Curtly Ambrose had the measure of most batsmen he bowled to © Getty Images

I was in for a surprise with my previous post. I never expected it to receive so many comments (nearly 200) many of which were quite complimentary. My favourite post so far has been the one on the Revised Batting Average. Possibly the reason for the mixed reactions on that post might have been the fact that the traditional definition of batting average exists in the mind of many people who are not going to accept a change quickly. On the other hand this idea of "Batsman wicket quality" is totally new and many people have appreciated the originality of the theme.

Many good suggestions were received. It was difficult to decide what to take up and what to discard. However I have taken up three tweaks for implementation, in increasing order of difficulty.

Since I do not want to post a follow-up to a follow-up, I will respond individually to comments which I feel deserve a further response.

Quite a few complex computational alternatives have been suggested. I have gone through all these, and most have some merit. However, I have decided to retain the easy-to-understand methodology adopted by me since it would be possible for everyone to follow the computations easily - that axiom has always been the cornerstone of my analysis. I must acknowledge the originality of some of the suggestions, though.

1. Raising the bar to 200 wickets (now only 54 qualifying bowlers in lists)


Quite a few readers have suggested raising the qualifying bar to 200 wickets. This request is like a half-volley outside the off stump, bowled to a set batsman, which would be instantly driven for four. Only a few minutes work was needed here. The revised table is presented below. It should be noted that only the qualifying bar is raised and no other change has been done. Of course, this is only a temporary exercise for this blog and my database table cut-off stays at 100 wickets.

Table 1: Ordered by BQI

SNo Bowler            Bow Cty Mat Wkt  Sum of   BQI

                                      BatAvge


  1.Caddick A.R       RFM Eng  62 234  7706.0  32.93

  2.Hoggard M.J       RFM Eng  67 248  8157.0  32.89

  3.McKenzie G.D      RF  Aus  60 246  8018.0  32.59

  4.Gough D           RF  Eng  58 229  7238.0  31.61

  5.Bedser A.V        RFM Eng  51 236  7456.0  31.59

  6.Thomson J.R       RF  Aus  51 200  6291.0  31.45

  7.Snow J.A          RFM Eng  49 202  6313.0  31.25

  8.Underwood D.L     LSP Eng  86 297  9212.0  31.02

  9.McDermott C.J     RF  Aus  71 291  8988.0  30.89

 10.Lillee D.K        RF  Aus  70 355 10919.0  30.76

...

...

 50.Abdul Qadir       RLB Pak  67 236  6516.0  27.61

 51.Waqar Younis      RFM Pak  87 373 10156.0  27.23

 52.Garner J          RF  Win  58 259  6903.0  26.65

 53.Wasim Akram       LFM Pak 104 414 10754.0  25.98

 54.MacGill S.C.G     RLB Aus  42 203  5231.0  25.77

One reason for the low placement of Muttiah Muralitharan, Wasim Akram and Waqar Younis in this table might be their skill in taking lower-order wickets quickly and effectively. This is indeed a great attribute of these bowlers, and not to be scoffed at. It is true these great bowlers would have taken many top-order wickets and quite a few lower-order wickets also.

Table 2: Ordered by Difference between BQI and Bowling Average

SNo Bowler            Bow Cty BowAvge  BQI    Diff


  1.Marshall M.D      RF  Win  20.95  30.06   9.11

  2.Ambrose C.E.L     RF  Win  20.99  29.85   8.86

  3.McGrath G.D       RFM Aus  21.64  30.43   8.79

  4.Donald A.A        RF  Saf  22.25  29.27   7.01

  5.Trueman F.S       RF  Eng  21.58  28.44   6.86

  6.Lillee D.K        RF  Aus  23.92  30.76   6.83

  7.Hadlee R.J        RFM Nzl  22.30  29.09   6.79

  8.Bedser A.V        RFM Eng  24.90  31.59   6.69

  9.Imran Khan        RF  Pak  22.81  29.44   6.63

 10.Pollock S.M       RFM Saf  23.12  29.62   6.50

...

...

