Character Optimization: highest DPR with the Shillelagh cantrip

Question

I'd like to optimize my character concept:

I want my main damage source to be a Shillelagh'd weapon and squeeze that source for all it's worth.

Table character limitations:

• Character is level 5
• Point buy for level 1 ability scores
• No multiclassing allowed
• Variant Humans and Duergar are banned
• Each character gets a free feat at level 1, provided they qualify for that feat at level 1
• All official sources are allowed and can be mixed, but UA is only allowed on a per case basis (so preferably not used), no homebrew

Optimization Goals:

• Highest average damage per round possible, using Shillelagh
• Secondary goal is highest effective number of hit points, assuming a well mixed pool of damage sources

Bonus points for:

• Not using UA
• Actually having a use for my Wisdom score besides whacking with Shillelagh

So far I have:

• Hill dwarf for the juicy Con and Wis + free HP
• Go Fighter, archetype Champion for extra attack DPR and heavy armor + shield + armored fighting style
• Take Magic Initiate feat level 1 for Shillelagh + absorb elements
• Pump Wis with ASI

Answer 1

Since you have a number of criteria, I had to go through each one by importance to find the best build (or builds in this case). You can find a TL;DR below with a description of my methods after.

TL;DR

The best build optimizing:

• DPR using shillelagh
• Effective HP
• Uses for Wisdom

Race: Envoy Warforged (secondarily: Simic Hybrid or Hill Dwarf)

Class: Ranger

Ability Scores: 8/16/16/8/16/8 (or 10/14/16/10/16/8 for 2 less EHP, non-Warforged also use this latter array)

Level 1: Magic Initiate (Druid): shillelagh spell
Level 2: Dueling Fighting Style, hunter's mark spell
Level 3: technically Gloom Stalker for uses of Wisdom, but Hunter and Monster Slayer are otherwise equal
Level 4: Polearm Master feat

Starting Equipment: (with just starting equipment, Hill Dwarf is a slightly better secondary race)
Scale Mail (not needed if Warforged)
Quarterstaff

Equipment Wishlist: (with this equipment, Simic Hybrid is a better secondary race)
Half Plate (not needed if Warforged)
Shield

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First, the DPR without using major resources, here are the best builds for each class:

I allowed for a margin of 20%, so any build that got within 20% of the best build is eligible since it may have other criteria that make up for its slightly less resource-less DPR. I skipped Monk and Sorcerer because they offer strictly less than Fighter and Wizard respectively no matter what build you choose.

You can check out the class name sheets of this spreadsheet for some other builds which were elimintated as well as how these builds were decided

Bard

• College of Swords with the Dueling Fighting Style and the Polearm Master feat.
  • Highest resource-less DPR
• College of Swords with the Dueling Fighting Style and the Elven Accuracy feat
  • Within 20% if Armor Class (AC) is 23 or higher and you have advantage
• College of Swords with the Dueling Fighting Style and +2 to Wisdom
  • Within 20% if AC is 24 or higher and you have advantage

Cleric

The clerics include either magic weapon or elemental weapon

• War or Forge Domain with Polearm Master
  • Highest resource-less DPR
• War Domain with Elven Accuracy
  • Within 20% if AC is 24 or higher and you have advantage
• Forge Domain with Elven Accuracy (with Elemental Weapon active)
  • Within 20% if AC is 20 or higher and you have advantage
• Forge Domain with +2 to Wisdom (with Elemental Weapon active)
  • Within 20% if AC is 23 or higher, but only if AC is 24 or higher if you have advantage

Druid

• Circle of Spores with Polearm Master and +2 to Wisdom
  • Highest resource-less DPR unless you have advantage and AC is 16 or higher; then it is within 20%
• Circle of Spores with Polearm Master and Elven Accuracy
  • Highest resource-less DPR if you have advantage and ACs is 16 or higher; within 20% otherwise
• Circle of Spores with Elven Accuracy and +2 to Wisdom
  • Within 20% if AC is 24 or higher and you have advantage

