Dungeons and Dragons - Memes and Comics

I'm curious of some math. So let's look at Fireball as a spell.

Fireball at 3rd level in 5e does 8d6 of damage in a 20 foot radius, with half-damage on a dex save. Then, each higher level gives it an extra 1d6 damage.

Two base fireballs is 16d6 while a 9th level fireball is only 14d6 so obviously the sorcerer can do more damage total, but the wizard only takes one round to cast theirs, while the sorcerer takes two.

If the wizard casts their fireballs in decending order of power, then its:

14d6+13d6+2(12d6)+2(11d6)+3(10d6)+3(9d6)+4(8d6)

Mapping that to rounds looks like this:

We can see on this chart that it takes the sorcerer 21 rounds to roll more dice than the wizard does at 16 after expending all spell slots.

Ergo, Wizard is better if combat is less than ~~17 rounds~~ 21 rounds