The D&D 5e DPR challenge! Can you make a level 5 character with more damage?

[GeneralVryth]

One thing I do think is worth pointing out is level 5 versus level 6 punishes a lot of the combat caster character types. Evokers, Bladesingers, Draconic Sorceres, Valor Bards, and Blades Bards are all full caster sub-classes that get a distinct damage buff at level 6. Not to mention the extra 3rd level slot. Level 5 also locks out any kind of multi-classing for melee classes that depend extra attack. I always thought the best levels for comparison were levels 3 (or 4), 6, 10 (or 12), 14 (or 16) for this kind of reason.

For Bladesingers especially things change significantly going from 11.75892 to 16.33338 for their default action (with only a +3 attack modifier and a +3 casting modifier, using a single d8 weapon).

One thing that is interesting that I realize when typing this, Wizards and Sorcerers don't really have a concentration spell that is worth casting versus dropping a blast because of the concentration limit. It would be interesting if con prof increased the concentration limit some along with having advantage on concentration checks. Though I am sure Clerics become really tough to beat in that case.

[GeneralVryth]

I submit artificer Artillerist, though I'm not the first to do so.

I'm making a few assumptions: I can use infusions and cannons, but not the Replicate Magic Item Infusion to maintain the spirit of simplicity. The cannons are, in my mind, acceptable because they aren't summoned by a spell, they are created by you as a class feature, and denying it would be akin to denying the beast master's pet or barbarian's rage. Assuming point buy, no feat, so INT 18.

At 5th level, with the ffree Cannon (which lasts an hour; far, far exceeding either 30 or 20 rounds)

2d8 (shocking grasp) +1d8 (arcane firearm) +2d8 (either DPS cannon). To-hit of 4 (int) +3 (prof) +1 (infusion).

So that's 22.5 DPR single-target, no concentration spells.

If, say, 6 bad guys conveniently group into a cone shape, then that amount increases by 9x5=45 (aka cone damage)

How could I increase that? I'm so glad you asked:
* bless increases to-hit
* Web causes restrained, granting advantage on attacks and disadvantage on fire cannon's Dex save
* kobold has pack tactics, though unlike the Steel Defender or Homunculous its cannon is not really a creature so might not count as ally
* faerie fire grants advantage though, and takes care of those pesky invisible arcane tricksters
* acid splash has higher dice and can hit two bad guys, making the potential base non-cone damage (2d12+1d8)x2 or 35 + 18 (still use fire for two baddies cause duh) for base 53 resourceless, continual damage as long as I have two bad guys beside each other.

All numbers should be adjusted by chance to hit, of course (I missed if there was an assumption on that) but don't forget that Infusion. Also don't forget I have several options for advantage, and not all require a spell slot, though advantage matters not at all for fire cannon or acid splash. It matters a lot lot more for fire bolt and bolt cannon, though.

18 AC with shield, 19 with defence Infusion, and Shield would also be damn strong if this were more than a DPR challenge.

I like this as another straight class, no feats or anything clever way to approach this. Things to note, the infusion bonus doesn't apply to spell save DCs (at least I couldn't find one that did) so your cannon and using acid splash wouldn't get a bonus. Even still just sticking with the simple Acid Splash (which is 1d6 not 1d12 btw) + Cannon route and the +7 equivalent DC you get 25.83 DPR, not using concentration or any tricks but your cannon really.

[Frogreaver]

Just to hit the Cleric comment from earlier:

Arcana Cleric:
Wis 18
Str or Dex 16 (with some method of having a 1d8 weapon, there are a few different ways to achieve this based off of race)

2 Spirit Guardians lasting 3 rounds and hitting 2 targets:
2 * 3d8 (13.5) * 3 * 2 = 162 * .815 = 132.03

20 rounds of Spiritual Weapon:
20 * .63 * (1d8 + 4 + (1d8 * .086) = 111.9762

Filling up the remaining actions with True Flame Blade:
18 * .63 * (3d8 + 7 + (2d8 * .086) = 241.24716

Add up and divide by 20 and you get a DPR of: 24.262668
If Spirit Guardians lasts 6 rounds you get: 30.864168
9 rounds: 37.465668

If Spirit Guardians lasts the whole 10 minutes and you don't bother to short rest you get to: 40.0563585

For a single level 3 spell slot I don't think anything comes close to Spirit Guardians for damage output even when you're just limited to 3 rounds and 2 targets (that's effectively 18d8 save for half).