Fighter

• Champion with the Dueling Fighting Style and the Polearm Master Feat
  • Highest resource-less DPR
• Champion with the Dueling Fighting Style and +2 to Wisdom
  • Within 20%
• Battle Master with the Dueling Fighting Style and the Polearm Master Feat
  • Within 20% if AC is 21 or less

Paladin

• Oath of Vengeance with the Dueling Fighting Style and the Polearm Master feat (using Hunter's Mark)
  • Highest resource-less DPR unless you have advantage and AC is 23 or higher; then it is within 20%
• Oath of Vengeance with the Dueling Fighting Style and +2 Wisdom (using Hunter's Mark)
  • Within 20% when AC is 11 or higher, but only when AC is 17 or higher if you have advantage
• Oath of Vengeance with the Dueling Fighting Style and the Elven Accuracy feat (using Hunter's Mark)
  • Highest resource-less DPR if you have advantage and AC is 23 or higher; otherwise only within 20% if you have advantage and AC is 13 or higher

Ranger

Each build includes Hunter's Mark damage. I used Colossus Slayer as the Hunter's Prey choice for simplicity, other options are explored later

• Hunter with the Dueling Fighting Style and the Polearm Master feat
  • Highest resource-less DPR if AC is 14 or lower when you have advantage, and when AC is 19 or less without; within 20% otherwise
• Horizon Walker (HW) with the Dueling Fighting Style and +2 Wisdom
  • Highest resource-less DPR if AC is 20 or higher and you don't have advantage; within 20% otherwise
• Horizon Walker with the Dueling Fighting Style and the Elven Accuracy feat
  • Highest resource-less DPR if you have advantage and the AC is 15 or higher; within 20% otherwise unless you don't have advantage and AC is 23 or higher
• Hunter with the Dueling Fighting Style and +2 Wisdom
  • Within 20%
• HW, Gloom Stalker, or Monster Slayer with the Dueling Fighting Style and the Polearm Master feat
  • Within 20% if AC is 23 or lower without
• Hunter with the Dueling Fighting Style and the Elven Accuracy feat
  • Within 20% if you have advantage

Warlock, Pact of the Tome

Each build includes Hex damage. I assumed that you could get one-fourth of your attacks on the target of Hexblade's Curse within short rests for the calculation. I assumed you could hit a second target with Green-Flame Blade on one-third of your attacks

• Hexblade with the Elven Accuracy feat and +2 Charisma using Green-Flame Blade
  • Highest resource-less DPR
• Hexblade with the Polearm Master and the Elven Accuracy feats
  • Within 20% if you have advantage, but only if AC is 22 or lower without advantage
• Hexblade with the Polearm Master feat and +2 Charisma
  • Within 20%, but only if AC is 17 or lower when you have advantage

Warlock, Pact of the Blade

Each build includes Hex damage. I assumed that you could get one-fourth of your attacks on the target of Hexblade's Curse within short rests for the calculation.

• Hexblade with Improved Pact Weapon, Thirsting Blade, and Eldritch Smite for Invocations and the Polearm Master feat
  • Highest resource-less DPR
• Hexblade with Improved Pact Weapon, Thirsting Blade, and Eldritch Smite for Invocations and +2 Charisma
  • Within 20% when AC is 12 or higher unless you have advantage; then it is only within 20% if AC is greater than 18
• Hexblade with Improved Pact Weapon, Thirsting Blade, and Eldritch Smite for Invocations and the Elven Accuracy feat
  • Within 20% if AC is 14 or higher and you have advantage

Wizard

I assumed you could hit a second target with Green-Flame Blade on one-third of your attacks

• Wizard with +2 Wisdom using Green-Flame Blade
  • Highest resource-less DPR
• Wizard with Elven Accuracy using Green-Flame Blade
  • Within 20% if AC is 23 or less when you have advantage, but only if AC is 21 or less without

Now let's eliminate any class whose best builds can't step to the better classes

You can check out the "Classes" sheet of this spreadsheet for which builds were considered

Going down the list...

