## On the batting h-index

Kartikeya Date has written a post applying the h-index, originally designed as a measure of academics' research impact, to batsmen. The basic idea isn't original (see, e.g., this blog post with a related h-based stat; that post also cites a paper by Gangan Prathap which I can't read because it costs 35 euros to download), but Kartikeya's implementation seems to be novel.

The definition of h-index is this: it is the largest integer h such that the batsman has made h scores of at least h. Combining Test and ODI cricket, Sachin Tendulkar has an h-index of 100, since he's made 100 scores of at least 100.

Kartikeya correctly notes that a batsman's h-index will tend to rise over the course of his career, and it can never decrease – if after 30 innings, he has 12 scores of at least 12, then he will never again have less than 12 scores of at least 12. The question then arises as to how to normalise the h-index, and Kartikeya proposes h^2 / innings, which "is a measure of consistency and quality without either privileging or penalizing a player for length of career".

I was initially very sceptical that such a normalisation could work. But it does, somehow. I'll split this post into two parts: in the first, I'll talk about why h^2 / innings is a decent metric over a range of different career lengths; in the second, I'll describe what I would do with an h-index, and show that my method doesn't give much (if any) improvement on h^2 / innings.

h^2 / innings

For ease of doing the maths, let's assume that a batsman's scores are exponentially distributed, so that the probability of a score greater than n is exp(-n / avg). This assumption is not particularly good for low scores, but it'll do for now.

For a career of N innings, the expectation value is for N * exp(-n / avg) scores of above n. Now we can write an equation to define what this idealised batsman's h-index will be:

N * exp(-h / avg) = h.

This sort of equation doesn't have a solution in terms of elementary functions, but it does using the ProductLog function that you can use in Wolfram Alpha. In any case, if you hold avg constant, and write h as a function of career length N, and square h, then this is the graph that you get:

That is remarkably close to a straight line. I don't know whether there's a good mathematical reason why it should be so close to linear, or whether it's just a coincidence. In any case, it shows that dividing h^2 by the number of innings will give you something roughly constant over a career, assuming an idealised batsman with constant ability.

It can't always be near-linear though. Obviously someone who's only batted in one innings can have an h-index of at most 1, and then h^2 / innings will also be 1. So early in a career, this won't be a reliable measure (though it does have the possibly desirable feature of preventing someone with an excellent start to his career showing up near the top of the all-time list after 20 innings). This is clearer if we plot h^2 / innings against innings, done here for an idealised batsman who averages 40:

There are two points to make here. The first is that for career lengths between about 50 innings and 300 innings, h^2 / innings doesn't vary too much: its maximum in this case is at about 14.7, its minimum over that range about 13. The second point is that this level of variability may be undesirable. An increase of 1.5 in h^2 / innings could send someone from being ranked 50th all-time to being ranked 23rd.

What I would do with the h-index

So let's instead go back to that equation, and solve instead for avg. This is straightforward:

avg = h / ln(N/h).

Essentially, then, for a given number of innings N, we are associating an h-index with some sort of effective average, which I'll call an h-average (it won't be defined if h = N). I think it's useful to do this, because the h-average is on the same scale as the regular average, which we're all familiar with. An h-average of 50 is very high; Chris Martin has an h-average of 1.8 (or at least he did whenever I last updated my database, in December 2010). A table of h- and regular averages is at the end of this post.

I expected that, for batsmen with 50 or more Test innings, the h-average would give a nicer all-time ranking than h^2 / innings. But while there was a bit of shuffling, overall the two measures are very closely correlated:

It is interesting to see how these h measures correlate with the regular batting average. Relaxing the qualification to just 20 Test innings, here are the two scatterplots (first the h-average, then h^2 / innings):

The wild non-Bradman outlier on the first plot is Jesse Ryder, who at the time of my last database update had an h-index of 20 after just 25 innings. In the second scatterplot, you can see that his (and a bunch of other high-h-average players) h^2 / innings is suppressed because of his low number of innings. But correlations are quite good – given a player's average, his h-average doesn't tell you that much extra information about his batting, and vice versa.

