The new, improved batting average
The batting average is a simple and convenient way of putting a number to a player’s ability with the bat, but often it doesn’t give the entire picture. One major problem with the conventional average – which is calculated by dividing the total number of runs scored by the number of completed innings – is the way it deals with not-outs. Consider the stats for two of the greatest batsmen in the modern era:
|Batsman||Tests||Innings||Not-outs||Runs||Average||Runs per Test|
Lara has scored nearly 750 more runs in ten fewer Tests than Tendulkar. His runs per Test is nearly 12 runs more than Tendulkar's. However his average is nearly two runs behind Tendulkar, primarily because of the number of not-outs that Tendulkar has had. It might be partly because of the way Lara played, almost always in an attacking mode. Possibly also because Tendulkar, with an average Batting Position Index, which is the average batting position at which a batsman has batted in, of 4.30 as against Lara's figure of 3.78, probably has a slightly higher chance of remaining not out.
I’ve developed a new measure, which I’ve named the extended batting average, that offers a solution to the problem created by the not-outs in the batting average. It is determined by allowing a batsman to complete his not-out innings in the fourth dimension, so to say, and then by dividing the new total of runs (current aggregate plus the additional runs deemed to have been scored) by the total number of innings played. This will be a fair measure of the batting average of batsmen.
The extension of an innings is done in a logical manner taking into account the batsman's form at the time he played the not-out innings. During the first 10 innings of his career, when an insufficient number of innings have been played to have a handle on his form, his not-out innings will be extended by his OBA (Out Bat Average, derived by dividing total number of runs in completed innings by the number of completed innings).
Afterwards, recent form takes over. The not-out innings is extended by a rolling innings average of his last 10 played innings. In this case even the not-outs are included so that a big not-out innings, indicating very good current form, is not ignored. Of course, a batsman might remain not-out on 10 and this will lower his recent form computation. However, that is more acceptable than ignoring an unbeaten 200.
Two examples illustrate this concept. Kumar Sangakkara, in the greatest form currently, has scored 984 runs in his last 10 innings at an innings average of 98.4. If he remains not out with, say, 32 in the next innings, it is fair to assume that he would extend his innings by another 98 runs, to 130, considering his outstanding form. A similar situation exists with Mohammad Yousuf and Kallis.
On the other hand, Sehwag is in the most wretched form of his career, having scored 189 runs in his last 10 innings with an innings average of 18.9. It is reasonable to expect that if he remained not out at 32, his innings will be extended by only 19 runs, to 51.
This is applied to each and every innings played by all the batsmen. Care is taken to ensure that the adjusted innings total does not exceed the batsman’s highest score. In other words, Lara's 375 will not be allowed to go past 400. However if the highest score by a batsman is a not-out innings, for example Lara's 400 not out and Tendulkar's unbeaten 248, that specific innings will be allowed to be extended. This, I think, is common sense.
Now the new total aggregate of runs is divided, this time with justification, by the total number of innings played.
Since this is a clear "what if", imagination-driven computation, practical factors such as the match getting over, the innings getting over, or a batsman running out of partners etc are ignored.
This is no mean task and there is no way can this be done manually since the "current form" computation has to be done for each and every innings played by a batsman.
The table for the top 25 batsmen (criterion 1500 Test runs), in order of extended batting average, is shown below. These are current up to the Delhi between India and Pakistan.
Now let’s apply the adjustments related to not-out innings, and then have a relook at the averages.
|Batsman||ORuns||NRuns||ARuns||TRuns||EBA||% of ave||Last 10 inngs|
"ORuns" are the Runs scored in the innings in which the batsman was dismissed. "NRuns" are the runs scored in the not-out innings. "ARuns" are the runs added to the not-out innings by extending these. "TRuns" are the new total runs, obtained by adding the runs in the previous three columns. "EBA" is the extended batting average, computed by dividing TRuns by the total number of innings played.
A few observations
In general the EBA benefits the batsmen with lower number of not-outs. Only five batsmen in this group, Headley, Sobers, Sangakkara, Lara and Pietersen, have benefited by the extended batting average, though in most cases the increase is marginal. Sangakkara has benefited quite considerably because of his recent form. The other batsmen have their extended batting averages lower than their normal batting averages by upto 5%. Hussey has lost the most, which is understandable since he has seven not-outs in the 29 innings he has played. Similarly Kallis has lost, which is explained by the fact that he has remained not out a whopping 31 times. However note Kallis' recent form.
Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems