The Rogue: DPR Examination

After a short discussion with a commenter, I decided to re-check my numbers and post a small build with the effective DPR for it. And let me clarify up-front that DPR means damage per round.

Lots and lots of math after the jump...

Relevant stats, not in an appropriate stat block:

Capn’ Jack

Rogue 10

Str 10

Dex 22 (16 + 2 level + 4 enhancement)

Con 13

Int 12

Wis 10

Cha 16 (14 + 2 enhancement)

Weapons: 2 +2 short swords

Relevant Feats: Weapon Focus (short sword), Piranha Strike, two-weapon fighting, improved two-weapon fighting

Relevant Rogue Talents: Bravado, bleeding attack, slow reactions, surprise attack, other stuff…

Relevant Rogue Abilities: Precise Strike, Sneak Attack +5d6

Okay. Now for the Breakdown.

The rogue, at level 10, has a Base Attack Bonus of +7. He also gains +6 to attacks from his dexterity bonus, +3 from his charisma bonus, +1 from his weapon focus, and +2 from his magical weapons. However, he takes a -2 penalty on attacks due to using Two-Weapon Fighting, so in the end he has a total bonus of…

+17/+17/+12/+12

And has 4 attacks.

Now, let’s see how much damage he does when flanking an enemy and dealing full Sneak Attack damage(which nets him an additional +2 to attack). We’ll be using this formula, as presented in the DPR Olympics thread on the Paizo boards.

The damage formula is 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.

So our variables are now:

h=.75 (+19 against a target AC of 24 means a 75% chance to hit)

d=11.5 (1d6 (3.5) + 8)

s=17.5 (5d6)

t=.1 (19-20 threat range means a 10% chance to critical threat)

c=1 (x2 bonus)

This means our equation is…

  

.75(11.5+17.5)+((.1)(1)(.75)(11.5)

Which means 22.6125

But he gets 2 attacks at +19, so that instead becomes 45.225

But we’re not done yet. The rogue still gets 2 more attacks, albeit at a +14 bonus.

Without going through all the math again, we’ll jus say that he now has a 50% chance to hit, since that’s the only changing variable, meaning our DPR for these two attacks comes out to…

15.075 each, or a total of 30.15 together.

Now, when we add all this damage together, we get…

DPR=75.375

That’s pretty far off my original estimate. And it’s much higher than the fighter’s average damage per round. However, let’s examine this for a second.

The rogue hits with his first two attacks 75% of the time. His second two attacks hit 50% of the time. This means that he has an average chance to hit of 62.5%.

The fighter, on the other hand, has a massive +26 attack bonus while flanking. This means that, at 2 attacks per round, he’s hitting 95% of the time on his first attack (since he always misses on a natural 1), and an 85% chance of the time on his second attack. That gives him an average chance to hit of 90%.

Let’s take note that the fighter’s DPR is somewhere around 59.25. This means that while the rogue might be out-damaging the fighter while flanking, it’s definitely not hitting as often. And the nature of Sneak Attack damage (you have to roll it) means that the damage it will be dealing won’t be nearly as consistent.

However, that’s not all our rogue can do. With my alterations, he still gets a nifty little boost to his damage even when not flanking. 2d6 damage, to be precise. So let’s see what he can do with that, shall we?

I’m not writing everything out again, but I’ll let you know what has changed:

d=.65 and .4 now (65% and 40%), since we’re no longer flanking

s=7 now, since we’ve only got 2d6 to roll.

And our final equations are…

.65(11.5+7)+((.1)(1)(.65)(11.5))

And

.4(11.5+7)+((.1)(1)(.4)(11.5))

Meaning that our total DPR is…

41.265

That seems good to me, especially since the rogue is only going to be hitting an average of 52.5% of the time.

Well…there it is. In black and white.

Keep in mind, all of you who read this and thought “Oh, hell. This guy is a total min/max-er. He doesn’t really understand the game at all” that this is an optimized rogue, and I have a feeling that most rogues, even with my modifications to the class, aren’t going to get anywhere near this kind of damage. I can assure you that I would almost never use a build like the one presented above in a real game. I’m far too much of a fan of rapiers and fencing rogues to go the “two-weapon meat grinder” route every time I build a rogue.

I don’t know that you all needed to know the exact DPR of these modifications. But I did, and I might as well share them.

Thanks for reading, if you did…

-Chris