard helps out immensely due to Bane of the Stricken.

Thanks to Iria#1342 for noticing a flipped sign in the target proof, a small notation error (both proofs) and a missed cancellation in the limit proof.
Written by sVr. Updated by Chewingnom.