5E Monoclass DPR Comparison: Eldritch Knight Archer vs Melee Arcane Trickster

Esker

Explorer
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.
 

Esker

Explorer
I realized toward the end of this writeup that I was not using magic initiate correctly: the eldritch knight would only have one use of Hex per day, since it is not on their spell list and so they can't use their own slots for it. They can cast Haste instead for similar damage a couple more times a day, but after those three fights they've got to do something else with their concentration. Are there other spells that would be good archer buffs that I'm forgetting about? This has me even more convinced that the battlemaster is going to do better here as a single classed comparison goes.
 

Gavin O.

Visitor
I feel like for an Arcane Trickster, you're better off using Haste instead of Shadow Blade when you get it. If you're hasted, you can ready a Booming Blade to use on another creature's turn and use the additional action from Haste to attack on your turn, which triggers sneak attack twice.
 

Esker

Explorer
I feel like for an Arcane Trickster, you're better off using Haste instead of Shadow Blade when you get it. If you're hasted, you can ready a Booming Blade to use on another creature's turn and use the additional action from Haste to attack on your turn, which triggers sneak attack twice.
I did include a note about readying an action to get a second sneak attack (it's a long post though, no worries). However, RAW you can't ready a booming blade while hasted, since readying a spell uses concentration. So at level 14 you give up 2d8 (~9) to gain 7d6 (24.5), netting 15.5 times your chance to hit (0.65 in this example, so roughly 10 eDPR) over using your main and hasted action to attack on your turn. But haste starts out down a few points compared to a 3rd level shadow blade to begin with, so you're really only gaining 7ish damage by spending your reaction that way, and need to leave yourself adjacent to the enemy with no reaction for shield or uncanny dodge to get it. I don't personally make a habit of that when hasted as a rogue, but it's a matter of style I suppose. You do get the +2 AC from haste that you don't get from shadow blade, but you have that if you attack on your turn too.
 

Gavin O.

Visitor
I did include a note about readying an action to get a second sneak attack (it's a long post though, no worries). However, RAW you can't ready a booming blade while hasted, since readying a spell uses concentration. So at level 14 you give up 2d8 (~9) to gain 7d6 (24.5), netting 15.5 times your chance to hit (0.65 in this example, so roughly 10 eDPR) over using your main and hasted action to attack on your turn. But haste starts out down a few points compared to a 3rd level shadow blade to begin with, so you're really only gaining 7ish damage by spending your reaction that way, and need to leave yourself adjacent to the enemy with no reaction for shield or uncanny dodge to get it. I don't personally make a habit of that when hasted as a rogue, but it's a matter of style I suppose. You do get the +2 AC from haste that you don't get from shadow blade, but you have that if you attack on your turn too.
Right, I forget that readying a spell breaks your concentration.
 

doctorbadwolf

Heretic of The Seventh Circle
Interesting! How does the AT rogue compare to a Swashbuckler with Magic Initiate (for BB and Find Familiar) and a rapier? (Or thief, I guess, but SB has much better ability to hit and run without reprisal, and is more likely to get the secondary BB damage as a result)
 

Esker

Explorer
Interesting! How does the AT rogue compare to a Swashbuckler with Magic Initiate (for BB and Find Familiar) and a rapier? (Or thief, I guess, but SB has much better ability to hit and run without reprisal, and is more likely to get the secondary BB damage as a result)
In other words take the above but remove shadow blade? I was assuming a 2nd level slot, so the extra d8 is worth about 5 average damage there (4.5 * (to-hit + to-crit)). So the rapier-wielding swashbuckler with owlvantage would get about 46 eDPR at level 14.

