D&D 5E The impact of overkill damage

[Weiley31]

Overkill=Epic DM kill descriptions.

 

[Todd Roybark]

The scenario that’s being challenged is not at all realistic. Far to many cases of extremely low hp.

A 10th Level party encountering a Hobgoblin/goblin tribe with 60 members is not an unusual setup for 1e and 2e, and 5e.

One aspect to be considered is that by RAW a PC can not breakup their movement between multiple attack rolls created by spell attacks. An 11th level Archer Fighter can shoot and move, between attack rolls, a Wizard with Scorching Ray cannot.

 

[FrogReaver]

I've put 5th level characters against groups that included lots of low HP monsters. I think that's a pretty reasonable use case for 5e.

The example would have generated about as many high HP creatures as low, since it's not a linear distribution. Given the large same size (3000) you'd have roughly as many high HP creatures as low HP, with many somewhere in the ballpark of 42. That doesn't seem particularly unrealistic to me.

Sure, you will sometimes encounter lower hp enemies usually in significant number, but in actual play a fireball or something equivalent will wipe them out or at least most of them. Which greatly skew the number of attacks you make toward being against enemies with higher hps. So I would say accounting for them as the simulation proposed did was actually the unrealistic version.

 

[FrogReaver]

This has been proven false in so many threads it is ridiculous - with math to back it up. Dismissing the math as irrelevant because you consider it 'unrealistic' (in your subjective lens) is not proving anything. We don't need to relitigate this every few months.

However, a good exercise to study this situation is to build an efficient 5th level rogue, and an efficient 5th level monk. The monk attacks 3 times, the rogue only twice, but gets to deal sneak attack damage once per round (assuming they hit at least once) and can use a main weapon and an off hand weapon. No magic items will be used, but a +1 bonus to the damage of the rogue main hand to balance out the simple DPR.

Now, have them cut down targets. These targets will have (2d4-1)d20 hps (a range of 1d20 to 7d20, with a tendency towards 4d20), and ACs of 8+2d6 (10 to 20 with a tendency towards 15).

To limit the influence of random chance, you'll have them each tackle the same targets in the same order (so if you roll a 46 hp target with an AC of 16, both will use their attacks to kill it and then will move on to the second one you roll so that their second one is also identical, even if they get to it at different rounds). You'll also record your d20 rolls and apply them to the attack rolls in the same order so that the first 6 d20 roll will cover 3 rounds for the rogue (who has main hand and off hand) and only 2 rounds for the monk (who has multi-attack and martial arts).

I've run this experiment. For 3000 targets. The monk killed 3000 targets in 9886 rounds. The rogue took 15,224 rds to kill the same number of targets.

The monk was attacking three times - twice at d8+4, and once at d6+4 for basic DPR of 24.5. The rogue was attacking for d8+5 (an extra plus one to balance out the DPR), d6, and 3d6 sneak. 24.5 for the rogue. Same DPR - massively different kill rates because of the overkill factor - even when we allowed a wide range of hps. However, I did not calculate DPR to include the criticals, which actually favors the rogue as they get to roll more additional dice on a crit.

Run the experiment. You'll see that lost efficiency due to overkill is a huge factor in balance.

So, I've been thinking more about the sim parameters. I've already mentioned I don't agree with the hp range you viewed, but that's easy enough to adjust.

However, I believe I've found a fairly major flaw in your version that I'll be attempting to rectify in mine. Encounters don't consist of fighting through a slew of 3000 enemies with no pause. The end of each encounter is a defacto hard stop where damage in your last round cannot be diverted to the next encounter. It's essentially the same principle as overkill waste but applied to encounters as well. A practical example. Let's say the monk kills the last opponent with his first attack on round 5. Your algorithm has those next 2 attacks applied to the next encounter when they really shouldn't be. If the rogue also defeated that encounter on round 5 the 2 combatants are equivalent as no damage gets applied to the next encounter to potentially lessen its number of rounds.

 

[MarkB]

Sure, you will sometimes encounter lower hp enemies usually in significant number, but in actual play a fireball or something equivalent will wipe them out or at least most of them. Which greatly skew the number of attacks you make toward being against enemies with higher hps.

As opposed to the times that a Fireball will knock half the health off of a group of slightly tougher enemies, skewing the numbers towards your attacks being against enemies with low HPs.

 

[Fanaelialae]

Sure, you will sometimes encounter lower hp enemies usually in significant number, but in actual play a fireball or something equivalent will wipe them out or at least most of them. Which greatly skew the number of attacks you make toward being against enemies with higher hps. So I would say accounting for them as the simulation proposed did was actually the unrealistic version.

Sometimes it will, sometimes it won't. For every time that you have a tight grouping of weakingling that's cries out for a fireball, you'll have a loose grouping of weaklings coming from multiple directions (such as if the PCs walk into the middle of an ambush). Presumably.

