Certainly everyone got a numerical score at the end... but what letter grade should, say, a 77 be? There were no departmental standards, I don't have any particular personal standards, and I hadn't tried to match the difficulty of the exams to what was done previously.

I could do something like 90-100 = A, 80-89 = B, etc., but that is no less arbitrary than any other system, and in my experience it is customary (as well as, IMHO, a good idea) to write harder exams and then make the cutoffs more generous.