Snooker Statistics and Zipf’s Law

Abstract

Zipf’s law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown that snooker statistics also follow such a mathematical pattern, but with varying parameter values. Two types of rankings (prize money earned and centuries scored), and three different time frames (all-time, decade, and year) are considered. The results indicate that the power law parameter values depend on the type of ranking used, as well as the time frame considered. Furthermore, in some cases, the resulting parameter values vary significantly over time, for which a plausible explanation is provided. Finally, it is shown how individual rankings can be described somewhat more accurately using a log-normal distribution, but that the overall conclusions derived from the power law analysis remain valid.