Measures of AoE damage

I want a "simple" measure of AoE Damage ability for the purpose of comparing individual powers and sets, mainly for the sake of gaguing performance in big-team/large-enemy-spawn/well-protected/rolling combats situations.

I propose to use R * D /T, where R = Radius (or radius of a circle of equivalent area, for Cones), D= Damage @ L50 & +95% Damage Enhancement, T = Cast Time + (Recharge Time at 95% recharge time redux), or for toggles, activation time.

Here are a few examples of figures I get:

Blaster/Archery/Fistfull Arrows: ~304
Blaster/Assault Rifle/Full Auto: ~189
Controller/Plant Control/Roots: ~186
Brute/Super Strength/Foot Stomp: ~140
Scrapper/Fiery Aura/Blazing Aura: ~107
Blaster/Fire Blast/Inferno: ~79
Blaster/Electrical Blast/Ball Lightning: ~59

Why ought I not be satisfied with this measure (what will be misleading about it), and is there a measure that seems preferable?

Though generally I would not be comparing across ATs, if I did use the measure as stated, what should my "simple way to compare apples to oragnes (AT to AT AoE damage)" guideline say?

I see two problems with your formula:
1) You're using radius rather than area, so you're undervaluing larger attacks.
2) You aren't accounting for the target cap, ranging from 5 targets for melee cones, to 16 for nukes and ranged AoE attacks.

I think it's also a bit misleading to use fully enhanced Damage and Recharge values.

The reason for radius (or radius equivalent) rather than area is that sq feet is, yanno, logarithmically "heavier" in the equation than damage. (It varies as a square of radius). I actually thought about going the opposite direction with it; maybe radius ^0.8 or something. IOW: considering there is soft floor on density of mobs, even radius over-values large attacks. Look at the values for roots, and then consider the fact that that figure does NOT include containment. Roots is a huMONgus damage tool, but with extensive experience with it and Rain of Arrows, probably two of my favorite powers in the game, I balk at saying Roots is 118% the tool RoA is.

I agree the target cap is something of an issue. But it's also in a sense redundant with the measure of area that radius provides, since there's an effective minimum density of mobs in realistic door-mission rolling play. Of course there're some powers that are way outside the "norm" for target-cap-per-square-feet-covered, and a detailed accouting of this would probably need footnotes on about a dozen powers like that.

I tend to think the damage enhancement thing is negligable, except in the rare conjunction with damage self-buff (pretty much Kinetics-- resist debuff is another story).

I agree that the decision to assume 95% recharge enhance is significant. Here's why I chose it: It's common, I think for good reason, to look at damage per cast on powers, and while that plays less of a role for my stated purposes, still it's significant, and unlike the issue with damage enhance it's not subsceptible to simple division by 1.95 to get the equivalent-- cast times are fixed value. So, it effectively hikes up the relative weight of differing cast times, and is closer to how the power will be realistically played.

I'm glad an effort is underway to improve upon past measures of AOE damage. I've found past efforts disappointing because the simplifications made promoted misunderstanding about the relative in-game value of different AOEs (ignoring the amount of area covered by an AOE when calculating damage, calculating damage for one foe while ignoring the maximum number of targets, and ignoring the gameplay implications of cone / PbAOE / AOE distinctions).

Probably the influence of the amount of area covered by an AOE on damage needs to be weighted on a sliding scale that is determined by spawn size. Values for AOE area coverage that are not weighted according to spawn size will inevitably be misleading because the effect of AOE area coverage is directly and heavily influenced by spawn size. If an interaction term can be worked out for area covered by an AOE and the maximum number of targets, then we'd be a significant step closer to AOE damage calculations that reasonably approximate the truth.

Incidentally, I agree with the decision to use enhancement values when calculating damage. It makes the numbers easier to interpret, as they can be compared against mob hit points to determine how many hit points are left after an AOE volley.

I feel sorry for whoever's attempting to get this numbers...

