When is it worth it to exchange hit to dmg?

[SangoProduction]

(I'm looking for verification on my methods here, so I'm perhaps more verbose than I need to be, for the sake of clarity.)

So, let's say I've got 2 attack options.
1 targets normal AC, but does 23 damage on average.
The other targets touch AC but does only 7 damage on average.

So, if x were the chance for the first to hit, and y is the chance for the second to hit, and I'm needing to find out how much more likely I'd need to be to hit, in order to, on average, break even on my expected damage.

x * 23 = y * 7
3.2 x = y

So, y needs to be 3.2 times as likely to hit as x, in order to make up the lost damage.

Using practical examples, if I had only a 25% chance to hit with the first option, then the second option would need to have an 82% (round up to 85%) chance to hit.

This passes the sanity test, as far as basic common sense. The lower damage option needs to hit more times to equal the higher damage one.


Now, how do I adjust this to factor in things like one attack option possessing multiple attacks? Because if you split an attack option evenly between two attack rolls, you are much more likely to do *something* on any given turn. But does it actually impact the math?

[Zaq]

It does impact the math. I will admit that I’m not super good at the specific formulas, but it does have an impact.

A really important step zero is to define your goal. “Most damage” seems obvious, but maybe it isn’t the best choice. Maybe you want to minimize turns with zero impact, or maybe you want to measure how many rounds it’ll take to drop a specified foe (this is related to DPR, but it’s potentially more useful because it devalues overkill). I personally like rounds-to-kill just because it helps contextualize things.

To use a hopefully silly extreme example of why simply “max DPR” might not be the best choice, if you have an attack option that does many hundreds or even thousands of damage on a success but only hits on a nat 20 (ignore surge of fortune and similar), a weighted average will probably have that win (for pure DPR) over a more reasonable option, but that’s clearly not a practical choice in most combats. (Again, intentionally using an extreme example for emphasis.) You might prioritize the option that lets you really participate in most combat rounds over something like this.

Again, not gonna get into the specific formulas, but if an option involves multiple attack rolls, you still want to account for all of them. Make a weighted average of “A hits, B hits, A and B hit, both miss” or whatever (gets slightly more complex with crits and stuff). And again, are you looking for a pure maximum, a maximum that reduces the value of overkill, something that avoids the subjective “welp, I missed, so this turn didn’t matter” feeling, or something else entirely?

Touch AC is hard because there isn’t always a clear relationship between regular AC and touch AC, so it’s very challenging to come up with a general formula unless you actually know the numbers for what you’re fighting. (Contrast with Power Attack, where if you know your target AC, you can just go from there and tweak a bit.)

In general, a weighted average / expected return formula that takes into account all possible combinations of outcomes from a given option will get you pretty far, but again, it’s important to really make sure you know what you care about.

[Esprit15]

Add the chance of each possible attack result multiplied by the amount of damage that would be done. So the odds that exactly one attack hits multiplied by the damage of one hit, the odds that exactly two attacks hit multiplied by the damage of two hits, and so on.

So with two attacks at 50% chance, you have a 50% chance that either the first or second attack hits, and a 25% chance that both attacks hit. If the attack does 10 damage, the average damage calc looks like this:

Exactly two hits:
0.5*0.5=0.25 chance

Exactly one hit:
(1-0.5*0.5)-(0.5*0.5)=0.5
Where the logic is:
[odds of any hit] - [odds of two hits] = [odds of one hit]

Total average damage:
0.25*20+0.5*10=10

So using one of your example numbers:

Odds of two hits from inaccurate but damaging attack
0.25*0.25=0.0625

Odds of one hit from inaccurate but damaging attack
(1-0.75*0.75)-(0.25*0.25)=0.375
You’ll note that the numbers in the first set of parenthesis look odd now. With this equation, we’re initially getting the odds that *anything* hits, and then subtracting out the odds that both hit. I’m pretty sure there’s a more elegant way to do this, but I can’t think of it right now. Anyways:

0.0625*46+0.375*23=11.5

Odds of two hits from accurate but low damage attack
0.85*0.85=0.7225

Odds of one hit from accurate but low damage attack
(1-0.15*0.15)-(0.25*0.25)=0.225

0.7225*14+0.225*7=11.9

You’ll note that the odds of both attacks hitting in in the latter is actually more likely than exactly one attack hitting. However because of this, the damage able to be done starts to matter way more - swing a big weapon around, and it’s gonna land eventually, even if it misses most of the time.