EDIT:


I have been assuming DC 15 = +7 for failure chance as that is what the equivalent ability scores work out to. All my numbers change if that is not true.

Unless we are prebuffing - which hasn't really been established then you may lose 3+ rounds of spiritual weapon and 2 rounds of True Flame Blade
Racial benefits are out according to the OP - so no d8 weapon?
What is True Flame Blade?

snip

Some classes like the gloomstalker ranger depends on the number of encounters for their abilities. How many encounters should we consider for his ability?

[GeneralVryth]

Unless we are prebuffing - which hasn't really been established then you may lose 3+ rounds of spiritual weapon and 2 rounds of True Flame Blade
Racial benefits are out according to the OP - so no d8 weapon?
What is True Flame Blade?

I meant Green-Flame Blade (the cantrip in SCAG and Tasha's). And no pre-buffing is needed for the Cleric build. You can use Spiritual Weapon first round along with a cantrip, Spirit Guardians second round and attack with Spiritual Weapon again. And then GFB until Spirit Guardians expires and you re-casts it. The missing rounds of GFB are already accounted for in the math which is why the 18 starts the GFB section and not 20. So the only real thing is d6 versus d8 weapon, which is worth ~.7 DPR on the rounds you use GFB (which is most).

Looking back I think there is actually a bigger error in my post, the accuracy number for GFB should be .58 and not .63 since it is only +6.

Redoing the numbers you get:

Spirit Guardians:
2 * 3d8 (13.5) * 3 * 2 = 162 * .815 = 132.03

Spiritual Weapon:
20 * .63 * (1d8 + 4 + (1d8 * .086) = 111.9762

Green-Flame Blade
18 * .58 * (1d6 + 2d8 + 7 + (1d6 + 1d8 * .086) = 210.76272

Add up and divide by 20 for: 22.738446 DPR

Personally I don't think assuming a d8 weapon is unreasonable considering the plethora of ways to get one from racial options, if you put that back you get: 23.337846 DPR

[Frogreaver]

I meant Green-Flame Blade (the cantrip in SCAG and Tasha's). And no pre-buffing is needed for the Cleric build. You can use Spiritual Weapon first round along with a cantrip, Spirit Guardians second round and attack with Spiritual Weapon again. And then GFB until Spirit Guardians expires and you re-casts it. The missing rounds of GFB are already accounted for in the math which is why the 18 starts the GFB section and not 20. So the only real thing is d6 versus d8 weapon, which is worth ~.7 DPR on the rounds you use GFB (which is most).

Looking back I think there is actually a bigger error in my post, the accuracy number for GFB should be .58 and not .63 since it is only +6.

Redoing the numbers you get:

Spirit Guardians:
2 * 3d8 (13.5) * 3 * 2 = 162 * .815 = 132.03

Spiritual Weapon:
20 * .63 * (1d8 + 4 + (1d8 * .086) = 111.9762

Green-Flame Blade
18 * .58 * (1d6 + 2d8 + 7 + (1d6 + 1d8 * .086) = 210.76272

Add up and divide by 20 for: 22.738446 DPR

Personally I don't think assuming a d8 weapon is unreasonable considering the plethora of ways to get one from racial options, if you put that back you get: 23.337846 DPR

Another minor nitpick. Shouldn't Greenflame blade be doing (1d6 + 2d8 + 6 ...)

Also we might want to double check that the OP intended for 5ft AOE's to be able to hit 2 targets.

Just for the sake of comparison basic Fiend Warlock not even trying to be clever just blowing things up at range:

Fiend Warlock
Cha = 18 (or +7 with prof)
Eldritch Invocations: Agonizing Blast...

