# The Overkill Damage Fallacy

#### Blue

##### Ravenous Bugblatter Beast of Traal
The calculation I did wasn't calculating overkill damage. It was calculating the rounds to kill an enemy. The point I'm making is that if you kill an enemy faster then any extra time the other build is spending killing the first enemy you are able to redirect whatever damage you can cause in that time to another enemy.
By definition you aren't measuring how overkill slows down your kill rate if you only have a single opponent. Because it ignore that with the two attacks if the first one kills the opponent, the second one can start on the next opponent which leads to quicker killing, while the wasted damage from a single large attack can't. If you want to look at overkill, you need to go to 3+ opponents so you can see the effect.

That said, I think I can adapt the formula I'm using to account for multiple enemies which would be the best way to tackle your question of if the first attack from the 2 attack PC kills an enemy then what happens.

I think I can determine the average number of rounds to kill 5 enemies with 5 hp each. I think that would be sufficient?
Yes - except for the 5 HPs because of the second issue.

Start simple and work toward more complex goals. Variable-Damage is not easy to deal with in a discrete way over multiple rounds. That is a goal I mentioned in my OP.

Eventually we will work our way up to such calcs.
Starting simple in this case is giving us a distorted view of the whole. Think like this - run your numbers with foes of 5 HPs and foes of 4 HPs - they have VERY different results with the 8 dmg & 2x 4 dmg attacks. When fit of the multiple of damage to the foe's HPs is causing such a large variation neither will give a representative result.

In other words, the simple calculations will give misleading results across thresholds where it changes the number of attacks to kill.

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#### Mistwell

##### Hero
Nope. I asserted that lone-character scenarios were less plausible.

The expectation that D&D is typically played by a group. Do you wish to argue that, to the contrary, solo play is the norm?
It had nothing to do with "lone character". It was "lone character fighting that particular foe" and not just "lone character in the scenario". If there are 10 foes and each PC is focused on a couple, that's the same as that scenario as well. And it's not that uncommon that different PCs might fight different foes. So yeah, your still asserting plausibility on the basis of nothing tangible.

#### Mistwell

##### Hero
My one hit kills were with the higher damage attack not the lower damage attack... I really don't expect you to understand the significance of that though
Again, you started the thread with one hit kills. When I spoke to the example you set you, you then claimed one hit kills wasn't a good representative example of the game. And now when I called you on that hypocrisy, you're insulting my intelligence in a personal attack?

#### FrogReaver

##### Hero
If you are going to use this reasoning, then you need to give PC 2 "credit" for kills on the half rounds because it is at that point that, as you say, PC 2 gets to start applying damage to the next enemy. For instance, instead of this entry in the PC 2 table:

 2 0.4608 (which contributes 0.9216 to the total)

 1.5 0.288 (contrib. 0.432) 2 0.1728 (contrib. 0.3456)

The total of these two is 0.7776, which is 0.144 less than 0.9216. That by itself brings the total for PC 2 down to ~ 1.682. The appropriate adjustments for the subsequent rounds would result in additional small downward adjustments to the total. It's just a guess, but I conjecture that adjusted in this way and carried all the way out as infinite series, the PC 1 and PC 2 scenarios actually converge to exactly the same number.

Although looking at your PC 2 table further, I'm not sure I can duplicate the calculation that leads to the numbers you have for Kill Chance on rounds 3 and 4. Could be my hand calculations are off; I will redo and check back later.
BINOMDIST(successes, trials, success chance, [0 for non-cumulative or 1 for cumulative])

Round1:= BINOMDIST(2;2;0.6;0)
Round 2:= BINOMDIST(1;2;0.6;0)*(1-BINOMDIST(0;2;0.6;0))+BINOMDIST(0;2;0.6;0)*(1-BINOMDIST(1;2;0.6;1))
Round 3:= BINOMDIST(1;4;0.6;0)*(1-BINOMDIST(0;2;0.6;0))+BINOMDIST(0;4;0.6;0)*(1-BINOMDIST(1;2;0.6;1))
Round 4:= BINOMDIST(1;6;0.6;0)*(1-BINOMDIST(0;2;0.6;0))+BINOMDIST(0;6;0.6;0)*(1-BINOMDIST(1;2;0.6;1))

Basic premise is 1 first round you have a chance to kill the enemy requires you hit with all your attacks.