Accuracy/rech/dam/range slotting priorities are a little more difficult to begin with, but I suppose in the end, it's going to be an average spawn death over time sort of calculation. I'd expect it to be possible to get a ranking of powers best for "3 targets" "5 Targets" "10 Targets" "16 Targets" "17+ Targets"

But due to so many more random factors using more enemies, (a huge number more random dice rolls) each powres gonna need to be tested a good many times to get a reliable average. Also each spawn contains different enemies, so somehow that'll need to be controlled to account for 'real' 8 man spawns having less lt's, but 2 bosses or, more lt's/minions but no bosses. (which will be very important since a boss in the mix is basically regular DPS rate after the rest are dead)

Then are the smaller spawns minions? lt's? bosses? mixtures? if radius is included does that mean cone size (which is enhanceable) included or should we pretend all enemies are stacked on eachother (herding position). Some AoE's are powerful at the center (Lightning Rod) but not so powerful towards the outer radius.

DPS is so easy because you can pick a single target that you know the stats of (like a pylon), and measure the time it takes to go down while seeing all the information played directly between you and that one target. This is gonna be all sorts of difficult.

Katten: I see no reason why this would have to be experimentally determined. The theoretical "pylon time" currently is quite close to measured pylon times, I think. Werner, BillZBubba and Arcanaville would have a better feel for that.

We've got good models, is what I'm saying.

OP: It's hard to say how to weight radius and max targets. Pardon me while I think in public.

1) Clearly, max=5 vs. max=10 is a much more significant effect than max=10 vs. max=16. Even a +0/x2 spawn (what we used to call "tenacious") can go over 5 enemies, while often "full team" spawns are under 10 enemies.

And I agree that area is disproportionate to "effective" area- that is, a 20' effect is not four times as useful as a 10' effect. Radius might be a good measure.

2) For toggles, I'd use "tick time" rather than activation time; we may be talking about the same number here. It takes (according to Red Tomax) 3.47 seconds to start up Death Shroud but it ticks every 2 seconds.

3) I've looked at your sample numbers and I think there's something off about either your math or your formula.

Fistful of Arrows is half the recharge of Ball Lightning and is a 50' cone at a 30 degree arc, so 1/12 the area of a 50' radius AOE, so about 50'/3.5 radius or close to a 15' radius sphere. No calculators were beaten in the making of this estimate.

So about half the cycle time, about the same damage (scale 0.91 vs scale 1.02), about the same "radius". Should have about twice the rating. And yet it's got a 304 vs. a 59. Did you include that Ball Lightning has multiple pulses over time?

4) I'm thinking that activation time MAYBE should be disproportionately represented. On one hand, there's "dead time" between spawns (so maybe reduce "Effective recharge" by 3 seconds?) On the same hand, you've also got... not an attack chain, exactly, of AOE, but definitely you can fire a second AOE and shrink the dead time between AOE's. Well, if you're Assault Rifle you can have an AOE attack chain... or maybe fire/mental/elec.

On the other hand I got nothing, but I feel like I'm overlooking something.

You'll get more usable results if you take actual play into account.

Full Auto and Rain of Arrows are usually cast after Aim and/or Build Up. Fistful of Arrows may not be. All secondary effects are not created equal. Sonic attacks should somehow account for the Damage Resistance debuff. Brute Foot Stomp should include Rage, and all Brute attacks need some Fury. You definitely need to include that, as well as things like Scrapper crits Blaster Defiance if you want to compare between ATs. Activation time is appropriate if you're looking at attack chains, but cycle time (taking into account Recharge) is probably a better measure of the total damage output of a power. Using cycle time for click AoEs lets you compare damage directly to toggles. Basically, think how the power is likely to be used in game. Large area long recharge AoEs are likely to be used as openers, meaning they'll hit the full number of targets. Inferno does great damage, but the long recharge significantly reduces its total output. Plus the crash may prevent you from doing more damage unless you're always prepared with Inspirations. Fast recharge attacks are likely to be used more often, meaning they'll hit fewer targets near the end of a spawn. But they usually put out more total damage because they are used so often.

Starsman did an analysis based on different Recharge levels and number of targets. See a sample HERE. But I don't really know how realistic it is.

I strongly believe target cap has more practical influence than square area. My Tankers can get lots of foes in close. I find the target cap of 5 on Pendulum from the Tanker Axe set to be much more restrictive to my damage output than War Mace's very similar power with a target cap of 10. Likewise, Shield Charge has a target cap of 16, but the following PBAoE has a target cap of 10; the difference is quite noticeable, even with a larger area PBAoE like Footstomp.

The place where large "square area" attacks make more difference, IMHO, is teams that don't allow the enemies to clump up (via tar patch, caltrops, Tanker, Rad herding, what have you) -- particularly teams with immob-happy Controllers, who lock everything down while it's still spread out. That's when I'm happy to have a big ol' target zone.