But using a rapier doesn't really take advantage of fancy footwork, since the arcane trickster can already disengage with their bonus action (granted, if using shadow blade, they can't do that on the turn they cast it). What fancy footwork buys you is the ability to quasi-disengage while also making an offhand attack. If you don't have a source of advantage, that second attack is valuable because it raises the chance of landing your sneak attack by up to 25 percentage points. But if you're assuming familiar help, particularly with elven accuracy, it's worse than a single rapier: shave off ~1 eDPR for having to downgrade your main hand to a shortsword, lose ~9 eDPR because booming blade doesn't allow an offhand attack, then add back (3.5 * to-hit + to-crit) for the offhand attack. On net you're down about 7 damage on average compared to rapier + BB (though you can spread your damage between two targets if you want, which is worth something).
 

doctorbadwolf

Heretic of The Seventh Circle
In other words take the above but remove shadow blade? I was assuming a 2nd level slot, so the extra d8 is worth about 5 average damage there (4.5 * (to-hit + to-crit)). So the rapier-wielding swashbuckler with owlvantage would get about 46 eDPR at level 14.

But using a rapier doesn't really take advantage of fancy footwork, since the arcane trickster can already disengage with their bonus action (granted, if using shadow blade, they can't do that on the turn they cast it). What fancy footwork buys you is the ability to quasi-disengage while also making an offhand attack. If you don't have a source of advantage, that second attack is valuable because it raises the chance of landing your sneak attack by up to 25 percentage points. But if you're assuming familiar help, particularly with elven accuracy, it's worse than a single rapier: shave off ~1 eDPR for having to downgrade your main hand to a shortsword, lose ~9 eDPR because booming blade doesn't allow an offhand attack, then add back (3.5 * to-hit + to-crit) for the offhand attack. On net you're down about 7 damage on average compared to rapier + BB (though you can spread your damage between two targets if you want, which is worth something).
I’d say rapier + BB and familiar is flat better than TWF, even if the damage were exactly equal. For one thing, you can let the familiar Help others on many rounds, since you can move freely and then hide as a bonus action, but you also can always dash, almost any round you need to, basically guaranteed. That means no rounds spent not attacking, and it means more room to make enemies choose between taking BB secondary damage, and staying put and taking suboptimal actions.

IME, a Swashbuckler or rogue with Mobile gets BB off significantly more times per combat.

I also wonder just how much of an impact Mage Slayer and War Caster have on spell casting rogues, but those are harder to accurately quantify.
 
I think you are vastly overestimating the amount of time you will get advantage. Familiars did all the time. Once your familiar is gone your source of advantage is gone. This benefits the rogue more than the fighter

you also ignore the fighters action surge which is a fairly large equalizer. 3 extra attacks per short rest average to 9 attacks per day. That’s a significant daily damage boost
 
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Esker

Explorer
I think you are vastly overestimating the amount of time you will get advantage. Familiars did all the time. Once your familiar is gone your source of advantage is gone. This benefits the rogue more than the fighter
This feels like a familiar caveat (pun certainly intended)...

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).
Owlvantage is clearly very much an issue of YMMV. My arcane trickster gets it a lot, as the DM rarely tries to kill the owl (smart owl tactics help too: it's generally pretty obvious if the enemy is readying a melee attack to swipe at it during a flyby, so just don't that round; then they waste their action which is even better than advantage. As for AoEs, camping out directly above the enemy is pretty useful to avoid those, since any AoE that would hit the owl either would also hit the caster or wouldn't hit any other party members. And how many enemies are going to spend a fireball just to kill a familiar, or fireball themselves to kill a familiar?

But again, even aside from the owl, the shadow blade wielding arcane trickster has a lot of other possible sources of advantage: dim light, versatile trickster, and anything an ally might do. Using the owl to help only to fill in the gaps likely also helps the familiar survive.

you also ignore the fighters action surge which is a fairly large equalizer. 3 extra attacks per short rest average to 9 attacks per day. That’s a significant daily damage boost
Not ignoring it...

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.
Not to mention, I did this analysis based on Hex assuming that the eldritch knight was using it all the time, but since the build in question got it from magic initiate, they can actually only use it an hour a day. So I was overstating the EK's damage a bit.
 
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TwoSix

The hero you deserve
Excellent analysis! My takeaway from this is:

1) In the most common situation, one attack per round with advantage, archer fighters and rogues are pretty similar in damage.
2) Fighters scale better with full round advantage, a fighter against a disabled boss is going to turn it into a pincushion.
3) Fighters lose less when they don't have advantage, although rogues have multiple utilities to gain advantage if their main trick is negated.
4) Basically, rogues are pretty competitive damage dealers. Fighters scale better when things go their way, and have the advantage of range, but rogues have lots of extra utility to compensate when things aren't going their way.
 
