D&D 5E (2014) An Argument for Why Paladins are the Strongest Class in 5E D&D

For simplicity's sake, I'll just model the Paladin's hit rate at 60%, and the spellcaster's DC results in an enemy failing the save 60% of the time ...

Fireball (3rd-level slot):
.6*28 + .4*14 = 22.4

Single Divine Smite (3rd-level slot)
(Paladin level is 9, has longsword w/ Dueling FS and 18 STR):
(1-(1-.6)^2) * 18) + (2 * .6 * (4.5+6)) = 27.72

So in this very simple scenario, the single Divine Smite turn is outdamaging the Fireball vs. single target by about 24%.

(Of course, the Paladin also keeps his spell slot if he misses both attacks, but I don't know how to model that part mathemetically.)

A caster will have 5th level slot by the time the paladin has 3rd level slots.
 

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An upcast Fireball, same conditions, deals avg. 28 damage. So slightly more than the 3rd-level single-smite turn.

Sounds good so far. Now The Paladin can miss his 2 attacks which will mean he doesn't use a spell slot 16% of the time in your example. To offset that he will need to smite twice 16% of the time. Since he only has an opportunity to smite twice 36% of the time. This means 16% of the time he will double smite (when both attacks hit) and 20% (he will hit with both attacks but single smite)
 
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I'm getting for a level 9 paladin that uses 1 spell slot on average a turn will deal 32.4 DPR (using his level 3 slots first and a 60% chance to hit). This can be further increased with hunters mark (at the cost of more spells per fight)

I'm getting a fireball upcast to 5th level will do 25.2 damage (assuming 60% chance for failed save).

Paladin in this example is doing 29% more damage than the fireball.
 






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