6 x Fireball is:
6 x 8d6 (28) x 2 = 336
336 * .815 (.63 + (1-.63)x.5) = 273.84

14 Eldritch Blasts for the remainder is:
14 x .63 x (11 + 8 + (11 x .086)) = 175.92372

(273.84 + 175.92372) / 20 = 22.488186
or ~22.5 DPR

Mind you if the AOE targets were 2.5 average that DPR goes up to ~26 and if they were 3 average it would be ~29.25

This character appears to fail the challenge by not getting 17 AC. Would be able to get medium armor feat to still compete but would likely lower damage quite a bit.

[borg286]

What percent of the time can we assume our target is prone? Let's say we have an ability to prone the target like tripping attack?

[pvcarrao]

What percent of the time can we assume our target is prone? Let's say we have an ability to prone the target like tripping attack?

If your target is prone I think we can assume it will be prone for one round extra, since getting up is pretty easy. You have to land your attack and the they have to fail the DC tought, so multiply your chane to hit by your spell DC fail chance and you got the chance for target beign prone.




I recently made a spreadsheet for calculating DPR, maybe it can help, it is not pretty but can do the job.
https://docs.google.com/spreadsheets...it?usp=sharing

[Frogreaver]

What percent of the time can we assume our target is prone? Let's say we have an ability to prone the target like tripping attack?

I'm not the OP but my take is that you only get 20 first attacks and on average about 12 of them will land. The naive assumption would then be you are in a position to use it on a first attack 12 times and you can use his bonus table to determine your chance to land - about 60% give or take a little. So you would benefit from the prone of trip attack about 8 times. OP may have different opinion

[pvcarrao]

One thing I do think is worth pointing out is level 5 versus level 6 punishes a lot of the combat caster character types. Evokers, Bladesingers, Draconic Sorceres, Valor Bards, and Blades Bards are all full caster sub-classes that get a distinct damage buff at level 6. Not to mention the extra 3rd level slot. Level 5 also locks out any kind of multi-classing for melee classes that depend extra attack. I always thought the best levels for comparison were levels 3 (or 4), 6, 10 (or 12), 14 (or 16) for this kind of reason.

For Bladesingers especially things change significantly going from 11.75892 to 16.33338 for their default action (with only a +3 attack modifier and a +3 casting modifier, using a single d8 weapon).

One thing that is interesting that I realize when typing this, Wizards and Sorcerers don't really have a concentration spell that is worth casting versus dropping a blast because of the concentration limit. It would be interesting if con prof increased the concentration limit some along with having advantage on concentration checks. Though I am sure Clerics become really tough to beat in that case.

Yep... that`s another error, level 6 is a lot better for hybrid subclasses. Buy now it is to late to change everything, again. Maybe we start the thing all over again...

[Frogreaver]

@pvcarrao I'm looking at a greatsword wielding hexblade that casts summon Fey. I normally calc DPR just fine but can't decipher how OP wants crits accounted for and also want confirmation that hexblade's curse lasts 3 rounds only per use.

[LudicSavant]

Incidentally, these white room DPR challenges tend to greatly underestimate the real world value of spells in my experience.

Some examples of troublesome parameters/assumptions that can lead to very non-representative results in these sorts of white room challenges include:

- Fixed rounds (in real games, the higher your output, the fewer important rounds there are, so burst damage tends to be undervalued by any "fixed round" challenge).

- Flat defenses. (In a real game, versatile characters can target a creature's weakest defense, while less versatile characters face a high defense more often. The more versatile the character, the more likely any given ability they use is going to be used in an 'ideal scenario' for that ability. And vice versa. As such, versatility tends to be undervalued in such challenges, and one-tricks tend to be overvalued).

- Long individual combats (10 rounds is a long time, especially if people are optimizing. This can lead to stuff like 1 minute durations getting overvalued).

- Initiative not mattering (init bonuses provide a meaningful action economy advantage, this just doesn't fit into damage "per round" because it effectively gives you an extra round each time you win initiative. Dexterity builds tend to be undervalued as a result).

- Flat Concentration duration (in real games, varies a lot based on build/tactics).

- No party involvement (an awful lot of effects have additional damage potential from party combos. Anything that knocks prone, stuns, creates a hazard, buffs multiple characters, etc etc).

[Hael]

I meant Green-Flame Blade (the cantrip in SCAG and Tasha's).

