D&D 5E The impact of overkill damage

[FrogReaver]

Why is that? This is exactly what's done with DPR, already. Why would we not look at overkill damage's effect on DPR the same way? You cannot hold out DPR as a valid statistic and then claim that it's inappropriate to evaluate DPR using similar metrics.

Let's start with the conclusion:

DPR is a per round metric. Overkill is a per kill metric. Mathematically You cannot add or subtract a per round metric from a per kill metric. You would need to determine your actual in game average kills per round after excluding any such kills that occur at the end of an encounter. That's the proper factor you would need to turn overkill into a per round metric from a per kill metric.

Let's examine the theory behind this:

DPR is an expected value calculation. Thus HP/DPR = Expected number of rounds to kill an enemy provided that the HP is sufficiently high. This calculation is independent of overkill. That is, no matter how much overkill you do, if you have the same DPR as another character you will on average over the long haul kill that enemy in the same number of rounds.

So while the first enemy is always killed in the same number of rounds, what overkill ultimately tells us is how much more damage can be passed along to the next enemy in a combat when you deliver the killing blow. It has a huge impact when your PC is killing low hp enemies that die in 1 hit. It has much less impact in many other scenarios.

One major challenge in determining impact is that the less often your PC delivers the killing blow while also having another enemy he can attack the overall overkill actually matters (it's essentially a per kill metric). Having party members in general tends to lower the impact of your overkill as you will be sharing kills with them. So in a 4 enemy encounter on average you will likely only see your overkill happen against 1 enemy (extremely abstract example).

 

[FrogReaver]

You want to prove that overkill doesn't matter, so you start by declaring that any circumstances where it does matter are corner case scenarios and aren't pertinent. That's very convenient, but anytime someone does that I tend to be suspicious of the reasoning involved.

And you want to prove it does matter - so you jump to the conclusion that I'm being unreasonable by pointing out that fireball and other aoe spells I'm using it to stand in for trivialize encounters against many low hp enemies. If they are doing that then you aren't getting killing blows against low hp enemies, which ends up lowering the overkill application factor as you only can apply overkill to enemies your PC kills.

Just as your suspicious of anyone bringing up a specific set of scenarios to bolster their point - I'm suspicious of anyone that falls back to claims of tactical inferiority to try and counter that point.

My move, your move.

I'm in three D&D groups right now. I have a solo side game going in one of the groups, so it's four parties total. Of those four parties, only one even has fireball IIRC, despite that three of those four parties have wizards. One group doesn't have a wizard at all. In the solo game, the wizard is a theurge (UA) so I'm having to make my spell selections very carefully so that I can eventually unlock her full potential (I'll hopefully find a scroll of fireball that she can transcribe into her book at some point). Another group has a wizard but he opted for lightning bolt because he prefers precision, over fireball's large area. The last group does have a wizard with fireball, but even in that case fireball wasn't always an option as he's had to miss several games while away on business trips.

That's four examples of groups that either don't have fireball at all, or don't always have access to it. An overall small sample size, but I think what it shows is that you can't just assume fireball to be a given. Just because tools like fireball exist, doesn't mean we can just assume that those cases are negligible. Not every party will have fireball, and not every tactical scenario will enable its use.

It's not just fireball though. It's any effective aoe. Anything that trivializes the encounter to the point where you are just going through the mop up motions. I've focused on the damage aspect because it's easier to show but it's really anything. Because we are talking about impact - what you accomplish in the mop up rounds means very little.

And to elaborate just a bit more, the point I'm making isn't that every single encounter against alot of foes will be decided by effective aoe's - just that many of them will. I'm talking about the factor most often overlooked in overkills impact - the factor you use to turn overkill from a per kill metric to a per round metric. Talking about the cases where it's going to be most effective being quite a bit less common (and less important) due to abilities that often trivialize those scenarios is a very important point.

Again - my case has never been that overkill doesn't have any impact - it's that it's impact on average over a campaign is minimal.

