D&D 5E Quantifying AOE impact

[NotAYakk]

Yes, calculating the average damage of a fireball spell is not the topic of this thread. This thread is about understanding shat the impact of AOE damage is, not calculating the anount. If you want to talk about that, can you start a thread on that topic, instead of doing it here?

I get it someone is wrong on the internet.

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Back on topic; I suspect the reason why the 50% rule works is that each AOE effectively shrinks a "triangle" of monstsr damage by reducing its height. And that reduces monster dmage half as a much just doing damage and eliminating monsters.

Now partial AOEs are interesting. 5 monsters, aoe hits 3; if those are the first 3 dropped, I suspect 1+.5+.5 is undervaluing the contribution.

 

[FrogReaver]

Let's look at a case with no AOE

Let 3N = Monster hp
Let 2N = party single target damage

3N/2N = 1.5 -> Round up = 2 -> The party will kill the first enemy at 2 rounds
2*1.5 = 3 -> The party will the next enemy at 3 rounds
Since remainder is 0 the cycle ends.
3+3+2+1+1 = 10

----------------------------------------------------------------

Let 10N = Monster Hp
Let 4N = party single target damage

10N/4N = 2.5 -> Round up = 3 -> The party will kill the first enemy at 3 rounds
2*2.5 = 5 -> The party will kill the next enemy at 5 rounds
Since the remainder is 0 the cycle ends
3+3+3+2+2+1+1+1 = 16

---------------------------------------------------

Let 10N = Monster HP
Let 3N = party single target damage

10N/3N = 3.33 -> Round up = 4 -> The party will kill the first enemy at 4 rounds.
2*3.33 = 6.67 => Round up = 3 -> The party will kill the next enemy at 7 Rounds
3*333 = 10 -> The party will kill the next enemy at 10 Rounds
Since the remainder is 0 the cycle ends
3+3+3+3+2+2+2+1+1+1 = 21

 

[Esker]

DPR in 5e dmg CR calculations does not take into acount hit rate.

Attack bonus is in the table though, so it's there, just separated.

 

[FrogReaver]

Let's look at a case with no AOE

Let 3N = Monster hp
Let 2N = party single target damage

3N/2N = 1.5 -> Round up = 2 -> The party will kill the first enemy at 2 rounds
2*1.5 = 3 -> The party will the next enemy at 3 rounds
Since remainder is 0 the cycle ends.
3+3+2+1+1 = 10

----------------------------------------------------------------

Let 10N = Monster Hp
Let 4N = party single target damage

10N/4N = 2.5 -> Round up = 3 -> The party will kill the first enemy at 3 rounds
2*2.5 = 5 -> The party will kill the next enemy at 5 rounds
Since the remainder is 0 the cycle ends
3+3+3+2+2+1+1+1 = 16

---------------------------------------------------

Let 10N = Monster HP
Let 3N = party single target damage

10N/3N = 3.33 -> Round up = 4 -> The party will kill the first enemy at 4 rounds.
2*3.33 = 6.67 => Round up = 3 -> The party will kill the next enemy at 7 Rounds
3*333 = 10 -> The party will kill the next enemy at 10 Rounds
Since the remainder is 0 the cycle ends
3+3+3+3+2+2+2+1+1+1 = 21

It seems to me that if one wanted to add some factor for not being able to perfectly move damage over to the next enemy that it could be done in the above equations. After the 1.5 or 2.5 or 3.5 value is calculated you simply decrease that by some amount (maybe 5% or 10%) to account for not all damage moving to the next target.

 

[FrogReaver]

So it's looking to me like fireball under fairly normal game conditions is going to typically save 2-3 attacks when facing 3 enemies.

I'll elaborate more on the trial methodology later.

Against 4 enemies fireball looks like it may reduce the number of attacks taken on average by 3-4.

These aren't perfect measurements, but they should give some insight into the benefits - at least enough to start comparing against a typical control spell against similarly sized groups.