Alternatively you could take booming blade and use the crusher feat (thus guaranteeing the rider). Depends how that is ruled.

[pvcarrao]

@pvcarrao I'm looking at a greatsword wielding hexblade that casts summon Fey. I normally calc DPR just fine but can't decipher how OP wants crits accounted for and also want confirmation that hexblade's curse lasts 3 rounds only per use.

I am not the king of DPR calculations, actually I am far from it.

Feel free to calculate the best you can. I am using this as a basis for crit dam modifiers:
https://amp.reddit.com/r/dndnext/com..._by_class_and/.

And yes, we are account 3 rounds per use for hexblades curse.

[Frogreaver]

• Hexblades Curse
• Blade Pact
• Warlock
• Thirsting Blade
• Eldritch Smite
• Improved Pact Weapon
• Great Sword - Elven Accuracy (Cha)
• 18 Cha

• Damage Baseline (18 Cha + Greatsword + Thirsting Blade)
  =11*.63*2 + 7*.05*2 = 14.56 DPR
  
• Improved Pact Weapon
  =2*(.05*11 + 1*.63 + .05*12) = +2.46 DPR
  
• Eldritch Smite Base DPR
  =6*18/20 = +5.4 DPR
  
• Eldritch Smite Crit DPR
  = 3*18/20 = +2.7 DPR (*3 because hexblades curse and prones will nearly double crit rate on around half of attacks)
  
• Eldritch Smite Prone DPR with elven accuracy
  = 4*(.97-.68)*12/20 = +0.70 DPR (*5 because can time 3 of the smites for first attack. The other 1 comes from assumption that at least 1 of the crit smites will be on first attack of the turn)
  
• Hexblade Curse DPR
  =3*2*3*3*.68 = +1.84 DPR
  
• Total DPR
  27.66

[Omni-Centrist]

Beast Barbarian Rogue
Beast 4 / Rogue 1 Half Elf Wood
18/16/16/8/8/8
Using Double Bladed Scimitar for attacks, you get 3d4+Str*2+d6 for an average of 25 DMG per turn, you also have the benefit of Tail form: d8 extra AC towards one attack of your choice. 17 AC with Revenant Blade feat.

[Frogreaver]

Beast Barbarian Rogue
Beast 4 / Rogue 1 Half Elf Wood
18/16/16/8/8/8
Using Double Bladed Scimitar for attacks, you get 3d4+Str*2+d6 for an average of 25 DMG per turn, you also have the benefit of Tail form: d8 extra AC towards one attack of your choice. 17 AC with Revenant Blade feat.

I think your str would be forced to be 16 for this as the OP has made clear no additional racial abilities including starting feats. Forgot Revenant blade feat was half feat. Though wouldn't you be getting 3*Str or are you assuming no beast claw attack with the blade? Nevermind, revenant blade doesn't give bonus attack.

Though I am curious, why go rogue instead of going Barbarian 5? 5d4+str*3 would be correct and that seems better?

[GeneralVryth]

Another minor nitpick. Shouldn't Greenflame blade be doing (1d6 + 2d8 + 6 ...)

Also we might want to double check that the OP intended for 5ft AOE's to be able to hit 2 targets.

This character appears to fail the challenge by not getting 17 AC. Would be able to get medium armor feat to still compete but would likely lower damage quite a bit.

It's +7, remember GFB uses casting stat which is +4 in this case (the Str/Dex is +3, for +7 total). Also, the 17 AC requirement was removed in the later update. Still if you wanted the AC 17 that is easy to do Half-Plate plus a Shield gets you there even without a dex bonus. So the only question is the 5 ft. AOE hitting 2 targets and that is following the rules. I agree it's kind of a perversion but then, I also think Fireball should hit 2.5 or 3 targets, and concentration spells should last longer (at least if you have things like Con prof or Adv. on Concentration).

Finally, the point of my builds so far hasn't been to try and be too clever, but more to show case how close a more standard thing gets.

Alternatively you could take booming blade and use the crusher feat (thus guaranteeing the rider). Depends how that is ruled.

Maybe, I would need to look into Crusher. But personally, like I said above I kind of like seeing how more standard things fare as a point of comparison as well.