This feels like a familiar caveat (pun certainly intended)...



Owlvantage is clearly very much an issue of YMMV. My arcane trickster gets it a lot, as the DM rarely tries to kill the owl...
I rest my case. If your DM doesn't attempt to kill your familiar then it likely is enough to put AT fully ahead.

But again, even aside from the owl, the shadow blade wielding arcane trickster has a lot of other possible sources of advantage: dim light, versatile trickster, and anything an ally might do. Using the owl to help only to fill in the gaps likely also helps the familiar survive.
Sure. I'm just saying the Owl won't be the primary source of the advantage in typical games. It will die, especially in tier 3 fights. If it isn't then DM is simply allowing it to live. That's fine but don't expect your whiteroom to be taken seriously if you are going into it with that assumption.

Not ignoring it...
You discounted it. The beauty of Action Surge is that you can start the fight and use it on turn 1 which makes a character like the rogue have to play major catchup the rest of the fight even if his DPR is slightly higher. Damage Now > Damage Later

Not to mention, I did this analysis based on Hex assuming that the eldritch knight was using it all the time, but since the build in question got it from magic initiate, they can actually only use it an hour a day. So I was overstating the EK's damage a bit.
Yep. That's why EK's really aren't all that special at damage (they are damn hard to kill though). Now a Battlemaster gets a lot more bang offensively (or even a Samauri).

However, the biggest flaw in your calculations is your assumption of 100% advantage for the AT. Dropping advantage down to 50% of the time drops DPR down to 42. That's probably a more realistic assumption IMO.

An EK without hex and never any advantage does 41 DPR. A Battlemaster does 53 (with precision attack and no advantage). Throw on some additional chance to hit or damage bonuses or even advantage and the battlemaster's damage will skyrocket.

That said, all this is without the haste off-turn attack for the AT...
 
Excellent analysis! My takeaway from this is:

4) Basically, rogues are pretty competitive damage dealers.
Past tier 1 rogues start sucking at damage. The only exception is the AT and that's solely because of booming blade and shadow blade. (till haste)
 

Gammadoodler

Explorer
I'm curious if there is a way to take an inability to engage at range into these calculations. I understand that the rogue is still a dex based class so they can just carry a hand crossbow or something. Just that they'll miss out on the feat support and the spell damage that seem to be propping the damage calcs thus far.

I understand that this isn't an issue exclusive to the rogue but leaving it out feels like we're making an apples to oranges comparison as a best case scenario.
 

Esker

Explorer
I'm curious if there is a way to take an inability to engage at range into these calculations. I understand that the rogue is still a dex based class so they can just carry a hand crossbow or something. Just that they'll miss out on the feat support and the spell damage that seem to be propping the damage calcs thus far.

I understand that this isn't an issue exclusive to the rogue but leaving it out feels like we're making an apples to oranges comparison as a best case scenario.
It's a very fair point. You expect a melee character to be able to do more damage, because they're taking more personal risk, and being at greater risk requires more investment in personal defense, perhaps at the expense of versatility. In the example, the AT had a spare feat, which I assumed would be spent on something like Tough, to boost their HP. But they already have a number of rogue abilities that help them avoid damage, like cunning action disengage and uncanny dodge (note that in the build I outlined, the rogue has their bonus action just sitting there). So they could instead spend that feat making themselves a better ranged combatant by taking crossbow expert. Alternatively, they could take something like Mobile, to reduce the number of situations where they're forced to engage from range: dash up to 80 feet and attack, and use any leftover movement to pull back again. Finally, as an arcane trickster, if they can't close to attack, maybe they can hide and cast a spell with disadvantage on the save (though that really is apples-to-oranges).

But even if they do none of that, and just hang back and just take a single shot with a longbow, they're still doing ok when they can get advantage (hiding or familiar): 37 eDPR, with zero investment in any archery-specific features. The EK with their fighting style and two feats invested in archery (if we take away Hex, which I used wrong), does 45 eDPR with advantage on the first shot, which they are going to have a harder time getting than the rogue, since they can't hide as a bonus action (and also don't have stealth expertise).

