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What is the most effective way to use a level 20 character's (with two or more levels in fighter for Action Surge ability) in order to maximize single target damage done in one round?

Rules/Restrictions:

  • Any race is allowed.
  • If there is a circumstantial bonus, such as Assassinate or Haste, please show each step in damage calculation
  • No magic items, charms, blessings, or epic boons.
  • No, the "damage done" can't be to yourself.
  • Vulnerability Damage caused by another player's action should not be considered.
  • Rogues may consider themselves to be targeting a Surprised creature.
  • You do not have advantage by default. If you can generate some advantage for yourself, then you may do so.
  • Consider your target to have AC20; Saving Throws Str +5, Dex +6, Con+5, Int +1, Wis +9, Cha +10; Skill Checks str(+5), dex(0), con(+5), int(+1), wis(+3), cha(+4); medium size... not dissimilar to a Death Knight.
  • You may have one non-combat round of setup.

(Again. Yes, I know this is alpha damage / nova damage and isn't sustainable.)

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17 Answers 17

10
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Expected Average Damage: 641.354, Maximum Damage: 1185

No items or spell components, no special circumstances. Legal for use in Adventurer's League. Attacking with Surprise.

Half-Orc (Arthur) (Savage Attacks add an extra die of damage on every critical hit)

Divine Soul Sorcerer 4 (Favored by the Gods, Shadow Blade spell, Subtle Spell meta-magic, ASI)

War Domain Cleric 1 (War Priest - make one weapon attack as a Bonus Action)

Assassin Rogue 3 (Assassinate - if surprised, advantage on all attacks, critical on all hits, 2d6 Sneak Attack with Finesse weapons per turn, Expertise: Stealth, Perception)

Battle Master Fighter 3 (Action Surge, 4 Maneuvers, including Precision Attack, Menacing Attack, and Disarming Attack, Fighting Style Dueling)

Paladin 2 (Divine Smite, Divine Sense, Fighting Style Armored)

Divination Tradition Wizard 2 (Portent)

Gloom Stalker Ranger 5 (Dread Ambusher: in the first round you gain an extra attack on every Attack action in the first round, +10 movement, extra 1d8 damage of the weapon's type on this extra attack, Primeval Awareness, Pass without a Trace, Longstrider, ASI, Fighting Style Archery)

Strength 14 + 2 + 2 ASI

Dexterity 13

Constitution 8 + 1

Intelligence 13

Wisdom 13

Charisma 13

  • To-Hit: +11, +12-19 with Precision Attack
  • Hit Points: 92
  • AC: 19 (Breastplate, Armored Fighting Style, Shield)
  • Stealth: +23 (Expertise and temporary boost from Pass without a Trace)
  • Initiative: +2 (+1 Dexterity, +1 Wisdom from Dread Ambusher)
  • Perception: +13 (Expertise)
  • Level 10 spellcaster (4 Sorcerer + 1 Cleric + (2 Paladin + 5 Ranger)/2 + 2 Wizard)
  • Movement speed: 40 feet (50 feet with Longstrider)
  • Darkvision: 90ft

The crux of it is that you have created a truly dreadful ambush character which has significant precision-boosting skills and tracking skills for his enemies. Beyond just being able to hit things hard, they also are able to do so with uncanny accuracy. This character goes patrolling for evil and predators in the woods, using his Primeval Awareness (L1 spell slot) to identify that there is evil in his land. As he uses his hunting ability to stalk his prey, his high perception and natural stealth make it difficult for his quarry to hide and make himself similarly difficult if not nearly impossible to spot. He'd use Pass Without a Trace, perhaps subtly, so that he could sneak up on his quarry. As he draws near and identifies his target, he casts Longstrider from his Ranger spells using the Subtle Spell meta-magic just to give himself that extra boost in movement that he'll need in order to close with his quarry before it realizes the danger. He knows how long it will take him to get into striking range, and stealthily moves to within 50 feet of his target. He has foreseen this day's events, and knows that death awaits his enemy. Patiently, he waits until it's his turn to strike. In terms of the sequence of events, I imagine it would look like this:

Primeval Awareness of the quarry, Subtle Pass without a Trace + Subtle Longstrider during the hunt for the quary. In the preparation round, cast Subtle Shadow Blade L5, from which the surprise round begins. Portent determines the initiative order for the target and the attacker: + Assassinating Critical: Action Surge + Dueling Attacks + Divine Smites + Dread Ambusher + Sneak Attack + Bonus Action War Priest weapon attack with Divine Smite.

Resource Expenditure:

  • Spending 2L5, 3L4, 3L3, Spell Slots, all maneuvers, action surge, divine favor, War Priest ability
  • Optional for flavor Spend another L2, 2L1 Spell slots: use a level 1 spell slot for Primeval Awareness to identify that your enemy exists nearby, then cast Pass without a Trace and Longstrider using Subtle Spell to hunt them and ambush them successfully.

Order of Events:

Preparation Round: Level 5 Shadow Blade. (4d8 psychic damage per melee attack)

Surprise Round: Initiative: Use Portent rolls to guarantee Assassinate feature works. Action: Attack action (2 attacks from Ranger, +1 attack from Dread Ambusher feature) *Bonus Action: 1 attack through War Priest Action Surge: Attack action (2 attacks from Ranger, +1 attack from Dread Ambusher feature)

The Math on the Damage:

(All dice are doubled because these are critical hits because of Assassinate)

Every attack that hits results in this: 2\$\times\$4d8 Psychic (Shadow Blade, Level 5) + 1d8 Savage Attack + 2 Dueling Fighting Style + 5 Strength modifier = 9d8 + 7 Psychic damage

7 attacks (3 attacks per action, plus 1 attack from War Priest) yield: 63d8 + 49 Psychic damage

Gloom Stalker Ranger allows us to adds 1d8 damage of the original weapon's damage type to the extra attack of every Attack action we take in the first round of combat through the Gloom Stalker feature. Since we take two Attack actions through Action Surge, we get extra 2d8 Psychic damage, which is doubled since they're critical hits. 67d8 + 49 Psychic damage

Assassin Rogue allows us to add 2d6 Sneak Attack damage because Shadow Blade is a Finesse weapon. Sneak attack rules for rogues do not require you to use Dexterity when using Finesse weapons. Since the attack is a critical hit, the damage gets doubled. 67d8 + 4d6 + 49 Psychic

As a paladin, every successful hit allows us to add 2d8 + (spell slot level-1)\$\times\$1d8 radiant damage, maxing out at 5d8 for an L4 spell slot or higher. As a 10th level spellcaster, after casting Shadow Blade at level 5, we can use 3 L4 spell slots, 1 L5 spell slot, and 3 L3 spell slots. All of this, of course, gets doubled on critical hits, which these will be. This results in the following additional damage: 2\$\times\$(3\$\times\$5d8 + 1\$\times\$5d8 + 3\$\times\$4d8) = 64d8 Radiant damage

Damage Total:

(67d8 + 4d6 + 49 Psychic) + (64d8 Radiant) = (67\$\times\$4.5 + 4\$\times\$3.5 + 49 Psychic) + (64\$\times\$4.5 Radiant) = 364.5 Psychic + 288 Radiant = 652.5 total

In order for the Assassinate feature to work, during the first round of combat the Assassin must act before their quarry. By having access to Portent, we will have two dice rolls which can be used for any ability check, which includes initiative. Because the quarry has a +0 to their initiative and our character has a +2 to initiative, regardless of what we roll, we can substitute the lower of the two Portent rolls to the target and use the higher of the two rolls for ourselves.

