Comparison of Batting "Average" in Professional Cricket (ODI)

Abstract:

In cricket, the specialist batsman’s ability can be evaluated by a single summary statistic: The Batting Average which is ubiquitous in professional cricket. Quantifying batting performance is therefore fundamental to help with in-game decisions, to optimize team performance and maximize the chances of winning as these metrics exist to summarise the individual batting performance. Since the batting average sometimes overestimates the individual batting performance all of a sudden especially in the limited over format of the game, a different modification over Runs Per Innings (RPI) has been proposed to the existing formula of batting average to circumvent this problem. An attempt has been made to study the effectiveness of the newly proposed measurement on some selected recognised batsmen worldwide.

Introduction

In every cricket match, some measurements are done by a statistician. A very common measure of batting performance viz. the Traditional Batting Average (TBA) is taken into consideration which is computed as follows.

Simplicity is one of the principal reasons behind the popularity of the batting average. It is used to signify the contribution of the batsman over some time or series, to draw a comparison between batsmen, at times conditioned on some specific opposition, specific venue etc. It is a quite useful measure (as opposed to the total runs scored) for drawing both short-term and long-term comparisons between batsmen (e.g. during a series or tournament, performance over a year, or a career span).

Suppose a batsman has played 10 innings. Among those, he was dismissed on only one occasion. Here, the Traditional Batting Average exceeds even the maximum score and it will become ∞ irrespective of the runs scored if the batsman does not get out in any of the innings. So, the question is how much he can score if he was allowed to finish the innings in an ideal case. From a statistical perspective, the expected scores from not out innings can be evaluated by attaching some weights according to their position of batting i.e. at which position of the innings he/she comes to bat. The position plays a crucial role in the scoring capability of a batsman. The top 3 batsmen have got enough opportunity or balls to score more runs according to their scoring ability. Sometimes the middle-order batsman remained “not out” at the end of the innings because of the end of the match or no more balls left to play or won the match by chasing. So their scoring ability gets surpassed as they do not get a chance to show their full potential. Hence their batting average is unjustified compared to the opening batsmen.

Proposed Measure of Batting Average

It is always expected to score more runs than the current ‘not out’ score if he was allowed to complete his innings in that particular match. More precisely, there is a relation between the position of batting and the runs scored in case of an incomplete inning. In a 50 over game, there are 300 balls to be bowled by the bowling side in each innings. Obviously, the number of balls faced by the batsman is not uniformly distributed among the batting side. The topper the order the more opportunity to face the balls. In this regard, the up-gradation of the ‘not out’ runs are evaluated by suitably attaching weights. A batsman can play at various positions throughout his career span. So, the expected runs will be computed position-wise i.e. the weights are to be attached at each position of batting. It is a well-established result that a batsman’s scoring ability highly depends on his strike rate. That is why “number of balls faced” is an important statistic to be considered as a weight to the runs. Then summing up the updated runs of incomplete innings and actual runs of complete innings and divided by total innings played, the Proposed Batting Average (PBA) has been computed.

The top 3 positions of batting have not been taken into account as we have seen that average 1st wicket partnership is 36 and average balls faced by the opener is 41 in ODI. So, on average, the number 3 batsman gets approximately 100 - 150 balls to face and has a tendency to score higher than the middle or lower-order batsmen.

A comparison of all three measurements (TBA, RPI, PBA) of 28 selected batsmen is shown in the table below.

The last column indicates corresponding p-values of the test of significance whether the updated runs are statistically significant or not.

Conclusion

The primary objective of this study is to formulate the newly proposed batting average by applying it to those selected 28 cricketers. This measurement gives the most suitable or appropriate outcomes to the middle or lower order batsmen unlike the top order batsmen though gives a reliable estimate of the true average.

For MS Dhoni and Michael Bevan, the p-values are nearly 0 (approximated up to 6 decimal), which truly indicates that the Traditional Batting Average is a highly overestimated measure, also for those who usually come to bat at middle order or lower order position as they have a high chance of remaining “not out”. On the other hand, for the top order batsmen like Sachin Tendulkar, Sourav Ganguly (most of the times they played as an opener) and Virat Kohli, Kane Williamson (regarded as one of the best No. 3 batsmen in recent times), PBA (over the RPI) gives a more or less good measure of the true batting performance.