Add in crossbow expert for the rogue, that brings them up to 43 eDPR with familiar help; 35 without any source of advantage.

Alternatively, the rogue could take sharpshooter, and use it to throw their shadow blade 60', ignoring cover (which would be a problem for them otherwise), for 42 eDPR when the familiar is up, and fall back on hiding with the longbow for 39 eDPR when the familiar is gone (maybe with a debuff thrown in, since they're not using concentration for anything in this case).

It's interesting to note that if they can be hasted, the AT might choose to stay at range so they can more comfortably spend their reaction readying a second attack. In this case, as long as they have a way to get sneak attack, the rogue with a longbow is even with the hasted EK at 54 eDPR (when both have advantage on one attack), and even with no source of advantage whatsoever, the hasted rogue gets 47 eDPR this way, which is also even with the hasted EK with no advantage. This is more of a side note to your point though, since if the rogue is in range by necessity rather than by choice, they likely can't get sneak attack if they don't have advantage.

Point is, a melee rogue is not bad at range even with no investment, and they have options to be better if they want, without sacrificing any melee offense. For big fights when they can afford to use Haste and spend their reaction readying a second sneak attack, they are dead even.

By contrast, what happens if the EK has to enter melee? They can make very good use of shadow blade too, making three attacks with it to the rogue's one, but if not in dim light, they're only doing 34 eDPR to the rogue's 51. Even in dim light, they only get up to 44, which is less than the rogue gets without shadow blade (provided they get advantage some other way).

What's the bottom line? I'm not trying to argue that the arcane trickster stands toe-to-toe with a fighter in doing damage. Under the right conditions they can, but the right conditions are narrower for them. Which is fine, because they bring vastly more to a party out of combat than a fighter. My point in writing this post in the first place was just to examine the notion that single classed rogues aren't good at doing damage at higher levels. Yes, they're dependent on getting that advantage. And yes, certain sources of advantage (namely, those that apply to all attacks in a turn) will enable the fighter to pull well ahead. But under a reasonably common circumstance of one attack per round with advantage, rogues really can be workhorse DPR members.
 

Esker

Explorer
Past tier 1 rogues start sucking at damage. The only exception is the AT and that's solely because of booming blade and shadow blade. (till haste)
That's overstating the case. Look at level 5, and let's compare a wood elf inquisitive rogue (widely considered a weak rogue subclass for combat) that uses a longbow and takes elven accuracy to a vuman fighter with GWF style, and PAM and GWM feats.

The rogue archer will usually get advantage on their one attack, given their ability to hide in lots of places. At a base 60% to hit, elven accuracy gives them a 96% chance to hit, with an average of 1d8+3d6+4 damage (19) per hit, plus a 14% chance to crit for an extra 1d8+3d6 (15). That's 20.3 eDPR at level 5. Meanwhile, the fighter gets three attacks, two at 1d10+13 and one at 1d4+13, at 35% to hit, which is 19.9 eDPR (after crits and rerolling 1s and 2s).

This is without either character using any resources. Obviously if the fighter is using resources to get advantage or reaction attacks, they'll pull ahead, but only when they (a) have those resources available and (b) are successful at getting advantage / reaction attacks (e.g., the opponent fails their trip attack save).

The vuman barbarian who takes PAM and GWM and always attacks recklessly is probably the single highest sustained DPR build, and can post truly outlandish at will damage (31.6 eDPR without rage, 36.1 with, at level 5). But not keeping up with that isn't tantamount to "sucking at damage", if you ask me.
 
That's overstating the case. Look at level 5, and let's compare a wood elf inquisitive rogue (widely considered a weak rogue subclass for combat) that uses a longbow and takes elven accuracy to a vuman fighter with GWF style, and PAM and GWM feats.