Subsequent rounds are divided 2 ways
1. Chance you landed exactly 1 attack on all your previous turns * the chance you hit with at least 1 of your attacks
2. Chance you landed exactly 0 attacks on all your previous turns * the chance you hit with both of your attacks

#### Mistwell

##### Hero
[MENTION=2525]Mistwell[/MENTION]

By the way why are you even here? I just told you on another thread:

My opinion since then has only hardened.
I thought you meant for that thread? I am fine not responding to you. But again, I am going to respond to threads you're in or ones you start. Hope that's OK with you.

#### Tony Vargas

##### Legend
It had nothing to do with "lone character".
Then there's no issue. I was pointing out that a lone PC whittling down a block of hp was implausible (mainly because of the lone PC) - Maybe I should have said an oversimplification?

If there are 10 foes and each PC is focused on a couple, that's the same as that scenario as well. And it's not that uncommon that different PCs might fight different foes.
Possibly, due to positioning or trying to occupy foes in melee so they don't focus on one PC - not that either is handled well by 5e in TotM mode.

Focus fire is just so effective under D&D style hp rules, though...

Either way a given PC dropping a given monster by inflicting exactly its remaining hp is going to be a pretty random event.

#### FrogReaver

##### Hero
By definition you aren't measuring how overkill slows down your kill rate if you only have a single opponent. Because it ignore that with the two attacks if the first one kills the opponent, the second one can start on the next opponent which leads to quicker killing, while the wasted damage from a single large attack can't. If you want to look at overkill, you need to go to 3+ opponents so you can see the effect.
Right, the argument wasn't that overkill damage doesn't exist and can't allow a multi attack character to sometimes kill an enemy faster than a single attack character of equivalent DPR.

The argument I am making is that there are also mechanisms in place that allow for the single attack character to kill an enemy a round faster and apply his next rounds damage to a new enemy while the two attack character is still killing the first enemy. At this point in time no one can say with any evidence that what they refer to as overkill is more important than the factor I've brought to light. Does the factor I'm talking about completely offset overkill? Is it more important than overkill? If so then mentioning overkill in isolation without this mitigating factor definitely is a fallacy, arguing that one option is superior than another based on 1 factor that is only part of the picture.

That said, more work needs done to work out the precise details. I also called that out in my first post.

Yes - except for the 5 HPs because of the second issue.
Actually I've just realized the way to account for it. He requires 2 hits to kill a 5 hp enemy. That means he needs 10 attacks to hit in total. I can easily calculate that for him. The single attack PC needs 5 attacks to hit in total. Any objections to this method?

Starting simple in this case is giving us a distorted view of the whole. Think like this - run your numbers with foes of 5 HPs and foes of 4 HPs - they have VERY different results with the 8 dmg & 2x 4 dmg attacks. When fit of the multiple of damage to the foe's HPs is causing such a large variation neither will give a representative result.

In other words, the simple calculations will give misleading results across thresholds where it changes the number of attacks to kill.
Sure. I'm sure you realize how complex the actual calculation will be. So arguing that I should have started there instead of building up to it seems more like a way to discount the work that has been done that is going to hopefully build up to that.

My initial working theory is that in actual play such threshholds will be encountered 50-50. This will occur because variable damage hits will tend to ultimately drop monsters hp to such a range that the value will be randomly distributed between the 2 thresholds.

Of course that brings up the more important and much more complicated scenario of variable damage which I don't plan to attempt to tackle till the end.

#### FrogReaver

##### Hero
I thought you meant for that thread? I am fine not responding to you. But again, I am going to respond to threads you're in or ones you start. Hope that's OK with you.
For everyone but you the block rules apparently prevent the blocked user from responding to a thread that the person blocking them has started. If you want to be special and refuse to abide by the apparent spirit of the block rules that's on you. I can't stop you and the mods don't appear interested in doing so either. But I will continue to call you out on it.

#### FrogReaver

##### Hero
Average Rounds to kill 5 different 5 hp enemies with PC 1 with a single attack doing exactly 8 dmg. PC 2 with a 2 attacks doing exactly 4 damage each. 60% chance to hit for both PC's.