EDIT: The “near infinite damage with a minimal chance of occurring” problem can easily be solved by remembering that the cap on damage that you can do is “Enemy HP+10.” Beyond that, there is no benefit to more damage.

[Ualaa]

I made a very basic spreadsheet, where values could be plugged in.

AC value of the target.
Your "to hit bonus".
The range that was a threat.

It was basically... a 20, 19, 18 (threat range 3) is a hit for (crit multiplier), x percentage of the time (the amount that the To Hit hits the AC value.

Other rolls are say 17, 16, 15, 14, 13, 12 are hits, so 1x average damage.
And 11 or lower are misses.

Then plug in numbers.

I never analyzed it in depth.
Iteratives weren't playing nice, so with haste I might be +23 to hit (twice).
And then +18 with the same formulas.
And finally a +13, and then add up all the totals.

When you're hitting on any number (other than a 1), damage is going to be king.
When you need to roll a decently high number to even connect, to hit is probably worth more.

Haven't really analyzed anything, it was rather basic.

[Crichton]

I

Touch AC is hard because there isn’t always a clear relationship between regular AC and touch AC, so it’s very challenging to come up with a general formula unless you actually know the numbers for what you’re fighting. (Contrast with Power Attack, where if you know your target AC, you can just go from there and tweak a bit.)




This seems like the most relevant point.


With Power Attack, you may not know the opponents exact AC (in fact, your character would never know this, at least not as a number), but you always know that you're stepping down your to-hit in 5% increments (down to the theoretical 'floor' of the point where your roll of a 2+your attack bonus is equal to the opponent's AC)

But with AC vs Touch AC, not only might you not know it, but it's gonna be different for every foe. For many monsters, Touch AC is equal to AC, if they don't have armor/shield/natural armor.

So between it being a different value for each monster, and not knowing either/both of the actual numbers, finding a 'universal' formula for this that's gonna be useful in actual play seems... difficult.


edit: not to say that your formula isn't correct, just that unless you know both values for every creature you face (and are willing/allowed to metagame so much as to make decisions based on AC values your character wouldn't know) I don't see how you can use this in actual at-the-table play in real-time.

[Esprit15]

Given that most monsters do have natural armor, and it’s the fringe cases where said natural armor isn’t the majority of their AC, I feel pretty okay saying that Touch AC is going to normally be markedly lower than regular AC.

Characters aren’t dumb, either. You at least know “That was a good swing and it hit.” We’re not throwing a dart at a board after all when we decide what penalties to take on Power Attack, and I have had very few combat encounters where we didn’t know the enemy’s AC down to at least a 2 point range. Knowing the numbers, even vaguely, is super helpful for decision making. Like I demonstrated out above, knowing “Hey, on just one hit, you’re probably better off with the accurate attack, but with multiple tries, you should go with the powerful one” is not metagaming, it’s almost just basic logic. You’d have to apply numbers to actually justify it, but the whole thing makes intuitive sense.

[Crichton]

Given that most monsters do have natural armor, and it’s the fringe cases where said natural armor isn’t the majority of their AC, I feel pretty okay saying that Touch AC is going to normally be markedly lower than regular AC.


Just pulled up 10 random CR 5 monsters on the SRD, and the difference between AC and Touch AC ranged from 2 to 8. A more thorough survey would turn up more definitive numbers, but that's a pretty big range, and it's definitely enough to make trying to use a universal calculation for the proposed two attacks pretty hard.



Characters aren’t dumb, either. You at least know “That was a good swing and it hit.” We’re not throwing a dart at a board after all when we decide what penalties to take on Power Attack, and I have had very few combat encounters where we didn’t know the enemy’s AC down to at least a 2 point range. Knowing the numbers, even vaguely, is super helpful for decision making. Like I demonstrated out above, knowing “Hey, on just one hit, you’re probably better off with the accurate attack, but with multiple tries, you should go with the powerful one” is not metagaming, it’s almost just basic logic. You’d have to apply numbers to actually justify it, but the whole thing makes intuitive sense.

Being able to apply logic like that isn't metagaming, you're right. But applying your OOC knowledge of a creature's AC, especially if that character hasn't encountered that exact creature before, very much is.

And while I don't necessarily subscribe to it, many DMs and players are of the opinion that there's a strong difference between 'that was a good swing and it hit' and 'you hit on a 15 and I missed on a 13, so we can determine its AC is between 14 and 15, which means I can use my lower bonus attack and still have a good chance to hit' Many would see the latter as absolutely metagaming. Characters don't know the numbers of the dice roll, and they don't know the numbers of their own attack bonus. They probably do know 'this attack hits harder but is harder to land hits with' though. It's all grey area, really.


