D&D 5E The impact of overkill damage

[Ovinomancer]

Right, that's why I am saying the overkill effect on the last enemy in the encounter is equal for all PC's so long as DPR is equal. That's an important point in this discussion IMO and why I insist on looking at overkill effects in terms of an infinite trial of encounters instead of an infinite trail of enemy after enemy.

Okay, let's look at this. First, this only applies when the PC in question scores the final blow on the final monster for the combat and has attacks remaining. How often does this occur? In a 4 PC party where the PC supplies an equal amount of damage output, then it will happen, over an infinite period of time, in no more than 1/8 of all combats. This is because the minimum case for this to happen is a PC with 2 attacks who will equally share with the others the final blow, for 1/4 x 1/2 (the times where the final blow is leaves an attack). The party damage assumption isn't terribly realistic, but it's good for back of the envelope (spherical cows). So, DPR will be lessened by 1 attack 1/8 of all combats. Using the 3 round assumption, that's 6 attacks per round 7/8ths of the time and 5 attacks per round 1/8 of the time for an average of 5.875 attacks per combat, or 1.96 attacks per round, or an adjustment factor to DPR of 98%. The impact of this case, over time, is a 2% reduction in DPR prior to overkill consideration.

Set this figher's DPA to X. Overkill for this 2 attack fighter is (X)/2, and if we assume, as previously, that 1 killing blow occurs per encounters, that's a DPA adjustment of -(X)/12. DPR would be base 2*[X-(X/12)] or 2X - (X)/6. If we rearrange a bit, you get DPR = (11X)/6. Adjust this for the above, and it's .98 times that.

For the single attack fighter, DPA is doubled, but there's only one attack. If we keep X the same as above and just double it for this fighter, we see that the overkill effect is 2X-(2X)/6. Rearranging like above, it's 5X/3. This, right here, is the crux of the point I was making -- the impact of overkill on the single big attack vs multiple small attacks is slight, but it cuts against single big attacks. Even factoring in the loss of the attack using the above assumption set, the difference is still that the multiple attacks, same DPR outperforms the single big hit, ceteris paribus.

 

[FrogReaver]

Okay, let's look at this. First, this only applies when the PC in question scores the final blow on the final monster for the combat and has attacks remaining. How often does this occur? In a 4 PC party where the PC supplies an equal amount of damage output, then it will happen, over an infinite period of time, in no more than 1/8 of all combats. This is because the minimum case for this to happen is a PC with 2 attacks who will equally share with the others the final blow, for 1/4 x 1/2 (the times where the final blow is leaves an attack).

I'm not sure with chance to hit and damage variability that 1/2 is correct but I don't know how to calculate the actual value yet. It should at least get us in the ballpark.

The party damage assumption isn't terribly realistic, but it's good for back of the envelope (spherical cows). So, DPR will be lessened by 1 attack 1/8 of all combats. Using the 3 round assumption, that's 6 attacks per round 7/8ths of the time and 5 attacks per round 1/8 of the time for an average of 5.875 attacks per combat, or 1.96 attacks per round, or an adjustment factor to DPR of 98%. The impact of this case, over time, is a 2% reduction in DPR prior to overkill consideration.

That 2% might change a little based on the above point but it's close enough for a rough estimation IMO.

Set this figher's DPA to X. Overkill for this 2 attack fighter is (X)/2, and if we assume, as previously, that 1 killing blow occurs per encounters, that's a DPA adjustment of -(X)/12. DPR would be base 2*[X-(X/12)] or 2X - (X)/6. If we rearrange a bit, you get DPR = (11X)/6. Adjust this for the above, and it's .98 times that.

Agreed and just to calculate:
Effective DPR = 89.8%

For the single attack fighter, DPA is doubled, but there's only one attack. If we keep X the same as above and just double it for this fighter, we see that the overkill effect is 2X-(2X)/6. Rearranging like above, it's 5X/3. This, right here, is the crux of the point I was making -- the impact of overkill on the single big attack vs multiple small attacks is slight, but it cuts against single big attacks. Even factoring in the loss of the attack using the above assumption set, the difference is still that the multiple attacks, same DPR outperforms the single big hit, ceteris paribus.

Agreed and just to calculate:
Effective DPR 83.3%

DPR difference. The 2 attack setup does 7.8% more effective DPR than the 1 attack setup. For a 3 round fight with a single kill that sounds reasonable to me. A few notables:
1. Fights that last more rounds would decrease the Overkill difference effect
2. Having more kills per encounter will increase the Overkill difference effect
3. Looking at a 3 attack vs 2 attack setup will decrease the overkill difference effect

Personally I find the 7.8% more effective DPR to be higher than I expected the effect to be but not so high it's game changing. It's still large enough to be significant.

So a 20 DPR character would do an effective 18 DPR with the 2 attack fighter and 16.7 DPR with the single attack fighter.

 

[Ovinomancer]

I'm not sure with chance to hit and damage variability that 1/2 is correct but I don't know how to calculate the actual value yet. It should at least get us in the ballpark.

The criteria you presented along with infinite trials demands it. The last blow being struck by the compared PCs will happen 1/4 of the time, given the assumption you appear to accept. This means that in cases where it matters, the hp of the last target is between 1 and the DPR of the single big hit fighter, which was 2X above, or 1 < hp < 2X. Given that range, and the lack of any process that would select for a subrange (unless you can provide one), then over infinite trials that range will be uniformly distributed. This then demands that 1/2 of the cases with have 1<= hp < X, and half the cases have X <= hp < 2X. Or, 1/2 the cases.

That 2% might change a little based on the above point but it's close enough for a rough estimation IMO.



Agreed and just to calculate:
Effective DPR = 89.8%



Agreed and just to calculate:
Effective DPR 83.3%

DPR difference. The 2 attack setup does 7.8% more effective DPR than the 1 attack setup. For a 3 round fight with a single kill that sounds reasonable to me. A few notables:
1. Fights that last more rounds would decrease the Overkill difference effect
2. Having more kills per encounter will increase the Overkill difference effect
3. Looking at a 3 attack vs 2 attack setup will decrease the overkill difference effect

Personally I find the 7.8% more effective DPR to be higher than I expected the effect to be but not so high it's game changing. It's still large enough to be significant.

So a 20 DPR character would do an effective 18 DPR with the 2 attack fighter and 16.7 DPR with the single attack fighter.

17.97 with the 2% adjustment, but yep.

 

[Ovinomancer]

Just thought of what was bothering me about attaching lost attacks to overkill -- lost attacks can modify calculated DPR whether or not you're accounting for overkill. Lost attacks isn't part of overkill analysis, it's just a different limitation on DPR.

 

[FrogReaver]

Just thought of what was bothering me about attaching lost attacks to overkill -- lost attacks can modify calculated DPR whether or not you're accounting for overkill. Lost attacks isn't part of overkill analysis, it's just a different limitation on DPR.

I dint care if we call it overkill or something else. Its based on a similar principle to overkill. It’s DPR that is taken into account in the DPR calculation but just like overkill isn’t actually applied.