I don't think I have a strong conclusion. The h-index rewards consistent scoring, and while consistency may be useful, I'm not sure that it's better or worse than scoring the same amount of total runs but with less consistency.

(Edit 1 April: I ignored not-outs, because they're annoying. You get slightly better agreement between the h-average and runs-per-innings than between the h-average and the regular average.)

Anyway, here is a nice big table. Qualification of 50 Test innings; stats current to late 2010.
`name               mat    inns      no    runs       h    avg  h^2/inns  h-avgDG Bradman          52      80      10    6996      44    99.9    24.2    73.6JB Hobbs            61     102       7    5410      47    56.9    21.7    60.7KF Barrington       82     131      15    6806      53    58.7    21.4    58.6H Sutcliffe         54      84       9    4555      41    60.7    20.0    57.2IVA Richards       121     182      12    8540      60    50.2    19.8    54.1SR Tendulkar       174     284      30   14366      73    56.6    18.8    53.7ED Weekes           48      81       5    4455      39    58.6    18.8    53.4L Hutton            79     138      15    6971      52    56.7    19.6    53.3SM Gavaskar        125     214      16   10122      63    51.1    18.5    51.5KC Sangakkara       94     156      12    8244      54    57.3    18.7    50.9RS Dravid          146     251      29   11920      67    53.7    17.9    50.7RT Ponting         149     253      28   12220      67    54.3    17.7    50.4SM Katich           55      97       6    4186      42    46.0    18.2    50.2KD Walters          74     125      14    5357      48    48.3    18.4    50.2BC Lara            130     230       6   11912      64    53.2    17.8    50.0CL Walcott          44      74       7    3798      36    56.7    17.5    50.0JH Kallis          141     239      35   11366      65    55.7    17.7    49.9Mohammad Yousuf     90     156      12    7530      53    52.3    18.0    49.1GS Chappell         87     151      19    7110      52    53.9    17.9    48.8EH Hendren          51      83       9    3525      38    47.6    17.4    48.6AD Nourse           34      62       7    2960      32    53.8    16.5    48.4JB Stollmeyer       32      56       5    2159      30    42.3    16.1    48.1AL Hassett          43      69       3    3073      34    46.6    16.8    48.0B Mitchell          42      80       9    3471      37    48.9    17.1    48.0S Chanderpaul      129     219      34    9063      61    49.0    17.0    47.7DPMD Jayawardene   116     190      13    9527      57    53.8    17.1    47.3Inzamam-ul-Haq     119     198      22    8829      58    50.2    17.0    47.2HM Amla             48      85       7    3647      38    46.8    17.0    47.2A Flower            63     112      19    4794      44    51.5    17.3    47.1EJ Barlow           30      57       2    2516      30    45.7    15.8    46.7CC Hunte            44      78       6    3245      36    45.1    16.6    46.6GS Sobers           93     160      21    8032      52    57.8    16.9    46.3Javed Miandad      124     189      21    8832      56    52.6    16.6    46.0Saeed Anwar         55      91       2    4052      39    45.5    16.7    46.0IR Redpath          66     120      11    4737      45    43.5    16.9    45.9SR Waugh           168     260      46   10927      64    51.1    15.8    45.7VVS Laxman         117     192      30    7707      56    47.6    16.3    45.4Younis Khan         65     116       8    5440      44    50.4    16.7    45.4G Boycott          108     193      23    8114      56    47.7    16.2    45.3MH Richardson       38      65       3    2776      32    44.8    15.8    45.2MEK Hussey          56      97      12    4420      40    52.0    16.5    45.2AR Border          156     265      44   11174      64    50.6    15.5    45.0ER Dexter           62     102       8    4502      41    47.9    16.5    45.0GC Smith            87     152       9    7302      50    51.1    16.4    45.0MC Cowdrey         