The rogue archer will usually get advantage on their one attack, given their ability to hide in lots of places. At a base 60% to hit, elven accuracy gives them a 96% chance to hit, with an average of 1d8+3d6+4 damage (19) per hit, plus a 14% chance to crit for an extra 1d8+3d6 (15). That's 20.3 eDPR at level 5. Meanwhile, the fighter gets three attacks, two at 1d10+13 and one at 1d4+13, at 35% to hit, which is 19.9 eDPR (after crits and rerolling 1s and 2s).

This is without either character using any resources. Obviously if the fighter is using resources to get advantage or reaction attacks, they'll pull ahead, but only when they (a) have those resources available and (b) are successful at getting advantage / reaction attacks (e.g., the opponent fails their trip attack save).

The vuman barbarian who takes PAM and GWM and always attacks recklessly is probably the single highest sustained DPR build, and can post truly outlandish at will damage (31.6 eDPR without rage, 36.1 with, at level 5). But not keeping up with that isn't tantamount to "sucking at damage", if you ask me.
I don't overstate cases.

The following chart assumes a fighter uses precision attack on near misses (until dice are expended which takes about 20+ rounds on average to do so) and that the rogue always gets advantage with elven accuracy. The fighter has SS + CE. The rogue has a longbow and elven accuracy always up. *Note crits were included. The chart shows how far behind in damage the rogue will be in perfect conditions. Truth is he won't have advantage every round and that will considerably cut into his expected damage output.

Capture21.PNG

The archer rogue is no where near the battlemaster fighter in damage at level 5.

Feel free to ask any questions if you want to know where any numbers came from
 
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Esker

Explorer
I don't overstate cases.
I'm assuming that is meant as tongue-in-cheek, since it's such a broad statement that it's very nearly proof of its own falsehood. Pretty much everyone overstates cases from time to time! I certainly do!

Feel free to ask any questions if you want to know where any numbers came from
Ok, I'm not able to quite replicate your numbers, but I come close in the end, but with a lower number before precision attack is factored in, and a greater impact of precision attack. Let me know if the following is close to how you are calculating things.

Here's my reasoning, walking through AC 16 which at level 5 was the reference AC I was using (since it corresponds to a baseline to-hit of 60% assuming +4 in the attack stat by level 5).

The fighter archer with 16 DEX should have a base attack bonus of +3+3+2 (proficiency + DEX + archery style), which becomes +3 when using the -5/+10. So to hit AC 16 they will need to roll a natural 13, which is a 40% to-hit chance, not 55%.

So before factoring in precision attack and action surge, they have DPR of 3 * (0.40 * 16.5 + 0.05 * 3.5) = 20.3, not 27.8.

Over 20 rounds, assuming two short rests and thus three action surges, they will have effectively 23 rounds of this, for a total of 23 * 20.3 = 467.

I'm not sure what your intended threshold for a "near miss" is to trigger a use of precision attack, but supposing 20 attacks per short rest, if rolls are perfectly uniformly distributed (which they aren't, but fine), if you use a die any time you're within 4 of a hit (so that it has a better than 50% chance of making a difference), that should happen on average about 4 times per short rest, which is exactly the number of superiority dice you have. Ok, so say you're within 1 once, within 2 once, within 3 once, and within 4 once (since each is equally likely), then you turn about 3.25 misses into hits per short rest, or 9.75 per day, for a total of 9.75 * 16.5 = 161 extra damage from precision attack (not bad!), assuming a picture-perfect distribution of turns and rests throughout the day. So that takes us to 628 total damage, or 31.4 per round. Somehow that's really close to your bottom line, so something must have cancelled out somewhere?

The rogue, meanwhile, vs 16 AC has a 93.6% chance to hit (not 90.9%), because elven accuracy boosts their DEX to 18, so they're working with a base 60% chance vs the fighter's 55%. Their damage on a hit is 19, not 18. So they're doing 0.936 * 19 + 0.1426 * 15 = 19.9 DPR.

