June 1, 2012

A statistical analysis dissecting the extraordinary Test batting career of Don Bradman

He scored heavily: Others also did.
He started well: Not at all, he was not a great starter.
His hundreds were big: So what, many other also had big 100s.
He had a great defence: Quite a few other batsmen probably had better defence.
His temperament was great: Maybe, but Hobbs and Gavaskar et al also had excellent temperament.
He scored fast: Yes, possibly, but quite a few others scored faster.

So where did he get his near-100 average, around 65% higher than the next best. I will try to answer this question in objective terms.

First the criteria for selection of the list of batsmen. I do not want to lower the level to 2000 Test runs. This is a career of around 25 Tests and is too short for a study like this. I know that I will lose Pollock and Headley when I go above this point, but they played too few Tests to be of any real help in this analysis. At the end of 20 Tests, Hussey averaged 80 and Trott, 65. So this is too low a level. After a lot of deliberation I have fixed 4000 Test runs, approximately a Test career of 50 Tests, as the cut-off. This gives me 112 batsmen, a very decent selection.

First let me look at areas in which Bradman was decidedly human and failed more than many other batsmen. I will demonstrate this through a special graph as well as a table. The graph is more a player positioning chart than a routine graph. There are 3 related charts in each graph. In general the batsmen shown in relative positions are Bradman, top three and bottom two batsmen. The mean is also shown. There is no need to anything other than the normal Arithmetic Mean.

Graph of zeroes and single-digit dismissals

Bradman had seven zeroes out of 80 innings, which works to 8.8%. He was worse than most batsmen in the selected group. Out of 112 batsmen, he was 97th. A very average performer indeed. The best time to get Bradman was before he scored: and this happened once in 11 innings.

Why zero? A 1 or 3 or 8 is also a failure. So I expand the definition of a real failure to a single digit dismissal. Very few will argue with this. There may be rare instances of single digit dismissals which are good innings but let us ignore those. Bradman had 14 such instances, more than once in six attempts. His average was a very poor 2.2. So low that he is ranked LAST in the list of 112 batsmen. Yes, last, I repeat. This average does not make much of a difference in the overall context. However that means the string of Bradman's low scores was really low. Ah! we have located another Achilles heel. Get that shorty before he reached 10. You probably have won the match.

But the numbers do not tell the complete story. The batsmen in our selected set have played between 80 and 311 innings. So what we need is a % of the total innings played. This is the correct method of measuring success or failure. Bradman has failed in 17.5% of his career innings. But now we begin to see some daylight. Bradman is slowly moving up. There are others better than him, but he is placed in the 6th position. Pretty good. This also gives us a clue to what we are looking for. The specific averages seem comparable but the frequency of failures or successes may provide the clue. Anyhow lot more work needs to be done. The related table is given below.

Zeros  Sub-10
BatsmanCtyInnsNum%AvgeNum%

Hobbs J.BEng10243.9%3.21312.7%
Sutcliffe HEng8422.4%4.41214.3%
Hammond W.REng14042.9%3.72417.1%
Hutton LEng13853.6%3.62417.4%
Kanhai R.BWin13775.1%3.42417.5%
Dexter E.REng10265.9%2.71918.6%
Sangakkara K.CSlk18373.8%3.53519.1%
Sobers G.St.AWin160127.5%3.23119.4%
Graveney T.WEng12386.5%2.82419.5%
Hayden M.LAus184147.6%3.13619.6%
Barrington K.FEng13153.8%3.62619.8%
Lloyd C.HWin17542.3%4.43520.0%
Katich S.MAus9944.0%3.02020.2%
Wright J.GNzl14874.7%3.23020.3%
Compton D.C.SEng131107.6%2.62720.6%
Smith G.CSaf174105.7%3.43620.7%
Kallis J.HSaf257145.4%3.65421.0%
Gower D.IEng20473.4%4.64321.1%

I am going to move forward a little to my next group of graph/table. Without in any way conferring any additional credit for crossing these landmarks, I will use 100 and 150 merely as convenient cut-off points.

Graph of 100-plus and 150-plus scores

Let us first look at the 100-plus scores. The additional cut-off is that there should have been ten such scores. The average of these scores for Bradman is an impressive 186.0. Quite impressive indeed, until you look at the others following close behind. Zaheer Abbas is quite close behind with an average of nearly 180. And then Sehwag and Lara follow closely and are within 10-12 runs of Bradman's average. So Bradman is leading here, but nowhere with a dominating lead.

