I think Laplace's Rule of succession [1] could be better here. It assumes there are binary "successes" and "failures" (e.g. thumbs up/down). Let s be the number of "successes", n be the total number of data points (successes+failures), and 1/x the prior probability of a success. Then the probability that the next data point will be a success is:
(s + 1)/(n + x)
E.g. for prior probability 1/2 (success and failure initially equally likely), x=2, so
(s + 1)/(n + 2)
For a cafe aficionado, who spends most of their time in cafes, reading HN and thinking about formulas, the probability that some random cafe becomes their new favorite is virtually zero.
In other words: The more cafes you already know, the closer to zero the chance that a random one will be the best of them all.
So yeah, it is a formula for cafe lovers. Not for the casual person who is happy with a random filtered coffee swill from the vending machine. Those would have to add a base probability, turning the formula into something like b+n/(n+x)*(1-b).