 50.Harbhajan Singh   ROB Ind  31.40  28.71  -2.69

 51.Sobers G.St.A     LM  Win  34.04  30.47  -3.57

 52.Danish Kaneria    RLB Pak  33.90  29.84  -4.06

 53.Abdul Qadir       RLB Pak  32.81  27.61  -5.19

 54.Vettori D.L       LSP Nzl  34.23  28.64  -5.59

A few suggested that instead of determining the measure of difference between BQI and Bowling Average, a measure of quotient, say BQI/Bowling Average can be determined. This has its own merits. However the differences are likely to be minimal: 40 minus 25 and 35 minus 20 both will work out to 15 while 40/25 will work out to 1.6 and 35/20 will work out to 1.75. It is difficult to select one method over the other. What I have done, however is to provide this information also in the Table. It can be seen that there is virtually no difference between Tables 2 and 2A.

Table 2A: Ordered by Quotient between BQI and Bowling Average

SNo Bowler            Bow Cty  BowAvge   BQI     Quot


  1.Marshall M.D      RF  Win   20.95   30.06    1.43

  2.Ambrose C.E.L     RF  Win   20.99   29.85    1.42

  3.McGrath G.D       RFM Aus   21.64   30.43    1.41

  4.Trueman F.S       RF  Eng   21.58   28.44    1.32

  5.Donald A.A        RF  Saf   22.25   29.27    1.32

  6.Hadlee R.J        RFM Nzl   22.30   29.09    1.30

  7.Lillee D.K        RF  Aus   23.92   30.76    1.29

  8.Imran Khan        RF  Pak   22.81   29.44    1.29

  9.Muralitharan M    ROB Slk   21.77   27.78    1.28

 10.Pollock S.M       RFM Saf   23.12   29.62    1.28

2. Taking into account the batsman score at the time of dismissal

Quite a few readers have also suggested that the batsman's score, at the time of dismissal, should be considered. This is an excellent idea and strengthens the concept of quality of wickets taken by bringing in a "when" factor in addition to the "who" factor. This suggestion falls smack in between the previous and the next suggestions in terms of implementation difficulties. I have gone over my notes and come out with the following methodology.

Assign a weightage of 50% to the dismissed batsman's average [current or career, whatever it might be]. Assign the other 50% weightage to the batsman score at the time of dismissal, ranging from 100% credit for dismissal at 0 to 0% credit for any dismissal at or above the batsman average. A few examples are given below.

Batsman   Avge    Score  BQI-Fixed  BQI-Variable  BQI-Total

Bradman   99.94   0      49.97      49.97         99.94

Bradman   99.94   67     49.97      16.47         66.44

Bradman   99.94   304    49.97      0             49.97 (any score above 99)

Tendulkar 55.58   0      27.79      27.79         55.58

Tendulkar 55.58   25     27.79      15.29         43.08

Tendulkar 55.58   75     27.79      0             27.79 (any score above 55)

Vettori   27.12   0      13.56      13.56         27.12

Vettori   27.12   11     13.56      8.08          21.64

Vettori   27.12   28     13.56      0             13.56 (any score above 27)

Based on the modified calculation methodology, the revised tables are given below. This modification now reflects a significant improvement. It must, however, be noted the revised report is not comparable with the earlier reports since the basis has changed significantly. Previously the bowler got 100% of the Batting Average as credit. Now he gets 50% + x% as credit. As such the average BQI values have dropped and this report should be seen on its own.

The only comparison possible will be between this option and the next option, to be done in future.

Table 4: Ordered by BQI (Revised)

SNo Bowler            Bow Cty Mat Wkt  SumAvge BQI


  1.Hoggard M.J       RFM Eng  67 248  6412.0 25.85

  2.Caddick A.R       RFM Eng  62 234  6045.2 25.83

  3.McKenzie G.D      RF  Aus  60 246  6146.3 24.98

  4.Gough D           RF  Eng  58 229  5618.7 24.54

  5.McGrath G.D       RFM Aus 124 563 13766.6 24.45

  6.Snow J.A          RFM Eng  49 202  4910.8 24.31

  7.Marshall M.D      RF  Win  81 376  8973.4 23.87

  8.Ambrose C.E.L     RF  Win  98 405  9650.2 23.83

  9.Bedser A.V        RFM Eng  51 236  5581.4 23.65

 10.Lillee D.K        RF  Aus  70 355  8314.5 23.42

...

...