EDIT:

And to stick with another simple build

Battle Master Fighter
Dex: 16
Fighting Style: Archery
Feat: Sharpshooter

Using all of the superiority dice to turn misses into hits (I will also a 10 or 12 fixes as well)

46 longbow attacks (2 per turn plus another 6 from 3 action surges):
46 * .43 * (1d8 + 3 + 10 + (1d8 * .086) = 353.80486

Superiority dice turning misses into hits:
12 * 1d8 + 3 + 10 = 210

Add up and divide by 20 for: 28.190243 DPR

If only 10 of 12 misses turn to hits: 26.440243 DPR

[Omni-Centrist]

I think your str would be forced to be 16 for this as the OP has made clear no additional racial abilities including starting feats. Forgot Revenant blade feat was half feat. Though wouldn't you be getting 3*Str or are you assuming no beast claw attack with the blade? Nevermind, revenant blade doesn't give bonus attack.

Though I am curious, why go rogue instead of going Barbarian 5? 5d4+str*3 would be correct and that seems better?

I like the 4 proficiencies you get from rogue a LOT, and it sets the tone for the class since my headcanon is a Barbarian 6/Assassin 14 split. I also love the idea of Level 6 opening up the 4 attacks per turn with the claws and DBS, 3d4 + 2d6 + 24 for 41 DMG per round with no real downside beside a limited resources.

[Frogreaver]

EDIT:

And to stick with another simple build

Battle Master Fighter
Dex: 16
Fighting Style: Archery
Feat: Sharpshooter

Using all of the superiority dice to turn misses into hits (I will also a 10 or 12 fixes as well)

46 longbow attacks (2 per turn plus another 6 from 3 action surges):
46 * .43 * (1d8 + 3 + 10 + (1d8 * .086) = 353.80486

Superiority dice turning misses into hits:
12 * 1d8 + 3 + 10 = 210

Add up and divide by 20 for: 28.190243 DPR

If only 10 of 12 misses turn to hits: 26.440243 DPR

On average you won't even be turning 10 of 12 misses to hits.

Example: Perfectly using precision attack when you miss by 1-3. We need to know 4 things:

How many superiority dice we have = 4 per short rest (and yes it matters that we look at this over a short rest period)
The chance we turn a miss by 1-3 to a hit = (1 + 7/8 + 6/8 ) / 3 = .875
The damage per attack = 4.5+3+10=17.5
The distribution of how often we miss by 1-3 in the given number of attacks = BINOM.DIST(X,16,0.15,FALSE), where X is the number of times you miss by 1-3. 16 is because 7 rounds of combat per short rest and 1 action surge makes 16 attacks. .15 because a miss by 1-3 has a .15 chance of occurring.

This weighted average ends up being about +35 Damage per short rest. So about +105 per day. Or +5.26 DPR due to precision attack. Total DPR this way comes to 22.9

We could expand our use case a little and get potentially better results. Going with using on a miss of 1-5 changes the number to +6.54 DPR. But we won't get much closer to the +10.5 DPR your method suggests. Total DPR this way comes to 24.2

[GeneralVryth]

On average you won't even be turning 10 of 12 misses to hits.

Example: Perfectly using precision attack when you miss by 1-3. We need to know 4 things:

How many superiority dice we have = 4 per short rest (and yes it matters that we look at this over a short rest period)
The chance we turn a miss by 1-3 to a hit = (1 + 7/8 + 6/8 ) / 3 = .875
The damage per attack = 4.5+3+10=17.5
The distribution of how often we miss by 1-3 in the given number of attacks = BINOM.DIST(X,16,0.15,FALSE), where X is the number of times you miss by 1-3. 16 is because 7 rounds of combat per short rest and 1 action surge makes 16 attacks. .15 because a miss by 1-3 has a .15 chance of occurring.