• The best bard, cleric, and druid builds do not meet the 20% threshold of the best fighter builds
• The best fighter builds stay within the 20% threshold of the best paladin builds when AC is 14 or higher (during advantage) or when AC is 17 or higher (without advantage)
• The best fighter and paladin builds do not meet the 20% threshold of the best ranger builds
• The best Pact of the Tome warlock builds do not meet the 20% threshold of the best ranger builds
• The best Pact of the Blade warlock builds challenge the best ranger builds on approximately the same level (the ranger builds are better at some ACs or advantage-statuses, and the warlock builds are better at others)
• The best wizard builds do not meet the 20% threshold for the best builds among either Pact of the Blade warlocks or rangers

Our final builds (weeding out the weak Ranger and Warlock builds)

You can check out the "Warlock vs Ranger" sheet of this spreadsheet for which builds were considered, as well as which builds are better with which combinations of AC and advantage

After placing the Ranger and Warlock builds into the same pool, and only accepting builds that satisfy the 20% threshold of at least half of the Armor Classes and advantage-statuses between AC 14 and AC 20 (where most enemies will be at level 5), these builds remain:

These builds are in order of the number of AC/advantage-statuses they satisfy the threshold for, with more weight placed if they have the highest value and slightly less value placed on advantage

• Hunter Ranger with the Dueling Fighting Style and the Polearm Master feat
• Hexblade Warlock with Improved Pact Weapon, Thirsting Blade, and Eldritch Smite for Invocations and the Polearm Master feat
• Horizon Walker (HW) Ranger with the Dueling Fighting Style and the Elven Accuracy feat
• Horizon Walker Ranger with the Dueling Fighting Style and +2 Wisdom
• HW, Gloom Stalker, or Monster Slayer with the Dueling Fighting Style and the Polearm Master feat

Second, the additional damage per day gained using other resources

Each of the five builds we arrived at have passable resource-less DPR, but they each have features that allow for other damage-increasing effects usually one or a few times before a short or long rest. It is all but impossible to evaluate which is best, so I will just give my thoughts:

• The Hunter Ranger with the Dueling Fighting Style and the Polearm Master feat has no extra damage throughout the day, but is the best overall damage (especially if you are in a campaign where you can take advantage of Giant Killer or Horde Breaker frequently, which can have more DPR than Colossus Slayer in the right situations)
• The Hexblade Warlock with Eldritch Invocations and the Polearm Master feat can use Eldritch Smite about 6-8 times per adventuring day and if you save them primarily for critical hits can deal about 70 extra damage throughout the day
• The Horizon Walker Ranger with the Dueling Fighting Style and the Elven Accuracy feat is only better than the Hunter Ranger above if you expect to get advantage more often than not; It also lacks additional DPR from other resources.
• The Horizon Walker Ranger with the Dueling Fighting Style and +2 Wisdom is only better than the Hunter Ranger and Horizon Walker Ranger above if you expect to have monsters of very high AC (22 and above) and don't expect to have advantage that frequently.
• If you are going to use a non-Hunter Ranger with the Dueling Fighting Style and the Polearm Master feat, you should either choose the Gloom Stalker or Monster Slayer. The Gloom Stalker gets an extra attack during the first turn of every combat, and the Monster Slayer gets to deal 1d6 damage per attack against one creature per short rest. Each of these bonuses will usually about catch them up with the builds above in most games, but in the right style of game they can even take the lead.