Damage, adjusted for accuracy:

The following probability calculations below were made with the help of the table in the article "D&D 5e: Probabilities for Advantage and Disadvantage" to figure out the likelihood of rolling particular numbers on a 20-sided die with advantage.

At least one attack will always hit. It's true that it's mathematically possible for a 1 to be rolled on every single attack die (7 attacks, all with advantage), but the odds of that are ridiculously low: \$\left(\left(\frac{1}{20}\right)^2\right)^7\$ = 0.0000000000000000006103515625. In other words, the Sneak Attack will always be added.

Precision Attack maneuvers and the Favored by the Gods feature allow the player to use them after the attack roll is made and any of these three abilities can be used in conjunction with one another.

With our target having an AC of 20, and our character having a starting +11 to hit, we need to roll 9 or higher in order to successfully land a hit, which from the table we can see that we have an 84% likelihood through advantage.

The Precision Attack maneuver from the Battle Master, adds 1d8 to attack rolls, yielding 4.5 average increase in likelihood. This can be used on 4 attacks, resulting in +15.5 to attack rolls, since we have 4 superiority dice from the Battle Master. In addition, the Favored by the Gods Divine Soul Sorcerer feature will allow us to add 2d4 to one attack that misses, turning it into a hit on average, due to effectively adding +5 to hit (resulting in a +16 to hit) for one of the two attacks which we cannot add the Battle Master die to. As a result, for 1 attack we need to roll 4 or higher through advantage to score a hit, and for 4 of the other 5 attacks we need to roll 4.5 or higher through advantage in order to score a hit.

The optimal strategy of their use should look something like this:

  1. Our attacks, whenever possible, should be sequenced from most damaging to least damaging, in order to take advantage of our ability to lazily add attack bonuses.
  2. Similarly, we should use our spell slots for Divine Smite in a decreasing progression. The Bonus Action attack will use the L5 spell slot, the first three attacks of the first Attack action will each use an L4 spell slot, and the three attacks of the second Attack action will each use an L3 spell slot.
  3. If an attack misses and we still have a superiority die, we should use the Precision Attack adds an average of 4.5 to the attack roll.
  4. If the total for the attack roll is still too low and we still can use Favored by the Gods, we should use it.
  5. If the number of attacks remaining is less than the number of superiority dice remaining and we haven't applied a maneuver to the attack, we should apply a damaging maneuver like Menacing Attack or Disarming Attack.

The Bonus Action weapon attack will average (2\$\times\$4d8 + 1d8 + 7) Psychic + 2\$\times\$5d8 Radiant = 47.5 Psychic + 45 Radiant = 92.5 damage. Adjusted for the likelihood of a natural 1, the accuracy adjustment reduces the expected damage total by: -92.5*(1-0.84) = -14.8

When using Favored by the Gods, our to hit becomes +16 on average, which means we need to roll 4 or higher through advantage. On the referenced table, we see that for this we have a 97.8% likelihood. The damage for this attack will be (2\$\times\$4d8 + 1d8 + 7) Psychic damage and (2\$\times\$5d8) Radiant = 9d8 + 7 Psychic + 10d8 Radiant = 47.5 Psychic + 45 Radiant = 92.5 damage. Adjusted for accuracy, this means that the damage total is lessened by -(1-0.978)\$\times\$92.5 = -2.035.

When using the Precision Attack maneuver, since the AC of the target is 20 and we will need to roll "5.5", the average (I think) will be (97.8% + 96%)/2 = 96.9%. This means that each of the 4 attacks with maneuvers has a 96.9% chance to hit. So, we will on average do 96.9% of the expected damage for those 4 attacks. The damage of these 4 attacks of the two Attack actions is: 4\$\times\$1d8 + 2\$\times\$4\$\times\$4d8 + 2\$\times\$1d8 + 4\$\times\$7 Psychic + 2\$\times\$(4d8 + 4d8 + 5d8 + 5d8) Radiant = (38d8 + 28) Psychic + (36d8 Radiant) = 199 Psychic + 162 Radiant = 361 total damage. Adjusting for accuracy, this means that the previously mentioned "total damage" is also lessened by -361\$\times\$ (1 - 0.969) = -11.191

On each of the 4 attacks on which we use a superiority die, if the attack doesn't need the accuracy boost, we can apply the die to the damage by using a different maneuver, such as Disarming Attack, doubling it because of the critical hit. This results in 2\$\times\$1d8 damage = 9 damage. How often would we get to add this extra damage? Since the original to-hit modifier is +11, hitting AC 20 would happen 84% of the time. Thus, 84% of the time, we can substitute a damaging maneuver instead of the Precision Attack Battle Master maneuver. Thus, the expected damage is increased by: 0.84\$\times\$9 onto every attack, for four attacks: 0.84\$\times\$9\$\times\$4 = +30.24

The 3rd attack from the second Attack can do (2\$\times\$4d8 + 1d8 + 7) Psychic damage and (2\$\times\$4d8) Radiant = 9d8 + 7 Psychic + 8d8 Radiant = 47.5 Psychic + 36 Radiant = 83.5 damage. As such, the damage expected for the last attack will be 83.5*(1-0.84) = -13.36.

Result:

Adjusted for accuracy, then, this means that the expected average damage of this character is 652.5 -14.8 - 2.035 -11.191 + 30.24 -13.36 = 641.354 total damage

Hope this math was relatively easy to follow, and hope you guys enjoyed the character and story setup as well. And be aware, the optimal use of the superiority dice and Favored by the Gods could improve this by a few more points.

*Note: Originally, I came up with a slightly higher number by using a Quickened Booming Blade. However, that spell is from Sword Coast Adventurer's Guide, and because many of the other features referenced here are from Xanathar's Guide to Everything, in Adventurer's League we wouldn't be able to use both for this character. *

It's worth noting, since the original poster mentioned this looking like a Death Knight, that this build would probably work even better against a Death Knight, because the latter's shield and sword can be removed through the Disarming Attack maneuver, thus lowering his AC and removing its ability to parry with his reaction.