This weighted average ends up being about +35 Damage per short rest. So about +105 per day. Or +5.26 DPR due to precision attack. Total DPR this way comes to 22.9

We could expand our use case a little and get potentially better results. Going with using on a miss of 1-5 changes the number to +6.54 DPR. But we won't get much closer to the +10.5 DPR your method suggests. Total DPR this way comes to 24.2

You have a good point but I think you are overthinking it. In layman's terms you are saying we need enough attacks to on average change 4 per short rest. And if we are only changing when we are 1 to 3 points off, only 15% of attacks while qualify. And 15% of 15 to 16 attacks is certainly not 4. You realistically need to risk changing 25% of all attacks to use all of the dice, or in other words make changes on a 1 to 5 miss. You will fix a hit that misses by 1 to 5 on average 75% of the time. Which means only 9 of the 12 superiority dice get used.

9 of 12 superiority dice working works out to: 25.565243 DPR

Still solid (if not potentially OP) for a straightforward build.

[Frogreaver]

You have a good point but I think you are overthinking it. In layman's terms you are saying we need enough attacks to on average change 4 per short rest. And if we are only changing when we are 1 to 3 points off, only 15% of attacks while qualify. And 15% of 15 to 16 attacks is certainly not 4. You realistically need to risk changing 25% of all attacks to use all of the dice, or in other words make changes on a 1 to 5 miss. You will fix a hit that misses by 1 to 5 on average 75% of the time. Which means only 9 of the 12 superiority dice get used.

9 of 12 superiority dice working works out to: 25.565243 DPR

Still solid (if not potentially OP) for a straightforward build.

First of all, 1 to 6 actually comes out slightly better than 1-5 ;)

More importantly though, you are only fixing part of the issue I'm describing. You've managed to better account for your conversion rate per dice used by realizing as you describe above that you're not making anywhere near enough attacks to use all your dice without expanding the range of the miss you will use them on. However, even after expanding that range there's still a significant chance you go through that whole short rest period without being able to use all your dice

For the 1-5 Case

Using no dice = 1%
Only using 1 dice = 5.3%
Only using 2 dice = 13.3%
Only using 3 dice = 20.8%
Only using 4 dice = 59.6%

This translates into an average dice usage rate of 3.32/4 per short rest = 83.1%

That is, by employing this specific strategy you will on average use about 3.32 of your 4 dice. Then, of the dice you use, you will only convert 75% of those to hits.

The DPR for this strategy comes out to the 24.2 that I posted earlier. The 25.56 you list above is too high.

Essentially precision attack becomes an optimization style problem, where one variable increases as the other decreases, leaving you with a relative maximum to find.

[GeneralVryth]

First of all, 1 to 6 actually comes out slightly better than 1-5 ;)

More importantly though, you are only fixing part of the issue I'm describing. You've managed to better account for your conversion rate per dice used by realizing as you describe above that you're not making anywhere near enough attacks to use all your dice without expanding the range of the miss you will use them on. However, even after expanding that range there's still a significant chance you go through that whole short rest period without being able to use all your dice

For the 1-5 Case

Using no dice = 1%
Only using 1 dice = 5.3%
Only using 2 dice = 13.3%
Only using 3 dice = 20.8%
Only using 4 dice = 59.6%

This translates into an average dice usage rate of 3.32/4 per short rest = 83.1%

That is, by employing this specific strategy you will on average use about 3.32 of your 4 dice. Then, of the dice you use, you will only convert 75% of those to hits.

The DPR for this strategy comes out to the 24.2 that I posted earlier. The 25.56 you list above is too high.

Essentially precision attack becomes an optimization style problem, where one variable increases as the other decreases, leaving you with a relative maximum to find.

Ah but you are assuming that the short rests need to be equally spaced, so you are doing a distribution to calculate the odds you will be able to use all 4 in a specific time period. For the sharpshooter archer, there is no reason to short rest until you have used all of your superiority dice. So you need to be looking at the usage over the day, and while you could do a distribution to calculate that, everything up until now has been averages. If you go by the averages you end up closer to the 25.56 number (which is still technically a little high because you don't have a full 48 attacks over the course of the day, but it's closer to the average case you would get if you rolled it out).

[Gignere]

Ah but you are assuming that the short rests need to be equally spaced, so you are doing a distribution to calculate the odds you will be able to use all 4 in a specific time period. For the sharpshooter archer, there is no reason to short rest until you have used all of your superiority dice. So you need to be looking at the usage over the day, and while you could do a distribution to calculate that, everything up until now has been averages. If you go by the averages you end up closer to the 25.56 number (which is still technically a little high because you don't have a full 48 attacks over the course of the day, but it's closer to the average case you would get if you rolled it out).

