D&D 5E Calculating Overkill Damage

[guachi]

You are wrong.

Let's take an extreme example. you are facing 65 1 hp creatures.

One person does 65 points of damage in a swing.

The other person does 65 1 point damage attacks.

What you are telling us is that we can derive nothing from showing that on any given hit the 65 damage person will have 64 points of overkill and that his average damage per attack will be 1 x hit chance (which is exactly what my calculations would show).And that we'd learn nothing by showing that the 65 1 point attack person would have 0 overkill and his average damage would be 65 x hit chance (which is exactly what my calculations would show).

Another example:

A character who does 40 points of damage per attack is fighting something with 93 hp. It will always, always, always take 3 hits to kill the target. Always. This means his effective average damage per hit is 31. (specifically, it's always 40, 40, 13). He does 93 points of damage and 27 points of overkill. Always.

Another person does 16 points of damage per attack and is fighting the same creature. It will always, always, always take 6 hits to kill the target. This means the effective average damage per hit is 15.5. He does 96 points of damage and 3 points of overkill.

What you are telling us is that knowing this is completely meaningless. Which is false.

Also, I'm not calculating DPR. None of my numbers are DPR. They are all damage per attack. The numbers don't care how many attacks you have per round. So I have no idea what your complaint is about.

My numbers do, in fact, attempt to take account the variable HP of the target by giving the target a random HP between 1 and its maximum HP. Sure, it's very unlikely a foe will have only one HP less than its maximum when you strike it but it's not completely unreasonable.

Here's another example of why blindly looking at DPR like you propose is absurd. You took GWM as a variant human at level one. You are fighting goblins who don't have a shield because, I don't know, they were using a bow. Using DPR shows that using -5/+10 does 8.95 DPR and not using it does 7.79. So what you're saying is that using GWM is the right way to go. You'd be so, so, so, so wrong.

Using GWM you'll automatically kill a 7 HP goblin just by hitting it. But you'll only hit 40% of the time so, using my calculations (and making the goblin's HP non-random. It's always 7 in this calculation) you get average DPS of 2.80. Which is exactly what you'd expect by trivially multiplying 7x.40. This indicates my calculations have some merit.

If you don't use GWM you hit 65% of the time and when you do hit you'll do 7 damage over 99% of the time. The average modified damage is 4.54 and you'll kill the goblin, like, 64.5% of the time. What you are telling us is that DPR is a better judge of whether you'll kill a goblin than my calculations are. Even though it's blindingly obvious that modified damage and having the ability to know the possibility of doing X damage on any given attack.

 

[guachi]

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.

1. Yes. But your average overkill per attack is dependent on accuracy. Just like your average damage per attack is.
2. Good thing I don't use number of attacks in any of my calculations.
3. Good thing I don't calculate DPR in any of my calculations. It's obvious to anyone that doing more damage per attack leads to more overkill. You aren't telling us anything we didn't already know. What I'm attempting is to put actual numbers to what we know.

 

[FrogReaver]

1. Yes. But your average overkill per attack is dependent on accuracy. Just like your average damage per attack is.
2. Good thing I don't use number of attacks in any of my calculations.
3. Good thing I don't calculate DPR in any of my calculations. It's obvious to anyone that doing more damage per attack leads to more overkill. You aren't telling us anything we didn't already know. What I'm attempting is to put actual numbers to what we know.

It's funny that 3 was my exact criticism of your focus on overkill. Overkill tells us nothing we don't already know because all it tells us is who has the higher base damage attack. Quantifying it is meaningless because trying to factor it into damage calculations as some kind of less modifier tells us nothing about what matters. What matters is how fast we are killing the monster and DPR coorelates very closely to that. Your Frankenstein statistic that calculates damage per attack and then removes overkill damage is just worse at predicting which attack will kill a monster faster than standard DPR calculations.

 

[guachi]

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

Yes. On one hand, using the -5/+10 might not be a good idea in and of itself On the other hand, if you can kill a foe you get an extra attack. For example, you have about a 50% of doing 12 or more points of damage with a greatsword without getting a critical hit and not using -5/+10. And if you get a critical hit you get an extra attack anyway. But you can't do more than 17 damage without a critical hit. So if your foe has more HP than that you'll only have a 5% chance of getting an extra attack.

On the other hand, you have the same chance of a crit using -5/+10 but about a 25% chance of doing at least 22 points of damage. And you can't do any LESS than 17 if you hit. Do you take the chance for an extra attack (assuming you don't already have it) or do you go with the higher average damage and leave a weakened foe for your ally to kill?

