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I see people toss this around a lot, and I thought I'd address it. It's not a universal situation that +1 hit is always superior to +1 damage. {Note this is a math post }

{Edit: In this case it's not a hard fallacy, as in: people are always mistaken in their belief. It's a contingent one, that depends on the situation. Above a certain average damage for the action used, +1 hit does indeed become more valuable than +1 damage. My intention is to point out that the break point exists, although it is a fairly low one that will mostly only affect Heroic characters.}

I figure CharOp is the best place to post this, because you guys are the most likely to be thinking about damage over status condition builds, and care about every little bit of math involved in making your decisions.

First of all, let's put in a qualifier, and a damn important one: +1 hit is infinitely superior to +1 damage when it comes to applying a status condition that won't apply on a miss. If that is your primary concern, there is no fallacy in the idea that +hit is god. It's absolutely correct. If you are primarily concerned with applying status conditions, please continue to get as much +hit as you can afford.

But for damage, which may or may not be a greater concern for you depending on your role, powers and inclination, you need to do the math.

Assumptions:
1) We're going to start the comparison vs equal level mobs, and the assumption that with an average build you will have 50% chance to hit. This bears out pretty well, since average build from the PHB pretty much seems to assume you have a base ability of 16 and improve it every chance you get, have the best possible magic item you can appropriate to your level, and use a +2 proficiency weapon (for weapon powers only obviously). If you do this and compare it to the mob equivilent AC 14+level (~12+level for NADs) you should hit on a about an 11+.

Here's the math.

B = Base hit chance (.5)
H = bonus hit chance (.05 for +1 to hit)
P = Power average base damage
D = bonus damage (1 for +1 damage)

To be exactly equal, B*D = H*P
Thus, P = B*D/H, or .5*1/0.05, or 10.

In other words, damage wise +1 to hit is only equal to +1 damage if the base damage you will do with the power is 10. It's only more if the base damage is greater than 10.

This number changes based on if you are fighting harder to hit creatures or easier to hit ones. As a general rule it goes down by 1 for every level higher than you the mob is, and up by one for every level lower than you it is. If you start with a lower/higher primary ability score, have a lower or higher magic item, etc, it also adjusts this number by 1 (up for higher and down for lower) your chance to hit is adjusted.




As an example, lets look at a Level 1 Ranger considering going Longswords vs Warhammers. Str 16, +5 to hit before the hit vs damage comparison. Remember, a Ranger typically get +3.5 damage from Hunter's Quarry once per round. Assume he's fighting level 2 mob (AC 16).

Twin Strike does on average 4.5 damage per attack with the longsword, and 8 with one of those on a quarry. The Warhammer is far superior for this At-will. Hit and Run does 9.5, or 13 to a quarry, advantage longsword. Dire Wolverine Strike and Two-Fang Strike also do a base 9.5 average damage, 13 to a quarry on one of the attacks, so it's a slight advantage longswords. Dailies however you have a damage advantage with swords, since they do 2[W] damage, or 9.5 before you even add in the ability modifier, 13.5 with it, and 17 vs quarry once per round.

So with this build, you have to consider the fact that your most common attack, Twin Strike, gets about double the benefit with +1 to damage over +1 to hit on at least one of the attacks. The converse is that your once an encounter abilities and dailies are weaker with +1 to hit.

Of course this whole equation changes based on the AC of his opponents and so forth, basically as he fights lower than AC 16 mobs warhammers become more attractive, higher AC longswords do, which is of course exactly what common sense would tell you.

Edit : Changed the Str and AC in the example to something a little more typical at 1st level.

I think it's assumed hitting is better for a couple different reasons: if you're getting a bonus to hit it's more likely you're using a daily or encounter power which is going to do significant damage or a useful effect on a hit, "extra" damage features of strikers (sneak attack, quarry, etc), other effects that only work on a hit (combat superiority, bolstering strike, etc). Not to mention that if a monster is at 5 hit points, it dosen't matter how much damage you do, just that you connect.


Cheers

Thing is, bonuses to hit are much better than bonuses to damage in general, but the ratio is not a constant. The higher your damage, the better a bonus to hit is; the lower your damage, the worse it is. At first level, a +2 bonus to damage is better than a +1 bonus to hit, but at 10th level, its the other way around because you deal so much more damage. At 30th level, when you can be dealing as much as +55 as a constant, plus your actual weapon damage (whose average may be as high as 8 per W, meaning 71 damage on an average hit) a +1 bonus to hit is massively better than a bonus to damage.

Basically, if I deal 71 damage on an average hit, a +1 to hit gives me +71 damage out of every 20 attacks. To make up for it, I have to deal +x * hits damage, where x = damage bonus and hits = number of hits you get out of 20. So if you get, say, 10 hits out of 20 (not unreasonable at 30th level), x has to be at least 7.1. That's a huge amount.

Even looking at a rogue, you see someone who deals 2d4 + 3d8 + str + dex + enh + bunch of other random stuff. With the proper equipment, you're looking at in the 50s, if not more.

But there are a lot of variables involved in all of this, and your base to-hit chance varies considerably across levels. At low levels, a 75% hit chance is not even all that unlikely; its fairly easily achieved by several classes. Conversely, at level 30, a 50% hit chance is not bad.

My general rule for my Rogue is: Lots of W's = Use my Rapier (Unless I'm really going for the effect.)

Few W's, an At-Will, etc. = Use my Dagger.

More hits is a higher chance to crit.

And this only becomes clear once you used a vorpal, really.