Let's assume the following:

1) D20 roll to hit vs. AC - standard D&Dism.
2) D6 for weapon damage
3) On average, a Level X Fighter vs. a Level X monster has a 30% chance to hit, aka hits on a 15+ on the D20.  

Here are my questions:

What is the value of a gaining +1 to hit bonus to the Fighter versus gaining a +1 bonus damage against a...

a) 5 HP monster?
b) 10 HP monster?
c) 25 HP monster?
d) 50 HP monster?

Does this value change if...

a) Monster has +1 AC so Fighter hits on 16+?
b) Monster has +2 AC so Fighter hits on 17+?
c) Monster has +5 AC so Fighter hits on 20+?


THANK YOU!!!

Quote from: Spinachcat;711197Let's assume the following:

1) D20 roll to hit vs. AC - standard D&Dism.
2) D6 for weapon damage
3) On average, a Level X Fighter vs. a Level X monster has a 30% chance to hit, aka hits on a 15+ on the D20.  

Here are my questions:

What is the value of a gaining +1 to hit bonus to the Fighter versus gaining a +1 bonus damage against a...

a) 5 HP monster?
b) 10 HP monster?
c) 25 HP monster?
d) 50 HP monster?

Does this value change if...

a) Monster has +1 AC so Fighter hits on 16+?
b) Monster has +2 AC so Fighter hits on 17+?
c) Monster has +5 AC so Fighter hits on 20+?


THANK YOU!!!

Every +1 to hit represents an extra 5% chance of doing d6 damage. The average amount of damage done on a d6 is 3.5. 5% of 3.5 is 0.175. So, in effect, each +1 to hit is worth an average of 0.175 extra points of damage per round.

If you have +1 damage instead, you need to hit first for that to matter. So if you have a 30% chance to hit, it's worth an extra 0.3 points of damage per round. If you have a 25% chance it's worth 0.25, if you have a 20% chance to hit it's worth 0.2, and if you have a 5% chance to hit it's worth 0.05.

So because your baseline damage is so low already, that +1 damage is actually better than +1 to hit unless you have a 15% chance to hit or less. Normally to-hit is way more important than to-damage, but that's because the baseline damage in most games is a bigger type of dice or has a bigger bonus attached to it. Once the average damage value of a hit goes up by a couple of points, the to-hit bonus will become more important again.

If hitting someone does other things, like disrupting spells, pushing people back, restricting their ability to attack you back or the like, then obviously to-hit becomes much more important again as well.

The hit point value of the monster doesn't really change the value because on average you're still going to need multiple hits to kill things so the longer term picture is what's important. D&D combat at mid level or higher is two big bars of soap shaving slivers off each other with razor blades, it's just a battle of attrition. If monsters are incredibly lethal but have really low HP then your damage value suddenly becomes more important, because from a gambling point of view you're going to lose the long game. You'd rather have a low to hit chance that ends the fight if it succeeds than a medium to hit chance for shitty damage that guarantees a long drawn out combat (which you'll lose).

Ok. My take on it...

Each +1 = +5% to hit. 30 to 35. A little better than a 1 in 3 chance to hit. On a d20 that is a hit on a 14+ at base and a 13+ with the bonus.
A +1 damage will increase a hits average damage from 3 to 4.

So a +1 weapon will hit 7 times in 20. or a little better than 1 in 3. So about every 3rd hit is going to connect. At base 30% ebout every 4th attack will hit. Little better than that though, more like 4/3/4 or somesuch.

So lets try this out
+1 to hit = 6 damage in 6 rounds, 9 damage in 9 rounds. 12 damage in 12 rounds. 15 in 15 rounds, 18 in 18. 21 in 21 rounds.
+1 Damage = 8 damage in 7 rounds, 12 damage in 11 rounds. 16 in 14 rounds. 20 in 18 rounds, 24 in 21 rounds

The +1 damage gradually outperforms the +1 hit.

Soviet and Omega, thank you both very much!!!

BTW, how do you view +1 to hit vs. +1 to AC???

Once you throw your own AC into the mix, the metric you need to maximize is the ratio of the damage you to that done by the enemy.

Somewhat bizarrely, +1 AC is worth more the higher your armor class is already, because as the range of d20 results the can strike you on gets smaller, each +1 AC represents a larger fraction.  (If the enemy can hit you on a roll of 2 or higher, and assuming rolling 20 implies double damage, +1 AC cuts enemy damage by one twentieth.  If the enemy needs 19 to hit on the other hand, +1 AC cuts enemy damage by a full third!)

All right, some variables:

x - average damage you inflict on a hit
X - average damage enemy inflicts on a hit
h - the target number, on d20, you need to hit the enemy
H - the target number, on d20, the enemy needs to hit you
p - your to-hit bonus
a - your AC bonus

The damage you do to the enemy is:
x(21-h+p)/20

The damage the enemy does to you is:
X(21-H-a)/20

The ratio you want to maximize - the rate at which you do damage divided by the enemy's damage rate - is therefore:

(x(21-h+p)) / (X(21-H-a))  [The twenties cancel out.]

You said you had to choose between +1 to hit and +1 AC.  Choosing the AC bonus is a good idea when it gives a better damage ratio for you.  So, it's a good idea when this is true:

(x(21-h)) / (X(21-H-1)) > (x(21-h+1)) / (X(21-H))

Using Wolfram Alpha's beta inequality solver, I get a whole ton of solutions, most of which we can discard (e.g. they assume negative damage and whatnot).  The interesting criterion seems to be this:

h-1 < H

Or, in other words,
 
h <= H

So, buff your AC unless you have an easier time hitting the enemy than it does you.

Awesome stuff!

Quote from: Spinachcat;711609Soviet and Omega, thank you both very much!!!

BTW, how do you view +1 to hit vs. +1 to AC???

Bonus to AC for the target or the attacker?

If the target then it will negate a +1 hit bonus, or slow down damage dealt. Treat + AC same as - to hit. Though localized to one target. It will cancel out a + to hit more or less.

Essentially ac bonuses will slow down damage dealt just like to hit bonuses speed it up.

Quote from: Omega;711773Bonus to AC for the target or the attacker?

The attacker.