*Note: Another poster, Herohersh (https://rpg.stackexchange.com/a/138689/49041), cleverly suggested that based on the guidelines for this math problem you could use your action to Create Bonfire during the setup round when you're casting Shadow Blade, step into the bonfire in order to trigger Absorb Elements through your reaction, and then proceed to attack using the bonus damage of Absorb Elements. In addition to probably not working mechanically due to stipulations regarding casting any other spell during the same round during which a Bonus Action spell is cast, for my personal taste I find this unsatisfying because it breaks the immersion and idea that you could still be hidden from your enemy the round before you attack if you conjure a bonfire that gives away your position. *

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  • 1
    \$\begingroup\$ This looks great! I'd love of another math savvy user could triple check your math, but I'll likely change the accepted answer sometime this week. \$\endgroup\$ – goodguy5 Jul 21 at 13:08
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    \$\begingroup\$ Math seems to check out. I got slightly different numbers (off by about 20), but I may have implemented the accuracy boosting differently. Bravo! [although don't think I won't be back to try to reclaim my throne ;)] \$\endgroup\$ – David Coffron Jul 22 at 15:56
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    \$\begingroup\$ I get an average damage of 655.240 based on my methodology and a maximum damage of 1185. I'm not too worried about the difference in average since that mostly comes down to methodological differences and is pretty close to what you estimate, but I can't account for 24 extra points of damage in your calculated maximum. It appears that you've accidentally doubled the Sneak Attack dice twice, instead of just once. \$\endgroup\$ – Xirema Jul 23 at 16:06
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    \$\begingroup\$ I added some MathJax to make some of your maths easier to read. Feel free to call me on it if I messed up any of the equations. \$\endgroup\$ – Someone_Evil Jul 23 at 20:24
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    \$\begingroup\$ The portent feature can only be used once per turn. While rolling initiative is before the rounds start, I think it is likely to be considered simultaneously so you might only be able to replace the role of one person. \$\endgroup\$ – findusl Nov 8 at 8:14
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Since the question states most effective way to deal max damage, I inferred that expected damage, which includes hit chance, critical hit chance, and saving throws, is the best metric (I have another answer for assuming perfect rolls, but that would be another question), so...

Expected damage is 564. Maximum is 648. Here's how:

The Character

Chloe is a level 20 Goblin {ASs: 9, 18, 10, 20, 8, 14} with these classes...

  • Wizard 17 ---------- [for Spells, Empowered Evocation, Alert feat and 3 ASI]
  • Fighter 2 ----------- [for Action Surge]
  • Warlock 1 ---------- [for Hexblade's Curse]

The Preparation

  1. Chloe casts wish replicating the effect of hallow with Energy Vulnerability on force damage within 60 feet of the target.

The Round

  1. Chloe uses Hexblade's Curse.
  2. Chloe casts magic missle (level 8 spell slot) applying Fury of the Small.
  3. Chloe uses Action Surge.
  4. Chloe casts magic missle (level 7 spell slot).

The Calculation

  • All force damage is doubled from hallow's Energy Vulnerability...
    • The target never enters the area
    • Chance target goes first: 15.125% (using optional rule for ties to avoid DM fiat)
    • Chance to save: +10 vs 19 DC = 60%
    • totals to 1 - (0.15125*0.6) = 90.925% chance
  • Each dart from the first magic missle deals...
    • 1d4 + 1 + 5 (Empowered Evocation) + 6 (Hexblade's Curse) force damage
    • 10 darts, doubled 90.925% of the time = 19.90925 multiplier
    • Expected: (2.5 + 12)*19.0925 = 276.84125 [Max: 320]
  • Each dart from the second magic missle deals...
    • 1d4 + 1 + 5 (Empowered Evocation) + 6 (Hexblade's Curse) force damage
  • 9 darts, doubled 90.925% of the time = 17.18325 multiplier
    • Expected: (2.5 + 12)*17.18325 = 249.157125 [Max: 288]
  • Fury of the Small deals...
    • 1 use per short rest, doubled 90.925% of the time = 1.90925 multiplier
    • Expected: 20*1.90925 = 38.185 [Max: 40]

Total expected: 564.183375 [Max: 648]

Note: This assumes that the target chooses to make the Charisma save against hallow; it doesn't have to. If not, the expected damage increases to 591


Rulings

How does Empowered Evocation work with Magic Missile?

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  • 1
    \$\begingroup\$ Is this allowed RAW? Pretty sure there's a rule against casting two non-cantrip spells in the same turn. \$\endgroup\$ – Nathan Sep 11 '18 at 18:01
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    \$\begingroup\$ @Nathan it is allowed. That rule only applies to bonus action spells. Chloe is casting 2 action spells here. See this question for more details. \$\endgroup\$ – David Coffron Sep 11 '18 at 18:06
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    \$\begingroup\$ Creature is a Tarrasque...wizards insta kills itself if the magic missile spell is reflected back \$\endgroup\$ – illustro Apr 13 at 18:25
  • \$\begingroup\$ It seems like you don't need the alert feat, or the calculation that the target may go first. Since the rouge is allowed to assume a surprise round presumably you can presume a surprise round as well to go first. That would give you ~ 4.5% increase on guaranteeing creature starts with vulnerability, plus ~6.9% increase for the extra ASI increase in place of alert, so ~11.7% more damage \$\endgroup\$ – dsollen May 7 at 20:39
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    \$\begingroup\$ @dsollen Even if the target is surprised, he still gets a turn in the first round. There is no "surprise round" in 5e where the surprised targets don't get a turn; they just don't get to act on the turn they are surprised. \$\endgroup\$ – David Coffron Jul 22 at 20:55
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249 expected, or 433 max damage

We are using a Scourge Aasimar Shadow Magic Sorcerer 18/Fighter 2, with a Charisma score of 20

The round before, activate Radiant Consumption. On your turn, move to within 5 feet of the target, use a bonus action to summon your Hound of Ill Omen next to the target, cast Disintegrate, action surge -> cast Meteor Swarm.

Scourge Aasimar Contribution:

Radiant Consumption:

  • At the end of each turn, you and each creature within 10ft of you take radiant damage equal to half your level: 10

  • Once on each of your turns, you can deal extra radiant damage to one target when you deal damage to it with an attack or a spell. The extra radiant damage equals your level: 20

Damage so far: 30

Fighter Contribution:

Action Surge

Damage so far: 30

Sorcerer Contribution:

Hound of Ill Omen:

  • Uses the statistics of a Dire Wolf
  • While the hound is within 5 feet of the target, the target has disadvantage on saving throws against any spell you cast.
  • On the hound's turn (it rolls initiative separately) it attacks.
    • The hound has +5 to hit and deals 2d6+3 damage. It has advantage if an ally is within 5 feet of the target (which you are).
    • Vs an AC of 20 the hound has a 49% chance of hitting with advantage, and deals 10 expected damage (max of 15, or 27 max on crit)

Damage so far: 40 (57 max), and target has disadvantage on its saving throws vs spells you cast.

Disintegrate:

  • 10d6+40 force damage, +3d6 for each level slot above 6th spent. Dex save negates
  • Cast using an 8th level slot, for 16d6+40 damage
    • Average damage is 16 * 3.5 + 40 = 96
    • Saving throw DC = 8 + proficiency + Cha mod = 8 + 6 + 5 = 19
    • Chance of making the ST = 40% (Target has +6 bonus).
    • Chance of making the ST with disadvantage = .4 * .4 = 16%
    • Expected damage = average damage * P(failing saving throw) = 96 * .84 = 80.64 (136 max)

Damage so far: 120.64 (193 max)

Meteor Swarm:

  • 20d6 Fire, 20d6 Bludgeoning, Dex save for half
    • Average damage is 40 * 3.5 = 140
    • Saving throw DC = 8 + proficiency + Cha mod = 8 + 6 + 5 = 19
    • Chance of making the ST = 40% (Target has +6 bonus).
    • Chance of making the ST with disadvantage = .4 * .4 = 16%
    • Expected damage = average damage * P(failing saving throw) + average damage/2 * P(making saving throw) = 140 * .84 + 70 * .16 = 117.6 + 11.2 = 128.4 (240 max)

Damage so far: 249 (433 max)

PS: You could get slightly higher damage using the Empowered Metamagic, but that complicates the calculations significantly. After some exhausting-looking calculations in chat and in a question, Empower will add ~12 expected damage to Meteor Swarm, and ~10 to Disintegrate, for ~22 more expected total.