I think that if you try to prove that overkill doesn't matter by disregarding any cases where it does matter, all you'll prove is that overkill doesn't matter in cases where it doesn't matter. Which is self evident.

So showing that overkill doesn't matter in cases it doesn't matter and then qualitatively and quantitively comparing those cases to the broader picture is precisely the point. Overkill is a per kill metric. We need a conversion factor to convert it into a per round factor. The argument is that you are weighting the cases where it's most useful much more highly than they should be weighted.

 

[Ovinomancer]

Let's start with the conclusion:

DPR is a per round metric. Overkill is a per kill metric. Mathematically You cannot add or subtract a per round metric from a per kill metric. You would need to determine your actual in game average kills per round after excluding any such kills that occur at the end of an encounter. That's the proper factor you would need to turn overkill into a per round metric from a per kill metric.

Let's examine the theory behind this:

DPR is an expected value calculation. Thus HP/DPR = Expected number of rounds to kill an enemy provided that the HP is sufficiently high. This calculation is independent of overkill. That is, no matter how much overkill you do, if you have the same DPR as another character you will on average over the long haul kill that enemy in the same number of rounds.

So while the first enemy is always killed in the same number of rounds, what overkill ultimately tells us is how much more damage can be passed along to the next enemy in a combat when you deliver the killing blow. It has a huge impact when your PC is killing low hp enemies that die in 1 hit. It has much less impact in many other scenarios.

One major challenge in determining impact is that the less often your PC delivers the killing blow while also having another enemy he can attack the overall overkill actually matters (it's essentially a per kill metric). Having party members in general tends to lower the impact of your overkill as you will be sharing kills with them. So in a 4 enemy encounter on average you will likely only see your overkill happen against 1 enemy (extremely abstract example).

This is fundamentally flawed. Yes, DPR is a per round metric, but it's built on per attack. Killing blows are also per attack. Both meteics are on the same level -- the attack. All DPR means is a summation of multiple attacks.

If you review my post above, you'll clearly see that it's premised entirely per attack and addresses the frequency of kill. It specifically modifies average attack damage. To get modified DPR, all you do is multiply by number of attacks.

The framewirk I present above also works for attacks the aren't even -- do a separate analysis for each and add for DPR.

 

[FrogReaver]

This is fundamentally flawed. Yes, DPR is a per round metric, but it's built on per attack. Killing blows are also per attack. Both meteics are on the same level -- the attack. All DPR means is a summation of multiple attacks.

If you review my post above, you'll clearly see that it's premised entirely per attack and addresses the frequency of kill. It specifically modifies average attack damage. To get modified DPR, all you do is multiply by number of attacks.

The framewirk I present above also works for attacks the aren't even -- do a separate analysis for each and add for DPR.

You do have a frequency of kill factor. The point is that you are applying it as if only the PC in question could be the one killing the enemy. In the actual game state that doesn't happen.

1. The benefits of doing less overkill only applies to enemies your PC actually kills - we agree there and you listed a factor for it.
2. Your PC will not be the one killing every enemy in an encounter. (Rule of thumb might be to estimate that he kills 1/4 of the enemies in the encounter).

You did not account for #2. Your calculation had the defacto assumption that your PC was killing every enemy encountered.

In general, it's never guaranteed that the 1 v N case can be substituted for the M v N case and yield correct results.

 

[Ancalagon]

No, I didn't say that. I said that if a fireball is always the solution to a group of weaker enemies, the DM is not playing them tactically. I never implied, or intended to imply, that this reflects your game.

However, it's a rather obvious sort of thing. Weak enemies CAN be played tactically in such a way that a fireball ceases to be a good option (ie. the creatures come from multiple directions, or in waves, such that it's impossible to get a majority of them with a fireball). Given that tactics exist to counter fireball, if the DM doesn't use such tactics then they aren't playing the creatures tactically.

Tactical considerations are not the only ones. roleplaying ones are too. The enemies may not know that you have a good AOE! Do goblins know about fireball and shatter?

