D&D 5E Attack bonus vs. damage bonus

[AverageCitizen]

How does an attack bonus stack up against a damage bonus? Which one is better, and by how much? I believe the conventional wisdom is that attack is better, but I don't know why. (Maybe because if you land a hit you can trigger your abilities?)

 

[Ryuutakeshi]

While I can't break down the math like some here can, it mostly works as follows: you can have all the damage bonuses in the world but it will do you no good if you can't hit anything. It's usually better to be more accurate and keep consistently hitting rather than hitting every other round for a little more damage. 5e's Bounded Accuracy also means you can target higher ACs more reliably with attack bonuses. Even a +1 can make a big difference

 

[TwoSix]

How does an attack bonus stack up against a damage bonus? Which one is better, and by how much? I believe the conventional wisdom is that attack is better, but I don't know why. (Maybe because if you land a hit you can trigger your abilities?)

It was more true in 3e and 4e when damage expressions were higher. It's still true in 5e when you're trying to land big hits, like sneak attack or attack spells or smite. It's not quite true for general weapon attacks, when the damage expression for a weapon attack only averages between 7 and 10. +1 to hit is only an 8-10% increase in DPS for normal hit chances (50-60%).

 

[mellored]

The more attack you have (archery style, reckless attack, precision strike, heightened spell) the better the damage bonus is.

The more damage you have (Sharpshooter, great weapon masters, sneak attack, 4e), the better an attack bonus is.


If your equal, attack is better. Since excess damage is effectively lost.
i.e. Better to hit a 4 HP kobold for 5 damage, then have a 50% chance at 10 damage.

 

[pukunui]

... you can have all the damage bonuses in the world but it will do you no good if you can't hit anything.

This.

 

[BoldItalic]

How does an attack bonus stack up against a damage bonus? Which one is better, and by how much? I believe the conventional wisdom is that attack is better, but I don't know why. (Maybe because if you land a hit you can trigger your abilities?)

Here's a formula for you:

Take the roll you need to hit the target you are facing and add the damage you would expect to do if you scored a hit. If the result is 22 or more, a +1 bonus to hit would be better than a +1 bonus to damage. If the result is 20 or less, the converse is true.

This ignores critical hits and assumes that the target can be hit at all.

Example: A creature with +3 to hit facing an AC 14 opponent does 6 damage on a hit. The roll to hit is 11, so you take 11+6 = 17 and that's less than 20 so a damage bonus would be better than a hit bonus. Without either bonus, the average DPR is 3.0. If you grant a +1 bonus to hit it goes up to 3.3 whereas if you grant a +1 bonus to damage it goes up to 3.5, which is better.

Second example: The same creature facing the same AC14 opponent switches to an attack that does 12 damage on a hit. You take the same roll to hit of 11 but add the 12 to get 23. That's greater than 22, so in this case a hit bonus would be better than a damage bonus. Without either, the average DPR is 6.0; with a +1 bonus to damage it would go up to 6.5 but with a +1 to hit it would go up to 6.6.

(edit) This also assumes that you don't do so much damage on a hit that it one-shots your opponent. If you did, a damage bonus would be wasted and a to-hit bonus would obviously be better.

 

[Xeviat]

It actually depends on what your attack bonus currently is. My standard calculations assume a 65% hit rate, but that's a character starting at 16 primary stat and increasing it at level 4 and 8, no magic items, fighting an "average" monster of equal CR. My guess is in actual play, the average AC you're facing will be lower, so your hit rate will be higher, since you're probably more likely to fight lower CR opponents than higher CR opponents (though there are some high AC opponents around).

Lets say you deal 10 damage per attack, with 65% hit rate. That's 6.5 average damage, minus crits. +1 to hit increases average damage by 0.5. +1 to damage increases damage by 0.65. In this case, damage is more important than to hit.

When you get 2 attacks, lets say you're now dealing 20 damage across two attacks. While the math above works for each attack, they add onto each other; the math would look the same if you had 1 attack for 20 damage vs 2 attacks for 10 each (though with 2 for 10, you have less chance of dealing 0, but less chance of dealing 20). Now, your average damage is 13. +1 to hit gets you +1 damage. +1 damage gets you +1.3 damage. That's actually the same ...

Lets say your damage is 15 per attack, then. At 65% to hit, your average damage is 9.75. +1 to hit is +0.65 damage; +1 damage is +0.65 ... we've found the balance point.

So if your damage is more than 15 per attack, to hit is more important. If your damage is less than 15 per attack, damage is more important.

Since most of the classes deal as much as 13.33 per attack (greatsword, great weapon fighter, +5 str), damage bonuses are actually pretty important. For characters with extra damage, like clerics, rogues, barbarians (after a point), paladins (at 11th level), rangers, etc.

 

[Saeviomagy]

Here's a formula for you:

Take the roll you need to hit the target you are facing and add the damage you would expect to do if you scored a hit. If the result is 22 or more, a +1 bonus to hit would be better than a +1 bonus to damage. If the result is 20 or less, the converse is true.

My calculations suggest that is wrong, probabilistically at least. The break even point is such that if (average damage) > (21 - target number) you should improve your attack bonus (up to your target number being 2). Otherwise increase your damage bonus.

... Which is precisely what you said +/- 1. Dur me. But at least there's some workings:

Maths:
Original average damage = (chance to hit) * (average damage roll)
= (21-(target number))/20 * (average damage)

We're looking for the point where
(21-(target number-1))/20 * (average damage) > (21 - target number)/20 * (average damage + 1)
(21-(target number - 1)) * (average damage) > (21 - target number) * (average damage + 1)
(21 - target number) * (average damage) +(average damage) > (21 - target number) * (average damage) + (21 - target number)

 

[BoldItalic]

My calculations suggest that is wrong, probabilistically at least. The break even point is such that if (average damage) > (21 - target number) you should improve your attack bonus (up to your target number being 2). Otherwise increase your damage bonus.

I'm not sure why you are disagreeing? Your formula is exactly equivalent to mine, with the terms rearranged algebraically ! Except that if the total is exactly 21, neither bonus is better than the other, which you haven't allowed for.

But you're right to pick out the case where the roll to hit (your target value) is 1 (or lower); in that case a bonus to hit is pointless even if the expected damage is more than 20. It could happen; a 20th-level PC with a STR of 20 attacking a goblin with a +3 greatsword is an extreme case but it does fall into that category. On the other hand, it also falls into the 'one-shot' category, so the upshot is, the goblin is dead 95% of the time regardless of any additional hit or damage bonus anyway.

An interesting, possibly counter-intuitive feature of the formula (yours or mine, doesn't matter) is that a bonus to hit and damage cancels out and doesn't affect the decision. (It affects DPR, obviously, but it doesn't affect the answer to the question). So it doesn't matter what Str or Dex adjustment the creature has, or if he has a magic weapon, the plusses and minuses cancel out. Weird, isn't it?

 

[AverageCitizen]

Here's a formula for you:

Take the roll you need to hit the target you are facing and add the damage you would expect to do if you scored a hit. If the result is 22 or more, a +1 bonus to hit would be better than a +1 bonus to damage. If the result is 20 or less, the converse is true.

My calculations suggest that is wrong, probabilistically at least. The break even point is such that if (average damage) > (21 - target number) you should improve your attack bonus (up to your target number being 2). Otherwise increase your damage bonus.

Could you guys walk me through this? Why 22 (or 21, according to Saeviomagy)?