Now, let's talk effective HP

Since all of these five builds are approximately equal when it comes to damage output, let's evaluate them based on your second criteria. The following table shows the effective HP (EHP) for an optimized version of each of our builds:

HW = Horizon Walker; GS = Gloom Stalker; MS = Monster Slayer

\begin{array}{c|r|r} \text{Build} & \text{EHP with best starting gear} & \text{EHP with best mundane gear} \\ \hline \text{Polearm Hunter} & 141 & 184 \\ \text{Polearm Hexblade} & 122 & 161 \\ \text{Elven HW} & 116 & 160 \\ \text{Wise HW} & 141 & 184 \\ \text{Polearm GS/MS} & 141 & 184 \\ \end{array}

I used this spreadsheet to calculate EHP, which assumes, among other things (source)...

• 75% of damage is physical, divided evenly between bludgeoning, slashing and piercing
• 25% of damage is elemental, divided evenly between all ten elements
• Characters are being attacked by creatures with attack bonuses and spell DCs that follow the DMG guidelines for a creature with a CR equal to character level – 2
• 80% of attacks are made against AC
• 10% of attacks require a Dexterity Save
• 5% of attacks require a Wisdom Save
• 5% of attacks require a Constitution Save
• A negligible amount of attacks require a Charisma, Strength or Intelligence Save

As you can see, the Warlock build falls behind the Rangers when it comes to EHP. Furthermore, the Elven Horizon Walker can't keep up because of the race restrictions of Elven Accuracy.

• The best race to be for Effective HP is an Envoy Warforged. You assign point buy and racial modifiers so that your ability scores are 8/16/16/8/16/8. This gives you an AC of 18 (20 with a shield), Maximum HP of 49, and resistance to poison.
  • note: you only lose 2 EHP if you go for 14 Dexterity and you can have two of your lesser stats at 10 instead of 8
• The Elven Horizon Walker's best alternate is a Sea Elf. You assign point buy so that your ability scores are 10/16/16/8/15/8 and then increase Wisdom with Elven Accuracy. This gives you an AC of 16 with scale mail (19 with half plate and a shield).
• The Warlock still uses the Warforged, but simply has less HP from his class, and worse starting equipment.

If Warforged are not an option for your table, there are two races to substitute depending on what equipment you get:

Simic Hybrid (10/14/16/10/16/8) gets +1 AC from Carapace and results in this table:

\begin{array}{c|r|r} \text{Build} & \text{EHP with best starting gear} & \text{EHP with best mundane gear} \\ \hline \text{Polearm Hunter} & 123 & 182 \\ \text{Polearm Hexblade} & 84 & 159 \\ \text{Elven HW} & 116 & 160 \\ \text{Wise HW} & 123 & 182 \\ \text{Polearm GS/MS} & 123 & 182 \\ \end{array}

Hill Dwarf (10/14/16/10/16/8) gets +5 HP from Dwarven Toughness and results in this table:

\begin{array}{c|r|r} \text{Build} & \text{EHP with best starting gear} & \text{EHP with best mundane gear} \\ \hline \text{Polearm Hunter} & 125 & 174 \\ \text{Polearm Hexblade} & 89 & 154 \\ \text{Elven HW} & 116 & 160 \\ \text{Wise HW} & 125 & 174 \\ \text{Polearm GS/MS} & 125 & 174 \\ \end{array}

The armors for these non-Warforged builds are Scale Mail for starting equipment (Leather for the Warlock), and Half Plate for best mundane.

With the considerations of EHP, the optimal builds for your criteria are narrowed down to:

• Hunter Ranger with the Dueling Fighting Style and the Polearm Master feat
• Horizon Walker Ranger with the Dueling Fighting Style and +2 Wisdom
• Gloom Stalker or Monster Slayer with the Dueling Fighting Style and the Polearm Master feat

Although, I'd recommend against the Horizon Walker Ranger with the Dueling Fighting Style and +2 Wisdom since it is only as effective in damage output when Armor Class is 22 or higher.

