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It can't depend on what the enemy's AC is. If they have AC 10 and you have +5 to hit, a +1 bonus changes your chance to hit from 80% to 85%.
If they have AC 20 and you have +5, a +1 bonus changes the chance to hit from 30% to 35%. The attack bonus and AC are irrelevant, +1 is always a 5% increase in chance to hit.
A +1 attack bonus makes your attacks 5% more accurate, meaning a +1 to hit is worth +5% of your average damage.WRONG
The value of a +1 to attack depends on the enemies AC and your to hit, but it will always be higher than 5%. Typically, its worth 8-10%.
It just depends on how you look at the math. A +1 to attack will usually only change the result of an attack roll 5% of the time.
For example, if you need to roll a 15 or higher to hit a target, then a +1 will only change the roll of a 14 from a miss to a hit. If you roll anything other than a 14, your result will be the same as if you didn't have the bonus.
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A +1 attack bonus makes your attacks 5% more accurate, meaning a +1 to hit is worth +5% of your average damage.WRONG
The value of a +1 to attack depends on the enemies AC and your to hit, but it will always be higher than 5%. Typically, its worth 8-10%.
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It can't depend on what the enemy's AC is. If they have AC 10 and you have +5 to hit, a +1 bonus changes your chance to hit from 80% to 85%.
If they have AC 20 and you have +5, a +1 bonus changes the chance to hit from 30% to 35%. The attack bonus and AC are irrelevant, +1 is always a 5% increase in chance to hit.
Going from a 30 --> 35% hit chance will increase your average damage dealt by around 16%.
The easiest counter example is going from only hitting on a 20 to hitting on a 19 or 20. This means you are hitting twice as often with the bonus. But the bonus still only changes your result 5% of the time, so on a roll of a 19.
If you want mathematical proof that a 5% in your hit chance doesn't equate to a 5% increase in average damage dealt, look at the old DPR formula:
h(d+s) + tchd
h = Chance to hit, expressed as a percentage
d = Damage per hit. Average damage is assumed.
s = Precision damage per hit (or other damage that isn't multiplied on a crit). Average damage is again assumed.
t = Chance to roll a critical threat, expressed as a percentage.
c = Critical hit bonus damage. x2 = 1, x3 = 2, x4 = 3.
Equivalently,
damage = h*(d*(1+tc) + s)
which is a convenient format for seeing how your hit chance affects your average damage per round.
Assuming d,t,c,s are constant, just take the ratio of your "to hit" values to see how much a change in hit chance changes your relative damage.
0.35/0.30 ≈ 1.17
So going from 30 to 35% hit chance, your damage went up by around 16.7% on average.
/endderail
Average damage per attack is useful to look at, but it's just an average. The usefulness will vary by quite a bit from session to session, because of the small set sizes. Think of it like this, a +1 to attack will benefit you about as often as you roll natural 20s. Some nights you will seem to roll that number every round, and some nights you won't roll it at all.
Hmm, I wasn't comparing the old DPR to the new. You are correct.
Man, this thread went off the rails, didn't it?
Chaotic threads for lawful monks!