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:

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.

	Brian Lara: only six not-outs in 232 Test innings © Getty Images

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.

"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.

	A familiar end to a Chris Martin innings © AFP

As Mathew Varghese pointed out in his post-match stats piece after the Johannesburg Test, Martin is already the proud holder of three records – the most number of pairs in Tests, the most zeroes in Tests between South Africa and New Zealand, and in Tests at the Wanderers.

The table below shows just how far ahead of the rest of the pack Martin is: in 25 completed innings, he has failed to get off the mark 19 times. Taking a cut-off of 20 dismissals in Tests, Martin is far ahead of his nearest competitor, Danish Kaneria. If he continues at his current rate of a duck every 1.79 Test, Martin will get his 44th – and go past Courtney Walsh’s world record – in his 79th match.

Meanwhile, here’s a response to the queries about genuine batsmen with the most propensity to score ducks. Taking a cut-off of 50 Test innings, and an average of at least 30, India’s Pankaj Roy comes out on top. Among specialist batsmen, Marvan Atapattu and Steve Waugh have the most number of ducks – 22 – but while Atapattu makes it to the list below, Waugh’s zeroes came over 260 innings, which means his percentage was only 8.46.

	Courtney Walsh: a true giant in the art of making zeroes © AFP

In 1996, Danny Morrison passed the record for most ducks in Test cricket amid a blaze of publicity and memorabilia. Bhagwat Chandrasekhar had held the record with 23 at that stage. Morrison subsequently passed the baton (if you will excuse the truly abysmal pun) to Courtney Walsh, who still holds the record with 43. Muttiah Murailtharan has been dismissed first ball for a duck on no fewer than 14 occasions in Test cricket.

But, what about ducks in first-class cricket? Reg Perks, of Worcestershire and England (twice, in 1939), collected 156 ducks in his first-class career, which is a record. Perks was not the world’s worst batsman: he scored 8956 runs, including 14 fifties, at an average of 12.20 in 595 first-class matches.

But a major candidate for champion duck maker in first-class cricket is Kevin Jarvis of Kent and Gloucestershire. Jarvis is the only batsman with over 100 dismissals in first-class cricket to have ducks as more than 50% of his dismissals. In his 199 first-class innings he was not out 87 times and made 59 ducks, which represents 52.69% of the total innings in which he was dismissed. In all, Jarvis scored 403 runs at an average of 3.59. He did, of course, make up for this by taking 674 wickets. He reached 20 for the first, and only, time in his 255th first-class match (Gloucestershire v Hampshire at Portsmouth in 1989) and played only 5 more matches before retiring.

And what of Seymour Clark? He played 5 first-class matches for Somerset (all in 1930) and in 9 innings (two of which were not outs) he did not score a run. He did not take a wicket either. He was a wicketkeeper and presumably must have been a very good one just to get a game.

Then there is the 1, the much-neglected score. If a century is a mark of batting excellence and a duck is a mark of batting ineptitude, then a 1 must be the non-batsman’s equivalent of 99. I briefly considered nominating the word ‘drake’ for ones to go with ducks for noughts. But it would probably be considered inappropriate, in these egalitarian times, for the male of the species to represent a higher value than the female.

The most dismissals for 1 in Test cricket is 12 by Javagal Srinath and Glenn McGrath.

Three players have been dismissed for 1 eleven times in Tests: Curtly Ambrose, Courtney Walsh and, surprisingly, Rod Marsh. And Adam Sanford was an impressive 1-maker. He was dismissed eight times for 1 out of his 15 Test dismissals (53.33%), including each of his last 4 innings. Then there’s Walter Reader-Blackton. In addition to having a name that was almost as long as his first-class career (8 matches for Derbyshire between 1914 and 1921), he was also the first player to be dismissed for 1 in five consecutive first-class innings.

And another world record for Shane Warne. He has been dismissed for 2 more often than anyone else in Test cricket – 11 times.

Cricket, more than almost any other sport, lends itself perfectly to analyses by numbers. The game has enough stats to satiate the most voracious appetite but there are so many delightfully different ways of looking at them that there’s always scope for debates, arguments and opinions. It Figures is a forum to rake up all those arguments, but also to delight in the quirks of all the trivia that so much stats can throw up. Read on ...