What is the expected average damage for an area of effect power?

Question

I have spent quite a bit of time coming up with an average damage document for my party and for several other characters. However, the one thing I have not been able to represent well is the average damage for attacks that have an area of effect.

For example a Level 1 Wizard at will such as Freezing burst that does 1d6 across all creatures in an Area burst 1 within 20 squares.

How do I best represent average damage for these. Should I represent it per target, for the max number of targets or is there a recommended general average that I should be using?

Answer 1

This answer is a conservative justification of the low values presented in DPR King 2.0:

Squares       Friendly     Unfriendly
4  (2x2)       1.2         1.1
9  (3x3)       1.45        1.3
16 (4x4)       1.8         1.5
25 (5x5)       2.25        1.7
36 (6x6)       2.8         1.9
49 (7x7)       3.45        2.1
64 (8x8)       4.2         2.3
81 (9x9)       5           3
a 9x9 is the cap.

After some deliberation, I agree with these assessments. Given that enemies will be avoiding bunching up save for the opportunity to flank, the heavy discount on unfriendly AoEs seems to correspond to how often there will be a combat where:

1. There are enough enemies

Given that the number of enemies in a fight optimally decreases with respect to time (you don't want to leave everyone on 1 hp until the last round) blasts and bursts have a decreased time where they can be effective.

Given that a non-trivial fraction of the fights are versus solo, elite, or small numbers of people, fulfilling the parent condition is difficult.

2. They are close enough without a party member in the way

Enemies will maneuver to avoid AoEs, just like party members. The most likely people to catch are the meleers flanking in the dogpile/scrum/charlie foxtrot, whatever you want to call the ball where all the melee happens. Targeting party unfriendly powers is hard, and almost certainly cannot happen every round.

Now, with that said, there are all kinds of ways to virtually expand the size of blasts and bursts, and anything that just adds "one square" onto a blast or burst can be said to upgrade its size for purposes of this chart.

Answer 2

If I were maintaining a list of my party's attacks and their average damages, I would list area effect attacks under multiple headings for the number of potential targets.

Let's take Freezing burst and assume the wizard has a 60% chance to hit and deals 1d6 + 4 damage. Here's how I'd list it in a document.

Freezing Burst (1 target) : 4.5
Freezing Burst (2 targets): 9
Freezing Burst (3 targets): 13.5
Freezing Burst (4 targets): 18
Freezing Burst (5 targets): 22.5
Freezing Burst (6 targets): 27
Freezing Burst (7 targets): 31.5
Freezing Burst (8 targets): 36
Freezing Burst (9 targets): 40.5

That way you can choose which power to use based on how many targets are in the area. This obviously gets a little crowded if you're using a Blast 5 or something like that. If you're using a spreadsheet you can just do something like this:

EDIT: Since your comment indicates that you aren't using this in game, and just for theoretical purposes, you're going to have to make an educated guess as to how many targets are in the area, on average. This obviously depends a lot on many different variables, so your best bet is one of the following:

1. Keep track of the maximum number of targets in the area on every turn during every encounter and average your results.
2. Ask the wizard what his criteria is for casting the burst. If he only ever casts it if 3 targets are in the area, use that for your calculations.
3. Read ahead and analyze every encounter, the terrain, the size of the combat location, the creatures, and their tactics ahead of time and theorize an average number of targets.

If you really want to boil it down to a single number...

...there are two things to look at.

1. The damage potential

This means given any round and any battlemap the average damage multiplied by the average number of targets in the area.

Using #1 above, keep track for a large sample of turns and tally up every time there were 1...9 targets in an optimally placed burst. Use that probability distribution and multiply it with the average damage for the corresponding # of targets, then add your results up.

Example:

1 Target : 77 of 200 turns = 0.385 * 4.5  = 1.7325
2 Targets: 65 of 200 turns = 0.325 * 9    = 2.925
3 Targets: 36 of 200 turns = 0.18  * 13.5 = 2.43
4 Targets: 15 of 200 turns = 0.075 * 18   = 1.35
5 Targets: 5  of 200 turns = 0.025 * 22.5 = 0.5625
6 Targets: 2  of 200 turns = 0.01  * 27   = 0.27 
7 Targets: 0  of 200 turns = 0     * 31.5 = 0
8 Targets: 0  of 200 turns = 0     * 36   = 0
9 Targets: 0  of 200 turns = 0     * 40.5 = 0

                                      Sum = 9.27 average damage potential

2. The damage of the spell when used

This one is a lot easier. Keep track over as large a sample as you can of how many targets are in the area only when the wizard casts the spell.

Example:

1 Target : 0  of 200 casts = 0     * 4.5  = 0
2 Targets: 79 of 200 casts = 0.395 * 9    = 3.555
3 Targets: 86 of 200 casts = 0.43  * 13.5 = 5.805
4 Targets: 18 of 200 casts = 0.09  * 18   = 1.62
5 Targets: 11 of 200 casts = 0.055 * 22.5 = 1.2375
6 Targets: 4  of 200 casts = 0.02  * 27   = 0.54 
7 Targets: 2  of 200 casts = 0.01  * 31.5 = 0.315
8 Targets: 0  of 200 casts = 0     * 36   = 0
9 Targets: 0  of 200 casts = 0     * 40.5 = 0
                                      Sum = 13.0725 average damage when used

Answer 3

I would strongly hesitate to put a number like that for average damage. You can't compare a sniper rifle to a grenade.

Instead, I would make it very clear what the a) average damage per effected target is and b) number of squares effected.

If I made a chart like this it would look like (just making up spells, anything after // wouldn't appear, it's just for showing here)

Magic Bolt - 4.5   // 1d6 + 1
Power Bolt - 6     // 2d4 + 1
Acid Spray - 5 (9) // 2d4 burst 3

Part of the whole point of these AoE spells is that they are DIFFERENT from a single target spell. As such, you shouldn't try to compare them.

Now, as shown above, you can approximate their value with some coefficients, but so much of it is circumstantial. But they are indeed intended to be circumstantial spells! It might not be all that often that you will have the opportunity to hit 3 enemies with a 3x3 attack, but when you do have that opportunity you should be prepared with that AOE spell for some encounter-deciding damage!

You're also looking at this from a purely roll-playing perspective (as opposed to role-playing.) The aoe spells might be very poor for damage, but when you need to get rid of incriminating documents fast, you might want that AOE fire spell. When you need to freeze a small lake to get across it, you might want that AOE frost spell.

My favorite part of table top games is doing fun, unexpected things, like hitting yourself in the face just to make your mace shine because you need some light. Having a diverse collection of spells will help you a lot more than just having the highest damage ones. I'm not saying always skimp on the damage, but just be aware of all the other things you can do with those spells. As a DM, I would totally consider giving your party a +2 to intimidate checks against goblins, commoners, or other people in some circumstances if you can conjure up some thunder in the background. And 'bar tricks' always go over good (and make for some very fun conversations!)