EDIT: The goal of the build is to optimize a gun-toting Giff. The Giff have a racial trait that specifically only applies to firearms, so I'm trying to determine how good it can be. I'm aiming for the highest infinitely sustainable damage possible with firearms, maintaining the damage output while expending no resources. Having expendable resources that can be used for several combats a day are bonuses, but for the base build I'm going for zero-resource expenditure.
And for a basis of comparison, I've added the DPR of a Warlock using only Agonizing Eldritch Blasts, without any resource expenditure to show how this stacks up. Keep in mind, Eldritch Blast can't harm non-creatures, and some creatures are immune to the effects of Cantrips, whereas nothing that I'm aware of that WotC has published is immune to magical weapons.
Background: Silverquill Student (For Silvery Barbs when he needs an enemy to fail the save against Faerie Fire)
L1-2 Class: Artificer: Taking the Repeating Shot and Mind Sharpener Infusions at L2. Prepare Faerie Fire spell.
L3+ Class: Fighter: Psy Warrior: The Fighter levels give the highest number of attacks possible, the Archery Fighting Style which grants a +2 on all ranged weapon attacks, and a few expendable resources that can significantly increase damage output.
L6 ASI: Sharpshooter Feat: deny enemies 1/2 & 3/4 cover, while already ignoring the disadvantage for long range with firearms for being a Giff. And the +1 from the Repeating Shot Infusion and the +2 from the Archery Fighting Style offset 3/5 of the penalty for getting the extra +10 on weapon damage
L8 ASI: Gunner Feat: only benefit here is not being at disadvantage for shooting within 5ft, and getting Dex to 18.
10 ASI increase Dexterity to 20 for maximum accuracy and damage.
L14, 16, & 18 ASIs increase Intelligence to 20 for highest effectiveness on Artificer Saves and Psy Warrior features. (Which can buff damage higher, but isn't part of the base I'm calculating for)
Artificers begin play with a Light Crossbow, and it's plausible to acquire a Heavy Crossbow by L3, when this character gains proficiency with Martial Weapons, and the character has the crafting proficiencies to hopefully build a Musket by L5
The following doesn't account for to-hit chance, because that would require a whole chart for low, mid, and high AC enemies, and if needed, the character can forgo the attack penalties and extra damage from Sharpshooter if needed to hit targets. And outside of the zero-resource-expenditure parameters, the character can give himself advantage via Faerie Fire on the target.
Level 1: Artificer 1
+5 Attack Bonus: +3 (Dex) +2 (Prof)
7.5 Avg DPR: 1d8 (Light Crossbow) + 3 (Dex)
(5.5 Avg DPR for L1 Character's Eldritch Blast, +5 Att Bonus)
(42 Avg DPR for L20 Character's Agonizing Eldritch Blast, +11 Att Bonus)
That's 337.5 average damage in half of a minute of combat. I don't think that's bad for no resource expenditure. Below I've provided how much damage the character can do with expenditure of resources.
Touching on the Expendable Resources this character has that can buff that damage to higher levels:
Faerie Fire: Gained at L1, The Mind Sharpener Infusion helps keep the concentration on this, and the advantage from this spell can help the character land more of his Sharpshooter shots.
Giff: Astral Spark: Adding the character's Proficiency Bonus as extra damage a number of times equal to his Proficiency Bonus is a nice, reliable bit of extra damage when needed. It is once-per-turn though.
Fighter: Action Surge: 1/Short Rest at L4, gain a second use per Short Rest at L19.
Fighter: Psy Warrior: Psionic Strike: The extra damage on the first hit per turn when a Psionic die is expended is significant, and it scales as the character levels.
Fighter: Psy Warrior: Telekinetic Master: At L20, can cast Telekinesis with no components, and for the duration of the concentration attack as a Bonus Action, bringing the attacks per turn up to 4 (or 7 when using Action Surge) At L20, if Psionic Dice aren't being used for other things, this easily allows this feature to be used for every combat, every day. And the Mind Sharpener Infusion from Level 2 helps ensure that the concentration isn't broken.
If the character uses the fact that Telekinesis lasts for up to 10 minutes to cast it just before Initiative is rolled, and uses all of the expendable resources, the damage output becomes the following:
L20: Artificer 2, Fighter: Psy Warrior 18
+9 Attack bonus, ignoring long range penalties, 1/2 cover and 3/4 cover.
Avg 22.5 damage on each of 2nd-7th Hits: 1d12 (Musket) +5 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)
Total Damage for 1st turn = 175 Average Damage.
Total Damage for 2nd turn = 175 Average Damage.
Total Damage for 3rd turn = 107.5 Average Damage.