PS2: The original specified target was a Death Knight, AC20, +6 to Dex saving throws.

PS3: If you are trying to find max damage (with all perfect rolls) you could swap Disintegrate for Scorching Ray, which brings the total up to 456 but only if every ray crits.

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11
+250
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Average 396, Max 1030

High Elf Eldritch Knight 12/Whispers Bard 5/Paladin 2/Hexblade Warlock 1, with Dexterity 20 and the Elven Accuracy, Lucky, Martial Adept and Savage Attacker feats.

Prep round: Bonus action: cast a 5th level Shadow Blade. Action: Apply purple worm poison to our blade.

Go Time: Bonus action: Apply Hexblade's Curse to our foe.

Action, Surge: We are going to make 6 weapon attacks. That is what is happening here.

To-hit: Assume dim light (given we can assume surprise, this seems fair)*. Now we have super elf-advantage on all of our attacks, giving us a to-hit of 94% and a crit chance of 27%. On any attacks we would miss, we apply Lucky, giving us a 60% chance of turning a hit into a miss, for a total to-hit chance of around 97%. (Given there is a 0.05% chance of missing three or more times, I will assume I will need at most two uses of it here.) We will also apply Lucky once our number of attacks left is equal to our number of Lucky uses left, for more crit chances.

On hit: Our sword does 4d8+13 (Dex 20, Hexblade's Curse, Dueling Fighting Style) damage, and we can pour all our high-level spell slots into Divine Smites. We have 4 4th-level or higher (5d8) and 2 3rd-level (4d8) slots to burn through. Finally, on one of our attacks (our first crit) we can use Bardic Inspiration to do an extra 3d6 damage. Thus, if all 6 attacks hit, we are dealing 52d8 + 3d6 + 78 damage as a baseline. This is average 270, but also slightly optimistic.

Critting: Our first crit, if it lands, will deal an extra 9d8 + 3d6 damage; we can also use Savage Attacker to reroll the 8d8 from our weapon, for a total average damage increase of 55. Our second, third and fourth crits, without Savage Attacker or Inspiration, do 41 on average. Subsequent crits will average 36 due to the lower level spell slots. This ends up giving us a total of 86 average damage.

Missing: Missing is interesting, because in order to maximise our crit damage, we have to save our high-level spell slots for later hits in case they crit. This means a miss is usually (and for the purposes of this model, always) one of our biggest attacks, losing us 53 damage. Of course, between a static miss chance of 97%, and a Precision Attack d6 that can save us from a miss with probability 81%, this is not a big difference. The chance of us missing once is 4%; the chance of us missing twice is negligible. That works out to about 2 lost damage.

Max: The maximum is just the maximum of 6 crits, which comes out to the max of 104d8 + 6d6 + 78, or 946.

Trip Attack: If all 6 attacks hit without needing our Precision Attack, we make our last attack a Trip Attack, dealing an extra 1d6 damage. This adds 3 to our average, and 12 to our max.

Poison: One of our attacks will hit. Then the purple worm poison kicks in, dealing 12d6 damage on a failed save or half on a success. If we use our third dose of Lucky here, our foe succeeds 12% of the time, so our poison does Average 39, max 72

Totals:

Average damage: 396

Max damage: 1030

*If we must have bright light, we can swap our Warlock level for an extra level of Paladin for Vow of Emnity, which gets us the advantage but not the other perks.

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7
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Average: 308.866 — Max: 470

  • Race: Protector Aasimar
  • Class Levels: Fighter (Battle Master) 3/Rogue (Assassin) 17
  • Feats: Crossbow Expert, Sharpshooter
  • Equipment: 2 Hand Crossbow, 3 doses of Purple Worm Poison (nonmagical) on 3 crossbow bolts.
  • Relevant ability scores: Dex +5
  • Fighting Style: Archery.

Step by step:

Previous turn

  • Radiant Soul: Your transformation lasts for 1 minute or until you end it as a bonus action. During it, you have a flying speed of 30 feet, and once on each of your turns, you can deal extra radiant damage to one target when you deal damage to it with an attack or a spell. The extra radiant damage equals your level (20).

PS: Why not Scourge Aasimar? Well, being an assassin and radiating bright light doesn't seem to be very functional since the character relies on surprise her foes.

This turn

  • Attack the surprised target with a poisoned bolt from the hand crossbow using Sharpshooter. Thanks to Assassinate, is a critical hit and thanks to Death Strike, it doubles the damage.

1d6(H.Crossbow) + 10(Sharpshooter) + 5(Dex) = 1d6+15

Chance to hit with Precision Strike: 1 - Chance to Miss: 1 - 35% * 35% = 87.75%

Critical: 2d6+15 -> Avg: 22 / Max: 27 -> Times 2 (Death Strike: chance is 65%)

Partial Total (multiplied by 87.75% and chance of death strike): Avg: 31.853 / Max: 54

  • Bonus Action: Attack the surprised target with a poisoned bolt from the other hand crossbow using Sharpshooter. Assassinate and Death Strike still applies.

1d6(H.Crossbow) + 10(Sharpshooter) + 5(Dex) = 1d6+15

Chance to hit with Precision Strike: 1 - Chance to Miss: 1 - 35% * 35% = 87.75%

Critical: 2d6+15 -> Avg: 22 / Max: 27 -> Times 2 (Death Strike: chance is 65%)

Chance to hit with Precision Strike: 1 - Chance to Miss: 1 - 35% * 35% = 87.75%

Partial Total (multiplied by 87.75% and chance of death strike): Avg: 63.706 / Max: 108

  • Action Surge: Attack the surprised target with a poisoned bolt from either hand crossbow using Sharpshooter. Assassinate and Death Strike still applies.

1d6(H.Crossbow) + 10(Sharpshooter) + 5(Dex) = 1d6+15

Critical: 2d6+15 -> Avg: 22 / Max: 27 -> Times 2 (Death Strike: chance is 65%)

Partial Total (multiplied by 87.75% and chance of death strike): Avg: 95.559 / Max: 162

  • Radiant Soul: Any attack hits, extra damage from Radiant Soul equal to character level (20)

Chance is 1 - Chances to Miss all 3 = 1 - 35% ^ 6 = 99.82%

Partial Total (multiplied by 99.82%): Avg: 115.523 / Max: 182

  • Sneak Attack: Any attack hits, extra damage is 18d6 x 2

Chance is 1 - Chances to Miss all 3 = 1 - 35% ^ 6 = 99.82%

Partial Total (multiplied by 99.82%): Avg: 241.296 / Max: 398

  • Purple Worm Poisons

Each attack hits 65% of the time: Half damage on 35% chance save

12d6* 65% * 65% + 12d6 * 65% * 50% * 35% = 22.5225 * 3 = Avg: 67.57 / Max: 72

Total: Avg: 308.866 — Max: 470

PS: Still working on improvements.

