Cross-Correlation in cricket data and RMT

TL;DR

This paper applies random matrix theory to analyze cross-correlations in cricket scoring data across different formats and periods, revealing universal spectral properties and a dominant influence factor.

Contribution

It introduces a novel application of RMT to cricket data, demonstrating universal eigenvalue distributions and identifying a common influence across matches.

Findings

Eigenvalues mostly follow Marchenko-Pastur distribution.

Fluctuations align with Gaussian Unitary Ensemble behavior.

Largest eigenvalue indicates a common influence across matches.

Abstract

We analyze cross-correlation between runs scored over a time interval in cricket matches of different teams using methods of random matrix theory (RMT). We obtain an ensemble of cross-correlation matrices $C$ from runs scored by eight cricket playing nations for (i) test cricket from 1877 -2014 (ii)one-day internationals from 1971 -2014 and (iii) seven teams participating in the Indian Premier league T20 format (2008-2014) respectively. We find that a majority of the eigenvalues of C fall within the bounds of random matrices having joint probability distribution $P(x_1...,x_n)=C_{N \beta} \, \prod_{j<k}w(x_j)| x_j-x_k |^\beta$ where $w(x)=x^{N\beta a}\exp(-N\beta b x)$ and $\beta$ is the Dyson parameter. The corresponding level density gives Marchenko-Pastur (MP) distribution while fluctuations of every participating team agrees with the universal behavior of Gaussian Unitary Ensemble (GUE). We analyze the components of the deviating eigenvalues and find that the largest eigenvalue corresponds to an influence common to all matches played during these periods.