The Overkill Damage Fallacy
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  1. #1
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    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:
    Name:  Capture1.PNG
Views: 1651
Size:  4.1 KB

    PC 2
    Name:  Capture2.PNG
Views: 674
Size:  3.6 KB

    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.
    Last edited by FrogReaver; Saturday, 8th June, 2019 at 09:56 PM.

  2. #2
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    If someone can help me fix the tables I would be appreciative

  3. #3
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    I would just post a screen shot of the tables as an image and it might look better.
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  4. #4
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    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.
    Last edited by FrogReaver; Saturday, 8th June, 2019 at 09:57 PM.

  5. #5
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    Quote Originally Posted by FrogReaver View Post
    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. .

  6. #6
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    Quote Originally Posted by 5ekyu View Post
    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

  7. #7
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    Quote Originally Posted by FrogReaver View Post
    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.

  8. #8
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    Quote Originally Posted by FrogReaver View Post
    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.
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  9. #9
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    Quote Originally Posted by Prakriti View Post
    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.

  10. #10
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    Quote Originally Posted by Harzel View Post
    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.

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