Total Damage for 4th turn = 107.5 Average Damage.
Total Damage for 5th turn = 107.5 Average Damage.
That's 672.5 damage in half of a minute, that could be put on a single target, but also has the versatility to be spread between as many as 26 targets.
@FayetteGamer I would drop the Artificer levels and go straighter 20 Fighter. Next (assuming you are using Tasha's option to move racial stat increases) I would drop STR or WIS by 2 in order to bump DEX up to 17. Finally I would replace one of the ASIs you used for a +2 to DEX and use it to take the Gunner feat. This build also nets you an extra ASI so you can also max your INT.
What the build gives up is a +1 to hit and damage from the infusion and the low level spellcasting from the Artificer class. But what it gains is 4 attacks per Action instead of 3 and no disadvantage to attacking enemies that are 5 ft from you, making you deadly from range or in close combat.
While I am too lazy to crunch the numbers, I think an extra attack per Action should more than offset the +1 bonus of the infusion.
I don't know why this is Giff-based, but the best firearms build I know of offhand is a half-elf samurai with Elven Advantage, Sharpshooter, and Gunner.
You might want to rework your numbers for AC 20 or 22, since a level 20 character isn't likely to face something with an AC of only 18.
Also, 100 damage at level 20 probably isn't that high.
But personally I've never played at level 20 so any "max damage at level 20" theorycrafting isn't useful to me.
Could you come up with a plan that would provide maximum DPS through all the levels of the class rather than only at level 20?
I've re-worked the original post, covering levels 1-10, as well as 20 for the zero-resource-expentiture build.
I wouldn't expect the zero-expenditure to be dealing as much damage as a resource-using build. That would be like a cantrip wizard trying to keep up with one using his spell slots. My goal is for the character's output without using resources to be high enough that there's only really motivation to use them for the big fights. He loses some of the high-end damage for the reliability of medium-high damage.
@FayetteGamer I would drop the Artificer levels and go straighter 20 Fighter. Next (assuming you are using Tasha's option to move racial stat increases) I would drop STR or WIS by 2 in order to bump DEX up to 17. Finally I would replace one of the ASIs you used for a +2 to DEX and use it to take the Gunner feat. This build also nets you an extra ASI so you can also max your INT.
What the build gives up is a +1 to hit and damage from the infusion and the low level spellcasting from the Artificer class. But what it gains is 4 attacks per Action instead of 3 and no disadvantage to attacking enemies that are 5 ft from you, making you deadly from range or in close combat.
While I am too lazy to crunch the numbers, I think an extra attack per Action should more than offset the +1 bonus of the infusion.
I tweaked the Ability Scores and added the Gunner Feat.
I've kept the Artificer levels primarily because the Repeating Shot Infusion removes the need for ammunition, which prevents the weapon from ever becoming dead weight due to lack of bullets, and it makes the weapon magical, which means it should be able to damage literally any creature. I may be wrong, but I don't think any creatures are immune to magical weapon damage.
The Mind Sharpener Infusion also helps keep up Faerie Fire, and at L20, Telekinesis. Each in their own way help improve damage output when concentrated on.
EDIT: The goal of the build is to optimize a gun-toting Giff. The Giff have a racial trait that specifically only applies to firearms, so I'm trying to determine how good it can be. I'm aiming for the highest infinitely sustainable damage possible with firearms, maintaining the damage output while expending no resources. Having expendable resources that can be used for several combats a day are bonuses, but for the base build I'm going for zero-resource expenditure.
And for a basis of comparison, I've added the DPR of a Warlock using only Agonizing Eldritch Blasts, without any resource expenditure to show how this stacks up. Keep in mind, Eldritch Blast can't harm non-creatures, and some creatures are immune to the effects of Cantrips, whereas nothing that I'm aware of that WotC has published is immune to magical weapons.
Starting Point:
Assuming no magic items awarded by DM.
Point Buy: (10 Str, 17 Dex, 14 Con, 14 Int, 12 Wis, 8 Cha)
Race: Giff
Background: Silverquill Student (For Silvery Barbs when he needs an enemy to fail the save against Faerie Fire)
L1-2 Class: Artificer: Taking the Repeating Shot and Mind Sharpener Infusions at L2. Prepare Faerie Fire spell.
L3+ Class: Fighter: Psy Warrior: The Fighter levels give the highest number of attacks possible, the Archery Fighting Style which grants a +2 on all ranged weapon attacks, and a few expendable resources that can significantly increase damage output.