In the real world, we call the fireball spell "hand grenades". But strangely enough, even though everyone knows about hand grenades, in a bar fight people don't consider that.

(btw don't get in bar fights, some jerk will pull a knife or break a bottle on your face).

 

[Ovinomancer]

You do have a frequency of kill factor. The point is that you are applying it as if only the PC in question could be the one killing the enemy. In the actual game state that doesn't happen.

1. The benefits of doing less overkill only applies to enemies your PC actually kills - we agree there and you listed a factor for it.
2. Your PC will not be the one killing every enemy in an encounter. (Rule of thumb might be to estimate that he kills 1/4 of the enemies in the encounter).

You did not account for #2. Your calculation had the defacto assumption that your PC was killing every enemy encountered.

In general, it's never guaranteed that the 1 v N case can be substituted for the M v N case and yield correct results.

Again, you do not ever care about overkill damage UNLESS the PC in question lands the killing blow. It does not matter what every other case is, it only matters when and if the given PC lands a killing blow. I did account for #2 in that I don't care about situations where the PC doesn't land the killing blow. This is covering in Assumption 1 -- we only care about overkill when a killing blow lands. After that, it's a matter of determining what frequency is appropriate, and here there is room for debate. If, as you say, a PC is assumed to land the killing blow on 1/4 of the enemies presented, and we assume 3 rounds of combat, that's 1.25 kills per combat per PC. If the PC in question has 2 attacks, that's 6 attacks total. If we eyeball it, that's an f of 6, which I happened to include in my example.

Now, I disagree that f should be 6, as a high average attack damage character has a wider kill range and so will more often land killing blows.

Fundamentally, what my analysis shows is that the overkill effect is dependent on two factors -- base average damage and frequency of killing blows. If is directly proportional to both -- as average damage increases, overkill effect increases and as frequency of killing blows increases, overkill effect increases. Nothing in this analysis says that the reference PC is doing all of the killing -- the rate of killing blows is an input variable, for goodness sakes!

If we take your assumptions above, and look at the previous example of rogue versus monk, we can do a rough analysis. Both have a +4 in the controlling stat, and both are 5th level. That's +8 to attack and +4 damage from stat with the Rogue at +3d6 sneak attack damage and using a +1 sword in the main hand. Let's assume the target is AC 14, so hit% is .75.

dmg(R1) = 1d6(weapon)+3d6(sneak)+4(stat)+1(magic) = 19
dmg(R2) = 1d6(offhand weapon) = 3.5
dmg(Rperround) = 22.5

dmg(M) = 1d6+4 = 7.5
dmg(Mperround) = 3*dmg(M) = 22.5

dmg(Rperround) = dmg(Mperround)

OAD(R1) = 6.625
OAD(R2) = 0.8125
OAD(M) = 2.3215

If we set frequency of killing blows to 1/4 over three rounds, the rouge makes 3 main hand attacks and 3 offhand attacks and the monk makes 9 attacks. The rouge has 2 cases now, one where the mainhand is the killing blow and one where the offhand is the killing blow. Let's assume this breaks according to the strength of the attack or that mainhand is going to be killing blow 19/22.5 times. Offhand the remaining 3.5/22.5 times. This is very close to .85 and .15. We'll adjust this when we solve.

This complicates the rogue, but we can do it using this split and calculating X' independently for each attack. The necessary step is in the calculation of X'. You have to multiply the OAD in that calculation by the split, so the new X' for the rogue looks like:

X'(R1) = X(R1) - ((.85*OAD(R1))/3) = 12.37

The frequency of 3 is used because the rogue makes 3 of these attacks. The percentage modifier adjusts this to reflect the times that one of these three attacks is the killing blow. X'(R2) is solved for the same way:

X'(R2) = X(R2) - ((.15*OAD(R2))/3) = 2.61

X'(Rperround) = 14.99

The monk is straightforward.