Fireball is a great spell, but if it's the solution to every mob of weak enemies then they DM is lobbing softballs IMO. So I mean, sure, if we assume that the DM never makes an effort to make groups of enemies tactical and tries to hammer on the PCs using only the toughest creatures they can, we can probably ignore overkill. However, that wouldn't be representative of my campaign, and I suspect the same would be true for many other campaigns.

 

[jgsugden]

So, I've been thinking more about the sim parameters. I've already mentioned I don't agree with the hp range you viewed, but that's easy enough to adjust.

However, I believe I've found a fairly major flaw in your version that I'll be attempting to rectify in mine. Encounters don't consist of fighting through a slew of 3000 enemies with no pause. The end of each encounter is a defacto hard stop where damage in your last round cannot be diverted to the next encounter. It's essentially the same principle as overkill waste but applied to encounters as well. A practical example. Let's say the monk kills the last opponent with his first attack on round 5. Your algorithm has those next 2 attacks applied to the next encounter when they really shouldn't be. If the rogue also defeated that encounter on round 5 the 2 combatants are equivalent as no damage gets applied to the next encounter to potentially lessen its number of rounds.

Go nuts. However, my monk only rarely fights solo monsters, and only rarely is unable to move on to a second target and attack. In a party of five, they're landing the last blow of the combat only about 25% of the time. Your assumption that the other attacks are wasted may help you 'prove' your initial point, but it isn't a common fact pattern - and when the math is as overwhelming as it is, I doubt it will override the imbalance that exists.

DPR, by itself, is a hugely flawed measuring stick for efficiency and overkill is a HUGE contributing factor into the flaws. As for the HPs not being realistic - poppycock. Look at monsters of CR 7 or lower in the DMG. Those are the monsters that the PCs in my comparison would be fighting. That spectrum of hps is quite reasonable for a level 5 foe.

Incidentally, I've also measured "effective damage" dealt at the table a number of times over the years. It was measuring which PCs dealt damage during an adventure and noting when the damage was overkill, and when it was effective against current or temp hps. I did it as early as 1995, and have repeated it in most editions. This is a looooooooooong term misunderstanding of people about the balance of the game that has resulted in countless ridiculous (but generally accepted) arguments, such as that Sharpshooter and Great Weapon Master are overpowered.

 

[Ovinomancer]

Here's a look at this issue. First, let's quantify what overkill damage is. Here's the assumption set:

Assumption 1: we only care about overkill damage when the attack reduces the target to 0 hp.

Assumption 2: we will be treating this an an infinite trial set and using average damages.

Given A1&2 above, defining overkill average damage (OAD) for a given attack is pretty easy. Due to A1, we're only looking at cases where the hp of the target is between 1 and X, where X is the average damage of the attack (you can add hit percentage multipliers, doesn't matter, we're looking at the average case). Given this, you can list out the options from 1 to X, and subtract that from X to find out what the overkill for that attack was. If you add all of those overkill damages up (which range from 0 to X-1), and average them, you'll get average OAD. Or, for a quicker way, just use (X-1)/2.

Great! Now we know the average overkill damage and can... well, what can we do with this number? Not much, by itself, because we haven't established how often A1 actually occurs. The frequency of A1 will majorly affect the impact of OAD. If you score the final blow with X 1 out of 3 attacks, then the impact of OAD will be reduced to OAD/3. This makes the impact X - (OAD/3). The general form of this is X - (OAD/f) = X', where f is the frequency, on average, of killing blows per attack, and X' represents the effective average damage of the attack.

You can use this to compare different attack schemes by computing the X' for two different attacks and comparing them. You can even set up differing hit percentages while doing so, to see what the impacts are. This is very helpful for things like SS and GWM. You'll have to guestimate f, though, as there's no way to determine a good rate for that. Party play can be captured using f as well.

To look at the GWM case, it's pretty interesting using this approach. GWM, when used for damage boosting, impacts X by increasing it by 10 but also decreasing it by the changed hit percentage. If you assume a base hit percentage of 85% (well within the recommend range for using GWM), the GWM hit percent is 60%. Let's set dmg(normal) to 2d6+4, a greatsword with 18 STR, which averages to 11 and makes dmg(GWM) 21.


I plugged this into a spreadsheet to calculate. If you assume that the normal greatsword user is killing once every three attacks and the GMW user is killing once every two attacks (seems fair), the OAD reduction in X' is such that the delta between them is reduces from a non-overkill of 3.25 DPR to 1.74 DPR.

