D&D 5E Quantifying AOE impact

[Cap'n Kobold]

DPR is not impact. I already illustrated why in the OP.

No, but AoE damage having twice the impact on an encounter as single-target damage is a pretty good starting point.

 

[Cap'n Kobold]

Yep, that's kind of where I'm going with this, except I'm not looking for one overall number to estimate. I want to know the interactions.

'm thinking about it like this. Relative to my AOE damage, how much single target party damage and how many enemies and how much hp per enemy do we need to get significant contributions from AOE.

For example.
Aoe Dmg = N
Party Dmg = 2N
Enemy Count = C
Enemy HP = 4N

How beneficial is casting a fireball in this situation? (assuming single target damage perfectly overflows to the next enemy).

Let C = 3
Then no AOE
3+3+2+2+1+1 (assumed the enemy gets turn on a round before death) = 12 enemy turns

With AOE = 3+3+2+1+1 = 10 enemy turns

However, if we change the relations of those variables then what happens. Can what's happening be generalized into a single multivariable equation?

***I think the example I provided is going to be close to a typical case.

Can you break down your "With AoE" example please? I'm not seeing how it turns out like that.

Two other potential variables to consider:
The ratio of enemies that can be caught in each AoE compared to the total number.

The point in the combat where switching from AoE to single target damage would be advantageous.

 

[dave2008]

I think the assumption is a 50% save chance

Per the 2nd post: "...To keep the problem workable I'm proposing to look at all damage sources as if they always do their DPR on each hit." I don't think he is assuming 50%. If @FrogReaver was it would be 14, not 21. So either way it is wrong.

 

[FrogReaver]

Per the 2nd post: "...To keep the problem workable I'm proposing to look at all damage sources as if they always do their DPR on each hit." I don't think he is assuming 50%. If @FrogReaver was it would be 14, not 21. So either way it is wrong.

The DPR of a fireball at 50% hit rate is 21.

 

[Krachek]

Yeah if you can't hit at least 2 don't bother with an AoE.

You don't really get to hit clusters that much based on encounter guidelines anyway.

I would go for at least 3, if not 4.
and casters are much more efficient at doing debuff or delay than damage.

 

[FrogReaver]

Can you break down your "With AoE" example please? I'm not seeing how it turns out like that.

Yes. All enemies die at the end of the round.
Round 1. 3 Enemies none die. 3 attacks on players. 1 enemy has N hp left. the other 2 enemies have 3N hp left.

Round 2. 3 enemies, 1 dies. 1 enemy drops to 2N hp left. The other enemy has 3N hp left. 3 attacks on players.

Round 3. 2 Enemies. 1 dies. The other has 3N hp left. 2 attacks on players

Round 4. 1 enemy. Has 1N hp left. 1 attack on players

Round 5. 1 enemy. It dies. 1 attack on the players

Total attacks = 3+3+2+1+1 = 10

Two other potential variables to consider:
The ratio of enemies that can be caught in each AoE compared to the total number.

Will be easy to do if we master the AOE hits all case. That's really the first step in this process. IMO.

The point in the combat where switching from AoE to single target damage would be advantageous.

AOE is typically resource driven and single target usually isn't. The real answer there would have to factor in how many resources you have remaining and how many encounters you have remaining - basically your asking about a far more complex problem than what we really need to solve for to obtain highly useful information.

If we know how impactful an AOE is then we as players in the game can evaluate the resource costs in relation to the known impact of the aoe.

 

[FrogReaver]

I would go for at least 3, if not 4.
and casters are much more efficient at doing debuff or delay than damage.

That can't be said for sure yet since we can't even relay the actually impact aoe damage is having yet.

 

[Esker]

Per the 2nd post: "...To keep the problem workable I'm proposing to look at all damage sources as if they always do their DPR on each hit." I don't think he is assuming 50%. If @FrogReaver was it would be 14, not 21. So either way it is wrong.

DPR is the average, factoring in chance to hit/save. The average damage roll is 28, so you average 28 per failed save and 14 per success. If saves succeed half the time the average damage is 21.

The simplification is to ignore the variability, which against specific monsters does matter (if the mob starts with 15 HP, you kill everything slightly less than half the time with 8d6 since you only need a slightly above average damage roll to make the save irrelevant, whereas if the damage were fixed at 28 only the save would matter. Of course, if they had 14 HP each, the variability works against you. My intuition is that these two types of scenarios roughly even out, so ignoring variability is reasonable in this case.

 

[DND_Reborn]

I think the assumption is a 50% save chance

LOL, that would do it.

 

[Esker]

For example.
Aoe Dmg = N
Party Dmg = 2N
Enemy Count = C
Enemy HP = 4N

Then no AOE
3+3+2+2+1+1 (assumed the enemy gets turn on a round before death) = 12 enemy turns

With AOE = 3+3+2+1+1 = 10 enemy turns

In this example, the AoE did 3N damage in total, and knocked off two enemy turns, compared to that character doing nothing. A useful comparison would be to look at the number of enemy turns if the caster instead were able to contribute 3N damage to a single target (but only once).

In round 1, the party does 5N damage, killing the first enemy and knocking the second down to 3N. In round 2 the party gets the second enemy down to N. Round 3, kills that one, third enemy to 3N. Round 4, down to N; Round 5, kills the last enemy.

3+2+2+1+1 = 9 enemy turns

So in that case the difference between the AoE and doing the same total damage but to a single target was a reduction by 3 enemy turns instead of 2, meaning the single target damage would have been 50% more impactful simply by being single target. Equivalently, the AoE damage was 2/3 as impactful per point as single target damage.

That actually works out exactly to @NotAYakk 's 50% discount rate on damage to targets after the first: You're getting N + (0.5)N + (0.5)N = 2N value out of your diffuse 3N damage.

Checking some more combinations would be helpful to see how well that holds up...