Esker
Hero
I see a lot of online discussion of different DPR-oriented builds that implicitly or explicitly accept some conventional wisdom about certain classes or feats being required to be optimized. I've read more than once statements to the effect that top tier DPR is reserved for builds with either Sharpshooter or Great Weapon Master. Also that rogues might start strong, but fall behind other martial classes in damage later unless they multiclass.
As a player with a fondness for the rogue class, and also an instinctively contrarian attitude toward both conventional wisdom and oversimplified calculations, I thought I'd do a numerical comparison of expected DPR between two single class builds, both of which make reasonable build decisions given their concept, but one of which is a pretty conventional DPR build and the other of which is, I think, generally considered to derive much of its value not from DPR but from its other utility.
Build 1: Eldritch Knight Archer
This character will be focused on DPR feats and spells. We'll obviously take the archery fighting style and the usual archer feats: crossbow expert, sharpshooter, and elven accuracy, as well as maxing our DEX, and taking Magic Initiate (Warlock) for Hex. We can have all of these things by level 14. We'll also assume an Owl familiar is available and will consistently take the Help action to give us advantage on our first attack on our turn, and that Haste is used instead of Hex if it would yield higher average DPR.
Build 2: Melee Arcane Trickster
This character will choose between a rapier with booming blade and two shortswords, as dicated by average DPR. They will also have a help-bot familiar, and pick up shadow blade and haste when they can, using whichever is better from a damage perspective. They'll also take elven accuracy and max DEX, which can be achieved by level 8, leaving them two spare ASIs or feats before level 14, which they could use to, for example, grab Tough and Resilient (CON), to compensate for their lower hit die and greater susceptibility to getting targeted than the archer.
Place Your Bets!
So, we've controlled for a bunch of things here: both characters are 1/3 casters with access to the same spell list (find familiar, shield, haste, mirror image, etc.). Both have elven accuracy and a maxed attack stat. They even have mostly the same pool of limited resources in their spell slots (action surge aside). So which one will do more damage over the course of an adventuring day?
It's obvious, right? The Eldritch Knight is considered one of the best single-classed archers in the game (probably rivaled only by the Battlemaster), and the crossbow expert + sharpshooter combo is considered the best archery setup. Throw in elven accuracy and an owl familiar... this character should wipe the floor with a mere rogue.
Well... let's do the math.
Methodology Notes: I'm going to set aside potential damage derived from off-turn attacks, as well as the possibility of the extra movement damage from Booming Blade, since these are situational. The rogue could use Haste and a readied action to get an off-turn sneak attack, but I'm not factoring that in. I'm also not factoring in synergies with other party members. That obviously matters, but is hard to account for. In any case, these other factors are likely to favor the rogue more than the fighter, so keep that in mind if you want.
I'll assume an enemy AC of 18, which should be reasonable at this tier.
Math: Eldritch Knight
At level 14, the EK has four attacks with a hand crossbow, one with advantage, and either a fifth from Haste or an extra 1d6 on each of the first four from Hex. With 20 DEX, +5 proficiency, and archery style, they'll have +12 to hit with a normal attack, or +7 with a sharpshooter power attack.
Against 18 AC, that's a 75% chance to hit with a normal attack with no advantage, and a 50% chance with a power attack. With advantage (and elven accuracy), those numbers go up to 98.4% and 87.5% respectively. On a hit, a normal attack will do 1d6+5, or 8.5 without Hex, and 12 with Hex. A power attack adds 10 to that, for 18.5 without Hex and 22 with Hex. It turns out we're better off always power attacking even when we don't have advantage. Hex and Haste yield almost exactly the same average DPR, so we'll assume Hex since it's a lower level spell slot and we're being purely offense-minded. I'll leave those claims as exercises for the reader, and assume below that we're always power attacking and have Hex up.
Attack 1: 0.875 * 22 = 19.3 eDPR
Attacks 2-4: 0.500 * 22 = 11.0 eDPR each
Total: 52.3 eDPR
Wait, but that doesn't factor in crits. With advantage we have a 14.3% chance to crit (and obviously 5% without) for an additional 7 damage on average per crit. That's 1.0 extra damage on average on the first attack and 0.35 on the next three, so about an extra 2 damage per round on average from crits.
Bottom Line: ~54 eDPR
Caveats: Once per short rest, action surge gives another three attacks without advantage, for an extra 34ish extra damage on average. A downside adjustment is that Hex uses a bonus action each time you select a new target, costing you 11ish damage on those turns. It seems reasonable to call these two things an approximate wash.
Math: Arcane Trickster
This character is either doing a single attack if using shadow blade, or two with a rapier if using Haste (only one of which can use booming blade). They could make an off-hand attack, but that's not a good option if not using Haste since it requires giving up Booming Blade; and even if using Haste is only going to add a little bit of damage.