I concur that target cap really does have more effect than Area.

My Arch/MM blaster duo's with a db/wp scrapper. I open with RoA ( if it's up) then hit fistfull of arrows then Psychic scream. Anything left over gets a few single target shots. I'm usually firing FoA before ROA lands. The 5 target cap absolutely affects the damage output of FoA. No matter how tightly packed the mobs are, I can't hit more than 5 ( and they do get packed in thanks to the AOE taunt in /wp)

With the cones, you have to use the target cap as part of the equation. It makes a difference.

Fulmens--
1) Maybe there's some overwhelming modal Target Cap per Sq Feet and a few outliers that will make the thing moot. Or, maybe not.

2) Yeah, I'm looking at the tick time. I never know what to call which thing-- I would call the 3.47 on Death Shroud the cast time. Thought that was the Red Tomax nomenclature. It's the 2 second intervals I'm interested in and use.

3) Archery/Fistfull = 50' radius with 30 deg cone. That's a radius equivalent of 14.4 Feet. It fires roughly every 5.3 seconds (at max recharge) for base 56.9 lethal. Ball lightning is 15' radius every 9.3 seconds for base 63.8 energy... Oh, I see, I hand-calculated the value for Ball Lightning, but left out the DoT. Zoink. Funny, because I specifically hand calculated stuff I noticed that had DoT because I was afraid the Damage Scaling thing was wrong. Ha.

4) Yeah, I agree activation time means something here, but I like the simplicity of emphasizing it by simply assuming max recharge. I certainly don't think it's as important as in actual chains. If you can think of a more elegant or convincing approach, lemme know.

Katten--

Right, well. As I said, I don't imagine I'm prepping a final way to "know what's what," but a starting point for numerical comparison, where we can then look at inherents, buildups, rages, Against All Odds, etc.

Some of those will be easy to eyeball alongside a rating, others less so. It's fairly straightforward to remark that "After containment's set (for sets that can do so AOE, anyhow), figure on doubling this value." Some will be hairy and impossible, and that's where you say, "Yeah, but remember you can get up to +300% damage" (or whatever) " out of fulcrum shift, so obviously plant/kin rox" or whatnot.

The goal is just a condensation of information to bring to those conversations that have to involve intuitions about real play. Do you want to bring huge but dangerous AoE DoT to uncontrolled mobs as a /kin controller? (I mean, yes, but.)

TopDoc--

I definitely mean to leave buildups, Rage, inherents, and other things distinct. Embedding them in a final rating of a power would add to the confusion, which is the opposite of what I intend. I definitely am interested in ways to make things like Fury and Containment easier to understand, to present alongside, and with things like buildup, possibly present a boost-per-time or maybe a boost-coverage-across-native-AoE-chains figure.

Actual play is obviously the ideal, but there's no way to measure that that's not prohibitively laborious, and I don't trust even the tools available for approximating such data collection. Science is half empiricism and theory for a reason.

Sailboat-- Yeah, a above, I'll be trying to decide on how diverse cap-per-area-coverage really is, and come up with... something, based on that.

Silverado-- No, you can see I didn't include rage or fury. If you have reasons you think I should, feel free to explain, but as I was saying, I think it would be more confusing to embed such things rather than to treat them distinctly.

xen10K--

Yeah, as above, I guess I'm goign to have to figure a way to incorporate cap explicitly, especially if cap-per-area is all over the place (I'm not sure).

I guess it's just that, going from three distinct factors (time, damage, and radius) to four factors, two of which are indistinct, seems like a mess.

Maybe I'll rate each power on DPS and some arcane composite rating of Area combined with target cap.

Ah forgot about this thread, noticed it before my move and didnt had much time to reply. Bumped into it again today.

I realized that I didnt made ever a dedicated AoE guide to back up my AoE calculation. I passingly explained it many times during discussions about my numbers but never actually posted my approach.

Let me explain how I do it in my spreadsheets:

First thing I do is to calculate the area of an AoE, I treat them all as cones (sectors) for simplicity. Won't get into the formula but you can go here if you need it.