PC 1:

PC 2:

This single attack PC still has the advantage in killing 5 different 5 hp enemies.

#### Tony Vargas

##### Legend
with the two attacks if the first one kills the opponent, the second one can start on the next opponent which leads to quicker killing, while the wasted damage from a single large attack can't.
That does seem like the crux of it.

The argument I am making is that there are also mechanisms in place that allow for the single attack character to kill an enemy a round faster and apply his next rounds damage to a new enemy while the two attack character is still killing the first enemy.
I think I finally get it...
Actually I've just realized the way to account for it. He requires 2 hits to kill a 5 hp enemy. That means he needs 10 attacks to hit in total. I can easily calculate that for him. The single attack PC needs 5 attacks to hit in total. Any objections to this method?
Just an observation: what you're measuring, there is chance to drop an enemy in the minimum time possible. Of course, the mechanic that calls for fewer checks will do that more often. But, it will also take /longer/ than the expected time more often, for the same reason.

So the dual attacker with the same DPR is more consistent, which, if you're facing multiple encounters each of which you're very likely to win, is slightly preferable.

variable damage hits will tend to ultimately drop monsters hp to such a range that the value will be randomly distributed
Multiple cooperating attackers will push it that direction, too.

#### the Jester

##### Legend
Sure. But are you really claiming such an encounter is anything other than an exception to the norm?
I will dispute that it's an exception to the norm. I'd say, depending on the campaign, it might even be quite a common type of encounter.

Just because you don't often see it doesn't mean it doesn't come up for others.

#### MonsterEnvy

I feel like the Cleave Rules are being ignored. While optional they are right there in the Core books.

Also I am not exactly sure what point is trying to be made.

#### Harzel

If it's of any interest, for the scenario in the OP, for PC 1 the exact value for expected rounds to kill is 1/0.6 = 5/3 = 1.66666... It's fairly easy to abstract the to-hit probability and the result is that for a hit probability p, the expected rounds to kill in the given scenario is 1/p.

The derivation is a little long but not hard. I'll provide it if anyone's interested (or skeptical ).

#### FrogReaver

##### Hero
I will dispute that it's an exception to the norm. I'd say, depending on the campaign, it might even be quite a common type of encounter.

Just because you don't often see it doesn't mean it doesn't come up for others.
Likewise, just because it's quite common for some others doesn't mean it's part of the norm.

#### MonsterEnvy

Likewise, just because it's quite common for some others doesn't mean it's part of the norm.
It's for sure part of the norm. Fighting a bunch of Kobolds or Goblins is super common.

#### FrogReaver

##### Hero
If it's of any interest, for the scenario in the OP, for PC 1 the exact value for expected rounds to kill is 1/0.6 = 5/3 = 1.66666... It's fairly easy to abstract the to-hit probability and the result is that for a hit probability p, the expected rounds to kill in the given scenario is 1/p.

The derivation is a little long but not hard. I'll provide it if anyone's interested (or skeptical ).
Yep. Though I don't think such a formula extends very easily to 2 and 3 hit cases.

#### FrogReaver

##### Hero
It's for sure part of the norm. Fighting a bunch of Kobolds or Goblins is super common.
Common in what sense. That it occurs. Sure. Common in the sense that most of the fights in a given campaign are against kobolds and goblins? no.

#### Nagol

##### Unimportant
Overkill control is pointless against a single enemy. The goal in that case is at-least-enough kill.

Overkill control becomes valuable when dealing with multiple enemies.

#### Garthanos

Focus fire is just so effective under D&D style hp rules, though...
Heck even ignoring hp oddities, attacks against an enemy tend to disrupt their attacks against you... ie you might have better effective armor class against any enemy you are attacking. So someone making broad sweeping attacks with a chance of hitting multiple enemies would be better defended from those enemies too.

Basically enemies not threatened have a significant advantage. So you want to threaten everyone even if your multistrike is itself at a penalty to hit.

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#### FrogReaver

##### Hero
Overkill control is pointless against a single enemy. The goal in that case is at-least-enough kill.

Overkill control becomes valuable when dealing with multiple enemies.
If that's your rebuttal then you don't understand the argument.