114     188      15    7624      55    44.1    16.1    44.7SJ McCabe           39      62       5    2748      31    48.2    15.5    44.7ML Hayden          102     182      14    8437      54    50.2    16.0    44.4CH Lloyd           110     175      14    7515      53    46.7    16.1    44.4V Sehwag            83     142       6    7467      48    54.9    16.2    44.3RC Fredericks       59     109       7    4334      42    42.5    16.2    44.0DCS Compton         78     131      15    5807      46    50.1    16.2    44.0ME Waugh           128     209      17    8029      57    41.8    15.5    43.9AH Jones            39      74       8    2922      34    44.3    15.6    43.7NS Sidhu            51      78       2    3202      35    42.1    15.7    43.7MA Taylor          104     186      13    7525      54    43.5    15.7    43.7AN Cook             62     111       7    4814      42    46.3    15.9    43.2PBH May             66     106       9    4537      41    46.8    15.9    43.2WR Hammond          85     140      16    7249      47    58.5    15.8    43.1AR Morris           46      79       3    3533      35    46.5    15.5    43.0RA Smith            62     112      15    4236      42    43.7    15.8    42.8WM Lawry            67     123      12    5234      44    47.2    15.7    42.8AC Gilchrist        95     135      20    5475      46    47.6    15.7    42.7G Kirsten          101     176      15    7289      52    45.3    15.4    42.6GR Viswanath        91     155      10    6080      49    41.9    15.5    42.5AW Greig            58      93       4    3599      38    40.4    15.5    42.5M Amarnath          69     113      10    4378      42    42.5    15.6    42.4AB de Villiers      63     108      13    4540      41    47.8    15.6    42.3TT Samaraweera      63      98      17    4395      39    54.3    15.5    42.3KP Pietersen        68     119       6    5576      43    49.3    15.5    42.2GP Thorpe          100     179      28    6744      52    44.7    15.1    42.1DI Gower           117     204      18    8231      55    44.3    14.8    42.0DR Martyn           67     109      14    4406      41    46.4    15.4    41.9M Leyland           41      65       5    2764      31    46.1    14.8    41.9NC O'Neill          42      69       8    2779      32    45.6    14.8    41.6GA Gooch           118     215       6    8900      56    42.6    14.6    41.6GM Turner           41      73       6    2991      33    44.6    14.9    41.6RR Sarwan           83     146       8    5759      47    41.7    15.1    41.5M Azharuddin        99     147       9    6215      47    45.0    15.0    41.2RB Simpson          62     111       7    4869      41    46.8    15.1    41.2MJ Clarke           65     106      12    4596      40    48.9    15.1    41.0Majid Khan          63     106       5    3931      40    38.9    15.1    41.0C Washbrook         37      66       6    2569      31    42.8    14.6    41.0CG Greenidge       108     185      16    7558      52    44.7    14.6    41.0Saeed Ahmed         41      78       4    2991      34    40.4    14.8    40.9BF Butcher          44      78       6    3104      34    43.1    14.8    40.9DL Haynes          116     202      25    7487      54    42.3    14.4    40.9MA Atherton        115     212       7    7728      55    37.7    14.3    40.8IR Bell             59     102      11    4007      39    44.0    14.9    40.6ME Trescothick      76     143      10    5825      46    43.8    14.8    40.6JL Langer          104     180      12    7674      51    45.7    14.5    40.4RN Harvey           79     137      10    6149      45    48.4    14.8    40.4RB Kanhai           79     137       6    6227      45    47.5    14.8    40.4PE Richardson       34      56       1    2061      28    37.5    14.0    40.4SP Fleming         111     189      10    7172      52    40.1    14.3    40.3KC Wessels          40      71       3    2788      32    41.0    14.4    40.2AI Kallicharran     66     109      10    4399      40    44.4    14.7    