All that said, you might be able to come up with some good rull-of-thumb for when to use which attack, in this scenario, but it's gonna be a lot harder than calculating how much PA to use, since there's more variables and you need them all in order to come up with a specific number to use.

[Esprit15]

I'm sorry, what? Judging what a good number to power attack for is metagaming? That's nonsense. Characters don't know any of the numbers, but they're how we as players interface with the game during combat. You might as well ask me to build a table without measuring anything.

[Drackstin]

Being able to apply logic like that isn't metagaming, you're right. But applying your OOC knowledge of a creature's AC, especially if that character hasn't encountered that exact creature before, very much is.

And while I don't necessarily subscribe to it, many DMs and players are of the opinion that there's a strong difference between 'that was a good swing and it hit' and 'you hit on a 15 and I missed on a 13, so we can determine its AC is between 14 and 15, which means I can use my lower bonus attack and still have a good chance to hit' Many would see the latter as absolutely metagaming. Characters don't know the numbers of the dice roll, and they don't know the numbers of their own attack bonus. They probably do know 'this attack hits harder but is harder to land hits with' though. It's all grey area, really.

As a DM, i can say my players don't do research on monsters, but finding the AC of a monster is rather easy because of course i need to tell them if they hit or miss. and in game they are not saying well i rolled a 13 so i missed, but they know they missed. that said in game if they are hitting consecutively, the character would realize this thing is easy to hit, ill put more force into it, sometimes that even internal. do you scream out every time your looking for something or flanking? most of the time my players just got full bore with PA on and if they don't hit they adjust then. ether way the rules of power attack is metagaming to a point but the players never have to say anything out loud other then, im only going -2 this turn.

[Crichton]

As a DM, i can say my players don't do research on monsters, but finding the AC of a monster is rather easy because of course i need to tell them if they hit or miss. and in game they are not saying well i rolled a 13 so i missed, but they know they missed. that said in game if they are hitting consecutively, the character would realize this thing is easy to hit, ill put more force into it, sometimes that even internal. do you scream out every time your looking for something or flanking? most of the time my players just got full bore with PA on and if they don't hit they adjust then. ether way the rules of power attack is metagaming to a point but the players never have to say anything out loud other then, im only going -2 this turn.


I don't take issue with anything there at all, and really, I fully expect players at my table, or any table probably, to easily suss out the approximate AC of anything they fight that they have a few hits and misses on. That's not an issue at all. I think the heart of my initial comment got sidetracked by the PA reference, but my point is that PA is a pretty easy on-the-fly estimation to make, since it's a static 5% increment for each point you use, but the OP's calculation is much harder to figure in real-time at the table, since it's much more of a moving target, and to really fulfill the X and Y of his formula, you need the precise AC and Touch AC of every monster you face, which, by the time you hit and miss enough times to get it, you've probably already killed said monster.

[SangoProduction]

I don't take issue with anything there at all, and really, I fully expect players at my table, or any table probably, to easily suss out the approximate AC of anything they fight that they have a few hits and misses on. That's not an issue at all. I think the heart of my initial comment got sidetracked by the PA reference, but my point is that PA is a pretty easy on-the-fly estimation to make, since it's a static 5% increment for each point you use, but the OP's calculation is much harder to figure in real-time at the table, since it's much more of a moving target, and to really fulfill the X and Y of his formula, you need the precise AC and Touch AC of every monster you face, which, by the time you hit and miss enough times to get it, you've probably already killed said monster.

Since chance to hit is static per enemy, per attack type, it's only tricky in that it would take more total attacks to figure out the chances of hitting with both.

[Crichton]

Since chance to hit is static per enemy, per attack type, it's only tricky in that it would take more total attacks to figure out the chances of hitting with both.

I mean, yeah, that's kinda what I was getting at. If that's what you call 'only tricky' then sure. By the time you've hit or missed enough times to get any usable data, surely you've killed the foe already? And there's no guarantee the next foe that appears visually similar has the same stats, so..... Not saying you can't use your knowledge of your attacks to make informed decisions, just that getting the precise data for every single foe you'll ever face, since, as you say, it's different for each enemy, is quite a process. Didn't say it was impossible, or even fruitless, just a lot more complex than the simple static 5% calculation for PA.

[Drackstin]

I say, instead of worrying about a fancy equation, just take the feat that puts the negative to AC, you can't get hit if they are dead.