You can also try and model quick toss maneuver along with precise for a BM archer. So if you don’t have enough misses to turn into hits you can also get a bonus action toss darts so sharpshooter and archery style both applies and they are finesse.

[Frogreaver]

You can also try and model quick toss maneuver along with precise for a BM archer. So if you don’t have enough misses to turn into hits you can also get a bonus action toss darts so sharpshooter and archery style both applies and they are finesse.

It's more than misses to turn into hits at that point though. The best strategy toward trying to tie in other maneuvers is going to be to check how many maneuver dice you have left and use another maneuver on the last few attacks if they hit. This will increase dice usage a little without impacting precision attack, but it still leaves a significant chance for dice to be left on the table (those last few dice miss by more than precision attack would help with). That is, the nature of maximizing DPR with precision attack leads us to strategies that leave dice on the table at the end of the rest period.

Ah but you are assuming that the short rests need to be equally spaced, so you are doing a distribution to calculate the odds you will be able to use all 4 in a specific time period.

Seemed to me the consensus up till now has been that we should space the short rests out equally.

I think you are right that unevenly spacing the short rests can increase dice usage - though not raise it to 100%. I don't see a way to mathematically model this though.

For the sharpshooter archer, there is no reason to short rest until you have used all of your superiority dice.

You'll be pushing back the unused dice to the last rest period. This still leads to unused dice. (Though potentially a bit less)

So you need to be looking at the usage over the day, and while you could do a distribution to calculate that, everything up until now has been averages. If you go by the averages you end up closer to the 25.56 number (which is still technically a little high because you don't have a full 48 attacks over the course of the day, but it's closer to the average case you would get if you rolled it out).

There are going to be unused superiority dice when you use any selective superiority dice strategy. Your method ignores any unused superiority dice. Thus, it is an overestimate of the DPR.

[Mitchellnotes]

I think your scenario is going to fundamentally be flawed based on your setup. You are designing a specific scenario that focuses on at will damage, then nerfing the classes that would be best suited to it. I'm seeing nerfs to druid summons, rogue sneak attack, and warlock hexing. If you wanted to check at will/attack damage, id focus on that

You may be better off identifying 3 iconic monsters and seeing how quickly they can go down. A hexblade/evoker or sorc/lock or paladin may not have they staying power for 30 rounds, but they may not need to given their ability to nova

[nathanv]

Just for the sake of comparison basic Fiend Warlock not even trying to be clever just blowing things up at range:

This sounded like a good base Warlock for testing a few things out. Fireball*6 is smart.

Warlock, Str 16 Cha 16, Fiend, Pact of Blade, Improved Pact Weapon, Polearm Master, Green Flame Blade, Glaive (or whatever). DC 14, attack +7, weapon damage D10+4 (=9.5). I gave full adjacent target damage to GFB due to AOE rules.

6*Fireball = 265.44
14*Green Flame Blade = 241.36
14*Bonus Action Attack = 60.34

DPR 28.357. Falls behind barbarian, as it should, but very respectable.

Green Flame Blade outperformed Thirsting Blade by a smidgeon. Shillelagh quarterstaff with Cha 18, Str 8 should be about the same, were that legal (it would be with VH feat). GWF fell behind by a bit, but would outperform PAM at lower AC or with reliable advantage (devil's sight + darkness; familiar help action.)

Good to know. Thirsting blade can come into its own later, with more invocations and better per-hit effects (incl. an all-day hex, not considered for this analysis where it'd only last three turns anyways.) The tiny price in dps for tome+shillelagh is certainly worth the SAD and the invocation saved. EB is still generally preferable because of ranged use + repelling blast and the feat saved. It seems that optimized warlock damage has a pretty tight spread.

If this were to go to lvl 6, I think you'd start to see some good bladesinger builds, with gfb + extra attack + whatever bonus actions they could scrounge up. Or, at 7, an eldritch knight build for BA GFB, which wouldn't need PAM. Under different testing circumstances, a GFB arcane trickster w/ familiar is pretty great at level 5.