 50.Muralitharan M    ROB Slk 118 723 14511.2 20.07

 51.Danish Kaneria    RLB Pak  51 220  4410.2 20.05

 52.Vettori D.L       LSP Nzl  78 241  4810.6 19.96

 53.Benaud R          RLB Aus  63 248  4925.8 19.86

 54.MacGill S.C.G     RLB Aus  42 203  3807.4 18.76

No one can have complaints on the top ten bowlers. The only surprise is the presence of Matthew Hoggard, Andy Caddick and Darren Gough in the top four. The only reason, as already surmised, could be their playing against Australia and India quite frequently recently. Another reason could be the generally high current batting averages.

Table 5: Ordered by Quotient of BQI and Bowling Average (Revised)

SNo Bowler            Bow Cty BowAvge BQI     Diff  Quot


  1.Ambrose C.E.L     RF  Win  20.99  23.83   2.84  1.14

  2.Marshall M.D      RF  Win  20.95  23.87   2.92  1.14

  3.McGrath G.D       RFM Aus  21.64  24.45   2.81  1.13

  4.Trueman F.S       RF  Eng  21.58  22.99   1.41  1.07

  5.Donald A.A        RF  Saf  22.25  22.41   0.16  1.01

  6.Hadlee R.J        RFM Nzl  22.30  22.49   0.19  1.01

  7.Pollock S.M       RFM Saf  23.12  23.06  -0.06  1.00

  8.Garner J          RF  Win  20.98  20.86  -0.12  0.99

  9.Holding M.A       RF  Win  23.69  23.37  -0.31  0.99

 10.Lillee D.K        RF  Aus  23.92  23.42  -0.50  0.98

...

...

 50.MacGill S.C.G     RLB Aus  28.15  18.76  -9.39  0.67

 51.Abdul Qadir       RLB Pak  32.81  20.64 -12.17  0.63

 52.Sobers G.St.A     LM  Win  34.04  21.11 -12.92  0.62

 53.Danish Kaneria    RLB Pak  33.90  20.05 -13.86  0.59

 54.Vettori D.L       LSP Nzl  34.23  19.96 -14.27  0.58

If one adds Wasim and Waqar to the top ten, this is almost a list of the top dozen pace bowlers of all time.

3. Applying the cumulative batsman average at the beginning of the Test (as against the career average)

Many people suggested applying "upto-current Test" batting average rather than the "career" batting average. This was the most voiced comment and deserves to be considered seriously. This has an impact at the early stages of a batsman's career. I had considered doing this earlier itself but ruled against it because of the complexity involved. Dynamic determination of the "upto-current Test" averages is very cumbersome. This method will slow down any analysis, even considering the high pentium speeds. The only alternative is to determine the "upto-current Test" averages as a one-off exercise for all 1866 Tests, store these static data within the match data for each player and use these any time required. Of course, the current averages will have to be created for each new Test as the data is appended. This exercise requires a redefinition of the database layout and considerable amount of programming since it is a systemic change. I will do this in the near future and make the results available to all the interested readers, even if not through a post in this blog.

Conclusion

It is amusing to see people complaining, even abusing the "Indian ***********" about the absence of their favourite bowlers from the list, most prominently Wasim Akram. Not having understood the analysis is a possible reason. The other reason is the difficulty in accepting any list which does not meet their perceived conclusions.

If I make a list of bowlers who have taken a hat-trick in Tests, Wasim Akram will appear twice. Dennis Lillee, Murali, Anil Kumble, Waqar and Richard Hadlee etc would not be on the list while Peter Petherick, Alok Kapali, Andy Blignaut, James Franklin and Irfan Pathan will appear in that list. Should one disown such a list because of the absence of the marquee names?

Just for the record, here is my own list, in alphabetical order, of the all-time great bowlers, taking all factors into consideration. This should satisfy the readers who should know that there is no narrow-minded chauvinism at work here.

Sydney Barnes, Bishan Bedi, Richard Hadlee, Michael Holding, Lillee, Malcolm Marshall, Glenn McGrath, Muttiah Muralitharan, Waqar Younis, Shane Warne, Wasim Akram.

A few have rightly commented on the dilution of the average because great bowlers tend to take lower-order wickets. Michael Clark and Onkar Walavalkar, among others, have given the example of someone taking all ten wickets would have the average batting average lowered significantly. My submission is that this list does not rate the bowlers at all. It is an alternative measure, hitherto untapped. The same Kumble whose ten-wicket haul in Delhi had an average batting average of 31 would have a higher average of batting average in the West Indies match in St Lucia - in which he took three wickets - of 41. It works both ways and over a long career, these variations even out. The points are well made, I concede.

