Anomalous Diffusion and Long-range Correlations in the Score Evolution of the Game of Cricket

TL;DR

This study analyzes cricket score evolution, revealing it as an anomalous diffusive process with super-diffusive behavior, long-range correlations, and universal Gaussian distribution, modeled effectively by a generalized Langevin equation.

Contribution

It uncovers the anomalous diffusion and long-range correlations in cricket scores and introduces a generalized Langevin model with power-law correlated noise to explain these phenomena.

Findings

Scores follow a super-diffusive power-law variance

Scores are statistically self-similar with a Gaussian distribution

Long-range correlations are present in score evolution

Abstract

We investigate the time evolution of the scores of the second most popular sport in world: the game of cricket. By analyzing the scores event-by-event of more than two thousand matches, we point out that the score dynamics is an anomalous diffusive process. Our analysis reveals that the variance of the process is described by a power-law dependence with a super-diffusive exponent, that the scores are statistically self-similar following a universal Gaussian distribution, and that there are long-range correlations in the score evolution. We employ a generalized Langevin equation with a power-law correlated noise that describe all the empirical findings very well. These observations suggest that competition among agents may be a mechanism leading to anomalous diffusion and long-range correlation.