Shadow Blade at a 2nd level slot and Haste at a 3rd level slot are pretty comparable for this character if they're already getting advantage from their owl (with a roughly 2 point edge for Haste). But let's just go with the 2nd level Shadow Blade.
With a +10 to hit, we have a 65% base chance to hit, going up to 95.7% with advantage.
Weapon Dice: 2d8 (average 9)
Booming Blade Dice: 2d8 (average 9)
Sneak Attack Dice: 7d6 (average 24.5)
Static Damage: +5
Total Per Hit: 47.5 on average
Average Per Round: 0.957 * 47.5 = 45.5
However, we have that 14.2% to crit, and do an extra 42.5 on average if we do crit, so on average we're doing 6 extra damage per round from crits.
Bottom Line: ~51 eDPR (going up to 56 when using a 3rd level spell slot)
Caveats: This character is using a second level spell slot each combat encounter compared to the fighter's 1st level slot. And they clearly lose much more when the owl is unavailable (though if in dim conditions they will still get advantage from shadow blade, and at this level they have versatile trickster as well). Conversely the fighter gains a lot if they can get a full turn source of advantage. Moreover they have less to gain from a weapon with a plus modifier. On the upside they are doing mostly psychic damage.
A Counterintuitive Result
The rogue at level 14 is, with a few caveats, doing nearly identical average damage compared to an optimized archer build much of the time (and in case you're wondering, no, the GWF+GWM+PAM eldritch knight isn't any better, though a battlemaster archer may well be), with only a single feat invested in damage vs the fighter's three. To be clear, this does not mean the rogue is equally good at killing things. Apart from the greater dependence on familiar help, the fact that the rogue's damage is single target, is more tied up in dice instead of static bonuses, and relies more on crits means they will put out more overkill damage as well as having more turns where they significantly underperform their average output. But the non-damage features they get are fantastic: expertise in 4 skills, cunning action (note that they aren't using their bonus action for anything right now, save the initial shadow blade cast), uncanny dodge, evasion, magical ambush, and reliable talent. Indomitable is lovely too, but I'll take the rogue's stack any day.
What About Level 20?
Out of curiosity, what happens if we project all of this up to level 20, when the fighter gets their fourth attack? The rogue gets a few more sneak attack dice and one more booming blade die in the mean time. Adjusting the enemy AC to 20, the rogue actually comes out ahead at this point, even when using only a 2nd level spell slot: about 66 eDPR vs the fighter's 60. Using a 3rd level shadow blade gets the rogue over 71, whereas the fighter using Haste doesn't improve compared to Hex. Now if the fighter has a +3 hand crossbow at this point, that's a whole other story, but still.
As a player with a fondness for the rogue class, and also an instinctively contrarian attitude toward both conventional wisdom and oversimplified calculations, I thought I'd do a numerical comparison of expected DPR between two single class builds, both of which make reasonable build decisions given their concept, but one of which is a pretty conventional DPR build and the other of which is, I think, generally considered to derive much of its value not from DPR but from its other utility.
Build 1: Eldritch Knight Archer
This character will be focused on DPR feats and spells. We'll obviously take the archery fighting style and the usual archer feats: crossbow expert, sharpshooter, and elven accuracy, as well as maxing our DEX, and taking Magic Initiate (Warlock) for Hex. We can have all of these things by level 14. We'll also assume an Owl familiar is available and will consistently take the Help action to give us advantage on our first attack on our turn, and that Haste is used instead of Hex if it would yield higher average DPR.
Build 2: Melee Arcane Trickster
This character will choose between a rapier with booming blade and two shortswords, as dicated by average DPR. They will also have a help-bot familiar, and pick up shadow blade and haste when they can, using whichever is better from a damage perspective. They'll also take elven accuracy and max DEX, which can be achieved by level 8, leaving them two spare ASIs or feats before level 14, which they could use to, for example, grab Tough and Resilient (CON), to compensate for their lower hit die and greater susceptibility to getting targeted than the archer.
Place Your Bets!
So, we've controlled for a bunch of things here: both characters are 1/3 casters with access to the same spell list (find familiar, shield, haste, mirror image, etc.). Both have elven accuracy and a maxed attack stat. They even have mostly the same pool of limited resources in their spell slots (action surge aside). So which one will do more damage over the course of an adventuring day?
It's obvious, right? The Eldritch Knight is considered one of the best single-classed archers in the game (probably rivaled only by the Battlemaster), and the crossbow expert + sharpshooter combo is considered the best archery setup. Throw in elven accuracy and an owl familiar... this character should wipe the floor with a mere rogue.
Well... let's do the math.
Methodology Notes: I'm going to set aside potential damage derived from off-turn attacks, as well as the possibility of the extra movement damage from Booming Blade, since these are situational. The rogue could use Haste and a readied action to get an off-turn sneak attack, but I'm not factoring that in. I'm also not factoring in synergies with other party members. That obviously matters, but is hard to account for. In any case, these other factors are likely to favor the rogue more than the fighter, so keep that in mind if you want.