39.9RB Richardson       86     146      12    5949      46    44.4    14.5    39.8Taufeeq Umar        27      50       2    1866      26    38.9    13.5    39.8DJ Cullinan         70     115      12    4554      41    44.2    14.6    39.8HH Gibbs            90     154       7    6167      47    42.0    14.3    39.6G Gambhir           36      64       5    2992      30    50.7    14.1    39.6DB Vengsarkar      116     185      22    6868      51    42.1    14.1    39.6WJ Cronje           68     111       9    3714      40    36.4    14.4    39.2SC Ganguly         113     188      17    7212      51    42.2    13.8    39.1SV Manjrekar        37      61       6    2043      29    37.1    13.8    39.0WM Woodfull         35      54       4    2300      27    46.0    13.5    39.0MS Dhoni            51      77       9    2746      33    40.4    14.1    38.9AJ Strauss          79     143       6    5888      45    43.0    14.2    38.9DC Boon            107     190      20    7422      51    43.7    13.7    38.8MJ Slater           74     131       7    5312      43    42.8    14.1    38.6CH Gayle            91     159       6    6374      47    41.7    13.9    38.6FMM Worrell         51      87       9    3860      35    49.5    14.1    38.4TL Goddard          41      78       5    2516      33    34.5    14.0    38.4CC McDonald         47      83       4    3107      34    39.3    13.9    38.1BL D'Oliveira       44      70       8    2484      31    40.1    13.7    38.1JH Edrich           77     127       9    5138      42    43.5    13.9    38.0A Ranatunga         93     155      12    5105      46    35.7    13.7    37.9Mohsin Khan         48      79       6    2709      33    37.1    13.8    37.8N Hussain           96     171      16    5764      48    37.2    13.5    37.8VS Hazare           30      52       6    2192      26    47.7    13.0    37.5KD Mackay           37      52       7    1507      26    33.5    13.0    37.5IM Chappell         75     136      10    5345      43    42.4    13.6    37.3TW Graveney         79     123      13    4882      41    44.4    13.7    37.3HW Taylor           42      76       4    2936      32    40.8    13.5    37.0B Sutcliffe         42      76       8    2727      32    40.1    13.5    37.0MD Crowe            77     131      11    5444      42    45.4    13.5    36.9AJ Stewart         133     235      21    8463      54    39.5    12.4    36.7Shoaib Mohammad     45      68       7    2705      30    44.3    13.2    36.7JM Parks            46      68       7    1962      30    32.2    13.2    36.7CPS Chauhan         40      68       2    2084      30    31.6    13.2    36.7Saleem Malik       103     154      22    5768      45    43.7    13.1    36.6EAB Rowan           26      50       5    1965      25    43.7    12.5    36.1FE Woolley          64      98       7    3283      36    36.1    13.2    35.9SM Nurse            29      54       1    2523      26    47.6    12.5    35.6NJ Astle            81     137      10    4702      42    37.0    12.9    35.5PD Collingwood      65     111      10    4222      38    41.8    13.0    35.4Rameez Raja         57      94       5    2833      35    31.8    13.0    35.4ND McKenzie         58      94       7    3253      35    37.4    13.0    35.4GN Yallop           39      70       3    2756      30    41.1    12.9    35.4Zaheer Abbas        78     124      11    5062      40    44.8    12.9    35.4KJ Hughes           70     124       6    4415      40    37.4    12.9    35.4DM Jones            52      89      11    3631      34    46.6    13.0    35.3Mushtaq Mohammad    57     100       7    3643      36    39.2    13.0    35.2ST Jayasuriya      110     188      14    6973      48    40.1    12.3    35.2LRPL Taylor         28      51       1    2077      25    41.5    12.3    35.1MP Vaughan          82     147       9    5719      43    41.4    12.6    35.0JG Wright           82     148       7    5334      43    37.8    12.5    34.8CG Macartney        35      55       4    2131      26    