Other interesting comments are by people complaining that the need is to enjoy the game and not reduce it to numbers or terming such analysis as useless or me as jobless (possibly I am !!!). Let me reply by saying that there are different types of cricket followers. There are those who only like to watch the game, they would not even bother about the batsman's strike-rate or some such simple measure. There are a few who are only number nerds. There are millions in between, the author included, who enjoy both watching the game and analysing it. If one does not want to see such analysis why get into this blog, which is purely an analyst's corner, at all? Entry to this blog is voluntary.

The comments for this post have been the most received so far for any post and have been very enjoyable, whether bouquets or brickbats. I have been made to think in a lateral manner and I thank all those who took the time to comment. It has been a great experience.

	Malcolm Marshall dismissed plenty of top-class batsmen without giving away too many runs © Getty Images

About a month back, I had done a post on the most consistent bowlers in Tests, as part of an analysis on bowlers. I had mentioned then that there would be two measures for bowlers - the second one is on the quality of wickets taken by bowlers.

In view of the very high number of comments received, we will close the comments by evening of Friday, 21 March so that a comprehensive follow-up can be posted.

Consider three recent innings summaries:

West Indies 215 all out (Sehwag 3-33, Patel 3-51, Kumble 3-57)
These numbers suggest Virender Sehwag was the best of the lot and Anil Kumble the worst. In reality, it was the other way around. Kumble took the wickets of Chris Gayle, Brian Lara and Dwayne Bravo. Munaf Patel took the wickets of Daren Ganga, Ramnaresh Sarwan and Denesh Ramdin, while Sehwag collected the tailenders - Ian Bradshaw, Jerome Taylor and Pedro Collins. Another example:

India 240 all out (Ntini 3-41, M Morkel 3-86)
Makhaya Ntini captured the wickets of Wasim Jaffer, Sachin Tendulkar and Sourav Ganguly while Morne Morkel captured the wickets of Mahendra Singh Dhoni, Kumble and Zaheer Khan. For that matter, the spell of Andre Nel, who captured only two wickets - those of Sehwag and Dravid - is better than that of Morkel.

Bangladesh 259 all out (Ntini 4-35, Steyn 4-66)
Here both bowlers took the same number of wickets, but Dale Steyn took the top four while Ntini mopped up the tail.

In the wickets column of scorecards there is the bland pronouncement that a bowler has captured x number of wickets. There is no information on whose wickets he captured. This analysis seeks to secure such information.

The computation is simple. Every wicket captured by a bowler in the 1865 Test matches played so far is analysed, and the sum of career batting averages of the batsmen dismissed is calculated. It is then divided by the number of wickets captured by each bowler and a Batting Quality Index (BQI) arrived at. It's a simple but exhaustive calculation, which is impossible manually.

The top ten bowlers in this list - criterion being at least 100 Test wickets - ordered by BQI is startling. (I would appreciate it if readers do not immediately write in saying "Wasim Akram is the greatest", "Who are these clowns", "Boje and Dillon could not find a regular place in their teams" etc.)

Table 1: Ordered by BQI

SNo Bowler            Bow Cty Mat Wkt  Sum of   BQI

                                      BatAvge


  1.Boje N            LSP Saf  43 100  3453.0  34.53

  2.Flintoff A        RFM Eng  67 197  6652.0  33.77

  3.Connolly A.N      RFM Aus  29 102  3444.0  33.76

  4.Giles A.F         LSP Eng  54 143  4812.0  33.65

  5.Dillon M          RFM Win  38 131  4366.0  33.33

  6.Collinge R.O      LFM Nzl  35 116  3825.0  32.97

  7.Zaheer Khan       LFM Ind  53 170  5599.0  32.94

  8.Caddick A.R       RFM Eng  62 234  7706.0  32.93

  9.Hoggard M.J       RFM Eng  66 247  8118.0  32.87

 10.Martin C.S        RFM Nzl  37 125  4086.0  32.69

The list is headed by virtually unknown bowlers. Why does this happen?

Possibly because they do not bowl at the end, picking up tail-end wickets. The other more established bowlers get the opportunity. These bowlers tend to bowl during the middle of the innings.