X'(M) = 5.37
X'(Mperround) = 16.11


As you can see the difference in effective DPR when accounting for overkill is slightly in the monk's favor by 1 DPR.

 

[Fanaelialae]

And you want to prove it does matter - so you jump to the conclusion that I'm being unreasonable by pointing out that fireball and other aoe spells I'm using it to stand in for trivialize encounters against many low hp enemies. If they are doing that then you aren't getting killing blows against low hp enemies, which ends up lowering the overkill application factor as you only can apply overkill to enemies your PC kills.

Just as your suspicious of anyone bringing up a specific set of scenarios to bolster their point - I'm suspicious of anyone that falls back to claims of tactical inferiority to try and counter that point.

My move, your move.



It's not just fireball though. It's any effective aoe. Anything that trivializes the encounter to the point where you are just going through the mop up motions. I've focused on the damage aspect because it's easier to show but it's really anything. Because we are talking about impact - what you accomplish in the mop up rounds means very little.

And to elaborate just a bit more, the point I'm making isn't that every single encounter against alot of foes will be decided by effective aoe's - just that many of them will. I'm talking about the factor most often overlooked in overkills impact - the factor you use to turn overkill from a per kill metric to a per round metric. Talking about the cases where it's going to be most effective being quite a bit less common (and less important) due to abilities that often trivialize those scenarios is a very important point.

Again - my case has never been that overkill doesn't have any impact - it's that it's impact on average over a campaign is minimal.



So showing that overkill doesn't matter in cases it doesn't matter and then qualitatively and quantitively comparing those cases to the broader picture is precisely the point. Overkill is a per kill metric. We need a conversion factor to convert it into a per round factor. The argument is that you are weighting the cases where it's most useful much more highly than they should be weighted.

It seems to me that you're cherry picking data, while I'm pointing out that you need to look at the game as a whole. Simply assuming that you can toss out everything to do with low HP creatures because of the existence of AoE is a gross oversimplification.

We're not talking creatures with a handful of HP. A creature with 15 HP will survive the average fireball on a save, whereas a creature with 29 HP will survive the average fireball on a failed save. These are not high HP numbers for 5e. You can't ignore the impact of overkill at these totals.

Assuming you have effective AoE available to the party, and assuming the creatures are in a formation that allows that AoE to be effective, it's still not a safe assumption that an AoE will kill them if they have 29 HP.

 

[Fanaelialae]

Tactical considerations are not the only ones. roleplaying ones are too. The enemies may not know that you have a good AOE! Do goblins know about fireball and shatter?

In the real world, we call the fireball spell "hand grenades". But strangely enough, even though everyone knows about hand grenades, in a bar fight people don't consider that.

(btw don't get in bar fights, some jerk will pull a knife or break a bottle on your face).

I made no claim that you should disregard roleplaying considerations for tactical ones.

 

[FrogReaver]

Again, you do not ever care about overkill damage UNLESS the PC in question lands the killing blow. It does not matter what every other case is, it only matters when and if the given PC lands a killing blow. I did account for #2 in that I don't care about situations where the PC doesn't land the killing blow. This is covering in Assumption 1 -- we only care about overkill when a killing blow lands. After that, it's a matter of determining what frequency is appropriate, and here there is room for debate. If, as you say, a PC is assumed to land the killing blow on 1/4 of the enemies presented, and we assume 3 rounds of combat, that's 1.25 kills per combat per PC. If the PC in question has 2 attacks, that's 6 attacks total. If we eyeball it, that's an f of 6, which I happened to include in my example.

Now, I disagree that f should be 6, as a high average attack damage character has a wider kill range and so will more often land killing blows.

Fundamentally, what my analysis shows is that the overkill effect is dependent on two factors -- base average damage and frequency of killing blows. If is directly proportional to both -- as average damage increases, overkill effect increases and as frequency of killing blows increases, overkill effect increases. Nothing in this analysis says that the reference PC is doing all of the killing -- the rate of killing blows is an input variable, for goodness sakes!

