FormerlyHemlock
Hero
If your goal is to deal maximum damage while still holding a shield, then yes, the paladins win.
If you factor in defense, then the fighter wins.
If your goal is to do maximum damage while holding a shield, a multiclass abomination (Fighter 2/Warlock 2/Sorcerer X Crossbow Expert) probably wins.
If your goal is to do maximum damage without magic while holding a shield, fighter wins (though barbarian is competitive at low levels). Smiting is magic. Some people don't enjoy magic.
Personally I think trying to turn sword-and-shield into a max DPR thing is optimizing for the wrong metric. You're a tank; be a tank. Bash some guy in the face with your shield, knocking him prone, then grapple his leg with your free hand and stick it under your armpit so he can't get up, and enjoy the fact that he now has disadvantage on all attacks while your GWM buddy gets advantage on all of his attacks. You can kick the guy a few times if you feel like it for some extra damage, but the point is that once you've grabbed him, the guy is toast and you're pretty much invulnerable to him, thanks to your shield.
Concrete example: defense fighter in plate armor and shield (AC 21) shield bashes an Earth Elemental Prone (say Athletics +8 vs. the elemental's Athletics +5 means 61% chance of victory, and the fighter gets up to three attempts per turn including Shield Master) and then grapples it. The elemental needs a 13 or better at disadvantage to hit, and it does 2d8+5 damage on a hit, twice per turn. Plug "avg.2.13D?2d8+5" into the dice tool (http://maxwilson.github.io/RollWeb/Roll/) and it turns out that the elemental will do 4.53 average DPR to the fighter. Against the GWM Reckless attacking barbarian he'd be doing 24.09 DPR (halved for rage), but now he will only do 8.52 DPR against that same barbarian (again, halved for rage). Your contribution to the fight is that you cut the damage your team takes by 65%! That is awesome!
BTW, without a shield you'd be taking 7.04 average damage from the elemental once it is proned/grappled, and without Shield Master you'd have a harder time knocking it prone in the first place, but you could use your free hand to stab it twice per turn at advantage for avg.2.9A?d8+5 = 16.84 damage per turn, half that if no magic weapon. This illustrates the awesomeness of grappling: it goes from a disadvantageous fight (11.85 inflicted for 14.90 taken) to a cakewalk (16.84 inflicted for 7.04 taken) as soon as you grapple/prone the earth elemental. The earth elemental can try to break out but at only one attempt per turn it will take it more actions to break out than it takes you to re-impose the condition, and meanwhile you are beating its face in. Lesson: tactics matter even in a one-on-one fight. Don't just start making attacks, stack the deck in your favor first if you can.
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