So if you KNEW a foe had 17 HP, you didn't already have an extra attack, and there were more foes out there that you could hit I'd go with the the -5/+10.

I think the bonus attack is really, really underrated. If an opponent had 15+ HP I'd probably go with -5/+10 because you'll have a 25-35% chance of dropping the foe (and that chance is higher than not using -5/+10). Anything less than that and you'd be better off not using it. But that's if you wanted to get that extra attack. Anything above 23 HP you won't have much chance of dropping it to zero barring a critical hit but you'll do more damage using -5/+10 anyway.

If you faced a target dummy that always had the same HP every time you attacked, the crossing point for where -5/+10 does more damage on average than not using it is a foe with 24 HP. This assumes +5 damage and a base 65% chance to hit. Though, as I said, GWM adds that bonus attack and any damage you lose by using -5/+10 (and it's not much) can be made up by dropping a foe and getting that extra attack.

So... don't have that extra attack - 15+ HP.
Do have that extra attack - 24+ HP.

This assumes you know exactly what the foe's HP is. Which you probably don't. But there's the cutoff for you.

 

[Aenorgreen]

I am not sure what is the point of these calculations. Those who do more damage per strike will also have more overkill. Wasn't that already obvious?

 

[FrogReaver]

You are wrong.

Let's take an extreme example. you are facing 65 1 hp creatures.

One person does 65 points of damage in a swing.

The other person does 65 1 point damage attacks.

What you are telling us is that we can derive nothing from showing that on any given hit the 65 damage person will have 64 points of overkill and that his average damage per attack will be 1 x hit chance (which is exactly what my calculations would show).And that we'd learn nothing by showing that the 65 1 point attack person would have 0 overkill and his average damage would be 65 x hit chance (which is exactly what my calculations would show).

Another example:

A character who does 40 points of damage per attack is fighting something with 93 hp. It will always, always, always take 3 hits to kill the target. Always. This means his effective average damage per hit is 31. (specifically, it's always 40, 40, 13). He does 93 points of damage and 27 points of overkill. Always.

Another person does 16 points of damage per attack and is fighting the same creature. It will always, always, always take 6 hits to kill the target. This means the effective average damage per hit is 15.5. He does 96 points of damage and 3 points of overkill.

What you are telling us is that knowing this is completely meaningless. Which is false.

Also, I'm not calculating DPR. None of my numbers are DPR. They are all damage per attack. The numbers don't care how many attacks you have per round. So I have no idea what your complaint is about.

My numbers do, in fact, attempt to take account the variable HP of the target by giving the target a random HP between 1 and its maximum HP. Sure, it's very unlikely a foe will have only one HP less than its maximum when you strike it but it's not completely unreasonable.

Here's another example of why blindly looking at DPR like you propose is absurd. You took GWM as a variant human at level one. You are fighting goblins who don't have a shield because, I don't know, they were using a bow. Using DPR shows that using -5/+10 does 8.95 DPR and not using it does 7.79. So what you're saying is that using GWM is the right way to go. You'd be so, so, so, so wrong.

Using GWM you'll automatically kill a 7 HP goblin just by hitting it. But you'll only hit 40% of the time so, using my calculations (and making the goblin's HP non-random. It's always 7 in this calculation) you get average DPS of 2.80. Which is exactly what you'd expect by trivially multiplying 7x.40. This indicates my calculations have some merit.

If you don't use GWM you hit 65% of the time and when you do hit you'll do 7 damage over 99% of the time. The average modified damage is 4.54 and you'll kill the goblin, like, 64.5% of the time. What you are telling us is that DPR is a better judge of whether you'll kill a goblin than my calculations are. Even though it's blindingly obvious that modified damage and having the ability to know the possibility of doing X damage on any given attack.

On example 1:
Your argument is that a character doing 65 damage in one attack a turn is worse than a character doing 65 attacks worth 1 point of damage each. Consider this: Assume a 50% chance to hit to each attack. Your character that does 65 damage in a single attack has a 50% chance to kill a 64 hp for in round 1. The other doing 65 1 damage attacks has virtually no chance of killing that 64 hp monster in round 1. The first character does 1 overkill damage. The 2nd character does no overkill damage. They both do the same DPR. Which is better in my scenario?

The point is that overkill damage predicted the 1 damage per attack character predicted the wrong character to win that contest.