Now we will take the innings in which the batsmen crossed 150. This time the cut-off is 5 such scores. The average of these scores for Bradman is an impressive 225.8. Very impressive, until we see that Chris Gayle (why isn't he in whites, walking in with Barath/Powell ?), who averages even higher. He clocks in at 231.8. Then Jayasuriya is closely behind at 225.0. So Bradman is not even the leader in this sub-analysis.

Now let us look at this from another angle. Let us look at the frequency of such occurrences. Again, there is clear daylight. Bradman has crossed the 100 mark on 36.8% of the occasions, nearly double that of the next batsman. He has scored 150+ in an astonishing 22.5% of the batting forays. Next placed is Weekes, with 8.6%. Now we are beginning to get a handle on what made Bradman click. His frequency of crossing high landmarks was well over double of the others. Once he reached there, he and the others performed at par.

100s  150s
BatsmanCtyInnsAvgeNum%AvgeNum%

Zaheer AbbasPak124179.8129.7%207.886.5%
Sehwag VInd167176.32213.2%209.5148.4%
Fleming S.PNzl189176.194.8%220.852.6%
Lara B.CWin232173.23414.7%214.0198.2%
Jayasuriya S.TSlk188168.3147.4%225.063.2%
Hammond W.REng140167.52215.7%222.7107.1%
Gayle C.HWin159166.8138.2%231.863.8%
Simpson R.BAus111164.6109.0%203.265.4%
Sangakkara K.CSlk183163.32815.3%204.5147.7%
Atapattu M.SSlk156161.51610.3%206.585.1%
Jayawardene D.PSlk217159.43114.3%210.4146.5%
Gibbs H.HSaf154159.0149.1%192.974.5%
Dexter E.REng102157.398.8%180.654.9%
Hutton LEng138156.11913.8%197.1107.2%
Younis KhanPak133155.52015.0%214.175.3%
Gooch G.AEng215152.1209.3%194.683.7%
de Villiers A.BSaf125151.51310.4%195.064.8%
Sobers G.St.AWin160150.72616.2%189.8116.9%

For the third set of table/graph, which is going to be the defining one, I am going to work on 50 as a cut-off point. In fact I am going to take 50 runs as a point at which the batsman can be said to have done well. 50 is anyhow the minimum average we expect in top batsmen. And since we are doing a comparison exercise, the figure of 50 will remain the same for all batsmen, Bradman to Healy.

And let me say this. If anyone comes out with a comment that there have been great 40s and awful 60s, the comment will not see the light of the day.

Graph of sub-50 and 50-plus scores

First let us take the sub-50 scores. Bradman averages 18.4, which is well below a few other batsmen, 32 to be exact. So even in this relatively acceptable failure category, Bradman is ordinary, as ordinary as many other batsmen.

Now we come to the crunch point. What about the 50-plus scores.

I think we have got it. Bradman's average for 50-plus innings is a huge 149.9, He is nearly 30% ahead of the next best. Translate this bland number. Every time he reached 50, 42 times in all, while he raised his bat, he was mentally taking guard to add 100 runs to his score, on an average. If this single statement does not prove Bradman's exalted status as a batsman, nothing else will.

But lo and behold, he has also done this a remarkable 52.5% of the times he batted in. This is 10% more than the next best batsmen.

This is the only analysis point wherein Bradman has averaged well above the next best and has had a frequency much higher than the next best. In all other criteria, either his average is comparable or the frequency is comparable. Not in this. And let me do a back-of-stamp calculation. When I multiply these two differential values for selected batsmen, I get 50-60% which is almost the same as his overall superiority.

Sub-50  50 +
BatsmanCtyInnsAvgeNum%AvgeNum%

Hammond W.REng14020.99467.1%114.94632.9%
Lara B.CWin23217.715064.7%113.48235.3%
Sehwag VInd16718.211367.7%113.35432.3%
Atapattu M.SSlk15614.412378.8%113.13321.2%
Zaheer AbbasPak12416.09274.2%112.23225.8%
Sangakkara K.CSlk18318.811763.9%108.86636.1%
Clarke M.JAus13817.19770.3%108.24129.7%
Jayawardene D.PSlk21718.614566.8%107.67233.2%
Younis KhanPak13317.78866.2%107.64533.8%
Crowe M.DNzl13118.09673.3%106.23526.7%
Sobers G.St.AWin16020.210465.0%105.85635.0%
Pietersen K.PEng14519.410069.0%105.84531.0%
de Silva P.ASlk15916.611773.6%105.34226.4%
EdeC WeekesWin8118.64758.0%105.33442.0%
Hayden M.LAus18419.412567.9%105.25932.1%
Tendulkar S.RInd31117.519562.7%103.911637.3%
Gibbs H.HSaf15417.911474.0%103.24026.0%
Smith G.CSaf17419.411867.8%102.85632.2%
Slater M.JAus13118.09673.3%102.43526.7%

Finally a table/graph looking at this from a different angle. This looks at the average number of balls he faced per innings and his average runs per innings, leading to the average scoring rate.

