Agreed.
But if you have just one encounter in a day, the wizard can cast those level 3+ spells every round, whereas the fighter can only use their resources once. The fighter only gets to use 1/3rd of their daily resources, but the wizard gets to use almost all of theirs.
Agreed. General wizard vs fighter power comparison is beyond the scope of this comparison. - However I am trying to show that the balance point does change with different numbers of encounters. (Or rounds of combat.)
The wizard dealing more damage than the fighter in the first encounter is less important than the wizard's power reducing with the number of encounters, whereas the Fighter's power remains steadier.
I was assuming the superiority dice were used in precision attack to turn misses into hits. Your earlier analysis showed the fighter seemed to be dealing 12 damage per attack, which translates to a rather unlikely 18 damage per hit given a 65% hit rate. If the hit rate was significantly improved through precision attack, that would explain the numbers.
However, the more attacks you make, the more SD you will need to burn to maintain that high DPR. Between level 6 and level 13, you get 50% more attacks, but only gain a single SD. Given the SD are a chunk of your effective damage, your DPR will go up by less than 50% when you get 50% more attacks.
Technically, the ballpark 150 damage in 3 rounds for a level 13 fighter that I estimated based on your figures was probably too high, because it depends on a hit rate that the fighter cannot maintain at that level.
Ah. That would explain the difference in our experiences. Generally if I do a single major encounter in a day, it will have more than just a couple of opponents in it.