The data available to the algorithm is the number of people in each age group, and the number of CEV, hopefully by age.
The assumptions of the model are
- how many are being vaccinated each day or week (some models allow you to change this according to what is being reported on the news)
- That priority groups are being vaccinated in order, eg all 80+s before they start on the 75-80
It then does the same calculation as you would, ie - there are X people in a higher priority group than you still waiting for a vaccination (and Y people in your group).
N people per week are being vaccinated, so you will have to wait at least X/N weeks (and you may have to wait (X+Y)/N weeks if you're the last person in your group to be vaccinated).
So it may be "just" a mathematical formula. But I can't see any better way of doing it short of today actually making an appointment for everybody in the country - and that would be liable to huge change because of missed appointments and re-bookings, fluctuations in the supplies of vaccine, staff administering the vaccines going off sick, etc.
They bear zero relation to the real world is a bit of an overstatement, to say the least.