The Overkill Damage Fallacy

Tony Vargas · Jun 10, 2019

FrogReaver said:
Being able to make 2 attacks instead of 1 is important because on some turns you will kill an enemy with your first attack and be able to attack another enemy with your 2nd while the comparison pc with a single attack doesn't get a chance to do damage except on the enemy you killed with your first attack.

The point I am making is that there is a similar scenario where the single attack PC is getting to do damage to another enemy while the two attack PC is still attacking the enemy the single attack PC killed the previous round.

I think that's actually a different scenario, that favors the Big Stick, and, there's another, corresponding one that favors the little sticks.

What you've been focusing on, AFAICT is the likelihood of finishing off an enemy in the shortest possible time, that is, of not missing from the time you choose to focus on that target until it drops. Assuming the same chance to hit, that will favor the character who can do it in the fewest hits.

But, most over time, on average, they will kill the same enemies at the same rate. But, the Big Stick will kill more of those in the minimum time possible.

You don't even need to do any math, just think about it: Big Stick will also take longer than average to kill an enemy more often.
His DPR is the same, but his dead-enemies/round distribution is flatter.

Nothing to do with Overkill.

Garthanos · Jun 10, 2019

Tony Vargas said:
Has any edition of D&D ever done anything to model those sorts of things?

Oh no I just think if one wanted a way to reduce the dominance of focus fire... that kind of thing might help.

FrogReaver · Jun 10, 2019

Tony Vargas said:
But, most over time, on average, they will kill the same enemies at the same rate.

...I edited your post down to the crux of my issue with it...

This is untrue. Please see the explanation below.

You don't even need to do any math, just think about it: Big Stick will also take longer than average to kill an enemy more often.
His DPR is the same, but his dead-enemies/round distribution is flatter.

Equal DPR PC's don't necessarily kill enemies at the same rate. In the first example I posted, on average the 1 attack PC killed the 5 hp enemies faster than the 2 attack PC. ON AVERAGE. Let that sink in. It's a non-intuitive result. On average a PC with the same DPR as another killed an enemy faster. I'm not saying that sometimes he killed it faster and then other times he killed it slower and those values all offset such that on average they killed them at the same rate. That's what we would intuitively expect. That's not what actually happens. On average one PC with the same exact DPR as another kills some enemies faster. Again, ON AVERAGE.

Celebrim · Jun 10, 2019

Mistwell said:
PC 1 does 6 units of damage with each hit, and has only one attack.
PC 2 does 2 units of damage with each hit, and has two attacks.
There are two foes, and each dies after taking 2 units of damage.
In this scenario, PC 2 can kill both foes. PC 1 cannot. Even though PC 1 does more total damage, it's meaningless as 4 units of their damage is wasted on a hit. Meanwhile, no units of damage from PC 2 is wasted on a hit.

So, overkill damage issues require an analysis of the different types of scenarios to see if they are meaningful or not. Picking an example where it doesn't matter isn't any more or less compelling than picking an example like this one where it does matter.

Bottom line, it CAN matter, depending on the scenario, and that has to be factored into broader analysis.

I haven't the foggiest clue why the argument in this thread is meaningful, but you seem to be well on top of it.

Conversely, we could have a single foe that dies after 5 units of damage, but reduces the damage from each attack by 1. Now Smough kills the target in a single blow, while Orenstein doesn't kill the target until the third round.

There seems to me to be way too many hypotheticals to do any sort of universal analysis and then claim hitting more often is better than hitting hard. For example, in 3e at least there was a surprise round where only a single attack could be made. This greatly favored hard hitting over rapid hitting if surprise was achieved, because any sort of 'first strike' scenario always favors hitting hard.

Similarly, to do a real analysis you have to start factoring in chances to hit, and similar issues come up with chance to hit. DPS by itself is derived from a formula like: DPS = <chance to hit> * <average damage>. But that formula if applied naively treats (0.1 * 95) as the same as (0.95 * 10) and the same as (0.01 * 950). In practice, those are going to produce very different chances that you've killed a foe by round N, depending on how much damage that the creature can absorb and random chance.

All of which should give people pause before attempting to prove something based on DPS.

Tony Vargas · Jun 10, 2019

FrogReaver said:
Equal DPR PC's don't necessarily kill enemies at the same rate.

Over a sufficiently large sample size, testing both tails of the distribution, they will.