[Dork_Forge]

This sounded like a good base Warlock for testing a few things out. Fireball*6 is smart.

Warlock, Str 16 Cha 16, Fiend, Pact of Blade, Improved Pact Weapon, Polearm Master, Green Flame Blade, Glaive (or whatever). DC 14, attack +7, weapon damage D10+4 (=9.5). I gave full adjacent target damage to GFB due to AOE rules.

6*Fireball = 265.44
14*Green Flame Blade = 241.36
14*Bonus Action Attack = 60.34

DPR 28.357. Falls behind barbarian, as it should, but very respectable.

Green Flame Blade outperformed Thirsting Blade by a smidgeon. Shillelagh quarterstaff with Cha 18, Str 8 should be about the same, were that legal (it would be with VH feat). GWF fell behind by a bit, but would outperform PAM at lower AC or with reliable advantage (devil's sight + darkness; familiar help action.)

Good to know. Thirsting blade can come into its own later, with more invocations and better per-hit effects (incl. an all-day hex, not considered for this analysis where it'd only last three turns anyways.) The tiny price in dps for tome+shillelagh is certainly worth the SAD and the invocation saved. EB is still generally preferable because of ranged use + repelling blast and the feat saved. It seems that optimized warlock damage has a pretty tight spread.

If this were to go to lvl 6, I think you'd start to see some good bladesinger builds, with gfb + extra attack + whatever bonus actions they could scrounge up. Or, at 7, an eldritch knight build for BA GFB, which wouldn't need PAM. Under different testing circumstances, a GFB arcane trickster w/ familiar is pretty great at level 5.

GFB/BB are not compatible with PAM as the PAM bonus attack require the attack action.

[nathanv]

GFB/BB are not compatible with PAM as the PAM bonus attack require the attack action.

Doh! Then I guess GWF would beat out PAM, and require recomputation with GFB vs TB.

[GeneralVryth]

Seemed to me the consensus up till now has been that we should space the short rests out equally.

I think you are right that unevenly spacing the short rests can increase dice usage - though not raise it to 100%. I don't see a way to mathematically model this though.

You'll be pushing back the unused dice to the last rest period. This still leads to unused dice. (Though potentially a bit less)

There are going to be unused superiority dice when you use any selective superiority dice strategy. Your method ignores any unused superiority dice. Thus, it is an overestimate of the DPR.

I went back to check the short rest thing just to be sure. Some classes can theoretically benefit from fewer short rests, the basic Arcana Cleric I posted earlier doesn't need a short rest, and would be hurt by it if the Spirit Guardians could last for all 20 rounds.

I don't have a good way to model it either, my instinct says the average approach I am using would get close though. You could use monte carlo to see if I am right though (though the odd hit chances and crit chances in the base post make this more difficult).

You are right about selective use potentially creating unused dice, that is why I mentioned 46 attacks causing the numbers to be a little off. By pure average you will have half a superiority unused while sticking to the 1 to 5 miss range for attacks. Which you could adjust the DPR to 25.127743 to account for that half a die. Ultimately it doesn't matter that much, as it's not going to be the best. It's a point of measure for more standard builds, that's also why I have offered up ranged of possibilities for things that could easily be different from the scenario and have a drastic impact on the build (Spirit Guardians lasting longer, Fireballs hitting more targets etc...).

[Frogreaver]

Level 5 Wizard - 16 str, 18 cha (after level 4 ASI)

Use Arcane Recovery to generate a level 3 spell slot.
Use Dragon's Breath with all your level 2 and level 3 slots on your familiar.
Use Burning Hands with your level 1 slots.
Use Greenflame blade with a quarterstaff

Burning Hands = (.081*10.5*2)*4 = 68.04
Greenflame Blade = [.058*[(4.5+3+4.5) + (4.5+4)] + .05*(4.5+4.5)]*16 = 197.44
Level 2 Dragons Breath = .081*(10.5*2*3)*3 =153.09
Level 3 Dragons Breath = .081*(10.5*2*3)*3 =204.12

Total Damage = 622.69
DPR = 622.69/20 = 31.13