## Best weapon (DPR, Pathfinder)

*It dawns upon me that various searchers may find this post. So bottom line up front: weapons, no mods or bonuses, the greatsword and the dwarven longhammer share the top spot. For one-handed it’s the bastard sword alone. If you can’t or won’t go exotic the one-handed highest DPR is shared between longsword and battleaxe.*

So the most recent number crunching I’ve done has been for pathfinder. That’s one of the Dungeons and Dragons editions for the one or two who don’t know. Now I’m not talking online gaming. I’m talking on the table-top – pen and paper (PnP) playing with a GM and a group of friends. What this means is that there are always a lot of caveats to apply. Every table has house rules, and the GM may be playing for god-slayers or E6ers, in low to epic magic levels, perhaps with dimensions, perhaps with a touch of steam, … yeah, you get the idea.

(God-slayers and E6ers are my terms so I’d better explain them. Godslayers are the players at level 20, who brag of killing various gods, who wander into hell to give Satan a wedgie. E6ers are the players using a variation that puts and mostly keeps them at the opposite end of the spectrum. I’ve got a post on E6 coming at some point, so I’ll refrain from full disclosure here.)

Despite all this making the correct answer ‘it depends’, there are continuous discussions of what weapon is best for various players. And despite knowing it depends, I’m going to take a whack at the answer.

The thing is I’m going to strip away as much flavor and variation as possible. I’m making a very specific definition of “best” for this post.

‘best’ is the weapon that does the highest DPR (damage per round) without any modifiers.

Before I get into the nuts and bolts and also-runs I’ll answer the question. There are two weapons that tie for the best DPR: the greatsword, and the dwarven long-hammer. The greatsword is a martial weapon found in the core rulebook, the dwarven longhammer is an exotic weapon found in the Advanced Race Guide.

Oh, ok. One-handed best DPR is the bastard sword wielded one-handed: core rulebook, exotic weapon. If you’re going to stick to martial weapons it’s tie between the longsword and the battleaxe.

Before I go into the crunch I can give a fast guide – a set of basic rules which I’ll be defending and expanding in the rest of this post.

Rule one: The higher the max damage the higher the DPR. If the top is 12 it beats 10. Seems obvious. What makes it not so obvious is criticals – see rule three. But first;

Rule two: If max is equal, multiple dice give a higher DPR. In other words, 2d6 beats 1d12. Again seems obvious (mean 7 beats mean 6.5). Again, criticals confuse. Fortunately it’s time for;

Rule three: The crit sequence is x2 < x3 = 19-20×2 < 18-20×2 < x4 = 19-20×3. Rephrased, the lowest is 20×2. Working upward there is a tie between 20×3 and 19×2, then 18×2 alone, then 20×4 which ties with 19×3. T

Onward for the crunchy goodness.

We begin with a verbal of the formula with definitions immediately following. Then I’ll put it together using spreadsheet notation so you can check my work and do it yourself.

Verbal formula:

For a given base target number, DPR is average damage times (chance to hit minus the chance of a crit), plus the average crit damage times the chance of a crit.

Breakdown definitions:

Average damage is (dmin + dmax)/2 or minimum damage plus maximum damage divided by 2.

Chance to hit is (21 – tgtnum)/20. Hitting is meet or exceed a target number on a 20 sided die, so I’m using 21 – the target number to get the hit range then dividing that by 20 to get the chance of hit.

Average crit damage is (dmin + dmax)/2 * X. That’s the average damage times the crit multiplier which I’m calling X.

Chance to crit is ((21 – pot_crit)/20 * (21 – tgtnum)/20)). It’s long because of the way the rules in pathfinder work. If you roll in the potential crit range you confirm the crit by rolling again and getting a to-hit or better. So it’s the pot_crit which is the crit target treated as a to hit target, then that’s multiplied by the chance of confirming a hit which is the chance to hit.

DPR = ((dmin + dmax)/2 * ((21 – tgtnum)/20 – ((21 – pot_crit)/20 * (21 – tgtnum)/20)) + ((dmin + dmax)/2 * X *(21 – pot_crit)/20 * (21 – tgtnum)/20))

I set that up in a spreadsheet, crossreferencing all 19 target numbers from 2 to 20 (1 is always a miss) by the damage dice/crit target/multiplier possibilities. Yes, that second is a lot of columns.

Now it’d be easy to average all these results to give a single number. But it’s not necessary (yet) as the relationship is stable across the table. 2d6 (for the available crit target/multiplies) always beats 1d12. 1d10 always beats 2d8. And the crit relationship is consistent as well, as stated in “rule three” above. 20×2 is on the bottom. 19×2 and 20×3 give equal averages and are next. And so on and so forth. Basically, add (21-crit_tgt) to the crit multiplier. The higher the score the higher the rank.

Keep that formula in mind by the way, because I’m going to use it in a few later posts. At least one big one to answer the perennial question: Which is better, 2H or TWF? (In pathfinder, is a honking big sword wielded in two hands better or worse than the whirling dervish with a weapon in each hand?)

Whee.