The other peculiarity is the presence of the three current England bowlers. Here the possible reason is that England has played Australia and India recently and the average of batting averages for these two teams is quite high.

I would be interested in reading comments from interested readers on possible reasons for this peculiar situation.

136.Steyn D.W         RFM Saf  20 105  2655.0  25.29
137.Barnes S.F        RFM Eng  27 189  4646.0  24.58
138.Blythe C          LSP Eng  19 100  2449.0  24.49
139.Wardle J.H        LSP Eng  28 102  2416.0  23.69
140.Noble M.A         ROB Aus  42 121  2859.0  23.63
141.Turner C.T.B      RFM Aus  17 101  2291.0  22.68
142.Giffen G          ROB Aus  31 103  2229.0  21.64
143.Peel R            LSP Eng  20 102  1960.0  19.22
144.Briggs J          LSP Eng  33 118  2025.0  17.16
145.Lohmann G.A       RFM Eng  18 112  1755.0  15.67

At the other end of the table we have the pre-World War-I players, indicating very low batting averages for batsmen playing at that time. Dale Steyn is a surprise inclusion, possibly because his last 54 wickets (over 50%) have been against the weaker batting teams of New Zealand, West Indies and Bangladesh, who have lower batting averages.

For a full list, please click here.

However let us seek to address this situation by looking at two other measures. The first is the difference between BQI and the career bowling average for the bowler. While it is true that having a high BQI means that the bowler has picked up better quality wickets, it might be more than offset by a high bowling average, which means the bowler has conceded a lot of runs for each wicket captured. The difference between these two figures will give a clear indication of the bowler's quality. The higher the difference, the better the bowler.

Table 1: Ordered by Difference between BQI and Bowling Average

SNo Bowler            Bow Cty   BowAvg  BQI    Diff


  1.Marshall M.D      RF  Win   20.95  30.06   9.11

  2.Davidson A.K      LFM Aus   20.53  29.51   8.97

  3.Ambrose C.E.L     RF  Win   20.99  29.85   8.86

  4.McGrath G.D       RFM Aus   21.64  30.43   8.79

  5.O'Reilly W.J      RLB Aus   22.60  31.12   8.53

  6.Barnes S.F        RFM Eng   16.43  24.58   8.15

  7.Laker J.C         ROB Eng   21.25  29.30   8.05

  8.Croft C.E.H       RF  Win   23.30  31.22   7.91

  9.Miller K.R        RF  Aus   22.98  30.65   7.68

 10.Adcock N.A.T      RF  Saf   21.11  28.17   7.07

Ha! The list looks a lot more 'normal'. This is certainly a list of the outstanding bowlers of all time. Again, no mails bringing up other bowlers' names please. These are great bowlers who will stand comparison with anyone outside the list.

136.Giles A.F         LSP Eng   40.60  33.65  -6.95
137.Yadav N.S         ROB Ind   35.10  28.14  -6.96
138.Wright D.V.P      RLB Eng   39.11  31.06  -8.06
139.Boje N            LSP Saf   42.65  34.53  -8.12
140.Venkataraghavan S ROB Ind   36.12  27.56  -8.56
141.Emburey J.E       ROB Eng   38.41  29.69  -8.71
142.Abdul Razzaq      RFM Pak   36.93  27.66  -9.27
143.Shastri R.J       LSP Ind   40.96  31.69  -9.27
144.Mohammad Rafique  LSP Bng   40.76  31.35  -9.41
145.Hooper C.L        ROB Win   49.43  31.52 -17.91

Again, one feels vindicated. Boje is at the end with a huge negative difference. There is no denying that these are bowlers of average skills and in case of Mohammad Rafique, playing for a weak team. The last in this list is Carl Hooper, a very ordinary bowler indeed.

For a full list, please click here.

Another analysis I have done is to consider the number of lower-order wickets taken by a bowler and determine a % of lower-order wickets taken.

Who is a lower-order batsman? For the purpose of this exercise, I have defined it as a batsman batting at positions 8 to 11, and averaging less than 25 [to take care of situations when a Adam Gilchrist or Kapil Dev or Ian Botham might have batted at No. 8 or lower]. Only Daniel Vettori, with a batting average of 26.39, goes out of this classification. But then who can say that Vettori, with two Test centuries, is not an allrounder.

