D&D 5E Quantifying AOE impact

[FrogReaver]

So far the best estimate we have:

So I guess we could say, roughly, that if the rest of the party's damage is D per round, then an AoE that does PD damage to each of M creatures (changing M here to be the actual number instead of half) should save the party around

P(M^2)/2

monster turns.

The impact of AOE damage is different than the impact of single target damage. For example, if there are 4 enemies with 100 hp each and you can do 100 damage to a single one or 25 damage to each then doing 100 damage to a single enemy is going to be more beneficial (at least absent some other party member having an AOE that could do 75 damage to each of the enemies).

The goal of this thread is to attempt to understand the various variables and relationships of those variables to AOE effectiveness.

So how to measure AOE effectiveness? To do that we need a "common currency". In this case the best "common currency" I can come up with is enemy damage output over the encounter - which if all enemies in a given encounter are identical equates to enemy turns.

***I want to note that a player group that has more of the enemy damage distributed to higher defense PCs will actually be less damage, but since the goal here is to evaluate AOE tactics and not party composition then I believe this variable can be safely ignored for this endeavor.

So what do I expect to see if we are able to achieve the quantification I hope we can? I expect to see that number of enemies is a strong variable. That hp of enemies compared with aoe damage and single target party damage per turn really drives the usefulness of aoe damage. I expect to be able to understand the exact nature of such relationships at least under some idealized conditions.

So let's begin this journey. Any assistance is greatly appreciated!

 

[FrogReaver]

To keep the problem workable I'm proposing to look at all damage sources as if they always do their DPR on each hit. It's not a perfect match to reality but should be enough to reveal trends!

I think fireball will be the best test cast AOE. I will use 21 damage as it's average.

 

[Phazonfish]

If I am not mistaken, one of the DMG tools for estimating DPR says assume it hits 2 targets.

 

[Zardnaar]

If I am not mistaken, one of the DMG tools for estimating DPR says assume it hits 2 targets.

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.

 

[FrogReaver]

If I am not mistaken, one of the DMG tools for estimating DPR says assume it hits 2 targets.

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

 

[Esker]

This would be really useful to be able to do.

Off the top of my head it feels like a good place to start is to index AoE damage to a level-appropriate baseline for single-target damage. That way, you're not trying to evaluate the impact of 21 damage per target to N targets, which is going to depend on how many HP per target is typical for the PC's level; instead you're comparing, say, doing X damage to one target to C*X total damage spread across N targets.

The total amount of damage is one relevant quantity, but it ought to be adjusted by the ratio C/N. If C/N > 1, the AoE is strictly better than doing X damage to one target, since (resource use aside) you'd prefer it even if you only hit one target; and if C/N <= 1/N it's almost strictly worse, since you're just doing X damage, but the chance of denying an enemy turn is lower than if you did all X damage to a single target (the exception being if multiple targets are below X/N HP at that point, though even then a single target damage dealer will often be able to pick off multiple enemies with multiple attacks).

But usually we'll have 1/N < C/N < 1, which is the interesting region, where we need to start making some assumptions.

... More later.

 

[DND_Reborn]

I think fireball will be the best test cast AOE. I will use 21 damage as it's average.

FWIW, unless I am missing something, fireball in 5E averages 28 damage, not 21 (which it averaged in earlier editions).

 

[Esker]

FWIW, unless I am missing something, fireball in 5E averages 28 damage, not 21 (which it averaged in earlier editions).

I think the assumption is a 50% save chance

 

[NotAYakk]

In 4e my rule of thumb was secondary targets where worth 50% of primary. You could probably use a harmonic sum or something instead, but 50% did a good enough job.

If you deal only aoe to N targets at Y total damage, or deal perfect single taget damage, the AOE case will result in twice as much damage from the enemies before they drop. This is because single target damage results in a triangle of monsters alice, while aoe results in a rectangle. The width is the same, but the area of the triangle is half of the rectangle.

If you do 1 monsters worth of single target damage per round, and there are 5 to start, you get 5+4+3+2+1 monster-rounds of atracks.

If instead your total damage is the same, except it is AOE, you take 5+5+5+5+5 damage.

One is a triangle of height and width 5, so area of 5*5/2. The other is a rectangle (well square) of area 5*5. So twice as much, so half as good.

In reality it gets messier, but this is good enough.

But this also aasumes you are a PC on the winning side. The DMG assumption of 2 targets is equivalent id we assume 4 PCs and 3/4 are hit by it.

 

[FrogReaver]

In 4e my rule of thumb was secondary targets where worth 50% of primary. You could probably use a harmonic sum or something instead, but 50% did a good enough job.

If you deal only aoe to N targets at Y total damage, or deal perfect single taget damage, the AOE case will result in twice as much damage from the enemies before they drop. This is because single target damage results in a triangle of monsters alice, while aoe results in a rectangle. The width is the same, but the area of the triangle is half of the rectangle.

If you do 1 monsters worth of single target damage per round, and there are 5 to start, you get 5+4+3+2+1 monster-rounds of atracks.

If instead your total damage is the same, except it is AOE, you take 5+5+5+5+5 damage.

One is a triangle of height and width 5, so area of 5*5/2. The other is a rectangle (well square) of area 5*5. So twice as much, so half as good.

In reality it gets messier, but this is good enough.

But this also aasumes you are a PC on the winning side. The DMG assumption of 2 targets is equivalent id we assume 4 PCs and 3/4 are hit by it.

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.