Which Polearm Dueler to choose (Hunter, Gloom Stalker, or Monster Slayer)

We've addressed your two main criteria and come to the conclusion that a Warforged (or Simic Hybrid/Hill Dwarf) ranger with the Dueling Fighting Style and the Polearm Master feat is the most fitting. As we've shown, the three Ranger Archetypes Hunter, Gloom Stalker, and Monster Slayer all are relatively equal. First of all, you should choose the one that is more fitting of your campaign.

• If you expect to be able to gain great advantage from one of the Hunter’s Prey features then you should choose Hunter.
• If you expect to have many combats throughout the day, you should choose Gloom Stalker to benefit more from the extra attack of Dread Ambusher.
• If you expect to have many short rests to refresh your uses of Slayer’s Prey and expect mostly single enemies as combatants, you should choose Monster Slayer.

If you don't expect any of these to present itself more than any other, then we move to your bonus criterion:

Actually having a use for my Wisdom score besides whacking with Shillelagh

If this is the last criterion, then Gloom Stalker is best.

• Dread Ambusher gives a bonus to initiative based on Wisdom
• Gloom Stalkers get disguise self, and the investigation DC will be based on Wisdom

Answer 2

Hunter Ranger

Wisdom is one of the Ranger's main stats, you get martial features that are very strong at this level, as well as very strong utility in the form of spells and abilities. Combat-wise, you get:

• Dueling fighting style
• Extra Attack, Hunter's Prey (your pick)
• Spells (like Hunter's Mark)

You also get Favored Enemy, Natural Explorer and non-combat spells, for utility. Assuming you have cast Shillelagh, Hunter's Mark (at level 5, you can do this 6 times a day) and chosen Colossus Slayer, this means you do 3d8 + 2d6 + 4 + (Wis mod * 2) damage when you land both your attacks on a single-target.

Compared with the Fighter, you lose some AC (medium-armor only), but you may not have disadvantage on Stealth checks, depending on which armor you choose to use. You also lose Second Wind and Action Surge (each once per short rest), and Improved Critical. I haven't done the math for Champion, but I think at level 5 you can out-DPR it as a Hunter Ranger.

As per comments suggested, this build takes Shillelagh from Magic Initiate if you're a Hill Dwarf. Otherwise, a Wood Elf has the Wood Elf Magic feat in Xanathar to take the cantrip (less HP than the Dwarf, but some extra Dex, and other Elf perks, like Elven Accuracy).

Answer 3

As an alternative to a generic anything-with-Extra-Attack-answer:

Draconic Sorcerer 5.

Benefits:
Twinned Booming Blade, allowing you to charge your stick with thunder and bash two people at once for 1d8 (bludgeoning) + 1d8 (thunder) + Wis-mod, and if those enemies move later an extra 2d8 thunder.
Draconic Sorcerer gets an increased AC and extra health (stack it with Hill Dwarf to have an unreasonably healthy sorcerer).
Haste will allow you to get another stickbash out every turn, while ensuring your enemies can't flee from your stick.
Shield will give you a ton of survivability to stick around in melee.

The downside of this is a bit of multi-ability-dependency in the build, but there are plenty of sorcerer spells that don't use charisma at all - selecting those (haste, blink, mirror image, blur, etc..) allows you to go all in on the Wisdom-melee style.

To maximize the DPR of this combination, you'd use the Magic Initiate feat to get Shillelagh and the level 4 ASI to bump Wisdom to +4

Action: Twin Booming Blade (4d8+2xWis)
Haste Action: Attack (1d8+Wis)
Bonus Action: Quickened Booming Blade (2d8+Wis)

AC10 DPR: 40.375
AC15 DPR: 28.5
AC20 DPR: 16.625

This is expensive though - at 3 sorcery points a round, you could only keep this up for 6 rounds each day.

Taking Polearm Master instead of the ASI nets you a 25% DPR decrease, but allows you to maintain this for a paltry 1 sorcery point per round.

