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[dhruvdeepak]

http://blogs.cricinfo.com/itfigures/archives/2007/11/the_new_improved_batting_avera.php#more

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:

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.

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.

[keep-it-cool]

If the difference is so marginal (0-2% either way), is the effort really worth it??

[dhruvdeepak]

If the difference is so marginal (0-2% either way), is the effort really worth it??

it proved conclusively that sachin is better than lara 

[LosingNow]

If the difference is so marginal (0-2% either way), is the effort really worth it??

Eggjacktly...

It is my view, that over a sufficient # of innings ..the current average (which is simple to calculate and well understood) does a good job.

[dhruvdeepak]

yes he sort of proved that his analysis is pointless

[keep-it-cool]

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.

How about the small fact that Lara has played 4 innings more than SRT? Of course SRT will not likely make 750 runs in his next 4 innings ... but, isn't this more relevant than not-outs and the way the two batsmen played and average Batting Position Index??

[broadbat]

Of course SRT will not likely make 750 runs in his next 4 innings

Well a triple and a quad are still awaited.

[broadbat]

Btw does everyone know that Lara has been involved in the maximum number of defeats for a player. Of course this is a reflection of the quality of the players around him than Lara himself.

[LosingNow]

yes he sort of proved that his analysis is pointless

Also, it is my hypothesis.. that MEDIAN would be a better measure of central tendency .. as it is less susceptible to outliers and hence more stable than AVERAGE
--
I think I did this analysis a long time ago for a few players and found that the current average and median yielded similar comparative results for that small sample.

[Libran]

Batsman               Tests   Innings  NOs  Runs       Avg

Rahul Dravid           113     193      23     9564      56.26

Sachin Tendulkar    141     228       24    11,207    54.94

No of innings rather than number of Tests should be the measurable criteria .... A batsman may play in a Test but may not play in a particular innings... but the test gets counted and his average drops...

Anyways coming to the point of this post......

The difference in # of innings and runs between RD and SRT is 35 and 2443. In simple terms, if SRT stops playing as of today, RD needs to score 69.8 runs per innings to equal SRT...

However, given that RD may continue longer than SRT, my feel is that he could end up overtaking SRT's aggregate score... started 5 - 6 years later...but has piled on the runs whenever the opportunity was provided 

[keep-it-cool]

Batsman               Tests   Innings  NOs  Runs       Avg

Rahul Dravid           113     193      23     9564      56.26

Sachin Tendulkar    141     228       24    11,207    54.94

No of innings rather than number of Tests should be the measurable criteria .... A batsman may play in a Test but may not play in a particular innings... but the test gets counted and his average drops...

Isn't that how it is always done?

The difference in # of innings and runs between RD and SRT is 35 and 2443. In simple terms, if SRT stops playing as of today, RD needs to score 69.8 runs per innings to equal SRT...

I think you still have a hangover from last night the difference in runs is only 1643 - so, RD has to score 47 runs per innings!!

[kban1]

Isn't that how it is always done?

Yes. but the author of this article uses the test criteria when comparing Lara vs SRT -- which is misleading to the reader. I believe that is what ravi was pointing out.

[keep-it-cool]

Isn't that how it is always done?

Yes. but the author of this article uses the test criteria when comparing Lara vs SRT -- which is misleading to the reader. I believe that is what ravi was pointing out.

yeah .. that is silly. and, the author clearly knows it given the calculations he has done later ... just trying to use something to show how much not outs change things ...and then himself goes on to prove that it does not make much of a difference

[kban1]

I also dont agree with the authors contention that the rolling average of the last 10 innings be added to the not out score. I think the rolling average of the last 10 innings should be used as the cap score.

So a batsman with a RA of 75 over the last 10 innings should have 65 added to his not out score of 10 to make it 75, not another 75 added to make it 85. Fail to see the logic behind that.

[justforkix]

The difference in # of innings and runs between RD and SRT is 35 and 2443. In simple terms, if SRT stops playing as of today, RD needs to score 69.8 runs per innings to equal SRT...

I think you still have a hangover from last night the difference in runs is only 1643 - so, RD has to score 47 runs per innings!!

Yes, looks like ravi had one too many 

[RicePlateReddy]

I also dont agree with the authors contention that the rolling average of the last 10 innings be added to the not out score. I think the rolling average of the last 10 innings should be used as the cap score.

So a batsman with a RA of 75 over the last 10 innings should have 65 added to his not out score of 10 to make it 75, not another 75 added to make it 85. Fail to see the logic behind that.

You may have a point that this is arguably a little bit more accurate.

But what I derived from this well articulated analysis (and worthy one in my opinion) is that with a large number of innings, the effect of average inflation due to not outs is marginal. Perhaps one could have deemed so even without this formal argument and calculations, but it is good to see someone do the hard miles to indicate that such adjustments don't make much of a difference for the majority.

As I have argued before, I think a valuable metric (or at the least a useful exercise to see if the resultant metrics are any more insightful) would be a weighed average. The weightage is determined by the quality of the opposition at that point. This would discount the so-called minnow effect. At the same time, a weightage should also be placed on relative contributions. So for example, if everyone is out cheaply against a so-called minnow like Bangladesh but one guy stands tall and saves the day, then that innings gets higher credit. Basically, the average is influenced by a combination of (a) strength of the opposition until that test (i.e. bowlers' records until that point), and (b) relative contributions of other team batsmen in that test.  A tweak of (a) to consider career average of the bowlers may be permissible. A tweak of (b) to consider relative contribution of batsmen across both teams with (a) considered is also possible.

The first requirement to make this feasible is to create a database of innings by innings progress of all players including keying the test match played along with a "moving record until that point in time". A few sites exist that can seed this data in a time-efficient manner. Then, it reduces to a good set of queries/aggregation against the data. Additionally it is important that "functions" are predefined, so that someone who makes new suggestions that seem more useful can leverage work already done.

I hope to do it someday and tie it in to a good analytics front-end also, all running on open source software. If this seems of interest to you too, and any of you have the technical background and would like to pitch in, please drop me a note -- we could collaborate and make it easier on any one of us. 

[natty]

Here's a proposal, not for "correcting" batting averages (like most others here, I agree that this isnt particularly flawed esp if there are many innings), but for a graphical representation that can be used to compare batting performances that, for lack of a better term, I will call "survival probability"

On the X axis, we'll have 100 points, from 1 to 100.  Each of these represent the exact runs scored.  The last point 100 covers the score 100 and all scores beyond that.

The Y axis represents the cumulative probability of surviving and reaching that score.   So the curve will have a negative slope (as zero will have the highest possible survival value.. so if a batsman has played 100 innings and got 10 ducks,  Y1 = 90% indicating a 90% probability of exceeding zero.  The curve will be smooth and for those folks who havent reached many centuries will approach zero percent around or even before X=100.

Using this graph one can compare many players "survival" curves easily as the graph scales similarly on both axes (100 runs on X and 100 percent on Y)..  It should be possible to see exactly where the curves are well separated vs. where they are not so well separated.

It is pretty trivial to churn these graphs but I shall resist the temptation and do real work.

[RicePlateReddy]

Good point Natty.

[Libran]

The difference in # of innings and runs between RD and SRT is 35 and 2443. In simple terms, if SRT stops playing as of today, RD needs to score 69.8 runs per innings to equal SRT...

I think you still have a hangover from last night the difference in runs is only 1643 - so, RD has to score 47 runs per innings!!

Yes, looks like ravi had one too many 

I don't lose count of how much I drink...but, yes... this calculation was absolutely roobish