I also want to answer the goblin example because its a more real world example. Your calculations aren't what is causing the problem on the goblin example. It's the differences in chance to hit (which shouldn't really impact your overkill calculations any). Why? Because chance to hit is infinitely more important in determining who wins a contest than overkill. You are giving a character a high chance to 1 shot a goblin and a higher chance to hit that goblin. Chance to hit really starts mattering when you get to 1 shot levels. As long as you have sufficient damage to 1-shot something then the driving efficiency factor will be chance to hit.

Of course for your goblin example I can just as easily pick an orc where the average GWF not using -5/+10 will likely not kill the orc in 1 hit. However, the GWM using -5/+10 will virtually 1 shot that orc. In which case the opposite would be true. Your overkill damage calculations would yet again fail and DPR would win out.

I guess the ultimate point is that for every example you can throw out where your method works better than DPR I can give an example where it works worse. Why? Because we are ultimately dealing with damage distributions and probabilities. Sometimes a method generating greater variance will be better than a method generating lower variance and other times vice versa. What I can say is that while DPR sometimes gets it wrong (as in your goblin example), those times mostly occur when we are talking about killing something in 1 hit. (It's really easy to take a closer look at chance to hit in such cases).

One other side point, example which focus on a single damage value aren't very helpful as D&D has damage ranges that generate a bell-like curve pretty quickly. This is why DPR is such a good guide in most cases, because that bell-like distribution of damage centralizes it very well and makes it hard to overcome the central tendencies of such a distribution after just a few attacks.

 

[FrogReaver]

I also want to ask:

What kind of bonus calculation are you giving for characters that have a higher chance of killing a foe quicker than another character. If you penalize them for overkill damage then you should award them for fast kills as their damage can start going to another target sooner. How would you factor this in?

 

[FrogReaver]

Yes. On one hand, using the -5/+10 might not be a good idea in and of itself On the other hand, if you can kill a foe you get an extra attack. For example, you have about a 50% of doing 12 or more points of damage with a greatsword without getting a critical hit and not using -5/+10. And if you get a critical hit you get an extra attack anyway. But you can't do more than 17 damage without a critical hit. So if your foe has more HP than that you'll only have a 5% chance of getting an extra attack.

On the other hand, you have the same chance of a crit using -5/+10 but about a 25% chance of doing at least 22 points of damage. And you can't do any LESS than 17 if you hit. Do you take the chance for an extra attack (assuming you don't already have it) or do you go with the higher average damage and leave a weakened foe for your ally to kill?

So if you KNEW a foe had 17 HP, you didn't already have an extra attack, and there were more foes out there that you could hit I'd go with the the -5/+10.

I think the bonus attack is really, really underrated. If an opponent had 15+ HP I'd probably go with -5/+10 because you'll have a 25-35% chance of dropping the foe (and that chance is higher than not using -5/+10). Anything less than that and you'd be better off not using it. But that's if you wanted to get that extra attack. Anything above 23 HP you won't have much chance of dropping it to zero barring a critical hit but you'll do more damage using -5/+10 anyway.

If you faced a target dummy that always had the same HP every time you attacked, the crossing point for where -5/+10 does more damage on average than not using it is a foe with 24 HP. This assumes +5 damage and a base 65% chance to hit. Though, as I said, GWM adds that bonus attack and any damage you lose by using -5/+10 (and it's not much) can be made up by dropping a foe and getting that extra attack.

So... don't have that extra attack - 15+ HP.
Do have that extra attack - 24+ HP.

This assumes you know exactly what the foe's HP is. Which you probably don't. But there's the cutoff for you.

I just want to point something out. You propose to do the opposite of what your new statistic tells you sometimes and not other times. Your statistic isn't what's guiding your decisions in these circumstances, it's the chance to kill probabilities you are calculating...

 

[FrogReaver]

I am not sure what is the point of these calculations. Those who do more damage per strike will also have more overkill. Wasn't that already obvious?

I think the thought is that he can remove overkill damage from DPR calculations to make them more accurate (it doesn't but I think that was his original belief / premise). It's probably best to let him answer for himself though...

 

[guachi]

I am not sure what is the point of these calculations. Those who do more damage per strike will also have more overkill. Wasn't that already obvious?

Yes. But to my knowledge no one has attempted to apply this to damage per attack for better comparisons between abilities. Is doing 120 damage in one attack better than doing 10 damage in each of 10 attacks? Maybe.

Can you tell me if it's better? I'll wait for an answer and your reasoning, with math, as to why.