A Ranger with Polearm Master, Dueling, Colossus Slayer, and Hunter's Mark is below for comparison:

Action: 2x Attack (3d8+2d6+2xWis+4)
Bonus Action: Polearm Master (1d4+1d6+Wis+2)

AC10 DPR: 33.2
AC15 DPR: 22.825
AC20 DPR: 12.45

This costs next to nothing to keep up - only a single 1st level spell that may be carried between encounters.

Answer 4

Monk is fun and competitive

A monk's AC is directly tied to its Wisdom score (and Dexterity)

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Race:

• Elf (Bishtahar, Joraga, Tirahar, Vadahar, or Wood) +2 Dex / +1 Wis
• Aarakocra: +2 Dex / +1 Wis / Flying 50'
• Aven (Hawk-headed) +2 Dex / +1 Wis / Flying 50'
• Genasi (Water) +2 Dex / +1 Wis / +Resistant to Acid
• Kenku +2 Dex / +1 Wis / Some interesting RP abilities
• Shifter (Wild Hunt) +2 Wis / +1 Dex / Bonus Action: Level + Con THP for 1 min (1/rest)

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Staring array:

• 15 (Dex or Wis) +1 from race
• 14 (Wis or Dex) + 2 from race
• 14 (Con)
• 10 (Cha)
• 9 (Str)
• 9 (Int)

Most of the races offer +2 Dex and +1 Wis. To be efficient, you'll probably want to match up the 15 stat with your +1 Wis so that it ends up an even number and nets you the next +1 to your mod without wasting a point. If you go Shifter, you'd just make Dex the 15 so that you end up with a pair of 16s for your top stats either way.

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Feats / ASI

Level 1: Free feat - Magic Initiate to make it a Shillelagh build.

Level 4: +2 Wisdom. This increases your hit and damage by +7/+4

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DPR / Features

• Three to four attacks (if you spend the Ki) @ +7 to hit, with two at d8+4 and two at d6+3 (~20 ADPR max)
• Standing AC: 16AC. If you go with Kensai, you can trade 1 club attack for an unarmed strike and add +2 and end up at 18AC. This does mean probably one or two fewer points of damage that round, though.
• If you go with Open Hand, your Stunning Strike save DC would be 15
• Several races offer flying speeds which allow you to rely on hit and run tactics at even greater distances to help keep you out of the frontline when it's not your turn. This makes your HP go further.
• If you land a stunning strike: Advantage for at least 3 or 4 attacks!

One thing to note is that, next level, you pick up Ki Powered Strikes which would be redundant with the benefit of Shillelagh (womp womp).

Answer 5

hexblade bladelock, something that gets +cha

Hexblade lets you attack with charisma. Quarterstaff is versatile rather than two-handed, so it's legit (you won't be using the versatile bit. It's redundant). For invocations, take Thirsting blade at level 5, giving you two attacks per attack action. Take Polearm mastery feat at level 4. That'll give you butt-stroke as a bonus action. With shillelagh, it's doing 1d8 rather than 1d4. Cast Hex

After a startup of one turn where you only hit twice, you get three attacks per round of 1d8+1d6+3(cha)... which is about on par with a ranger who's doing the same thing, except that your hex spells refresh on a short rest, and you have hexblade's curse to play with if the fight is going to be long enough to deserve two setup turns.

Really, though, you're trying to optimize the wrong thing. Optimization for melee damage is never going to get you a druid or a cleric. Beyond those, the only class that cares about wisdom is monk, and they can already use the staff with dex. They also don't have any reason to not use it two-handed, which makes it 1d8 damage anyway... so monks have no need for shillelagh. The non-monk melee heavy-hitters out there can all use martial weapons one way or the other, which will get you that 1d8 damage pretty readily, which means that the only thing it nets you there is the ability to take polearm mastery and deal damage on the butt-stroke... if you have that feat. Glaive does it better, too, which means that you pretty much also need to be using a shield.

Basically, shillelagh is there to give druids something they can do in melee. It's good at that. It's not good at anything else.

You can do this, but there's really not much there to squeeze.