Graph of runs per innings, balls per innings and scoring rate

Bradman averages 149 balls per innings. This is 12% ahead of the next best one. His career strike rate is 58.3, which, if not the best, is in the top-15 out of the 112 selected batsmen. The way-out BpI value coupled with the quite high Strike rate leads to the impressive value of 87.5 runs per innings.

BatsmanCtyRuns/InnsBalls/InnsSt Rate

EdeC WeekesWin55.0115.347.7
Sutcliffe HEng54.2134.140.4
Hobbs J.BEng53.0110.148.2
Barrington K.FEng52.0123.242.2
Hammond W.REng51.8115.844.7
Lara B.CWin51.585.160.5
Sangakkara K.CSlk51.394.754.2
Hutton LEng50.5127.139.7
Sobers G.St.AWin50.2103.048.7
Tendulkar S.RInd49.791.954.1
Sehwag VInd49.059.782.0
Kallis J.HSaf48.2105.645.6
Younis KhanPak48.190.353.3
Jayawardene D.PSlk48.192.951.8
Ponting R.TAus47.380.558.8
Chappell G.SAus47.192.251.1
Richards I.V.AWin46.972.564.8

Now for a final collection of related figures. I am sure readers might want to know about the quality of bowling faced by Bradman. First let me say this. Only a cricketing ignoramus would say that the bowling faced by Bradman was not good. Amongst the bowlers Bradman faced were Larwood, Verity, Bowes, Voce, Robins, Alec Bedser, Griffith, Constantine, Laker and Mankad: most of these bowlers had bowling averages below 30.0. Only the South African bowlers were average. Overall the average quality of bowling (AQB) faced by Bradman works out to 35.9. This is based on the CTD bowling figures and the reciprocal method of working. The range of AQB is 28.5 to 46.6 and the mean is 34.4. So one could say that Bradman faced, on the whole, slightly below-par bowling. Just to give a reference point, the AQB values for Jayawardene, Sangakkara and Graeme Smith are above 36.0.

Let me do a final summary.

1. When Bradman failed, he failed in a big way. He failed often, more than the others. Until he reached 50, he was quite human.
2. When he posted big scores, he was very good but only comparable to the other equally good players in these aspects of the game.
3. It is at the level of 50 that he completely overshadowed others. He reached this level over 50% of the time and posted an average of nearly 150 when he crossed 50. These two factors together account for the 60% increase he had in the key measures.
4. From a different angle, he posted a way-above figure on the Balls per innings and boasted of a very high career strike rate. These two factors together also account for the 60% increase he had in the key measures.

To download/view the Special table containing the information requested for by Arjun (Averege of innings factors based on innings highest score at 1.00) and Gerry (Average Bowling Quality faced for scores of 50 and above), please click/right-click here. This also contains an additional data field which is Batting Average * 30.0 / Career ABQ.

It is certain that Bradman possessed non-quantifiable skills which enabled him to reach the pinnacle, leaving everyone far behind. Enough has been written about that. Here I have only tried to look at the mundane figures. Somewhere earlier in the article I had mentioned shorty in a flippant manner. Short Bradman might have been in stature, but he stands tall, very tall indeed. And hopefully now we know why Bradman clicked.

### Easier analysed than done !!!

Since my tennis elbow is troubling me a lot I will be responding to many remarks with pre-formed boiler-plate responses generated through a key macro program. However let me assure the readers that I always read the responses in full.

Without bringing in anything else into the picture, it is necessary to briefly recapitulate the wonderful performance of Anand, winning his fifth World Chess title, fourth in succession and the toughest to date. Gelfand proved to be a tough nut to crack and Anand, to his credit, has said so right from he beginning. He is adding a few very significant bold lines to his biography and strengthens his claim to being called India's best sportsman ever. The only appropriate words needed during this epic occasion are expressions of recognition, approbation and appreciation.

Anantha Narayanan has written for ESPNcricinfo and CastrolCricket and worked with a number of companies on their cricket performance ratings-related systems