41.8    12.3    34.7JR Reid             58     108       5    3428      37    33.3    12.7    34.5WJ Edrich           39      63       2    2440      28    40.0    12.4    34.5Hanif Mohammad      55      97       8    3915      35    44.0    12.6    34.3PA de Silva         93     159      11    6361      44    43.0    12.2    34.2PH Parfitt          37      52       6    1882      25    40.9    12.0    34.1KR Miller           55      87       7    2958      33    37.0    12.5    34.0DJ McGlew           34      64       6    2440      28    42.1    12.3    33.9HP Tillakaratne     83     131      25    4545      40    42.9    12.2    33.7MA Butcher          71     131       7    4288      40    34.6    12.2    33.7Asif Iqbal          58      99       7    3575      35    38.9    12.4    33.7TM Dilshan          66     105      11    3990      36    42.4    12.3    33.6AL Logie            52      78       9    2470      31    35.8    12.3    33.6Aamer Sohail        47      83       3    2823      32    35.3    12.3    33.6Nawab of Pataudi    46      83       3    2793      32    34.9    12.3    33.6PR Umrigar          59      94       8    3631      34    42.2    12.3    33.4CL Hooper          102     173      15    5762      45    36.5    11.7    33.4GRJ Matthews        33      53       8    1849      25    41.1    11.8    33.3AP Sheahan          31      53       6    1594      25    33.9    11.8    33.3C Hill              49      89       2    3412      33    39.2    12.2    33.3Sadiq Mohammad      41      74       2    2579      30    35.8    12.2    33.2WW Armstrong        50      84      10    2863      32    38.7    12.2    33.2MJ Prior            37      57      11    1923      26    41.8    11.9    33.1AP Gurusinha        41      70       7    2452      29    38.9    12.0    32.9KWR Fletcher        59      96      14    3272      34    39.9    12.0    32.8JN Rhodes           52      80       9    2532      31    35.7    12.0    32.7W Bardsley          41      66       5    2469      28    40.5    11.9    32.7HA Gomes            60      91      11    3171      33    39.6    12.0    32.5Shoaib Malik        32      54       6    1606      25    33.5    11.6    32.5DJ Bravo            40      71       1    2200      29    31.4    11.8    32.4VL Manjrekar        55      92      10    3208      33    39.1    11.8    32.2CL Cairns           62     104       5    3320      35    33.5    11.8    32.1AJ Lamb             79     139      10    4656      40    36.1    11.5    32.1FM Engineer         46      87       3    2611      32    31.1    11.8    32.0AC Hudson           35      63       3    2007      27    33.5    11.6    31.9APE Knott           95     149      15    4389      41    32.8    11.3    31.8DN Sardesai         30      55       4    2001      25    39.2    11.4    31.7PJP Burge           42      68       8    2290      28    38.2    11.5    31.6AG Prince           59      94      15    3435      33    43.5    11.6    31.5GP Howarth          47      83       5    2531      31    32.4    11.6    31.5MA Noble            42      73       7    1997      29    30.3    11.5    31.4MJK Smith           50      78       6    2278      30    31.6    11.5    31.4A Flintoff          78     128       9    3795      38    31.9    11.3    31.3BE Congdon          61     114       7    3448      36    32.2    11.4    31.2TW Hayward          35      60       2    1999      26    34.5    11.3    31.1MW Tate             39      52       5    1198      24    25.5    11.1    31.0NJ Contractor       31      52       1    1611      24    31.6    11.1    31.0MW Gatting          79     138      14    4409      39    35.6    11.0    30.9DL Vettori         102     155      22    4045      41    30.4    10.8    30.8MJ Horne            35      65       2    1788      27    28.4    11.2    30.7CD McMillan         55      91      10    3116      32    38.5    11.3    30.6CG Borde            55      97      11    3061      33    35.6    11.2    30.6KR Stackpole        43      80       5    