 

[Esker]

To remove the impact of overkill, let's use an even number of monsters -- say 2M -- leaving the party damage at 2N and the AoE per target at N, and set the number of HP per monster to KN. That way, with no contribution from the caster, the party will take MK rounds to go through the monsters' 2MKN HP with no overkill damage, and with the one-time 2MN contribution from the caster they will take MK-M rounds, with none left over (regardless of whether the caster is doing single target or AoE damage).

Assuming no contribution from the caster, it takes ceiling(K/2) rounds to kill the first monster, then floor(K/2) rounds to kill the second, ceiling(K/2) to kill the third, and so on, so the number of turns by each monster, as a function of the order in which they get attacked, is

1. ceiling(K/2) = 0K + ceiling(K/2)
2. ceiling(K/2) + floor(K/2) = 1K
3. K + ceiling(K/2) = 1K + ceiling(K/2)
4. K + ceiling(K/2) + floor(K/2) = 2K
5. 2K + ceiling(K/2) = 2K + ceiling(K/2)
6. 2K + ceiling(K/2) + floor(K/2) = 3K
...

for a total of

M*ceiling(K/2)+[(1-1)*K+1*K + (2-1)*K+2*K + ... + (M-1)K + MK]

which simplifies to M*ceiling(K/2) + M^2 * K enemy turns.

An AoE from the caster is equivalent to reducing K by 1, since we are starting out subtracting N from each monster's HP, so we wind up preventing either M^2 or M^2+1 enemy turns, depending on whether K is even or odd (respectively).

 

[FrogReaver]

To remove the impact of overkill, let's use an even number of monsters -- say 2M -- leaving the party damage at 2N and the AoE per target at N, and set the number of HP per monster to KN. That way, with no contribution from the caster, the party will take MK rounds to go through the monsters' 2MKN HP with no overkill damage, and with the one-time 2MN contribution from the caster they will take MK-M rounds, with none left over (regardless of whether the caster is doing single target or AoE damage).

Assuming no contribution from the caster, it takes ceiling(K/2) rounds to kill the first monster, then floor(K/2) rounds to kill the second, ceiling(K/2) to kill the third, and so on, so the number of turns by each monster, as a function of the order in which they get attacked, is

1. ceiling(K/2) = 0K + ceiling(K/2)
2. ceiling(K/2) + floor(K/2) = 1K
3. K + ceiling(K/2) = 1K + ceiling(K/2)
4. K + ceiling(K/2) + floor(K/2) = 2K
5. 2K + ceiling(K/2) = 2K + ceiling(K/2)
6. 2K + ceiling(K/2) + floor(K/2) = 3K
...

for a total of

M*ceiling(K/2)+[(1-1)*K+1*K + (2-1)*K+2*K + ... + (M-1)K + MK]

which simplifies to M*ceiling(K/2) + M^2 * K enemy turns.

An AoE from the caster is equivalent to reducing K by 1, since we are starting out subtracting N from each monster's HP, so we wind up preventing either M^2 or M^2+1 enemy turns, depending on whether K is even or odd (respectively).

The actual results I'm getting don't appear to be going up quadratically with number of monsters. Though it could just be that the 3 and 4 monster case isn't far enough out to really reveal that behavior. Or else there's some mitigating factor like monster hp that decreases with the number of monsters being fought.

 

[Esker]

The actual results I'm getting don't appear to be going up quadratically with number of monsters. Though it could just be that the 3 and 4 monster case isn't far enough out to really reveal that behavior. Or else there's some mitigating factor like monster hp that decreases with the number of monsters being fought.

Keep in mind that my M is half the number of monsters, so 4 monsters is just the M=2 case.

 

[FrogReaver]

Keep in mind that my M is half the number of monsters.

Ah yea, Then not far enough out.

 

[Esker]

So, against 2 monsters, an AoE that does damage to each creature equal half the rest of the party's DPR (e.g., a fireball in a scenario where the rest of the party puts out a combined 42 DPR) should prevent 1-2 monster turns.

Against 4 monsters, it should prevent 4-5 monster turns.

Against 6, it should prevent 9-10 monster turns.