Math needed! Bonus to hit vs Bonus to damage

[cdrcjsn]

A friend and I were having a discussion as to which is preferable, a bonus to hit or a bonus to damage.

I thought I saw someone do an analysis where it showed that a bonus to hit is preferred as long as you're not hit capped (i.e. you would only miss on a 1 vs. level appropriate foes).

He says that +1 damage is better than +1 to hit due to the binary nature of attacks (i.e. hitting half the time against level appropriate foes).

Anyone know the math behind this?

 

[MwaO]

In general, assuming that there's a 50% chance of hitting, an increase of +1 to hit means you hit 11 times out of 20 instead of 10. On the other hand, you should hit 10 times with the +1 to damage - i.e. per 20 swings, you do an extra 10 hp of damage.

So if you can do more than 10 hp of damage with that extra hit, then it is better to have the +1 to hit. Which isn't especially hard to do, even at low levels.

If on the other hand, you had a 75% chance of hitting, you'd hit 15 times out of 20 for an extra 15 hp of damage. A little harder to do, but not out of reach for even a 1st level character. A Rogue 1 with a Rapier who gets sneak attack damage can do 1d8+2d6+4 or 15.5 damage as an example.

And this is ignoring that often, hitting is important not just because of the damage, but the other benefits you get(confirming an encounter/daily, imposing a condition or effect that only happens on a hit, etc...)

 

[Bison]

well, taking your base assumption that on average you hit level appropriate creatures exactly 1/2 the time (I am not sure if this is true or not, it would depend on your build i think)

so if you take a bonus of +1 damage, and you hit 50% of the time, you are doing an extra 0.5 damage per round from the baseline.

on the other hand, if you take +1 to hit, you are going to hit 5% more often (1 out of 20 attacks). so if you take your average damage bonus, and divide it by 20, that is how much more damage you are going to do on an average swing.

so if your damage pre-bonus on a hit comes out to be 10, then you break even on average damage, if your average damage on a hit is less than 10 you are better off with a damage bonus, if it is more than 10 you are better off with a to hit bonus.

edit: sorry for the double info here, server took a while to post this but at least you can see there is some agreement