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Using a plain vanilla fighter from the PHB, you pick Str 14 for one of your stats, pick a race like Mountain Dwarf or Half-Orc that gives you +2 to Strength for a starting Stength of 16. Use Half-Orc for Savage Attack (thanks to Someone_Evil for pointing that out).

Critials: You get an extra d6 on these from Savage Attacker. You roll a total of 15 d20 (12 attacks with advantage, 3 Lucky dice), and have 1/20th on each to crit, so you add 15/20 * 4d6 from critical damage, or about 15.3 points (with Great Weapon Fighting style).

Possible Improvements. It may be possible to eke out a few more points of optimization here and there, maybe by taking Archery for the +2 to hit vs Great Weapon Fighting for the +1.33 damage from die rolls, but then you would need another way go get adavantage on your attacks, as Mounted Combatant only works for melee.

Goodguy5 reports that in the new Mordenkainen Presents, the once-a-turn limit has been lifted on the Bugbear's Surprise Attack. This makes a large difference: pick Bugbear instead of Half-Orc and add +2d6 to all six attacks for an extra 42 * 95.9% = 40.28. Replace 3.125 points on crits from 1d6 Savage Attacker, with 5.25 points from 2d6 Surpise Attack, for another 2.125 and a total of +42.4 damage over the Half-Orc. This on top of the 192 gets you to 234 expected damage.

Using a plain vanilla fighter from the PHB, you pick Str 14 for one of your stats, pick a race like Mountain Dwarf or Half-Orc that gives you +2 to Strength for a starting Strength of 16. Use Half-Orc for Savage Attack (thanks to Someone_Evil for pointing that out).

Criticals: You get an extra d6 on these from Savage Attacker. You roll a total of 15 d20 (12 attacks with advantage, 3 Lucky dice), and have 1/20th on each to crit, so you add 15/20 * 4d6 from critical damage, or about 15.3 points (with Great Weapon Fighting style).

Possible Improvements. It may be possible to eke out a few more points of optimization here and there, maybe by taking Archery for the +2 to hit vs Great Weapon Fighting for the +1.33 damage from die rolls, but then you would need another way go get advantage on your attacks, as Mounted Combatant only works for melee.

Goodguy5 reports that in the new Mordenkainen Presents, the once-a-turn limit has been lifted on the Bugbear's Surprise Attack. This makes a large difference: pick Bugbear instead of Half-Orc and add +2d6 to all six attacks for an extra 42 * 95.9% = 40.28. Replace 3.125 points on crits from 1d6 Savage Attacker, with 5.25 points from 2d6 Surprise Attack, for another 2.125 and a total of +42.4 damage over the Half-Orc. This on top of the 192 gets you to 234 expected damage.

Our build beats the wizard soundly for a single target, and just barely beats a vanilla wizard when adding a second target. It does not beat an Evoker, who deals 240.

Maybe there is another fighter subclass or combination in auxiliary books that is even better, and more books are being printed. I'm sure if there is or will be a way to improve on this damage, some clever min-maxer will add a better answer.

You can easily see this is skewed: for the maximal number of about 800 opponents that could be hit by Meteor Swarm (assuming each needs at least 5x5 foot of space) we'd be looking at more than 92,000 damage. It would be very likely impossible to do as much damage with the fighter in a single turn without preparation.

Possible Improvements: Maybe there is another fighter subclass or combination in auxiliary books that is even better, and more books are being printed. I'm sure if there is or will be a way to improve on this damage, some clever min-maxer will add a better answer.

Our build beats the wizard soundly for a single target, and just barely beats a vanilla wizard when adding a second target. It does not beat an Evoker on two targets, who deals 240.

You can easily see this is skewed: if we had to beat the wizards on three targets, we would fail by wide margin. For the maximal number of about 800 opponents that could be hit by Meteor Swarm (assuming each needs at least 5x5 foot of space) we'd be looking at more than 92,000 damage. It would be very likely impossible to do as much damage with the fighter in a single turn without preparation.

Pick the combat style Great Weapon Fighting on level 2 and the Battlemaster subclass on level 3.

Pick the combat style Great Weapon Fighting on level 1 and the Battlemaster subclass on level 3.