Ok, so comparing pure damage is easy. Take 1d12+6 to 2d8+8, it's 12.5 vs 17 average damage and the 2d8+8 wins.
But what if the 1d12+6 is a single attack at an attack bonus of +10, while the 2d8+8 is actually two separate attacks (TWF) at +7 with 1d8+4 each ?
I'm fairly sure the 1d12+6 wins in that case.
What if the 1d12 is a 20/x3 crit weapon and the 1d8 is a 19-20/x2 weapon?
I'm also sure you people here have already developed a formula to calculate all these things fairly easily and compare them to each other.
So my question: Can someone of you tell me that formula (and maybe explain it too)? Would be great.
The DPR formula is for just this purpose.
The 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.
You determine h (chance to hit) by picking a target AC (usually average for the level you're comparing at. 23 at level 10 is the accepted norm IIRC).
Ah, that's exactly what I was looking for.
Thank you very much!
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Shouldn't that second h be a new variable, since there are quite a few things that grant you a bonus to confirm critical hits, and even a few that impose penalties?
And h = min(max(20/(AC - to_hit_bonus), 0.05) 0.95), right?
The min/max represent 1 and 20 always missing/failing. (AC - to_hit_bonus) is the number you need to roll to hit. 20/roll is the probability of such a roll or higher.
Otherwise that formula looks about right to me.
Ah, yes special crit confirmation feats aren't important for me, but I suppose you're right.
However, how do I compare a single 2hd attack vs two TWF attacks?
Simply use the formula for each hand separately and then add the results together?
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I got a present for you!
Here is a spread sheet with average numbers for CRs.
You know, average AC, average saves, average HP, ect.
I use it when making a higher level character to make sure they're capable of affecting enemies of appropriate CRs (CR=Character Level +/- 2)
I would honestly suggest not getting overly wrapped up in the DPR Dogma. As I've said elsewhere, it can lead to looking at one number (DPR) as "the answer" when in fact one of the numbers in the formula can compensate for the other in a theorycrafting-a-thon and be misleading
e.g. really high to hit with low damage or really low to hit with high damage.
Weigh the numbers separately before looking at them together and consider other important factors like your skills, your AC, HP, saves etc.
When people start mashing it all together like if one number is a 2 and the other is a 20, yes the average is an 11....but is that 2 a relevant statistic on its own? Something to think about.
I use the 50/50 rule
I use the chart I posted and see if I have at least a 50% chance to hit, preferably higher. In actual play I assume party buffs will happen and increase my relative chances, but if a character can't even succeed 50% on his own, then he's probably dragging the group down.
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Ah, yes special crit confirmation feats aren't important for me, but I suppose you're right.
However, how do I compare a single 2hd attack vs two TWF attacks?
Simply use the formula for each hand separately and then add the results together?
Yes.
Note that as soon as you're comparing sequences of more than 1 attack, there's some noise in the math if you're also fighting more than one opponent.
For example: you're fighting two goblins (in reach), who each have 1 hp left. It doesn't really matter that your greatsword has better DPR, because your two short swords stand a better chance of killing them both this round. In this case it's much more important how accurate your to-hit is with the shorts swords vs. the greatsword.
However, DPR calculations do have their uses, for example when you're trying to make up your mind whether you should use Power Attack.
However, DPR can be misleading; sometimes accuracy is more important than damage, for example if another party member can reliably do a bit extra damage to finish up after you (with a Magic Missile, perhaps). Killing a monster in this round for certain can be worth a lot, because that's one fewer round of the monster hitting back at you.
Another thing to consider is probability distributions. A weapon that does 1d12 damage will do 6.5 damage on average, while a 2d6 weapon will do 7 damage on average. But the 2d6 weapon is much more likely to deal close to that 7 damage than it is to deal 2 or 12 damage. The d12 however is equally likely to do roll a 1 as it is to roll a 7 or a 12, making that average damage a much less solid figure.
Suppose you're fighting enemies with 4hp; suppose that your to-hit with the 2d6 weapon is a little bit worse than with the 1d12 weapon, and therefore your DPR a little bit lower; the 2d6 weapon might still be the better choice because it's much more likely to kill the monster with a single blow.