So the battlemaster archer, when everything is included, comes out about 58% ahead against a reference AC; more against lower AC, less against higher AC. (Note that they're probably optimized in the wrong direction re: difficulty of opponent; all else equal you'd like to be doing relatively better against tougher enemies, since those are the ones where DPR matters more, though I recognize that AC is an imperfect reflection of encounter difficulty)

So yes, fine, the best fighter archetype meticulously optimized and using their resources very efficiently can do significantly more damage than a baseline rogue when both are using their favorite weapon from a distance*. That's not a surprise. But it doesn't seem to establish "rogues suck at damage in tier 2". If doing 5/8 the damage of the carefully optimized battlemaster archer with the investment of half a non-weapon-specific feat constitutes "sucking at damage" then how many other classes "suck at damage"? Do agonizing blast + hex warlocks "suck at damage"? They're doing less than the rogue with 2 attacks at 60% to-hit and 5% to-crit, with 13 damage per hit and an extra 9 per crit, for a total of 16.5 eDPR.

*Here's something to think about: what happens if one of the other party members knocks a key foe prone? The rogue can do exactly the same damage if they run up and pull out a rapier (using their bonus action to dash if needed). But the battlemaster has to choose between (a) switching targets, (b) attacking at disadvantage, or (c) also running up and pulling out a rapier (if they can even reach). Being less feat-dependent than the fighter, the rogue is more flexible and adaptable, which is one of its main strengths.
 
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Ok, I'm not able to replicate your numbers, which overstate the fighter's damage slightly and understate the rogue's slightly (so much for not overstating cases?). I don't think they're too far off, but in the fighter's case they start out quite far off and then mostly catch up somehow, so I guess I'm curious about the logic.
The numbers are 100% correct. I'll be happy to explain my methodology.

Here's my reasoning, walking through AC 16 which at level 5 was the reference AC I was using (since it corresponds to a baseline to-hit of 60% assuming +4 in the attack stat by level 5).

The fighter archer with 16 DEX should have a base attack bonus of +3+3+2 (proficiency + DEX + archery style), which becomes +3 when using the -5/+10. So to hit AC 16 they will need to roll a natural 13, which is a 40% to-hit chance, not 55%.
I stated the fighter was using precision attack. Precision attack effectively adds about +3 to chance to hit over the entire adventuring day. Thus the fighter gets +3 to attack listed in his effective attack column over his actual attack - thus why I labeled the column effective attack instead of attack.

So before factoring in precision attack and action surge, they have DPR of 3 * (0.40 * 16.5 + 0.05 * 3.5) = 20.3, not 27.8.
I have no doubt you are right - but I was accounting for precision attack in that step.

Over 20 rounds, assuming two short rests and thus three action surges, they will have effectively 23 rounds of this, for a total of 23 * 20.3 = 467.
you left off the impact of precision attack

I'm not sure what your intended threshold for a "near miss" is to trigger a use of precision attack, but supposing 20 attacks per short rest, if rolls are perfectly uniformly distributed (which they aren't, but fine)
Rolling a d20 does form a uniform distribution

, if you use a die any time you're within 4 of a hit (so that you have at least a 50% chance of succeeding), that should happen on average about 4 times per short rest, which is exactly the number of superiority dice you have. Ok, so say you're within 1 once, within 2 once, within 3 once, and within 4 once (which is not how RNG works, but I'm making some idealizations too, so again, fine),
You've gotten the basic concept. Some days all your rolls will be 1 away from hitting. Some all will be 4 away from hitting etc. Etc. Overall though if you roll long enough you will expect to see very close to 1 in 20 misses by 1 and 1 in 20 misses by 2 etc.

then you turn about 2.5 misses into hits per short rest, or 7.5 per day, for a total of 7.5 * 16.5 = 123.75 extra damage from precision attack (not bad!), assuming a picture-perfect distribution of turns and rests throughout the day. So that takes us to 590.5 total damage, or 29.5 per round. Somehow that's really close to your bottom line, so something must have cancelled out somewhere?
You can attempt to turn it into damage that way - it loses some nuance that the basic +3 estimate was tuned with. Simulations helped a lot there. Basically using it optimally changes a bit between number of attacks and how many superiority dice you have and their size - but if you do use it more or less optimally (or close to that) then that's the expectation.