Initially I did this analysis based on batting average. However, that distorted the complete picture since the batting averages of batsmen during pre-WW-I and recently those from Bangladesh and Zimbabwe have been quite low. Hence I have gone back to the batting position.

In addition, any nightwatchman, determined through a proprietary algorithm, is considered as a lower-order batsmen.

Table 3: Ordered by % of lower-order wickets

SNo Bowler            Bow Cty Mat Wkts LowOrder Wkts

                                          & %age


  1.Zaheer Khan       LFM Ind  53  170    23 (13.5)

  2.Collinge R.O      LFM Nzl  35  116    18 (15.5)

  3.Boje N            LSP Saf  43  100    16 (16.0)

  4.Martin C.S        RFM Nzl  37  125    22 (17.6)

  5.Edmonds P.H       LSP Eng  51  125    22 (17.6)

  6.Flintoff A        RFM Eng  67  197    36 (18.3)

  7.Reid B.A          LFM Aus  27  113    21 (18.6)

  8.Pathan I.K        LFM Ind  28  100    19 (19.0)

  9.Intikhab Alam     RLB Pak  47  125    24 (19.2)

 10.Ghavri K.D        LFM Ind  39  109    21 (19.3)

 11.Hall W.W          RF  Win  48  192    37 (19.3)

 12.Mushtaq Ahmed     RLB Pak  52  185    36 (19.5)

 13.Allen D.A         ROB Eng  39  122    24 (19.7)

 14.Srinath J         RFM Ind  67  236    47 (19.9)

 15.Thomson J.R       RF  Aus  51  200    40 (20.0)

This is a very good table, showing bowlers whose tally of lower-order wickets is less than 20% of the career wickets. It shows the value of Zaheer Khan to the Indian attack, as also Flintoff, Martin and Pathan to their respective teams.

134.Vettori D.L       LSP Nzl  77  238    81 (34.0) 
135.Gupte S.P         RLB Ind  36  149    51 (34.2) 
136.Rhodes W          LSP Eng  58  127    44 (34.6) 
137.Mallett A.A       ROB Aus  38  132    46 (34.8) 
138.Johnson I.W       ROB Aus  45  109    39 (35.8) 
139.Adams P.R         LSP Saf  45  134    48 (35.8) 
140.Giffen G          ROB Aus  31  103    37 (35.9) 
141.MacGill S.C.G     RLB Aus  42  203    74 (36.5) 
142.Wardle J.H        LSP Eng  28  102    38 (37.3) 
143.Noble M.A         ROB Aus  42  121    47 (38.8) 
144.Briggs J          LSP Eng  33  118    50 (42.4) 
145.Lohmann G.A       RFM Eng  18  112    52 (46.4) 

At the end of the table, these are bowlers whose tally of lower-order wickets is greater than a third of their total. It looks as if these bowlers have often been brought in to clean up the tail. There are quite a few pre-WW-I bowlers. A surprise is the presence of Vettori and MacGill, especially, who seems to have been brought in to bamboozle the tail despite the presence of other fast bowlers.

For a full list, please click here.

Some possible reader queries are anticipated and answered below.

1. At what individual score does the bowler dismiss the batsman. It is true that, for the fielding team, it is better for a batsman to be dismissed at 10 rather than 100. However, that is a more complex computation and has been done in a different context.

2. Whatever happens, capturing Tendulkar's wicket, even when he is on 100, is invaluable since he is capable of scoring a lot more runs than, say, when Dinesh Kartik has scored 25. It has been assumed that Tendulkar's wicket is Tendulkar's wicket, whatever be his individual score. Also, it might be true, in certain cases, that capturing Brad Haddin's wicket at 10 might be more valuable than capturing Matthew Hayden's wicket when he is at 100.

3. What about current form? While it may be true a few matches back Sehwag's wicket was going quite cheaply, his potential, as shown in the Adelaide Test, can never be underestimated. It is also true that even when Rahul Dravid or Ricky Ponting are going through indifferent form, their wickets are extremely valuable, because of their potential to score big.

	When Virender Sehwag gets a hundred, he usually goes on to make it a big one © Getty Images

In this table, Sehwag has scored 912 runs after reaching 100, while Hayden has mustered only 219. In fact, Hayden has converted only one of his last 15 Tests centuries into a 150, whereas Sehwag has clocked up nine conversions in a row (a world record; not even Bradman managed this).

