The Overkill Damage Fallacy

[cmad1977]

Anytime anyone brings up DPR in a discussion I know who’s opinions on the efficacy of characters I should ignore.

I’ve always thought the idea of ‘overkill’ was ridiculous. Overkill is just moar kill.

 

[jaelis]

Compare that to a 4 hp opponent.

Better, compare to a whole range of opponent hp and see who does better on average across the range.

 

[FrogReaver]

Compare that to a 4 hp opponent.

Better, compare to a whole range of opponent hp and see who does better on average across the range.

I already derived the general case for who is better and who is worse for those PC's. It was in the OP.

hp values 1-4 favor PC 2. values 5-8 favor PC 1. values 9-12 favor PC 2. values 13-16 favor PC 1. etc.

 

[Dausuul]

Is it not significant that the two characters in your example do the same amount of overkill (3 damage)?

Yeah, it blows the whole argument out of the water. If you compare two PCs with exactly the same amount of overkill, of course your analysis will find that overkill is not a factor. If we're going to use silly white-room examples, why not have the PCs deal 5 and 10 damage instead of 4 and 8? Suddenly PC #2 has an 84% chance of killing a monster on the first round, and a 36% chance of killing a second monster, while PC #1 has a 60% chance of killing one and a 0% chance of killing a second. Thus, we can "prove" that overkill is THE dominant factor in combat, with just a small change to our rectally generated values.

In actual play, I have found that overkill is a minor factor, but not for the reason OP claims. Monsters usually have a lot more than 4-5 hit points, and PCs tend to use their big guns - fireballs, assassinate attacks, et cetera - early in the fight when the monsters are at or near full hit points. As a result, the vast majority of damage goes to the monsters' hit points and very little is wasted. The only time I see a lot of overkill damage is when the wizard catches a lot of low-level monsters in a fireball, and in that scenario, the fireball is still generating good value because it hit so many targets.

 

[Prakriti]

Compare that to a 4 hp opponent.

...such as kobolds, a common low-level enemy. There, the multi-attacker has a chance to kill two kobolds in one round, whereas the single-attacker can only ever kill, at most, one.

Edit: I see FrogReaver accounts for this in his original post, and the "fallacy" in the title is somewhat misleading. He admits that the issue is more complicated than I gave him credit for.

 

[Blue]

[MENTION=6795602]FrogReaver[/MENTION], Serious reply, not an "instant naysayer". I'm commenting to improve your calculations so we can get a clear view. I see two things I don't think were taken into consideration and I would be interested in how much or how little they impact the end results.

First issue is that overkill is about damage wasted. The calculations shown do not differentiate for the twice-attacker between if the kill is done by the first attack or the second attack. Because if done with the first attack, then there is an additional attack that can be used to start damaging the next. If that's ignored, that's being treated as "overkill" (wasted") damage just like any extra done by the killing blow, but it actual play that is the opposite of overkill, that's damage that can be redirected to another target.

Perhaps a better way would be to see how many can be killed in 5 rounds. Or if you want to keep it on killing, then assume 5 opponents and count how many are (statistically) alive each round to make attacks against you.

Another issue that isn't being taken into consideration is that damage isn't static, and that aspect not being modeled in your calculations has an impact on the result.

If the single attack was 5-11 damage (avg 8) and the two attacks were 2-6 damage (avg 4), I think you'd find overkill matters a lot more. Because 1 hit from the first would always kill, but 40% of the time one hit from the second would also kill. The flip side is that 4% of the time it takes three attacks from the double-attack character, when a 2, 2, and anything are the damage rolls. But that's a lot less likely than that 40% when the overkill isn't important.

This won't be as large a change once you reach higher levels and HPs that greatly exceed damage of a single blow, but it does still have an impact.

 

[jaelis]

The main way overkill comes into play is when there are multiple opponents, so that there is another target that the “overkill “ damage could have gone too

 

[5ekyu]

Maybe you should read the whole analysis before you comment negatively... replying to the tldr version you miss alot

I did before posting, like I said, it helps greatly to show how confident we should be in your analysis. .

 

[UngeheuerLich]

Frogreaver actually has a point:

some people rate DPR too high. It is a complex scenario and you can find some situations where the "optimal choice" is worse than the "suboptimal coice".

Many DPR discussions chose the circumstances in a whiteroom that support their opinion. You know that GWM is highly rated because of the massive increase in DPR... Which is a fair point, and still all cases where -5 to hit might be relevant are often neglected.

 

[FrogReaver]

[MENTION=6795602]FrogReaver[/MENTION], Serious reply, not an "instant naysayer". I'm commenting to improve your calculations so we can get a clear view. I see two things I don't think were taken into consideration and I would be interested in how much or how little they impact the end results.

Thanks.

First issue is that overkill is about damage wasted. The calculations shown do not differentiate for the twice-attacker between if the kill is done by the first attack or the second attack. Because if done with the first attack, then there is an additional attack that can be used to start damaging the next. If that's ignored, that's being treated as "overkill" (wasted") damage just like any extra done by the killing blow, but it actual play that is the opposite of overkill, that's damage that can be redirected to another target.

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.

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.

Perhaps a better way would be to see how many can be killed in 5 rounds. Or if you want to keep it on killing, then assume 5 opponents and count how many are (statistically) alive each round to make attacks against you.

I think I can determine the average number of rounds to kill 5 enemies with 5 hp each. I think that would be sufficient?

Another issue that isn't being taken into consideration is that damage isn't static, and that aspect not being modeled in your calculations has an impact on the result.

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.

If the single attack was 5-11 damage (avg 8) and the two attacks were 2-6 damage (avg 4), I think you'd find overkill matters a lot more. Because 1 hit from the first would always kill, but 40% of the time one hit from the second would also kill. The flip side is that 4% of the time it takes three attacks from the double-attack character, when a 2, 2, and anything are the damage rolls. But that's a lot less likely than that 40% when the overkill isn't important.

Eventually we will work our way up to such calcs.

This won't be as large a change once you reach higher levels and HPs that greatly exceed damage of a single blow, but it does still have an impact.

I did my example with a 45 hp enemy instead of a 5 hp enemy. The 1 attack PC killed the enemy about .5 rounds faster. I'm just guessing but I don't think whatever is gained by possibly being able to split attacks when an enemy dies will be worth that difference.