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November 28, 2007

The new, improved batting average

Anantha Narayanan

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:

Brian Lara and Sachin Tendulkar in Tests
Batsman Tests Innings Not-outs Runs Average Runs per Test
Brian Lara 131 232 6 11,953 52.89 91.2
Sachin Tendulkar 141 228 24 11,207 54.94 79.5

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 prepares to pull in the Hong Kong Sixes, Kowloon Cricket Club, October 28, 2007
 © AFP
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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.

Top 25 batsmen in terms of averages
Batsman Tests Innings Not-outs Runs Average
Don Bradman 52 80 10 6996 99.94
Michael Hussey 18 29 7 1896 86.16
George Headley 22 40 4 2190 60.83
Herbert Sutcliffe 54 84 9 4555 60.73
Graeme Pollock 23 41 4 2256 60.97
Everton Weekes 48 81 5 4455 58.62
Ricky Ponting 112 186 26 9504 59.40
Wally Hammond 85 140 16 7249 58.46
Garry Sobers 93 160 21 8032 57.78
Ken Barrington 82 131 15 6806 58.67
Eddie Paynter 20 31 5 1540 59.23
Jack Hobbs 61 102 7 5410 56.95
Jacques Kallis 111 189 31 9197 58.21
Len Hutton 79 138 15 6971 56.67
Kumar Sangakkara 68 112 9 5741 55.74
Clyde Walcott 44 74 7 3798 56.69
Rahul Dravid 113 193 23 9564 56.26
Mohammad Yousuf 77 130 10 6686 55.72
Sachin Tendulkar 141 228 24 11,207 54.94
Dudley Nourse 34 62 7 2960 53.82
Brian Lara 131 232 6 11,953 52.89
Kevin Pietersen 30 57 2 2898 52.69
Greg Chappell 87 151 19 7110 53.86
Matthew Hayden 91 162 13 7833 52.57
Javed Miandad 124 189 21 8832 52.57

Now let’s apply the adjustments related to not-out innings, and then have a relook at the averages.

Extended batting averages: top 25
Batsman ORuns NRuns ARuns TRuns EBA % of ave Last 10 inngs
Don Bradman 5868 1128 829 7825 97.81 97.87 565
Michael Hussey 1519 377 463 2359 81.34 94.39 757
George Headley 1642 548 263 2453 61.33 100.81 389
Herbert Sutcliffe 4098 457 530 5085 60.54 99.67 406
Graeme Pollock 2014 242 191 2447 59.68 97.88 677
Everton Weekes 4171 284 286 4741 58.53 99.85 455
Ricky Ponting 7913 1591 1381 10,885 58.52 98.52 520
Wally Hammond 5728 1521 931 8180 58.43 99.95 256
Garry Sobers 6124 1908 1273 9305 58.16 100.64 406
Ken Barrington 5843 963 807 7613 58.11 99.05 315
Eddie Paynter 1256 284 249 1789 57.71 97.43 511
Jack Hobbs 5067 343 355 5765 56.52 99.25 353
Jacques Kallis 6703 2494 1468 10,665 56.43 96.94 937
Len Hutton 5890 1081 813 7784 56.41 99.53 270
Kumar Sangakkara 4754 987 560 6301 56.26 100.93 984
Clyde Walcott 3419 379 356 4154 56.14 99.03 493
Rahul Dravid 8092 1472 1156 10,720 55.54 98.73 329
Mohammad Yousuf 5861 825 500 7186 55.28 99.21 510
Sachin Tendulkar 9044 2163 1082 12,289 53.90 98.11 438
Dudley Nourse 2612 348 351 3311 53.40 99.23 393
Brian Lara 11,245 708 337 12,290 52.97 100.16 634
Kevin Pietersen 2774 124 114 3012 52.84 100.29 450
Greg Chappell 5883 1227 862 7972 52.79 98.02 478
Matthew Hayden 7329 504 672 8505 52.50 99.87 448
Javed Miandad 7051 1781 925 9757 51.62 98.20 263

"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

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Posted by arun pathania on (October 18, 2008, 12:12 GMT)

king of kings

Posted by Prashant on (December 19, 2007, 14:27 GMT)

Forget the runs per test and calculate runs per innings... Lara is 51.52 and Tendulkar is 49.15. Given that lara bats at 3 and tendulkar at 4, the opportunity of scoring lara gets is more than tendulkar - especially if it is the last innings of a test. So there is hardly any difference between the two....

Posted by Goyal on (December 19, 2007, 14:07 GMT)

Hi,

Congrats on the lovely blog. Geeky and nerdy. However, one complaint. Can you guys do the right thing and enable full feeds instead of stupid partial feeds?