If we take your assumptions above, and look at the previous example of rogue versus monk, we can do a rough analysis. Both have a +4 in the controlling stat, and both are 5th level. That's +8 to attack and +4 damage from stat with the Rogue at +3d6 sneak attack damage and using a +1 sword in the main hand. Let's assume the target is AC 14, so hit% is .75.

dmg(R1) = 1d6(weapon)+3d6(sneak)+4(stat)+1(magic) = 19
dmg(R2) = 1d6(offhand weapon) = 3.5
dmg(Rperround) = 22.5

dmg(M) = 1d6+4 = 7.5
dmg(Mperround) = 3*dmg(M) = 22.5

dmg(Rperround) = dmg(Mperround)

OAD(R1) = 6.625
OAD(R2) = 0.8125
OAD(M) = 2.3215

If we set frequency of killing blows to 1/4 over three rounds, the rouge makes 3 main hand attacks and 3 offhand attacks and the monk makes 9 attacks. The rouge has 2 cases now, one where the mainhand is the killing blow and one where the offhand is the killing blow. Let's assume this breaks according to the strength of the attack or that mainhand is going to be killing blow 19/22.5 times. Offhand the remaining 3.5/22.5 times. This is very close to .85 and .15. We'll adjust this when we solve.

This complicates the rogue, but we can do it using this split and calculating X' independently for each attack. The necessary step is in the calculation of X'. You have to multiply the OAD in that calculation by the split, so the new X' for the rogue looks like:

X'(R1) = X(R1) - ((.85*OAD(R1))/3) = 12.37

The frequency of 3 is used because the rogue makes 3 of these attacks. The percentage modifier adjusts this to reflect the times that one of these three attacks is the killing blow. X'(R2) is solved for the same way:

X'(R2) = X(R2) - ((.15*OAD(R2))/3) = 2.61

X'(Rperround) = 14.99

The monk is straightforward.

X'(M) = 5.37
X'(Mperround) = 16.11


As you can see the difference in effective DPR when accounting for overkill is slightly in the monk's favor by 1 DPR.

I'm going to assume your math is 100% right for a moment (I haven't checked it yet). Let's talk about what the conclusion means. You showed an effective 1 DPR difference due to overkill. I would consider that result as supporting my claim that overkill doesn't really matter. I've not claimed that it doesn't have any impact afterall, just a minimal impact that can be safely ignored.

On a side note - your work shows something else very interesting. Overkill depends on your chance for a killing blow and average damage. You said that yourself. But let's think about this for a moment. As DPR increases your average damage increases which increases your overkill. However, at the same time, doing more DPR increases your chance of landing a killing blow which decreases your overkill.

 

[FrogReaver]

It seems to me that you're cherry picking data, while I'm pointing out that you need to look at the game as a whole. Simply assuming that you can toss out everything to do with low HP creatures because of the existence of AoE is a gross oversimplification.

We're not talking creatures with a handful of HP. A creature with 15 HP will survive the average fireball on a save, whereas a creature with 29 HP will survive the average fireball on a failed save. These are not high HP numbers for 5e. You can't ignore the impact of overkill at these totals.

Assuming you have effective AoE available to the party, and assuming the creatures are in a formation that allows that AoE to be effective, it's still not a safe assumption that an AoE will kill them if they have 29 HP.

You seem to be cherry picking counter examples. Again, my assessment isn't that we can fully ignore all these cases. My assessment is that we need to be weighting them much less than we are.

You also seem to ignore my point that doing more damage in easier encounters also deserves less weight - including encounters made easy via aoe abilities (like fireball) whether they outright kill the enemies or not.

The issue is one where you are wanting certain things weighted much higher when they really shouldn't be. That's why I proposed leaving off the lower hp values in the sim, because they deserve significantly less weight due the the factors I am discussing above. If you have a good well reasoned suggestion for what weight to give them I'm open to that instead.