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Seb-wejem
(Why would anyone cast burning hands at level 3 when they could cast fireball at level 3????) So why even compare a level 3 burning hands with a level 3 thunderwave? ...very unrealistic comparison there.....
I tried to pick aoe spells or single target spells at each level.
Level 1
Burning hands = 3d6 (10.5)
Thunderwave = 2d8 (9)
Level 2
Scorching Ray = 6d6 (21)
Melf's Acid Arrow = 6d4 (15)
Level 3
Fireball 8d6 (28)
**Really no AOE spell to compare this with at this level
Level 4
Icestorm 6d8 (27)
*a level higher and lower damage than fireball
Level 5
Cone of Cold 8d8 (36)
We could go on but the point is that fire spells just do more damage at comparable levels for when you get them and other similar spells. There may be other affects involved or whatever, but fire spells just tend to do more damage.
Lightning bolt deals the same as fireball, although I will admit it is more likely easier to hit more targets with fireball.
I think it is worth comparing spells at higher levels as well, particularly ones in comparison to an upscaled fireball spell. I think there could be plenty of occasions where casting an upscaled burning hands or thunderwave would be better than fireball, generally it comes down to location of allies and enemies, not every wizard is an evoker able to exclude their allies from the effects of a fireball.
Other spells worth looking at:
Level 2
Aganazzar's Scorcher: 3d8 fire
Shatter: 3d8 thunder
Snilloc's snowball swarm comes in a bit underpowered at only 3d6 cold
Level 4
Storm sphere: 2d6 bludgeoning to all in area (save for none) each round and 4d6 lightning 1/round for up to 1 minute. Area inside the sphere is also difficult terrain.
Vitriolic sphere: total 15d4 (37) acid
I would not be surprised if a spell called icy rays is eventually created which, unless it has an additional effect, deals the exact same damage as scorching ray except with cold damage. Fire just isn't the powerhouse that people seem to think it is and really doesn't deal more damage than other damage types, except in cases where the other spells have an additional effect that warrants a reduction in spell damage.