L6 ASI: Sharpshooter Feat: deny enemies 1/2 & 3/4 cover, while already ignoring the disadvantage for long range with firearms for being a Giff. And the +1 from the Repeating Shot Infusion and the +2 from the Archery Fighting Style offset 3/5 of the penalty for getting the extra +10 on weapon damage
L8 ASI: Gunner Feat: only benefit here is not being at disadvantage for shooting within 5ft, and getting Dex to 18.
10 ASI increase Dexterity to 20 for maximum accuracy and damage.
L14, 16, & 18 ASIs increase Intelligence to 20 for highest effectiveness on Artificer Saves and Psy Warrior features. (Which can buff damage higher, but isn't part of the base I'm calculating for)
Artificers begin play with a Light Crossbow, and it's plausible to acquire a Heavy Crossbow by L3, when this character gains proficiency with Martial Weapons, and the character has the crafting proficiencies to hopefully build a Musket by L5
The following doesn't account for to-hit chance, because that would require a whole chart for low, mid, and high AC enemies, and if needed, the character can forgo the attack penalties and extra damage from Sharpshooter if needed to hit targets. And outside of the zero-resource-expenditure parameters, the character can give himself advantage via Faerie Fire on the target.
Level 1: Artificer 1
+5 Attack Bonus: +3 (Dex) +2 (Prof)
7.5 Avg DPR: 1d8 (Light Crossbow) + 3 (Dex)
(5.5 Avg DPR for L1 Character's Eldritch Blast, +5 Att Bonus)
Level 2: Artificer 2
+6 Attack Bonus: +3 (Dex) +2 (Prof) +1 (Repeating Shot Infusion)
8.5 Avg DPR: 1d8 (Light Crossbow) + 3 (Dex) + 1 (Repeating Shot Infusion)
(8.5 Avg DPR for L2 Character's Agonizing Eldritch Blast, +5 Att Bonus)
Level 3: Artificer 2, Fighter 1
+8 Attack Bonus: +3 (Dex) +2 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style)
9.5 Avg DPR: 1d10 (Heavy Crossbow) + 3 (Dex) + 1 (Repeating Shot Infusion)
(8.5 Avg DPR for L3 Character's Agonizing Eldritch Blast, +5 Att Bonus)
Level 4: Artificer 2, Fighter 2
+8 Attack Bonus: +3 (Dex) +2 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style)
9.5 Avg DPR: 1d10 (Heavy Crossbow) + 3 (Dex) + 1 (Repeating Shot Infusion)
(9.5 Avg DPR for L4 Character's Agonizing Eldritch Blast, +6 Att Bonus)
Level 5: Artificer 2, Fighter Psy Warrior 3
+9 Attack Bonus: +3 (Dex) +3 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style)
10.5 Avg DPR: 1d12 (Musket) + 3 (Dex) + 1 (Repeating Shot Infusion)
(19 Avg DPR for L5 Character's Agonizing Eldritch Blast, +7 Att Bonus)
Level 6: Artificer 2, Fighter Psy Warrior 4
+4 Attack Bonus: +3 (Dex) +3 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
20.5 Avg DPR: 1d12 (Musket) + 3 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)
(19 Avg DPR for L6 Character's Agonizing Eldritch Blast, +7 Att Bonus)
Level 7: Artificer 2, Fighter: Psy Warrior 5
+4 Attack Bonus: +3 (Dex) +3 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
41 Avg DPR: 2x [1d12 (Musket) + 3 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)]
(19 Avg DPR for L7 Character's Agonizing Eldritch Blast, +7 Att Bonus)
Level 8: Artificer 2, Fighter: Psy Warrior 6
+5 Attack Bonus: +4 (Dex) +3 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
43 Avg DPR: 2x [1d12 (Musket) + 4 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)]
(21 Avg DPR for L8 Character's Agonizing Eldritch Blast, +8 Att Bonus)
Level 9: Artificer 2, Fighter: Psy Warrior 7
+6 Attack Bonus: +4 (Dex) +4 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
43 Avg DPR: 2x [1d12 (Musket) + 4 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)]
(21 Avg DPR for L9 Character's Agonizing Eldritch Blast, +9 Att Bonus)
Level 10: Artificer 2, Fighter: Psy Warrior 8
+7 Attack Bonus: +5 (Dex) +4 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
45 Avg DPR: 2x [1d12 (Musket) + 5 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)]
(21 Avg DPR for L10 Character's Agonizing Eldritch Blast, +9 Att Bonus)
And...
L20: Artificer 2, Fighter: Psy Warrior 18
+9 Attack Bonus: +5 (Dex) +6 (Prof) +1 (Repeating Shot Infusion) + 2 (Archery Fighting Style) - 5 Sharpshooter
67.5 Avg DPR: 3x [1d12 (Musket) + 5 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)]
(42 Avg DPR for L20 Character's Agonizing Eldritch Blast, +11 Att Bonus)
That's 337.5 average damage in half of a minute of combat. I don't think that's bad for no resource expenditure. Below I've provided how much damage the character can do with expenditure of resources.