But that includes things like wiffing multiple rounds in a row.

For instance, in your first example, 16% of the time Big Stick will take at least 3 rounds to kill one enemy, while for Little sticks, that same 16% is the chance to take at least 2 rounds...

FrogReaver · Jun 10, 2019

Tony Vargas said:
Over a sufficiently large sample size, testing both tails of the distribution, they will.

this is is untrue. I’ve provided concrete examples that demonstrate this to be untrue.

But that includes things like wiffing multiple rounds in a row.

ive included all that in my counter example proof. It’s like your not listening to what I’m saying...

For instance, in your first example, 16% of the time Big Stick will take at least 3 rounds to kill one enemy, while for Little sticks, that same 16% is the chance to take at least 2 rounds...

Mans the average of all those situations favors the single attack character in the example I provided. On average he kills the single 5 hp enemy faster. On any given trial he may kill it slower or faster. But on average he kills it faster. That’s accounting for everything.

the Jester · Jun 10, 2019

FrogReaver said:
Common in what sense. That it occurs. Sure. Common in the sense that most of the fights in a given campaign are against kobolds and goblins? no.

I don't think very many campaigns use the same enemies for most fights, but I'd say the "horde of bad guys" trope is well represented in most campaigns. In this context, I would define "Common" as "Most campaigns feature this type of fight with relative regularity." Pretty much any adventure that features kobolds or goblins uses it, as do most that are focused on other humanoids as foes; the horde of skeletons or zombies is a common enough trope that we've seen both zombie and skeleton swarms statted up in multiple editions; the G series had giant slaves such as orcs, bugbears, and ogres fill this role; various parts of the Temple of Elemental Evil adventure have large groups of bandits, orcs, etc; etc.

The trope is so common that 4e actually made minion rules to reflect it.

I would be willing to bet that you'd be hard pressed to find too many published D&D adventures that don't feature at least one encounter with lots of foes at once.

So, that's what I mean when I say this is a common encounter type.

Tony Vargas · Jun 10, 2019

FrogReaver said:
It’s like your not listening to what I’m saying...

Just what you were /trying/ to say wasn't clear.

You're on about that oddity of D&D hps that an enemy is still fighting at full power even at 1 hp, which introduces a sort of rounding effect. Wounded rounds down to alive, so if your attack can only kill, never wound, your curve remains smooth & symmetrical, but if it can wound, it gets pulled in, becomes lopsided, because wounded enemies are counted the same as untouched enemies.

I still don't see what it has to do with the 'overkill' issue, though. In your example, both hypothetical characters overkill the same hypothetical enemies by the same amount when they drop them. When overkill is eliminated for one, but not the other - 4 hp enemies, was the first instance someone brought up - it flip-flops.

jgsugden · Jun 10, 2019

Meet Bob. Bob is an optimizer. Bob plays a fighter. While most fighters of Bob's character's level deal about 15 damage a round, Bob cranks out 30. Go Bob.

Meet DM. DM sees Bob's party cut through his encounters with ease. DM adjusts the encounters to make them toucher by adding more or tougher enemies.

Meet Squidface. He isn't real - he is just an illithid in an encounter DM made. Squidface is leading a bunch of ogres. This should be an insane combat for a party of Bob's PC's level, but not with Bob there. It is just a reasoably tough one.

Encounter. Squidface blasts Bob and Bob fails his save. Oh NOSE! Suddenly, we're bak to this being an insane combat. Down Goes Gary's cleric. Then Gloria's mage. Then Charlotte's rogue. Then Timmy's monk. And then Bob's fighter. TPK.

Greetings Professor Optimization

Hello

A Strange Game.
The Only Winning Move Is
Not To Play.

Fenris-77 · Jun 10, 2019

If we looked at some of the actual high end nova builds and what they are pumping out at mid-high levels I think this conversation would mean more. The more individual attacks a players has (nova or not) the better the chance that at least in some encounters you will fail to find optimal targets for your optimal damage. Seriously though, you want to piss off an Assassin? Send him 50 goblins. Nova away sir. Jokes aside, I'd bet that the genesis of this kind of question comes from people looking at immense novas and thinking well isn't that ... silly. 500+ damage?! Jesus murphy. Can I think of a way to at least kinda convince myself that it's not silly? Hmm .... maybe an overkill fallacy will help me sleep at night.