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5
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212.5 points of damage on average (or 644 maximum)

Okay, I'll bite. A Paladin/Fighter (18/2) with Str 20, Cha 20, and Great Weapon fighting style can make 4 attacks and deal 644 points of damage in a single turn:

  1. On the prior turn, activate Sacred Weapon (+Cha to hit) and cast Holy Weapon (+2d8 damage to every attack).
  2. Attack and extra attack, pumping a divine smite at 4th level into both attacks.
  3. Action surge to do all that again, except one divine smite at 3rd level (having run out of 4th-level slots).
  4. Use a bonus action to dismiss Holy Weapon and deal 4d8 more points of damage (16.38 average against a Death Knight).

Given the parameters you provided (death knight: AC 20, undead creature), this comes out to 212.5 points of damage on average.

The maximum amount of damage you can do with this combo is 644.

enter image description here

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4
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189 damage dealt on average (or 301 max).

Without factoring in magic items or artifacts, including Unearthed Arcana, and using a 20th-level straight Fighter build specifically, and not assuming you gain surprise for the attack, the answer appears to be using a 20-Dex Sharpshooter (Martial Archetype) with the fighting style Archery, a longbow, and the feats Sharpshooter (yes, confusing), Silver-Tongued, Elven Accuracy, Lucky, and Martial Adept (Menacing Attack and Pushing Attack). You didn't provide skill values for the opponent, so for simplicity I'll assume any non-combat skill checks are successful.

Your bonus action is Steady Aim, which adds +12 damage to every hit on your turn. Your first attack will be Menacing Attack at a +13, which if it hits (if you have an Inspiration, your odds of missing are right around 1%) will give your opponent disadvantage on all ability checks against you for the rest of the turn. You'll replace your second attack with Silver-Tongued's action, giving you advantage on all attacks for the rest of the turn. Every subsequent attack will be made at +8 (13-5 for the Sharpshooter feat) with up to four dice (advantage + elven accuracy + lucky), giving you approximately 87% chance to hit and... well, we'll say 14% chance to crit, although that's not quite right because you'll sometimes have a fourth die.

Your damage for the 'back six' hits is 1d8+5+10+12 which averages to 27.95 each with miss and crit chances factored in, or 167.7; we add to this the initial, assumed hit at 1d8+5+12= ~21.5 for a grand total of 189 damage dealt on average (or 301 max).

Of course, if they're standing on the edge of a long drop, you can use Pushing Attack on the final shot and add 20d6 to that.

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3
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Average 443 damage, maximum 1438 damage

Protector Aasimar Paladin 2/Warlock 11/Fighter 3/Ranger 3/Sorcerer 1 (now with less multiclassing (but only slightly))

AS Requirements: Str 20 Cha 20, Wis 13, Dex 13

Required Choices: pact of the blade (warlock pact boon), Tenser's transformation as 11th level Mystic Arcanum (warlock feature), Battle Master (fighter archetype), Disarming Attack (or any other Battle Master talent that adds your superiority die to damage), hunter's mark (ranger spell), Hunter (ranger archetype), colossus slayer (ranger feature), wild magic (sorcerer bloodline), Dual Wielder (Feat), Two-Weapon Fighting (fighting style)

Required Equipment 2 lances, warhorse mount (i realized you can have this because its technically not magical)

Setup: Radiant Burst, Hunter's mark the target and cast Tenser's transformation on yourself. Because Tenser's transformation is technically a wizard spell, roll on the Wild Magic table and get a 93-94, increasing your size to Large.

The Round of Truth: This is surprisingly similar to the other setup. First, make 3 lance attacks (one normal, one TWF, one Tenser's), burning all of your 2nd level spell slots to Divine Smite and all of your warlock slots to Eldritch Smite, and adding all your superiority dice to damage, giving you, per attack:

18 (2d12+5) base + 13 (2d12) Tenser's + 3.5 (1d6) Hunter's Mark + 4.5 (1d8) Colossus Slayer + 27 (6d8) Eldritch Smite + 13.5 (3d8) Divine Smite + 4.5 (superiority die) = 84 damage per attack * 3 attacks + 20 from Radiant Burst = 272 damage, before even Action Surging.

Then you Action Surge, using 3 1st-level slots to Divine Smite (and unfortunately, you're out of slots to Eldritch Smite and superiority dice) but you can still deal:

18 (2d12+5) base + 13 (2d12) Tenser's + 3.5 (1d6) Hunter's Mark + 4.5 (1d8) Colossus Slayer + 9 (2d8) Divine Smite * 3 attacks = another 147 damage.

Add on the 23 damage your horse averages in a turn, the grand total is 272 + 147 + 23 = an average of 443 damage per turn.

Of course I'm not done. I have to calculate what the maximum damage with crits. Here it is in all its glory:

(53+48+12+16+96+48+16)*3+20+(53+48+12+16+36)*3+56 = 1438 maximum damage with crits!

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2
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Average 329, Max 628

Goblin Radiant Sorcerer 17/Fighter 2/Hexblade Warlock 1, with 20 Charisma and the Lucky feat, aided by our plucky Owl familiar, Trilby.

Setup round: use our action to cast Heightened Empowered Delayed Blast Fireball, bonus action to apply Hexblade's Curse to our foe. Trilby takes the Help action, giving my next attack against our foe advantage.

Go time:

Action: Cast Heightened Empowered Meteor Swarm, dealing 40d6+6 damage, with up to 5 rerolls, and a 94% save failure chance (with disadvantage from Heightening and Lucky - 14% chance of using Lucky up)... average 153, max 246

Free: Trigger Delayed Blast Fireball on ourself and our enemy. That's 13d6+6, with up to 5 rerolls, and an 94% chance of them failing the save, gives average 58 max 84. Also hits us, at which point we cast a 6th level Absorb Elements to gain fire resistance.

Action Surge: Cast an 8th level Inflict Wounds on our foe, hitting on a 9+. With Lucky and advantage from Trilby, this is pretty likely (94%). We also have a 27% crit chance, which is pretty great. So we deal 1.21*(10d10 + 6d6) + .94*6 damage, which is average 98, max 278

Fury of the Small: We use this any one time we deal damage to do an extra 20 damage.

Total Average: 329

Total Max: 628

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2
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Average 997.5,Max 1785 Race/Classes/Stats: Very lenient, pick most any race, get to 20. Fighter-2, Cleric-1 (Arcana Domain), Druid-17 (Circle of Twilight from Unearthed Arcana).

Classes explained: As per the rules we grab 2 fighter minimum, which gets us action surge. Cleric Level 1 gets us into the arcana domain, detect magic and Magic missile are always prepared for us. We max out druid levels otherwise, picking the circle of twilight from Unearthed Arcana. Their feature Harvester's Scythe is vital to maximizing our damage. We get a pool of d10's equal to our druid level. Up to half of our maximum may be spent at a time when we roll for damage on a spell, rolling those additional dice and adding them to the damage as bonus necrotic. Yes, we plan on stacking the bonus damage from multiple magic missile darts as with some of the other methods.