The contrast might be more understandable if Sehwag was by far the superior batsman, but of course this is not the case. Hayden scored his last ten centuries in the space of just 45 innings, where Sehwag needed 68 innings; Hayden averaged 60.0 in that time to Sehwag’s 54.2. Sehwag even spent some time on the Indian reserves bench in that time.

A deeper understanding of this might require an excursion into psychology; it’s better for the moment to leave it simply as an intriguing difference between two great players.

A wider examination of such differences is quite straightforward; just calculate the “century average” of all players. One way is to take a simple average of all Test centuries (ignoring the effect of not-outs); the leaderboard looks like this:

Now any measure of scoring that puts Don Bradman on top is all right by me, but there are better ways of doing this. Bradman, after all, made some very big scores in “timeless” Tests that would be curtailed under modern conditions, and that would bring down the average size. An alternative is to take a standard batting average of the centuries, accounting for not-outs.

Some care is required. For a proper comparison of the ability to progress beyond 100, the first 100 runs of each century must be set aside, otherwise anomalies occur. (For example, a batsman scoring 100 not out, 100, and 100 not out would end up with a century average of 300 even though he has never scored a single run past 100.) By ignoring the first 100 runs in each century, a score of exactly 100 becomes equivalent to a duck in a normal batting average, while a score of 100 not-out will have no effect on the average, equivalent to a score of 0 not-out. This is fair enough, since a score of 100 not-out tells us nothing about a player’s ability to score after reaching 100.

It is interesting that, when you calculate such averages, many batsmen come up with a century average similar to, or just a little higher than, their ordinary batting average (for example, Jacques Kallis 57.4, Greg Chappell 56.1, Allan Border 55.0, Sunil Gavaskar, 51.9, Adam Gilchrist 49.6, Marcus Trescothick 45.1; this applies even to Bradman, 108.0). However, there are notable exceptions, and Sehwag is among them.

When it comes to converting hundreds into giant scores, Kumar Sangakkara is a phenomenon. In his last thirteen Test centuries, he has been dismissed below 150 only once, while scoring six double-centuries plus that umpire-truncated 192 against Australia. It is also quite curious that, in addition to Sangakkara and Marvan Atapattu, the Sri Lankans Sanath Jayasuriya (68.3) and Mahela Jayawardene (67.2) are also in the all-time top 20.

At the other end of the scale, while it is not surprising to see Mark Waugh (highest score 153) near the extreme, it is intriguing to compare his century average with his brother, who averaged 67.2. Honourable mention should go to Graeme Wood, who, with only nine centuries, did not qualify for the list, but whose century average was only 17.4. Wood was out for exactly 100 in three of his nine tons.

And what of Matt Hayden? His century average is 39.0, quite low, but it would be much lower still without his 380 against Zimbabwe. In fact, imagine if Hayden’s 380 had never happened, and we were to try to predict the major Australian batsmen most likely to ever make such a score. Hayden would have to be just about the least likely, with the exception of Mark Waugh.

Finally, here is a similar list for half-century averages, the batsmen most likely to go on to big scores after reaching 50.

Postscript

My previous post on the fastest and slowest innings attracted some lively comments. Some thought that the calculation was too complex, others thought that it needed more sophistication. The numbers of these comments seemed about equal, so perhaps I was doing something right.

Some pointed out that, because the distributions are skewed, comparing scores of different sizes could be unreliable. This is valid, up to a point. One could probably normalise the distributions, perhaps by taking the logarithms of the balls faced. This is a nuance that must await some future day; this is a cricket blog, not a statistics journal. My gut feel is that the results would not be significantly different if a fancier approach was taken.

Someone asked about Hanif Mohammad’s epic 337 against the West Indies. This is tricky, firstly because we don’t know the balls faced, and secondly because there are so few innings of similar size to compare it with. However, the z-score can be estimated at 6.42.

If you like, check out a detailed analysis of this innings on my blog. Scroll down to 23 June 2007.

Inevitably, there are those who come onto blogs like this to cleverly inform us that “statistics don’t tell the whole story” (or words to that effect). I have been following cricket stats for 40 years or so, and I have never heard anyone, statistician or otherwise, claim that stats DID tell the whole story. Just enjoy stats for what they are, an important dimension of the game.