Good answer, but the criteria of belt promotion are really subjective from an academy to another one. There are so many criteria of attribution (example age, previous grappling/judo/sambo/luta livre/wrestling background, natural aptitudes like superb coordination movements, rapid learning, exceptionnal physical condition).
I remember in my former academy that a young girl in her early twenties got her purple in 3 years ( 1 year white belt and 2 years blue belt) despite starting one year before me because she becomes so addict that she trains twice a day/ 5 days a week and competes a lot (from IBJJF Europeans, Nationals, Abu Dhabi, Rio....etc).
As well a guy starting at his forties but is a crossfit / pilates instructor and got his purple belt in a little more than 3 years and half after earning a bronze medal at the IBJJF Europeans Master 3 blue belt.
At my current academy, I had a purple belt from another academy in the late forties he earned after 3 years and half due to his age and 15 years of judo and competed a few in BJJ but he does a lot of errors and his level is below the average.
The average criteria in my current academy is 3 years as white belt, 3 years as blue belt, 2 years as purple 2 years brown but again it depends on the age and the progress / consistency in training, a woman in her early forties who competes often got promoted blue belt after 2 years of white belt, It took me less than a 1 year and a half to be promoted blue belt before I left to return to my country and at my current academy, I got trashed as a blue belt and I spent 3 years and 3 months as a blue belt (and competing more than a dozen of times) before being promoted purple belt so you see the criteria are very subjective from an academy to another!