Prep round: :)

Go Time- Action: Use 9th level spell slot to cast Magic Missile, creating 3+8 darts, for a total of 11. Roll for damage, add 8d10 to the roll. (17/2=8.5 rounding down for 8 bonus dice maximum) Damage calculation:

D1= 11(1d4+1)+11(8d10), D1avg= 11(2.5+1)+11(8x5.5)= 522.5, D1max= 11(4+1)+11(8x10)= 935

Action Surge: Use 8th level spell slot to cast Magic Missile, creating 3+7 darts, for a total of 10. Roll for damage, add 8d10 to the roll. (17/2=8.5 rounding down for 8 bonus dice maximum) Damage calculation:

D2= 10(1d4+1)+10(8d10), D2avg= 10(2.5+1)+10(8x5.5)= 475, D2max= 10(4+1)+10(8x10)= 850

Totals

Maximum Damage= D1max+D2max = 935+850= 1785

Average Damage= D1avg+D2avg = 522.5+475= 997.5

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  • 1
    \$\begingroup\$ Interesting Answer. I suppose Unearthed Arcana wasn't explicitly banned, but I chose not to use it for my answers since it is playtest material. If you are allowed Unearthed Arcana, a higher value can be reached with other techniques. ( @goodguy5 any thoughts?) \$\endgroup\$ – David Coffron Apr 29 '18 at 0:57
  • \$\begingroup\$ I agree. Interesting answer, but UA isn't technically "released" and wouldn't apply. No need to delete or anything. \$\endgroup\$ – goodguy5 May 3 '18 at 1:15
  • \$\begingroup\$ Your pool of d10s is only 17d10 from being a 17th lvl druid. It recharges on a long rest. There's no way you can spend 8 * 21 d10s in a single round, because that's about 10x more than you have in your pool. You spend d10s on a damage roll, not on a whole spell, so they don't get multiplied across multiple damage rolls for a single spell. (I think you could spend them on an AoE, though, and have multiple targets affected by the same damage roll all take the necrotic damage.) \$\endgroup\$ – Peter Cordes Jan 5 at 21:10
2
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Level 2 Fighter, Level 2 Wizard (Loremaster), Level 6 Cleric (Tempest), Level 10 Druid (Twilight)

  • First action, Cast Magic Missile as a 9th level spell. 11 * (1d4+1 force) damage.

  • Use Circle of Twilight's Harvest Scythe to add 5d10 to MM damage. 11 * (1d4+1 force + 5d10 necrotic) damage

  • Use Loremaster's Spell Secrets to turn necrotic damage to lightning 11 * (1d4+1 force + 5d10 lightning) damage

  • Use Tempest's Destructive Wrath to change 5d10 to 50 damage. 11 * (1d4+1 force + 50 lightning) damage

Use Action Surge to repeat above with an 8th level spell, your remaining Harvest Scythe dice, Spell Secrets, and second Destructive Wrath for the following:

10 * (1d4+1 force + 50 lightning) damage.

We can rewrite that as 21 * (1d4+51)

At a minimum you will do 1,092 damage to a single target, at most you will do 1155 damage. Thankfully there isn't much variation, you only have 4 values your damage will be: 1092, 1113, 1134, and 1155.

An average of 1,123.5 isn't bad. If we use the hypothetical death knight with average hp as a target, please line up 5 of them, because this character will only need 4 missiles to down one death knight it can kill all five in a single turn. Since the death knight doesn't have shield as a reaction, resistance to force or lightning damage, there is no question about whether or not it will die from the attacks. If you have doubts on how to apply magic missile damage please see the following:

https://www.sageadvice.eu/2016/10/17/magic-missile-do-you-roll-the-same-d4-for-all-darts/

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  • 1
    \$\begingroup\$ Welcome to RPG.SE! Take the tour if you haven't already and see the help center if you need more guidance. Good Luck and Happy Gaming! \$\endgroup\$ – Someone_Evil Apr 13 at 19:35
  • \$\begingroup\$ It might be worth clearly delineating which of the content in your answer (i.e. Lore wizard and Twilight druid) are UA-only content. \$\endgroup\$ – V2Blast Apr 13 at 19:52
  • \$\begingroup\$ Oh its UA all over and some questionable interpretations of rules at that. Is it too much to have faith that someone can google the bold text if they don't know where something came from? Have we that little faith in the general population? \$\endgroup\$ – enki Apr 14 at 23:58
  • \$\begingroup\$ There are actually sixteen different damage results you can get with this build, not only four. You'd roll two different d4s, one for each Magic Missile casting, and since they get multiplied by different numbers of darts, it matters which die is which. Each pair of results on the dice gives a slightly different amount of damage. This doesn't change the average or maximum damage, it just means there are more values in between the min and max you've shown. The full damage is 1050 lightning and 11*1d4 + 10*1d4 + 21 force. \$\endgroup\$ – Blckknght Jul 21 at 20:08
1
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For my own personal baseline:

Level 20 Fighter - Champion
20 Strength
7 ASIs - +2str, Mounted Combat, Lucky, +1str/+1con, Great Weapon Master, Lucky, Blade Mastery
Greatsword attack - +12 to hit (or +7 with GWM), 2d6ish+5 (or +15 w/GWM)

Things doing: 1. walk horse up to target.
2. Attack with advantage.
3. Action Surge
4. Attack with advantage.

5*.64*(2d6+15+.28*2d6) + 3*.78*(2d6+15+.39*2d6)

For an expected 144 in one round. 312 Max

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1
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Thought I'd try a stab at this. I know there is a lot of multi-classing, but the goal was to create the biggest expected one turn hit.

Expected damage is 584.29. Maximum: 1044; here’s how:

The Character

Goblin (13, 20, 14, 8, 13, 13) + alert feat (Level 11 Spellcaster)

Fighter 5: Battle Master (Action Surge, Multi-attack, Superiority Dice, Dueling, ASI)

Bard 4: College of Whispers (Jack of All Trades, Psychic Blades, ASI)

Sorcerer 4: Divine Soul (For Spells, Quicken/Empowered, 4 Sorcery Points, Favored by the Gods, ASI)

Rogue 3: Assassin (Assassinate, Sneak Attack)

Cleric 2: Grave Domain (Channel Divinity: Path to the Grave)

Paladin 2 (Smite)

The Preparation

Action: Create Bonfire

Movement: Walk in to Bonfire and choose to fail save

Reaction: Absorb Elements: level 6

Bonus Action: Shadow Blade: level 5 (C)

The Round

Action Surge: Channel Divinity: Path to the Grave

Bonus Action: Green Flame Blade

Action: Multi-attack

The Calculation

Quickened, Empowered Green Flame Blade w/ Shadow Blade w/ Empowered Absorb Elements, Smite, Psychic Blades, Sneak Attack, Superiority Die, Fury of the Small (Autocrit, Vulnerable, 4 Sorcery Points)

