A Probabilistic Approach to Identifying Run Scoring Advantage in the Order of Playing Cricket

TL;DR

This paper introduces a probabilistic model to analyze how batting order and venue influence scoring advantages in cricket, revealing potential biases from toss decisions and proposing a Bayesian method to equalize scoring chances.

Contribution

It develops a Bayesian model to adjust target scores based on venue-specific scoring patterns, aiming to eliminate batting order bias in cricket match outcomes.

Findings

Winning teams batting first have a significant scoring advantage.

The likelihood of high scores is much lower if teams bat second.

A Bayesian model can standardize scoring chances across venues.

Abstract

In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big target for the opponent. However, the opponent may fail to show their natural batting performance in the second innings due to a number of factors, including deteriorated pitch conditions and excessive pressure of chasing a high target score. The advantage of batting first has been highlighted in the literature and expert opinions, however, the effect of batting and bowling order on match outcome has not been investigated well enough to recommend a solution to any potential bias. This study proposes a probability theory-based model to study venue-specific scoring and chasing characteristics of teams under different match outcomes. A total of 1117 one-day international matches held in ten popular venues are analyzed to show substantially high scoring advantage and likelihood when the winning team bat in the first innings. Results suggest that the same 'bat-first' winning team is very unlikely to score or chase such a high score if they were to bat in the second innings. Therefore, the coin toss decision may favor one team over the other. A Bayesian model is proposed to revise the target score for each venue such that the winning and scoring likelihood is equal regardless of the toss decision. The data and source codes have been shared publicly for future research in creating competitive match outcomes by eliminating the advantage of batting order in run scoring.