That sounds about right.
I want to avoid the dry, stats heavy discussion about drop rates that occurs in this
post.
So the short answer is: If drop rates are random, than you will sometimes gets stuff very early (lucky!) and sometimes have trouble getting one to drop (unlucky) but most the time you'll be about average (middle of the bell curve, right along the expected line).
Given the game has a lot of items to drop, an average play through will have a handful of really luck drops and a handful of unlucky drops. That is just part of the expected randomness.