For an example, Foot Stomp is a 15ft radius attack, being a full circle and having a 360 degree angle, i get an area of 706.86


Now comes the fun part, figuring out how many critters fit in there. For the most part, the average humanoid critter has a diameter of 3 ft, some are bigger (tarantulas for example.) So we get to calculate the area each average critter covers too.

Before jumping to that though, I also take into assumption that foes tend to leave 3.5 ft in between each-other. The number is really guesswork more than analytic and I keep it as a variable in my spreadsheets I can dynamical modify. Herding situations, for instance, may set this spacer to zero.

So this means that I consider critters to have 6.5 ft diameters, or 3.25 radius, therefore take 33.18 ft in area.

The next is simple: divide the area of my AoE by the area of the critters and we get how many critters the AoE can really hit without too much maneuvering. In the case of foot-stomp, we talking about 21.3 foes.

Ah but wait a minute, there is one complication that requires an exception: PBAoE have ME at the center meaning I take one spot. This spot must be subtracted from the foes that fit, turning our 21.3 into 20.3. This is not an issue with cones, as I have confirmed with the devs in the past that all cones start at the tip of the extended bone (hand) and not at the center of your entity.

So far we got AoEArea / CritterArea - 1 (if PBAoE)

Now I add one last touch: target caps. Foot stomp will simply be lowered to 10 foes since that's the true max. At this point I may multiply damage by "True Max Cap".

This all may seem redundant since I just ended with the foe cap, but that's just because FootStomp is huge. Let's try any whirling attack, that are only 8 ft, and we see a difference. The area of an 8ft radius PBAoE is only 201.06 and that yields 6 before substracting yourself from the equation for a total of just 5 foes hit in average.

Frozen aura is another interesting case as it covers 10 feet. That adds up to 314.16 square feet covered, or enough to feet 9.5 critters. 8.5 once you exclude yourself from the area.

And finally a cone example, one I like due to it being full of Fun: Crowd Control. This one is 8 Ft radius and has a 180 angle, making it's covered area 157.08 square feet. That's enough to hit 4.73 critters in average, being a cone it does not suffer from me being at the center. Blasts don't suffer this either.

Shadow Maul, with it's 45 degrees and 7ft radius will have a hard time hitting anything more than 1 (hits .57)

Off course, you can always maneuver and get a better hit count, but should your goal be to see how much you can cram in you can always set Foe Spacing to zero. At zero foe spacing Shadow Maul can hit 2.7 foes comfortably.

There is an additional artifact but it's mostly an outlier. In the game engine, things will be hit even if there is just a hair-thin inside the area of the AoE. This means that, aligned properly, 3 foe max can easily become 5 hit max (push half of the leftmost to the left, then squeeze half a new one on the right, play the same on other angles and voala, 5 foes,) but its mostly so hard to do intentionally that it's better to not even consider them when you are just benchmarking average performance.

Can't we just make a table and view all the appropriate numbers side by side in order to gauge their effectiveness?

I mean, let's say we have 2 powers: Power A and Power B. People all assume power A is better. But seeing the base numbers side-by side, we'd get this:

Power | Dam | End | Cast | Recharge | Range | Radius | # targets
---A---- | -60-- | -10- | 3sec |15seconds| 30ft--- | 10feet---| 8
---B---- | -40-- | --7-- | 1.5s- | 9seconds | 45ft--- | 20feet--| 16

Power B suddenly looks a lot better. It can be cast more often, hits more foes, and costs less to do so. Though with enhancements, things like endurance and recharge become nill... but we still don't need a formula to determine that B has an advantage numerically, unless you have 8 or less foes in the shorter range with only 60 HP left, in which case power A is preferable.

Also note that this chart doesn't take into account DoT or how long that DoT takes to finish. Couldn't be arsed.

But still, why wouldn't something like this be workable?

Dont forget to add in average spawn size for average party size, for average difficulty (at least it used to be diff difficulty setting affected what spawns and how much), also youll need to look at mob density.

Just because a power has 17 targets and 10 ft range doesnt mean you can say it will hit all 17 targets and is more or less valuable than something that hits 5 targets in a 40 ft range. you rarely will get to use 17 targets within 10 ft or the full 40 ft range on 5 targets. the fact that its rare to see more than about 8-12 mobs togeather (much less on small or non teams), that on outdoor maps they are very far apart, etc, makes any numbers almost void.


Its like saying an unusable golden statue is better than a usable toilet. One is worth alot if you can sell it, the other youll use every day.