Snooker Statistics and Zipf's Law

TL;DR

This paper demonstrates that snooker statistics follow Zipf's law, revealing that the frequency of certain game outcomes adheres to a power law pattern, with parameter values influenced by ranking type and time-frame.

Contribution

It extends the application of Zipf's law to snooker statistics, analyzing how power law parameters vary across different rankings and time periods.

Findings

Snooker prize money and centuries scored follow power law distributions.

Parameter values vary significantly with ranking type and time-frame.

Temporal variations in parameters suggest changing dynamics in snooker statistics.

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 (estimated) parameter values. Two types of rankings (prize money earned and centuries scored), and three 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.