Measuring batting consistency and comparing batting greats across eras in Test cricket: Innovative application of statistical tools

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Australian cricketing great Don Bradman’s batting average could be 109.42, instead of the famed 99.94, according to a new study by the Indian Institute of Management Calcutta (IIM-C).

While there have been calculations by ICC and ESPN Cricinfo on who is the best batsman across cricketing eras, the study maintains that comparing batsmen like Gary Sobers, Viv Richards, Sachin Tendulkar, Brian Lara, Ricky Ponting and Rahul Dravid has proved to be a challenge on account of various dimensions of batting statistics such as batting average, batting consistency and longevity of careers. In addition, there are also challenges in comparing the quality of opposition bowlers across eras and the quality of runs scored against strong or weak opponents in home or away matches.

On the contrary, the research paper titled ‘Measuring batting consistency and comparing batting greats in Test cricket: Innovative applications of statistical tools’ by faculty members Sahadeb Sarkar and Anirban Banerjee of IIM-C has devised its own methodology to compare great batsmen in Test cricket across eras.

Based on the Weibull distribution model for a select group of batsmen, the study has come out with what it claims to be more accurate statistics. For instance, the study finds that while Bradman is outstanding for his batting average and quality of runs scored, Tendulkar is exceptional for his longevity and the opposition diversity he faced.

“Traditional methods of calculating a player’s batting average require assumptions that may not often be justified. Furthermore, a measure of batting consistency of a player is generally not provided, for example, by ICC or ESPN Cricinfo. Our work successfully addresses both of these issues using the Weibull distribution model for a select group of Test batsmen. It provides a reliable estimate of batting consistency which is statistically more rigorous than what is available in the existing literature. Batting average values produced by our statistically more rigorous method are different from those provided by the traditional method,” says Sarkar, a professor of the operations management group at IIM-C. As a result, Bradman’s batting average becomes 109.42 instead of 99.94. Based on Mahalanobis distance used for overall ranking of a select group of batting greats on the back of various combinations of the five criteria, the paper ranked Bradman (Australia) at the top, followed by Sachin Tendulkar (India), Len Hutton (England), K F Barrington (England) and Jacques Kallis (South Africa).

“Our study analyses batsmen’s performance in terms of five criteria, namely batting average, consistency or dependability, longevity, quality of runs scored and opposition diversity,” Sarkar explains.

The paper’s results show this through Bradman’s batting average being about five standard deviations above the averages of 32 top players while Tendulkar’s longevity is three standard deviations above the average longevity of others.

Instead of judging a batsman’s performance against individual bowlers, the paper takes into consideration the strength of the opposition team. Hence, runs scored by a batsman against a stronger opposition team, having a higher winning percentage, are given more weight than those scored against weaker opposition.

“We also consider if the runs were scored at home or away, and how well the opposition fared in such situations. This is done through our criterion called ‘index for quality runs scored’. For example, runs scored against an Australian side weigh more than those scored against a Bangladesh or a Zimbabwe team,” Sarkar adds.

The paper’s findings also reveal that Tendulkar outperforms his contemporaries like Lara, Ponting, Dravid and Kallis in terms of career records against the toughest opponents, both home and away.

Also, though knighted for his contributions to cricket and voted one of the five Cricketers of the 20th century by a 100-member panel of experts in 2000, Richards ranks below average in all categories, barring home Test second innings.

"Close inspection indicates that quality runs scored by Richards, as measured by the overall composite performance index value of 0.89, appear to be below average. Further, compared to other star players in our study, Richards’ batting average appears to be high only against England in both home and away matches, and against New Zealand and India only in home matches," the paper notes.

Going forward, the same methodology may be applied to study players of the IPL era who have played a sufficiently large number of innings (say, 50 innings or more), says Sarkar.