4d8 + 1d8 + 2d6 + 2d6 + 7 psychic + 3d8 + 6d6 Fire + 5d8 Radiant + 20

(26d8 + 20d6 + 27 + (2.8058 + 2.3763 average damage from empowering)) x2

438.3642 Avg (710 max) (59.6116 from GFB)

Attack w/ Shadow Blade, Superiority Die, Smite (Autocrit) x2 Attacks

4d8 + 1d8 + 7 psychic + 5d8 Radiant

(20d8 + 7) x2

97 Avg (167 Max) PerAttack

Chance to 1st Hit (Advantage + Favored by the Gods): 97.15%

Chance to 2nd Hit (Advantage + Favored by the Gods if unused): 95.046%

Chance to 3rd Hit (Advantage + Favored by the Gods if unused): 93.279%

Chance at least 1 hits: 99.94%

Chance at least 2 hit: 99.67%

Chance all 3 hit: 86.13%

Initiative + 13 (dex +5, alert +5, Jack of All Trades +3)

94.75% of going first

(378.7526*0.9994 + 59.6116*0.9715 + 97*0.9967 + 97*0.8613) * 0.9475

584.29 Expected (1044 Max)

Caveat: Assumed damage done if second on initiative is 0, thus true value is somewhat higher. Also if enemy is holding shield disarming strike could be used to lower AC on subsequent attacks.

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  • 2
    \$\begingroup\$ "Movement: Walk in to Bonfire and choose to fail save" - By RAW, you can't choose to fail a saving throw. \$\endgroup\$ – V2Blast Jan 12 at 5:36
  • \$\begingroup\$ Also, welcome to RPG.SE! Take the tour if you haven't already. \$\endgroup\$ – V2Blast Jan 12 at 5:39
  • \$\begingroup\$ I suppose instead of using Create Bonfire you could use a Firebolt to shoot your own hand. \$\endgroup\$ – noisebelt Jul 21 at 16:59
1
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Expected damage is 709.82. Maximum: 1256; here’s how:

The Character

Wood Elf (13, 20, 11, 8, 14, 13) + alert, elven accuracy (Level 11 Spellcaster)

Ranger 5: Gloom Stalker (Dread Ambusher, Multi-attack, ASI)

Bard 4: College of Whispers (Jack of All Trades, Psychic Blades, ASI)

Cleric 4: War Domain (Magic Weapon, War Priest, Channel Divinity: Guided Strike, ASI)

Rogue 3: Assassin (Assassinate, Sneak Attack)

Fighter 2: (Action Surge, Great Weapon Fighting)

Paladin 2 (Smite)

The Preparation

Action: Apply Purple Worm Poison

Bonus Action: Magic Weapon: level 6 (C)

The Round

Action: Attack

Action Surge: Attack

Bonus Action: War Priest bonus attack

The Calculation

Chance to hit: 98.4375% Chance to miss: 1.5625%

Chance to hit 7 times: 89.562%

6 Times: 9.951%

5 Times: 0.474%

4 Times: 0.013%

With Channel Divinity 99.513% to hit 7 times

65% to fail DC 19 save against poison

Double-Bladed Scimitar, Smite, Psychic Blades, Sneak Attack (Autocrit, Advantage)

2d4 + 8 + 2d6 Slashing + 5d8 Radiant + 2d6 Psychic + (12d6) Poison

2d4 + 8 + 5d8 + (12d6)

2d4 + 1d8 + 8 + 5d8 + (12d6)

2d4 + 8 + 5d8 + (12d6)

2d4 + 8 + 5d8 + (12d6)

2d4 + 1d8 + 8 + 4d8 + (12d6)

2d4 + 8 + 4d8 + (12d6)

If going first:

Total: 28d4 + 70d8 + 8d6 + 56 + (12d6*4.55 fails + 2.45*21 successes)

483 + (4.55*42 + 2.45*21)

722.55 * .99513 chance to hit all 7

Expected 722.016

If going second (no advantage, no crits, 5 hits)

Total: 10d4 + 25d8 + 4d6 + 40 + (60d6)

196.5 + (3.25*42 + 1.75*21)

369.75

Expected: 233.98

Initiative + 15 (dex +5, wis +2, alert +5, Jack of All Trades +3)

97.5% of going first

0.975*722.016 + 0.025*233.98

709.82 Expected (1256 Max)

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  • 1
    \$\begingroup\$ The double-bladed scimitar is not a finesse weapon and therefore cannot be used with sneak attack. \$\endgroup\$ – David Coffron Feb 14 at 14:51
  • 1
    \$\begingroup\$ Also, are your calculations using Channel Divinity more than once? A level 4 cleric can only use it once \$\endgroup\$ – David Coffron Feb 14 at 14:54
  • 1
    \$\begingroup\$ I recalculated your damage (using a rapier with dueling instead of a double-bladed scimitar with GWM) and got 474.67 expected. I'm not sure who's right, but you can check my work. I'd love to see how you calculated differently. \$\endgroup\$ – David Coffron Feb 14 at 15:43
  • 1
    \$\begingroup\$ You should have 66d8 not 70. \$\endgroup\$ – David Coffron Feb 14 at 15:45
  • 1
    \$\begingroup\$ I think I see the problem. Purple worm poison can only apply once. "Injury poison can be applied to weapons, ammunition, trap components, and other objects that deal piercing or slashing damage and remains potent until delivered through a wound or washed off." (emphasis mine). You've applied it multiple times \$\endgroup\$ – David Coffron Feb 14 at 15:48
1
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The maximum expected damage is 850.077 [2800 with ideal rolls]. Here's how:

The Character

Camila is a level 20 Goblin {ASs: 10, 20, 12, 10, 10, 18} with these classes...

  • Bard (College of Valor) 18 ---------- [for Spells, Battle Magic, the Alert feat, and 3 ASI]
  • Fighter 2 ------------------------------ [for Action Surge and the Archery Fighting Style]

...the following Magical Secrets:

  • inflict wounds
  • conjure woodland beings
  • wish

...the following equipment:

  • 24 holly berries
  • 2 antimatter rifles
  • ample energy cells

...and she has participated in downtime Training to gain proficiency with antimatter rifles.

The Preparation

  1. Camila casts wish replicating the effect of hallow with Energy Vulnerability on necrotic damage within 60 feet of the target.
  2. Camila uses Action Surge.
  3. Camila casts conjure woodland beings with an 8th level spell slot conjuring 24 pixies.
  4. The pixies who have lower initiative use Superior Invisibility.

The Round

  1. Camila flanks with one of the pixies and casts inflict wounds with a 7th level spell slot.
  2. Camila steps away and attacks with an antimatter rifle using Battle Magic.
  3. The pixies take turns picking up, firing, and then dropping the other antimatter rifle (reloading when necessary).