Posted by hemant on (December 19, 2007, 8:42 GMT)

These stats do not tell how many times sachin was the beneficiary of the lax umpiring.117 (vs WIN),109(vs SL),94(vs PAK) &50(vs NZ) are only some of the innings which should have been restricted to only single digits but weren't.Also he has always played to remain not out. Remember his comments after he scored 241* against Oz.

Posted by Vivek Gupta on (December 18, 2007, 22:18 GMT)

Interesting read. One suggestion- I think extending the N.O. innings BY the current form average overestimates the potential number of runs scored. A better measure would be to extend the inning TILL the current form average. For example, if the batsman's current form indicates 100 and batsman has scored only 10 when his inning was terminated then he should get 90 more runs NOT 100 more. In case, if the batsman has already scored more than his current form average then his incomplete inning should not get any more runs. I think this system is "fairer". However, I suspect that doing this will probably align the EBA closely with BA itself.

Posted by Vivek Gupta on (December 18, 2007, 22:15 GMT)

Interesting read. One suggestion- I think extending the N.O. innings BY the current form average overestimates the potential number of runs scored. A better measure would be to extend the inning TILL the current form average. For example, if the batsman's current form indicates 100 and batsman has scored only 10 when his inning was terminated then he should get 90 more runs NOT 100 more. In case, if the batsman has already scored more than his current form average then his incomplete inning should not get any more runs. I think this system is "fairer". However, I suspect that doing this will probably align the EBA closely with BA itself.

Posted by salman on (December 15, 2007, 13:33 GMT)

For proper alignment of averages of batsmen, a better suggestion would be to adjust their averages by excluding all innings V the rank minnows - Zimbabwe and Bangladesh. Now Tendulkar has played these two quite a lot as compared to Ponting, and I believe after excluding these puny bowling-attack oppositions, Ponting's average is still near a staggering 58, while Tendulkar's is around 52 - the gulf in their averages increases further.

Posted by salman on (December 15, 2007, 13:30 GMT)

Why question a "not out" if the batsman in question has not deliberately played out for a "not out" innings near the end - for example an accomplished Number 6 batsman not only returns not-out disproportionately more than any of the top order, but also in the process of his many innings has to sacrifice runs in order to shield the tail, even playing unorthodox at times to farm the strike. Imran's Khan's extra-ordinary batting average of 62 playing at Number 6 for Pakistan, happens to be n all-time best for all Test batsmen in history at that position, yet he returned not-out quite a few times, although hardly anyone can recall a single "selfish" innings during which he returned "not out" due to a conscious effort - he was left to shepherd the tail and the lower-order ever so often as a matter of fact.

Posted by mel pereira on (December 11, 2007, 5:40 GMT)

kudos for all the work put in, if you did it to stimulate discussion - it succeeded. Beyond that it's all for nothing. The present method is just fine. Nobody seems disturbed by it. If someone like a Lara were to feel slighted there is a simple solution: bat lower down in the order and increase one's chances of NOs. And for crying out loud, how in the world can you compare Bradman's averages when he did not have Bangladesh or Zimbabwe to beat up, like our present guys do.

Your system, though, may have some merit in setting a 'new' standard for ODIs, and even more in 20-20s. The latter is a new concept and averages can easily be adjusted to reflect your system, if chosen. It truly is worth a try as it makes a lot of sense. For example a Dhoni or a Hussey have a great advantage in this form of cricket coming in so late in the batting order.

Posted by Srivathsa on (December 3, 2007, 18:30 GMT)

We can add more confusion to the calculations. Why should each not out be extended by the average of the final 10 innings. Each not-out ought to be extended by the average of it's previous 5/10 out innings. Then we could check if the batsman had enough partners remaining and multiply the additional runs by a factor between 0.3 and 0.7 depending on how many batsmen were left. This can go on and on.

Even if Jacques Kallis had an average of 80 and Viv Richards had an average of 40 after doing all this - who would we go to watch?

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ABOUT THE AUTHOR

Anantha Narayanan
Anantha spent the first half of his four-decade working career with corporates like IBM, Shaw Wallace, NCR, Sime Darby and the Spinneys group in IT-related positions. In the second half, he has worked on cricket simulation, ratings, data mining, analysis and writing, amongst other things. He was the creator of the Wisden 100 lists, released in 2001. He has written for ESPNcricinfo and CastrolCricket, and worked extensively with Maruti Motors, Idea Cellular and Castrol on their performance ratings-related systems. He is an armchair connoisseur of most sports. His other passion is tennis, and he thinks Roger Federer is the greatest sportsman to have walked on earth.

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