Data type	variable	value		differences
Input	dmg(1)	11​		dmg diff
Input	dmg(2)	21​		10​
Input	hit(1)	0.85​		hit% diff
Input	hit(2)	0.6​		0.25​
Calculated	X(1)	9.35​		DPR diff
Calculated	X(2)	12.6​		3.25​
Calculated	OAD(1)	4.175​		OAD diff
Calculated	OAD(2)	5.8​		1.625​
	f	2​	3​	4​	5​	6​
Calculated	X'(1)	7.2625​	7.95833333​	8.30625​	8.515​	8.654167​
Calculated	X'(2)	9.7​	10.6666667​	11.15​	11.44​	11.63333​
Calculated	difference	2.4375​	2.70833333​	2.84375​	2.925​	2.979167​

It would appear that overkill does make a difference. Even assuming f of 4 for both, the delta is 2.84 from 3.25, a difference of .6 which is substantial in these kinds of arguments.

It's all a bit silly, but I like the thinking challenge.

 

[FrogReaver]

Here's a look at this issue. First, let's quantify what overkill damage is. Here's the assumption set:

Assumption 1: we only care about overkill damage when the attack reduces the target to 0 hp.

Assumption 2: we will be treating this an an infinite trial set and using average damages.

Given A1&2 above, defining overkill average damage (OAD) for a given attack is pretty easy. Due to A1, we're only looking at cases where the hp of the target is between 1 and X, where X is the average damage of the attack (you can add hit percentage multipliers, doesn't matter, we're looking at the average case). Given this, you can list out the options from 1 to X, and subtract that from X to find out what the overkill for that attack was. If you add all of those overkill damages up (which range from 0 to X-1), and average them, you'll get average OAD. Or, for a quicker way, just use (X-1)/2.

Great! Now we know the average overkill damage and can... well, what can we do with this number? Not much, by itself, because we haven't established how often A1 actually occurs. The frequency of A1 will majorly affect the impact of OAD. If you score the final blow with X 1 out of 3 attacks, then the impact of OAD will be reduced to OAD/3. This makes the impact X - (OAD/3). The general form of this is X - (OAD/f) = X', where f is the frequency, on average, of killing blows per attack, and X' represents the effective average damage of the attack.

You can use this to compare different attack schemes by computing the X' for two different attacks and comparing them. You can even set up differing hit percentages while doing so, to see what the impacts are. This is very helpful for things like SS and GWM. You'll have to guestimate f, though, as there's no way to determine a good rate for that. Party play can be captured using f as well.

To look at the GWM case, it's pretty interesting using this approach. GWM, when used for damage boosting, impacts X by increasing it by 10 but also decreasing it by the changed hit percentage. If you assume a base hit percentage of 85% (well within the recommend range for using GWM), the GWM hit percent is 60%. Let's set dmg(normal) to 2d6+4, a greatsword with 18 STR, which averages to 11 and makes dmg(GWM) 21.


I plugged this into a spreadsheet to calculate. If you assume that the normal greatsword user is killing once every three attacks and the GMW user is killing once every two attacks (seems fair), the OAD reduction in X' is such that the delta between them is reduces from a non-overkill of 3.25 DPR to 1.74 DPR.

Data type	variable	value		differences
Input	dmg(1)	11​		dmg diff
Input	dmg(2)	21​		10​
Input	hit(1)	0.85​		hit% diff
Input	hit(2)	0.6​		0.25​
Calculated	X(1)	9.35​		DPR diff
Calculated	X(2)	12.6​		3.25​
Calculated	OAD(1)	4.175​		OAD diff
Calculated	OAD(2)	5.8​		1.625​
	f	2​	3​	4​	5​	6​
Calculated	X'(1)	7.2625​	7.95833333​	8.30625​	8.515​	8.654167​
Calculated	X'(2)	9.7​	10.6666667​	11.15​	11.44​	11.63333​
Calculated	difference	2.4375​	2.70833333​	2.84375​	2.925​	2.979167​

It would appear that overkill does make a difference. Even assuming f of 4 for both, the delta is 2.84 from 3.25, a difference of .6 which is substantial in these kinds of arguments.

It's all a bit silly, but I like the thinking challenge.

I don't think looking at averages and then comparing them actually helps answer the question here.

 

[FrogReaver]

As opposed to the times that a Fireball will knock half the health off of a group of slightly tougher enemies, skewing the numbers towards your attacks being against enemies with low HPs.

We can break fireball up into 3 distinct ranges.
1. Enemies fireball normally kills most of outright. Let's say 20 hp and below.
2. Enemies fireball normally reduces to below the hp threshold I'm wanting to look at. In this case I think I had said 37 hp which would be anything with 57 hp and below.
3. Enemies over 57 hp.

1. This is basically enemies in the CR 2 and below range
2. This is basically enemies in the CR 2 and 3 range.
3. Nearly every enemy CR 4+ range.

So yes, you bring up an excellent point, but I'm not sure that extending the CR range from 2 and below to 3 and below actually is substantial enough difference.