I'll assume an enemy AC of 18, which should be reasonable at this tier.
Math: Eldritch Knight
At level 14, the EK has four attacks with a hand crossbow, one with advantage, and either a fifth from Haste or an extra 1d6 on each of the first four from Hex. With 20 DEX, +5 proficiency, and archery style, they'll have +12 to hit with a normal attack, or +7 with a sharpshooter power attack.
Against 18 AC, that's a 75% chance to hit with a normal attack with no advantage, and a 50% chance with a power attack. With advantage (and elven accuracy), those numbers go up to 98.4% and 87.5% respectively. On a hit, a normal attack will do 1d6+5, or 8.5 without Hex, and 12 with Hex. A power attack adds 10 to that, for 18.5 without Hex and 22 with Hex. It turns out we're better off always power attacking even when we don't have advantage. Hex and Haste yield almost exactly the same average DPR, so we'll assume Hex since it's a lower level spell slot and we're being purely offense-minded. I'll leave those claims as exercises for the reader, and assume below that we're always power attacking and have Hex up.
Attack 1: 0.875 * 22 = 19.3 eDPR
Attacks 2-4: 0.500 * 22 = 11.0 eDPR each
Total: 52.3 eDPR
Wait, but that doesn't factor in crits. With advantage we have a 14.3% chance to crit (and obviously 5% without) for an additional 7 damage on average per crit. That's 1.0 extra damage on average on the first attack and 0.35 on the next three, so about an extra 2 damage per round on average from crits.
Bottom Line: ~54 eDPR
Caveats: Once per short rest, action surge gives another three attacks without advantage, for an extra 34ish extra damage on average. A downside adjustment is that Hex uses a bonus action each time you select a new target, costing you 11ish damage on those turns. It seems reasonable to call these two things an approximate wash.
Math: Arcane Trickster
This character is either doing a single attack if using shadow blade, or two with a rapier if using Haste (only one of which can use booming blade). They could make an off-hand attack, but that's not a good option if not using Haste since it requires giving up Booming Blade; and even if using Haste is only going to add a little bit of damage.
Shadow Blade at a 2nd level slot and Haste at a 3rd level slot are pretty comparable for this character if they're already getting advantage from their owl (with a roughly 2 point edge for Haste). But let's just go with the 2nd level Shadow Blade.
With a +10 to hit, we have a 65% base chance to hit, going up to 95.7% with advantage.
Weapon Dice: 2d8 (average 9)
Booming Blade Dice: 2d8 (average 9)
Sneak Attack Dice: 7d6 (average 24.5)
Static Damage: +5
Total Per Hit: 47.5 on average
Average Per Round: 0.957 * 47.5 = 45.5
However, we have that 14.2% to crit, and do an extra 42.5 on average if we do crit, so on average we're doing 6 extra damage per round from crits.
Bottom Line: ~51 eDPR (going up to 56 when using a 3rd level spell slot)
Caveats: This character is using a second level spell slot each combat encounter compared to the fighter's 1st level slot. And they clearly lose much more when the owl is unavailable (though if in dim conditions they will still get advantage from shadow blade, and at this level they have versatile trickster as well). Conversely the fighter gains a lot if they can get a full turn source of advantage. Moreover they have less to gain from a weapon with a plus modifier. On the upside they are doing mostly psychic damage.
A Counterintuitive Result
The rogue at level 14 is, with a few caveats, doing nearly identical average damage compared to an optimized archer build much of the time (and in case you're wondering, no, the GWF+GWM+PAM eldritch knight isn't any better, though a battlemaster archer may well be), with only a single feat invested in damage vs the fighter's three. To be clear, this does not mean the rogue is equally good at killing things. Apart from the greater dependence on familiar help, the fact that the rogue's damage is single target, is more tied up in dice instead of static bonuses, and relies more on crits means they will put out more overkill damage as well as having more turns where they significantly underperform their average output. But the non-damage features they get are fantastic: expertise in 4 skills, cunning action (note that they aren't using their bonus action for anything right now, save the initial shadow blade cast), uncanny dodge, evasion, magical ambush, and reliable talent. Indomitable is lovely too, but I'll take the rogue's stack any day.
What About Level 20?
Out of curiosity, what happens if we project all of this up to level 20, when the fighter gets their fourth attack? The rogue gets a few more sneak attack dice and one more booming blade die in the mean time. Adjusting the enemy AC to 20, the rogue actually comes out ahead at this point, even when using only a 2nd level spell slot: about 66 eDPR vs the fighter's 60. Using a 3rd level shadow blade gets the rogue over 71, whereas the fighter using Haste doesn't improve compared to Hex. Now if the fighter has a +3 hand crossbow at this point, that's a whole other story, but still.
