The Overkill Damage Fallacy - Page 11
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  1. #101
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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. 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:
    Attachment 106907

    PC 2
    Attachment 106908

    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.
    It took me a bit to figure out what you did to get it, but I did recreate your numbers. First, let me explain what I understand you did so we're on the same page.

    The above charts look only at the chance that the PC kills the target in that round. For the single big attack, it's straighforward enough. You kill it or you don't. The cases are round 1 hit, round 1 miss round 2 hit, round 1&2 miss round 3 hit, and so on.

    The second case has more cases to consider, and these expand rapidly per round. You still kept the analysis at the single point where PC 2 kills the creature in that round. So, on round 2, you consider the case for round 1 - 2 misses and round 2 - 2 hits, round 1 - 1 hit and round 2 - 1 hit and 1 hit round 2, and, finally, round 1 - 1 hit and round 2 - 2 hits. And so on.

    However, in both cases, I think you've made an error in analysis. Each round should have the cumulative chance that the creature is killed in that round or in any previous round, not just the chance that the target is killed in that round. You're essentially ignoring all the cases where the killing is done already. But, let me drop some illustrations first.

    Here is 3 rounds of expanded hit cases and associated odds for each for PC 1:
    Name:  Kill cases PC1.jpg
Views: 65
Size:  124.2 KB

    And here is the same for PC 2:
    Name:  Kill cases PC2.jpg
Views: 118
Size:  296.6 KB

    You can see that the column marked % Kill the round shows the numbers you presented. The column marked % Kill Overall is the total odds at the end of each round that the PC is standing over a dead body. As you can see, PC 1 is ahead in rounds 1 and 2, but starts to lag behind in round 3. This continues, although it remains close, because the number of successful kill cases for the 2 attack character grows faster. This is why there is a larger delta in round 1, where PC 2 has 1 kill case out of 4 and PC 1 has 1 kill case out of 2, and almost none in 3 and four due to the similarity in kill cases. Past 3 rounds, the % Kill Overall is essentially 1 for both characters.

    So, overall, your average rounds to first kill seems a bit wonky, as it's ignoring the odds of a previous round resulting in a kill already. I'm not sure that your number tells us anything, and, honestly, I'm not sure you can just add up your percentages to get to an average time to first kill. The extended results above, though, do suggest that the single big hitter will kill first, and possible more often. I crunched some more numbers to look at this in a case where there's always at least one more foe to attack. So, over 3 rounds:

    PC 1 kills none 6% of the time, 1 29% of the time, 2 43% of the time, and 3 22% of the time. This is an 'at least 1' of 94% and an at least 2 of 65%.
    PC 2 kills none 4% of the time, 1 41% of the time, 2 50% of the time, and 3 5% of the time. This is an 'at least 1' of 96% and an at least 2 of 55%

    It's very interesting, I'd say. The single big attack spends more time at the ends than the multiple attacks and less time in the middle. What's also interesting is that the average damage output per round for both PCs remains constant and equal -- as you might expect. This was one of my primary checks for my maths - did I maintain expected average damage per round?

    And, all of this is using your numbers. Some have advanced this use case is maximized for the big hitter based on target hp, but the analysis is stable for all x less than 9 and greater than 4. Until you get into the hp that PC 1 can't kill with 1 hit or into hp that PC 2 can kill with one hit, the numbers don't change. However, if you use different numbers, the analysis will change. This assumes that big hit precises doubles little hit, and that's not a valid assumption, nor is it valid that big hit will always kill and little will not. Different cases may yield very different outcomes. It should be possible to build an expanded case chart that could handle very different numbers, but it would take more work than I've done so far (a good bit) so unless there's a lot of interest, I'm not going to try.
    XP Mistwell, Fanaelialae gave XP for this post

  2. #102
    Overkill to me seems like more a side issue than anything, and one of the less important parts of any sort of analysis. It seems to be context dependent, rather than an objective metric.Is that the point you're trying to make, or am I mistaken?
    XP FrogReaver gave XP for this post

  3. #103
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    Quote Originally Posted by Tony Vargas View Post
    You can trust it as far as you can mod it.
    I prefer solid foundations for modding with instead of having to shore it up before building off of it.

  4. #104
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    Quote Originally Posted by Tony Vargas View Post
    I know you're indirectly advocating for game balance
    I said what I meant.... keeping optimizations from creating things like instant party death spirals (per the anecdote), is to keep things from becoming not fun, it's not praying to a non D&D god or whatever there are very real values involved.

    I have been putting some thought into techniques to fight party death spiral effects even when there isn't party ability disparity, and which also allow a downed ally a form of participation.

  5. #105
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    Quote Originally Posted by Garthanos View Post
    My son seemed to be able to accidentally optimize a Paladin for his first character enough to defeat enemies which were designed for a full party several levels higher by himself ... which either defeats the fun of optimizing or just seems mildly like they reduced the character balance significantly from 4e. (or designed for a full party 3 levels higher doesn't mean the same thing when you can supernova trivially).

    I know its just an anecdote but one that makes me less than convinced I can trust this latest edition.
    Would you mind a specific example? What was the level of the paladin and the build? What monsters several (3? 5?) levels higher than him did he slay by himself?

  6. #106
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    Quote Originally Posted by jgsugden View Post
    Would you mind a specific example? What was the level of the paladin and the build? What monsters several (3? 5?) levels higher than him did he slay by himself?
    If I get reasonable details I will start a new thread - I remember there was a feat that contributed and his subclass or oath? and they were 3 levels higher.

  7. #107
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    @Ovinomancer

    i will reply more detail later

    to find weighted average you dont use cumulative probabilities. Doesnt that affect your analysis?

  8. #108
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    Quote Originally Posted by FrogReaver View Post
    @Ovinomancer

    i will reply more detail later

    to find weighted average you dont use cumulative probabilities. Doesnt that affect your analysis?
    Sorry, was meant to be XP.

    Um, not sure where you're going here. Weighted average of what? Depends on what question you're asking. I don't think "chance to kill this round only" does a good job of illuminating your premise. Actually, I don't think this entire exercise illuminates your title premise at all, although it is interesting and different from previous looks at damage per round.

  9. #109
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    Quote Originally Posted by Garthanos View Post
    If I get reasonable details I will start a new thread - I remember there was a feat that contributed and his subclass or oath? and they were 3 levels higher.
    You can start a new threat or just PM me. Sounds like Great Weapon Master and Oath of Vengeance? That is generally the power combo... If around 6th level, a sweet spot for a paladin with those high saves, enough slots to smite, etc... you'd be talking about a foe like a Glabrezu, Fire Giant, Treant or Cloud Giant. I'm not putting money on your kid's PC in that fight once, much less routinely. What am I missing?

  10. #110
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    Quote Originally Posted by Ovinomancer View Post
    Sorry, was meant to be XP.

    Um, not sure where you're going here. Weighted average of what? Depends on what question you're asking. I don't think "chance to kill this round only" does a good job of illuminating your premise. Actually, I don't think this entire exercise illuminates your title premise at all, although it is interesting and different from previous looks at damage per round.
    Weighted average of the round you are killing the enemy on.

    If im looking for that then I literally cant use cumulative percentages as I need to know the exact chance I have of killing an enemy on exactly round X so I can use that value as my weight for round X

    on a phone so lengthy math discussion is hard. Hopefully that helps

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