In the case of level 5, you would want to basically use it on misses of 1-4. So then on average when you use the dice you will turn ( 8/8+7/8+6/8+5/8 ) / 4 = 81.25% of misses into hits. (Of course you could run out a little early, so you also want to lower your near miss threshold a little if you use the dice to fast at the start). Anyways the miss by 4 or less strategy at level 5 equates to 9.75 misses turned into hits. Roughly 10 additional hits - Roughly 10 less misses. Do you know how many attacks a 5% chance of hit turns into a hit? 1 out of 20 = 3 out of 60. So for a standard adventuring day of 20 rounds (with 3 total attacks per round) then hitting with 9 additional attacks while missing with 9 fewer would be a +3 to hit. As you noted earlier, action surge essentially makes our day 23 rounds. We could factor that in and get it exactly precisely correct but it's much easier and plenty accurate to just remember the +3 attack for precision attack estimate.

The rogue, meanwhile, vs 16 AC has a 93.6% chance to hit (not 90.9%), because elven accuracy boosts their DEX to 18, so they're working with a base 60% chance vs the fighter's 55%. Their damage on a hit is 19, not 18. So they're doing 0.936 * 19 + 0.1426 * 15 = 19.9 DPR.
My calculations were with the PC's started with 16 dex. You are correct that having 18 dex would increase that slightly. Though if you want to get really nitpicky, do you know how much not having advantage on 25% of your turns will cause your DPR to drop? ALOT! Having advantage on most rounds but not all is a much more realistic expectation. I would use 75% of the time you will have it and 25% of the time you will not as my rule of thumb estimate but I wanted to show that even in the most idealized circumstances for the rouge the normal damage builds were far superior. I accomplished that goal.

So the battlemaster archer, when everything is included, comes out about 48% ahead against a reference AC; more against lower AC, less against higher AC. (Note that they're probably optimized in the wrong direction re: difficulty of opponent; all else equal you'd like to be doing relatively better against tougher enemies, since those are the ones where DPR matters more, though I recognize that AC is an imperfect reflection of encounter difficulty)
I don't know that we can really correlate really high ac with really difficult opponents. I think you'll fight plenty of really tough enemies in each segment of 15-20 AC's. Keep in mind encounters can be hard because of a number of weaker enemies as well instead of 1 large enemy.

So yes, fine, the best fighter archetype meticulously optimized and using their resources efficiently can do significantly more damage than a baseline rogue when both are using their favorite weapon from a distance*. That's not a surprise.
In all fairness - you were acting earlier like it was closer than people thought....

But it doesn't seem to establish "rogues suck at damage in tier 2". If doing 2/3 the damage of the carefully optimized battlemaster archer with the investment of half a non-weapon-specific feat constitutes "sucking at damage"
I didn't actually try to calculate a realistic value for the rogue. The rogues realistic value is certainly lower than what I calculated. Missing out on advantage on rounds will do that.

then how many other classes "suck at damage"? Do agonizing blast + hex warlocks "suck at damage"? They're doing less than the rogue with 2 attacks at 60% to-hit and 5% to-crit, with 13 damage per hit and an extra 9 per crit, for a total of 16.5 eDPR.
Yes. Eldritch Blast + Hex basically sucks at damage too. The biggest factor for it IMO isn't the at-will numbers, it's the lack of any kind of ability to front load the damage.

*Here's something to think about: what happens if one of the other party members knocks a key foe prone? The rogue can do exactly the same damage if they run up and pull out a rapier (using their bonus action to dash if needed). But the battlemaster has to choose between (a) switching targets, (b) attacking at disadvantage, or (c) also running up and pulling out a rapier (if they can even reach).
Pick option d) run up to being 5ft away and shoot with hand crossbows. You will have advantage due to being 5ft away from a prone enemy and disadvantage for firing into melee. This will cancel out leaving you with a normal attack.

More importantly though, your no longer arguing about the rogues damage but whether there's some edge cases where the rogue is better than the damage number shows. I certainly agree. An archer rogue (even without elven accuracy) is by no means a bad character. It's effective in combat, packs great out of combat skills and is tons of fun to play. It doesn't take high damage output to be effective in combat. Only moderate.