The Calculation

  • All necrotic damage is doubled from hallow's Energy Vulnerability...
    • The target never enters the area
    • Chance target goes first: 6.125% (using optional rule for ties to avoid GM fiat)
    • Chance to save: +10 vs 19 DC = 60%
    • totals to 1 - (0.06125*0.6) = 96.325% chance
  • Inflict wounds deals...
    • 9d10 necrotic damage with a +10 chance to hit (+4 Charisma, +6 Proficiency Bonus) and advantage on the attack roll since it is almost impossible that Camila acts before every pixie.
    • Vulnerability * Regular Damage * Regular Hit Chance + Critical Damage * Critical Hit Chance (CHC)
    • Expected: 1.9265*[(9*5.5)*(1-45%2-CHC) + (18*5.5)*(1-95%2)] = 88.3575 [Max: 360]
  • Camila's antimatter rifle attack deals...
    • 6d8 necrotic damage with a +13 chance to hit (+5 Dexterity, +6 Proficiency Bonus, +2 Archery)
    • Expected: 1.9265*[(6*4.5)*(65%) + (12*4.5)*(5%)] = 39.01163 [Max: 96]
  • Fury of the Small deals...
    • 20 necrotic damage, relies on either inflict wounds or the antimatter rifle attack to hit
    • Expected: 1.9265*[20*(1-(16%*35%)] = 35.94752 [Max: 40]
  • The pixies' antimatter rifle attacks deal...
    • 6d8 necrotic damage with a +5 chance to hit (+5 Dexterity) and advantage on any with lower Initiative than Camila due to Unseen Attackers
    • Expected for invisible pixies: 1.9265*[(6*4.5)*(1-70%2-CHC) + (12*4.5)*(1-95%2)] = 31.59941 [Max: 96]
    • Expected for visible pixies: 1.9265*[(6*4.5)*(25%) + (12*4.5)*(5%)] = 18.20542
    • Expected number of invisible pixies is 19.68
    • Overall expected damage is 19.68*31.59941 + 4.32*18.20542 = 700.5238 [Max: 2304]

Total expected: 860.07684 [Max: 2800]

Note: This assumes that the target chooses to make the Charisma save against hallow; it doesn't have to. If not, the expected damage increases to 889.7

Other Summons

Spells like conjure woodland beings don't give the player full control over what creatures specifically get summoned as discussed in this Q&A. If the GM decides to cause a different CR 1/4 or lower creature, the expected damage changes as follows:

  • Sprites yield an expected damage of 783.06009 (using Invisibility instead of Superior Invisibility).
  • Blink dogs yield an expected damage of 206.62289 (flanking with Bite instead of using the antimatter rifle).
  • Boggles yield an expected damage of 692.97184 (using Dimensional Rift to attack without being seen, 11 boggles have to reload instead).

If the GM chooses randomly, you get...

  • An expected damage of 635.68291 when all fey at or below CR 1/4 are eligible.
  • An expected damage of 616.5866 when only fey at exactly CR 1/4 are eligible.
  • An expected damage of 778.70292 if you can guarantee you won't get blink dogs.
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  • \$\begingroup\$ This is a fantastic idea that will almost certainly make your DM say "that was funny, never again." \$\endgroup\$ – goodguy5 Nov 7 at 13:44
0
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I will start by giving credit where it is due. I can't comment yet (new account) but most of the setup was thought of by David Coffron, I just found a way to improve his damage with Unearthed Arcana's Lore Mastery wizard. Give him all the love please! If I made an error when modifying his approach please let me know.

Expected damage is 782. Maximum is 1238.

Here's how:

The Character

Chloe is a level 20 Goblin {ASs: 9, 18, 10, 20, 8, 14} with these classes...

Wizard 17 (Lore Mastery subclass) - [for spells, Alchemical Casting, Alert feat and 3 ASIs]
Fighter 2 - [for Action Surge]
Warlock 1 - [for Hexblade's Curse]

The Preparation

Chloe casts wish, replicating the effect of hallow with Energy Vulnerability on force damage within 60 feet of the target.

The Round

Chloe uses Hexblade's Curse.
Chloe casts magic missile (level 8 spell slot). Chloe uses Alchemical Casting on magic missile (level 1 spell slot)
Chloe uses Action Surge.
Chloe casts magic missile (level 7 spell slot). Chloe uses Alchemical Casting on magic missile (level 1 spell slot)

The Calculation

All force damage is doubled from hallow's Energy Vulnerability...

  • The target never enters the area
  • Chance target goes first: 15.125% (using optional rule for ties to avoid DM fiat)
  • Chance to save: +10 vs 19 DC = 60%
  • totals to 1 - (0.15125*0.6) = 90.925% chance

Each dart from the first magic missile deals...

  • 1d4 + 1 + 2d10 (Alchemical Casting) + 6 (Hexblade's Curse) force damage
  • 10 darts, doubled 90.925% of the time = 19.90925 multiplier
  • Expected: (2.5 + 7 + 11(2*5.5))*19.0925 = 391.39625 [Max: 610]

Each dart from the second magic missile deals...

  • 1d4 + 1 + 2d10 (Alchemical Casting) + 6 (Hexblade's Curse) force damage
  • 9 darts, doubled 90.925% of the time = 17.18325 multiplier
  • Expected: (2.5 + 7 + 11)*17.18325 = 352.256625 [Max: 558]

Fury of the Small deals...

  • 1 use per short rest, doubled 90.925% of the time = 1.90925% multiplier
  • Expected: 20*1.90925 = 38.185 [Max: 40]

Total expected: 781.837875 [Max: 1238]

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  • 1
    \$\begingroup\$ You only roll damage for magic missle once so Alchemical Casting could only add 11 damage since it makes the spell do added damage rather than adding to the damage roll itself, similar to what Fury of the Small does (much less than the benefit from Empowered Evocation); not to mention Lore Mastery is play test material. \$\endgroup\$ – David Coffron Mar 14 '18 at 14:51
-1
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Expected damage: 446.5

Max damage: 1788

Max with 2 turn set up: 2592

How:

Goblin: Bard 13/sorc 4/fighter 2/ warlock 1

Expected damage:

Turn 1: hex blade curse, contagion (flesh rot for vulnerable all damage) gained through being a bard

Turn 2: bestow curse -> scorching ray (lvl9) -> action surge -> scorching ray (lvl8)

Lvl 9 shoots 10 rays, level 8 shoots 9 so there are 19 rays total and eavh ray each ray does

(2d6+1d8(bestow)+6(hexblade)x2

One ray does 40 extra because of fury of the small and vulnerability

Assuming a 60% hit rate because of their 20ac and us not having magical items

Works out to: 446ish

If you have an extra turn (and access to the spelldriver feat):

Turn 1: contagion, hexblade curse

Turn 2: bestow curse, hex

Turn 3: scorching ray (9), AS, scorching ray (8), quicken scorching ray (2)

With max dice and crits you get:

((((2d6+1d6+1d8)x2)+6)x2)x22rays +40

Or

2592

(This is assuming pheonix sorcerer from unearthed arcana is NOT allowed, because it allows you to add your cha to each fire damage roll you make... adding another 22x10 damage and making the total 2812)

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    \$\begingroup\$ Welcome to RPG.SE! Take the tour if you haven't already. Note that you can't quicken a spell and cast another leveled spell as an action on the same turn, due to the bonus-action spellcasting rule. (You can cast two spells as actions using Action Surge, though.) Also, it seems odd to assume that an unofficial (third-party) feat would be allowed in your calculations. \$\endgroup\$ – V2Blast Jan 19 at 10:54
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    \$\begingroup\$ Hello and Welcome! Comtation was erratad. You need at least 3 turns before the flesh rot sets in. \$\endgroup\$ – Ruse Jan 19 at 11:14

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