Simple algorithm to estimate probability based on past occurences?

Question

Suppose after N occurrences, there are P times that an event happens. The "naive" approach to estimate the probability of that event happen again the next time is P/N, but obviously the higher N is, the better our estimation.

What is a practical approach to model that "sureness" in the real world? I don't need something mathematically perfect, just something to make it a little bit more realistic. For example:

• if a footballer scores 9 goals in 40 matches then I want the algorithm to rate him higher than a footballer who scores 1 goal in 4 matches
• a movie with a rating of 8.0 with 100k votes should be placed higher than a 8.2 movie with 2k votes
• etc...

Answer 1

This looks like the wilson-score interval: http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval. The wilson-score solves the problem how to sort a 2d array.