Being less feat-dependent than the fighter, the rogue is more flexible and adaptable, which is one of its main strengths.
Fighters have more feats though. They literally can take such feats and not be set back like other classes. But this sounds more like you are justifying playing a rogue when that doesn't need justified. Rogues don't suck. They are awesome. It's just rogues damage is just not impressive (outside having haste).

Pick option d) run up to being 5ft away and shoot with hand crossbows. You will have advantage due to being 5ft away from a prone enemy and disadvantage for firing into melee. This will cancel out leaving you with a normal attack. --- actually scrap that, you have crossbow expertise, you will have advantage
 
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Esker

Explorer
The numbers are 100% correct. ... You've gotten the basic concept. ... Do you know how many attacks a 5% chance of hit turns into a hit?
I don't know if you realize it or not, but when you say things like this (and things like "I don't overstate cases") it comes across as pretty arrogant and condescending. I don't think I was doing the same; maybe I was, but if so I didn't mean to be.

Rolling a d20 does form a uniform distribution
In probabilities, but not in actual rolls, which is what I was referring to. The reason this may matter is that by conserving your superiority dice for near misses like that you run the risk of not using them all, because you might not have enough rolls that miss by 4 or less. In fact, that will happen about half the time (the other half of the time you will burn through them quickly, which doesn't balance out the other case since it's a finite resource). That's why your calculation is optimistic, because you are finding an optimal threshold to use and then assuming you will be able to use your dice optimally in practice, which isn't going to be the case in general. It probably doesn't make a huge difference, but it's one reason why I think it muddies things to treat precision attack dice as a fixed boost to your to-hit chance instead of thinking about it in terms of an expected number of attacks that go from misses to hits.

In the case of level 5, you would want to basically use it on misses of 1-4. So then on average when you use the dice you will turn ( 8/8+7/8+6/8+5/8 ) / 4 = 81.25% of misses into hits. (Of course you could run out a little early, so you also want to lower your near miss threshold a little if you use the dice to fast at the start). Anyways the miss by 4 or less strategy at level 5 equates to 9.75 misses turned into hits.
Yeah, we had crossed edits there. I realized I was adding 1+3/4+1/2+1/4 for some reason to get 2.5 instead of 1+7/8+6/8+5/8 to get 3.25, but fixed it in the edit.

Though if you want to get really nitpicky, do you know how much not having advantage on 25% of your turns will cause your DPR to drop? ALOT!
Not all that much. The rogue loses about 2 DPR at level 5.

I don't know that we can really correlate really high ac with really difficult opponents. I think you'll fight plenty of really tough enemies in each segment of 15-20 AC's. Keep in mind encounters can be hard because of a number of weaker enemies as well instead of 1 large enemy.
Right, hence the "all else equal" qualifier in my statement. But on average, if you divide up the encounters you see in a day into easy, medium and hard, I would bet that the hard ones consist of higher ACs generally than the easy ones.

In all fairness - you were acting earlier like it was closer than people thought....
I mean, it is (in terms of averages) if you don't artificially restrict the rogue from using booming blade, etc., or if you look at fighters that don't take the best combination of fighting style, archetype, maneuver, maneuver deployment strategy, and feats. What I'm taking issue with is the conventional wisdom that the single classed rogue is a particularly weak combat class. Not that it doesn't contain the very-top-tier-optimized-for-DPR-at-the-expense-of-all-else single classed build within it.

You said that "Past tier 1 rogues start sucking at damage. The only exception is the AT and that's solely because of booming blade and shadow blade," but it could just as easily be said that "Fighters are not that much better than rogues at (average) damage. The only exception is the Battlemaster, and that's solely because of the interplay between precision attack and the -5/+10 feats."

I'd be fine if you wanted to say "If you're trying to optimize a build for damage, then a single classed rogue doesn't offer you a way to do that (though an AT using booming blade and shadow blade can do pretty well)." But it sounded like you were making a blanket statement about the class in general as compared to other classes in general (which I think is the conventional wisdom! and which is what I was aiming to critique in the OP)

More importantly though, your no longer arguing about the rogues damage but whether there's some edge cases where the rogue is better than the damage number shows.


That's why it was in a footnote: it was tangential to the original average DPR discussion.
 

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