The Overkill Damage Fallacy

Overkill Damage is often brought up in DPR discussions as a theoretical offset to the damage that characters with fewer harder hitting attacks are doing. The basic concept seems reasonable on the surface but what never gets accounted for is that a character with a single attack can kill enemies faster on average than a character with 2 attacks even when they do the same DPR.

Proof:
Enemy has 5 hp
PC1: 60% chance to hit. 8 Damage (no variation). 1 Attack
PC2: 60% chance to hit. 4 Damage (no variation). 2 Attacks

PC 1:
Capture1.PNG

PC 2
Capture2.PNG

As you can clearly see above, the Character that makes a single attack actually kills the 5 hp enemy faster on average than the PC making 2 attacks. (In the example provided both PC's have the same overkill damage whenever this particular enemy dies). So why is PC 1 killing this enemy faster? Because the chance to kill on rounds X distribution.

Why do we consider PC 1's overkill damage to be higher than PC 2's (given that it was the same in the example provided)? Because the other half of enemies PC 1 fights will leave him doing more overkill damage. Thus, on average PC 1 does more overkill damage than PC 2

On the enemies where PC 1's overkill damage is higher, what causes that? Basically it happens because the hp value fell is such a place that PC 1 needed X hits to kill it on average but PC 2 only needed 2X-1 attacks. This occurs any time an enemies hp divided by 4 is an even number. When the enemies hp divided by 4 is an odd number PC 2 needs 2X attacks.

Why do I discount overkill damage? Because, the most important factor is how fast the enemy dies. If the enemy dies faster then you get to start applying your damage to the next enemy that much faster. Since equal DPR characters kill different enemies faster or slower on average (and their chance to kill an enemy on round X distributions are never the same) then looking at overkill ignores the most important factor. In fact, that's why I call overkill damage a fallacy. It's a nearly meaningless stat in the grand scheme of things that some individuals regard as providing a significant insight in analysis. It can't do what they want it to do because equal DPR characters don't kill enemies at the same rates. Oftentimes the fewer attacking higher damage character will on average kill enemies faster.

What more work needs done in this area?
Adjust the results for different chances to hit. Different numbers of attacks. Probably most importantly would be to adjust for variable damage dice as opposed to a specific damage value for every hit. It would also be helpful to compare a few enemies that PC 1 kills faster and some PC 2 kills faster and see if the magnitudes and relative values of such faster average kills are much different.
 
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dnd4vr

Supercalifragilisticexpialidocious!
I would just post a screen shot of the tables as an image and it might look better.
 
TLDR:

PC's with equal DPR don't kill enemies at the same rate
Thus, looking at overkill damage without looking at average round to kill an enemy doesn't reveal anything important - it's kind of looking at the reaminder of a dividion problem without looking at how many times something went into it.
 
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5ekyu

Adventurer
TLDR:

PC's with equal DPR don't kill enemies at the same rate
Thus, looking at overkill damage without looking at average round to kill an enemy doesn't reveal anything important - it's kind of looking at the reaminder of a dividion problem without looking at how many times something went into it.
Uhh... ok, so you cherry picked one example with the target number between the two "per attacks" and eherevonly one hit was needed for the ko and that's all you needed to call overkill a fallacy?

Great job at showing us how much confidence we should have in your analysis of expected results.

I thank you for that and I mean it sincerely. .
 
Uhh... ok, so you cherry picked one example with the target number between the two "per attacks" and eherevonly one hit was needed for the ko and that's all you needed to call overkill a fallacy?

Great job at showing us how much confidence we should have in your analysis of expected results.

I thank you for that and I mean it sincerely. .
Maybe you should read the whole analysis before you comment negatively... replying to the tldr version you miss alot
 

Harzel

Adventurer
TLDR:

PC's with equal DPR don't kill enemies at the same rate
Thus, looking at overkill damage without looking at average round to kill an enemy doesn't reveal anything important - it's kind of looking at the reaminder of a dividion problem without looking at how many times something went into it.
So you picked a particular scenario in which overkill damage doesn't matter and you've concluded that overkill damage doesn't matter. I'm shocked - shocked.

You have to include scenarios with two or more opponents for overkill to matter.

EDIT: Oh, and yes I did read the whole, rather redundant, OP. Just quoted the wrong one.
 

Prakriti

Hi, I'm a Mindflayer, but don't let that worry you
Overkill Damage is often brought up in DPR discussions as a theoretical offset to the damage that characters with fewer harder hitting attacks are doing. (...)
Enemy has 5 hp
PC1: 60% chance to hit. 8 Damage (no variation). 1 Attack
PC2: 60% chance to hit. 4 Damage (no variation). 2 Attacks
Is it not significant that the two characters in your example do the same amount of overkill (3 damage)?

Also, I'm going to withhold judgment until some more math-minded individuals weigh in. But at least to my untrained eyes, your argument looks... highly questionable.
 
Is it not significant that the two characters in your example do the same amount of overkill (3 damage)?

Also, I'm going to withhold judgment until some more math-minded individuals weigh in. But at least to my untrained eyes, your argument looks... highly questionable.
1. It doesn't change the fact that overkill damage is meaningless if the rounds to kill isn't the same.
2. PC 1 does more overkill damage in general than PC 2.
 
So you picked a particular scenario in which overkill damage doesn't matter and you've concluded that overkill damage doesn't matter. I'm shocked - shocked.

You have to include scenarios with two or more opponents for overkill to matter.

EDIT: Oh, and yes I did read the whole, rather redundant, OP. Just quoted the wrong one.
Overkill damage mattering in the general sense is wholly based off the idea that 2 equal DPR PC's will kill enemies at the same rate. The example I provided crushed that premise.
 

cmad1977

Adventurer
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

Explorer
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.
 
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

Legend
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.
 
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Prakriti

Hi, I'm a Mindflayer, but don't let that worry you
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.
 
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Blue

Ravenous Bugblatter Beast of Traal
[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

Explorer
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
 

UngeheuerLich

Adventurer
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.
 
[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.
 

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