If all you care about is observable evidence then you should start taking note of every run you do, the time you finish at and the number of deaths as well as the rewards. That's the only way you will yield a % drop rate and the only way you can prove it as being random.

Unfortuneately there is no such thing as random in game programming. In FFXI crafting we had the Tiers to go by, but we also had the Law of the Averages which dictates that if you have a 10% drop/HQ rate, you could fail 90 times in a row, then pop 10HQ/drop in a row and you average out 10%. You could just as well go 20 NQ, followed by 2 HQ, ad infinum.

At the end of a day there is a % drop rate, and the only thing that applies is the Law of the Averages according to you. The only pertinent question at hand is the average drop rate. And the only way to get a definite average drop rate is by taking notes of your runs.

Otherwise your speculative 2-3% is as unfounded as my hidden reward factor based on performance.