D&D 5E Calculating Overkill Damage

[guachi]

When we do our white room calculations for damage I've never seen any calculations done to account for overkill damage. That is, damage done over and above what is necessary to bring a foe to 0 HP.

Generally, we assume our foe has infinite HP. This is, of course, not the case but it certainly simplifies our calculations.

I have, however, attempted to calculate it and give myself a robust spreadsheet to if I need to change parameters.

I chose a GWF GWM greatsword wielder as my first victim. Because there's nothing like starting with the hardest one first. First up is finding the chances of doing each potential value in your damage range. This is harder for a greatsword as it deals 2d6 damage on a normal hit and, thus, isn't linear Further, and the real pain, is accounting for the rerolls. But I did it! Despite a range (before static bonuses) of 2-24 about 60% of your values will range from 7-10.

Assumptions:
STR 20
hit chance 65%
hit chance post -5/+10 usage 40%
crit chance 5%always use -5/+10
target HP: 100 (roughly CR 5)

All of these are relatively easy to change so if anyone wants different results, I can give them to you.

Foe is a target dummy with a randomly determined HP at time of swing ranging from 1 to its maximum value (in this case 100). This is an attempt to simulate that your target can have variable HP when you attack it and aren't intentionally targeting a foe with high or low HP.

Given the above, our GWM, GWF, STR 20 greatsword user will average 1.16 points of overkill damage per swing, accounting for misses (which, obviously, have no overkill damage). Our attacker averages 9.75 damage per swing so his average damage per swing is reduced by 11.9% to 8.59.

When I get a free minute at work I'll see see how things change simply by removing the usage of the -5/+10 portion of the feat.

 

[guachi]

Changing nothing other than not using the -5/+10 portion of the feat.

Our attacker now does an average 0.62 points of overkill damage per swing. Our attacker averages 9.08 damage per swing so his average damage per swing is reduced by 6.8% to 8.46

Before making any attempt to account for overkill, not using GWM was .67 points behind. Now he is only 0.13 points behind.

 

[guachi]

Changing a few more parameters:

You are lower level so your STR is 18
hit chance still 65%
Target HP 50 (so about CR 2 or 3)

Not using -5/+10:
Average Damage: 8.43
Overkill Damage: 1.07
Modified Damage: 7.36

Using -5/+10:
Average Damage: 9.35
Overkill Damage: 2.06
Modified Damage: 7.29

Huh.

You actually do less damage.

According to the math, you only have a 7% chance of doing 10 or more points of damage above your minimum. So if you know or suspect the enemy has at least 10 or more HP than your minimum using GWM then you can use GWM with high confidence you won't have any overkill damage. Otherwise you might want to consider using a normal attack instead.

 

[Wiseblood]

Interesting. What does this tell us? Is it that the optimal strategy with this feat is based loosley on the targets HP?

 

[guachi]

More fun:

11th level Rogue (The first two posts were assuming level 11 like in vonklaude's examples. GWM + 2 ASIs for a 20 STR)
d6 weapon (because the math was easier with all those d6 sneak attack dice)
65% hit chance
100 HP foe

Average damage: 20.40
Overkill damage: 3.31
Modified Damage: 17.09

Damage reduction: 16.2%

If it's a 50 HP foe:

Average damage: 20.40
Overkill damage: 6.60
Modified damage: 13.80

Damage reduction: 32.3%


Sword & Board
DEX/STR 20
duelist style
d8 weapon
65% hit chance
100 HP foe

Average damage: 7.70
Overkill damage: .44
Modified damage: 7.26

Damage reduction: 5.72%

50 HP foe:
Average damage: 7.70
Overkill damage: .88
Modified damage: 6.82

Damage reduction: 11.44%

I think it's a shock to no one that a rogue with a high single damage attack gets hosed if he just attacks targets at random. A rogue is better off attacking high HP targets and a duelist fighter (for example) is better mopping up the low HP targets.

So our summary damage of what we've calculated so far. Assuming 11th level (so the fighters actually get three attacks. The rogue numbers aren't taking advantage or wielding two weapons.)

100 HP foe/50 HP foe:

GWF + greatsword + GWM: 8.59/7.29
GWF + greatsword: 8.46/7.36
duelist + longsword/rapier: 7.26/6.82
rogue + d6 weapon: 17.09/13.80

 

[FrogReaver]

Overkill damage is meaningless. I will explain why later

 

[Krachek]

Should we start to count half and quater hit point?

 

[FrogReaver]

Overkill damage is meaningless. I will explain why later

To elaborate:

1. Overkill damage is totally independent of accuracy.
2. Overkill damage is totally independent of your number of attacks.
3. Overkill damage is DEPENDENT on your damage per attack (not DPR). High overkill damage tells us is that we do a lot of damage per attack. That is something we can already tell by looking at listed damage on such an attack. High listed damage will always lead to higher overkill damages. Those stats are directly proportional.

More elaboration coming soon...

 

[mellored]

Interesting. What does this tell us? Is it that the optimal strategy with this feat is based loosley on the targets HP?

Don't use GWM or Disintegrate on a target with 5HP.

 

[FrogReaver]

To elaborate:

1. Overkill damage is totally independent of accuracy.
2. Overkill damage is totally independent of your number of attacks.
3. Overkill damage is DEPENDENT on your damage per attack (not DPR). High overkill damage tells us is that we do a lot of damage per attack. That is something we can already tell by looking at listed damage on such an attack. High listed damage will always lead to higher overkill damages. Those stats are directly proportional.

More elaboration coming soon...

In D&D killing a monster is what's important. The faster you kill a monster the better off you are. DPR is generally the statistic we look at for how quick we can kill a monster. We do this because it's an easy and simple measure to calculate even though it would be more accurate to calculate our chances of killing the monster each turn (accuracy and total damage and number of hits all factor in if we try to calculate the chances). The modified DPR stat the OP proposes to use would tell us less about how fast we kill any particular monster. Heck, it won't even bring us closer to the truth about whether a high single attack character has a better chance of killing a particular monster faster than a 2 attack character at the same chance to hit and same DPR. (In fact it may hide the truth by showing the high single attack character has a lower "effective DPR" after overkill damage is taken in, even though the reality may have the high single target attack character more effective against that particular enemy).

I will give the OP's proposal for overkill damage 1 thing. It should model a characters effectiveness against any enemy a character is guaranteed to kill in 1 hit pretty well. Once you start getting into chances to kill it in one hit due to your damage spread and chances to kill it in 2 and etc then things far to complex to fast to make any realistic use of the overkill damage idea.