Touching on the Expendable Resources this character has that can buff that damage to higher levels:
Faerie Fire: Gained at L1, The Mind Sharpener Infusion helps keep the concentration on this, and the advantage from this spell can help the character land more of his Sharpshooter shots.
Giff: Astral Spark: Adding the character's Proficiency Bonus as extra damage a number of times equal to his Proficiency Bonus is a nice, reliable bit of extra damage when needed. It is once-per-turn though.
Fighter: Action Surge: 1/Short Rest at L4, gain a second use per Short Rest at L19.
Fighter: Psy Warrior: Psionic Strike: The extra damage on the first hit per turn when a Psionic die is expended is significant, and it scales as the character levels.
Fighter: Psy Warrior: Telekinetic Master: At L20, can cast Telekinesis with no components, and for the duration of the concentration attack as a Bonus Action, bringing the attacks per turn up to 4 (or 7 when using Action Surge) At L20, if Psionic Dice aren't being used for other things, this easily allows this feature to be used for every combat, every day. And the Mind Sharpener Infusion from Level 2 helps ensure that the concentration isn't broken.
If the character uses the fact that Telekinesis lasts for up to 10 minutes to cast it just before Initiative is rolled, and uses all of the expendable resources, the damage output becomes the following:
L20: Artificer 2, Fighter: Psy Warrior 18
+9 Attack bonus, ignoring long range penalties, 1/2 cover and 3/4 cover.
Action Surge for first two turns of combat.
Avg 40 damage on 1st Hit: 1d12 (Musket) +1d12+5 (Psionic Strike) 5 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter) +6 (Astral Spark)
Avg 22.5 damage on each of 2nd-7th Hits: 1d12 (Musket) +5 (Dex) + 1 (Repeating Shot Infusion) +10 (Sharpshooter)
Total Damage for 1st turn = 175 Average Damage.
Total Damage for 2nd turn = 175 Average Damage.
Total Damage for 3rd turn = 107.5 Average Damage.
Total Damage for 4th turn = 107.5 Average Damage.
Total Damage for 5th turn = 107.5 Average Damage.
That's 672.5 damage in half of a minute, that could be put on a single target, but also has the versatility to be spread between as many as 26 targets.
You might want to rework your numbers for AC 20 or 22, since a level 20 character isn't likely to face something with an AC of only 18.
Also, 100 damage at level 20 probably isn't that high.
But personally I've never played at level 20 so any "max damage at level 20" theorycrafting isn't useful to me.
Could you come up with a plan that would provide maximum DPS through all the levels of the class rather than only at level 20?
@FayetteGamer I would drop the Artificer levels and go straighter 20 Fighter. Next (assuming you are using Tasha's option to move racial stat increases) I would drop STR or WIS by 2 in order to bump DEX up to 17. Finally I would replace one of the ASIs you used for a +2 to DEX and use it to take the Gunner feat. This build also nets you an extra ASI so you can also max your INT.
What the build gives up is a +1 to hit and damage from the infusion and the low level spellcasting from the Artificer class. But what it gains is 4 attacks per Action instead of 3 and no disadvantage to attacking enemies that are 5 ft from you, making you deadly from range or in close combat.
While I am too lazy to crunch the numbers, I think an extra attack per Action should more than offset the +1 bonus of the infusion.
I don't know why this is Giff-based, but the best firearms build I know of offhand is a half-elf samurai with Elven Advantage, Sharpshooter, and Gunner.
I've re-worked the original post, covering levels 1-10, as well as 20 for the zero-resource-expentiture build.
I wouldn't expect the zero-expenditure to be dealing as much damage as a resource-using build. That would be like a cantrip wizard trying to keep up with one using his spell slots. My goal is for the character's output without using resources to be high enough that there's only really motivation to use them for the big fights. He loses some of the high-end damage for the reliability of medium-high damage.
I tweaked the Ability Scores and added the Gunner Feat.
I've kept the Artificer levels primarily because the Repeating Shot Infusion removes the need for ammunition, which prevents the weapon from ever becoming dead weight due to lack of bullets, and it makes the weapon magical, which means it should be able to damage literally any creature. I may be wrong, but I don't think any creatures are immune to magical weapon damage.
The Mind Sharpener Infusion also helps keep up Faerie Fire, and at L20, Telekinesis. Each in their own way help improve damage output when concentrated on.