2807      30    37.4    11.3    30.6Imran Farhat        39      75       2    2327      29    31.9    11.2    30.5MG Burgess          50      92       6    2684      32    31.2    11.1    30.3Wasim Raja          57      92      14    2821      32    36.2    11.1    30.3GM Ritchie          30      53       5    1690      24    35.2    10.9    30.3SV Carlisle         37      66       6    1615      27    26.9    11.0    30.2ML Jaisimha         39      71       4    2056      28    30.7    11.0    30.1AL Wadekar          37      71       3    2113      28    31.1    11.0    30.1MV Boucher         135     190      22    5223      44    31.1    10.2    30.1Habibul Bashar      50      99       1    3026      33    30.9    11.0    30.0IT Botham          102     161       6    5200      41    33.5    10.4    30.0BM McMillan         38      62      12    1968      26    39.4    10.9    29.9HH Dippenaar        38      62       5    1718      26    30.1    10.9    29.9Salman Butt         33      62       0    1889      26    30.5    10.9    29.9DL Amiss            50      88      10    3612      31    46.3    10.9    29.7M Prabhakar         39      58       9    1600      25    32.7    10.8    29.7GT Dowling          39      77       3    2306      29    31.2    10.9    29.7RJ Shastri          80     121      14    3830      36    35.8    10.7    29.7GA Hick             65     114       6    3383      35    31.3    10.7    29.6Kapil Dev          131     184      15    5248      43    31.1    10.0    29.6AW Nourse           45      83       8    2234      30    29.8    10.8    29.5VT Trumper          48      89       8    3163      31    39.0    10.8    29.4MS Atapattu         90     156      15    5502      40    39.0    10.3    29.4JA Rudolph          35      63       7    2028      26    36.2    10.7    29.4GW Flower           67     123       6    3457      36    29.5    10.5    29.3BA Young            35      68       4    2034      27    31.8    10.7    29.2Mudassar Nazar      76     116       8    4114      35    38.1    10.6    29.2GS Blewett          46      79       4    2552      29    34.0    10.6    28.9P Roy               43      79       4    2442      29    32.6    10.6    28.9RES Wyatt           40      64       6    1839      26    31.7    10.6    28.9JV Coney            52      85      14    2668      30    37.6    10.6    28.8WW Hinds            45      80       1    2608      29    33.0    10.5    28.6GM Wood             59     112       6    3374      34    31.8    10.3    28.5Ijaz Ahmed          60      92       4    3315      31    37.7    10.4    28.5JHB Waite           50      86       7    2405      30    30.4    10.5    28.5AD Gaekwad          40      70       4    1985      27    30.1    10.4    28.3CJ TavarÃ©           31      56       2    1755      24    32.5    10.3    28.3GR Marsh            50      93       7    2854      31    33.2    10.3    28.2SL Campbell         52      93       4    2882      31    32.4    10.3    28.2BB McCullum         55      93       6    3232      31    37.1    10.3    28.2Yuvraj Singh        34      52       6    1639      23    35.6    10.2    28.2WR Endean           28      52       4    1630      23    34.0    10.2    28.2AC MacLaren         35      61       4    1931      25    33.9    10.2    28.0JP Crawley          37      61       9    1800      25    34.6    10.2    28.0MJ Greatbatch       41      71       5    2021      27    30.6    10.3    27.9RW Marsh            96     150      13    3633      38    26.5     9.6    27.7ADR Campbell        60     109       4    2858      33    27.2    10.0    27.6LEG Ames            47      72      12    2434      27    40.6    10.1    27.5Imran Khan          88     126      25    3807      35    37.7     9.7    27.3JC Adams            54      90      17    3012      30    41.3    10.0    27.3J Dyson             30      58       7    1359      24    26.6     9.9    27.2BA Edgar            39      68       4    1958      26    30.6     9.9    27.0SM Pollock         108     156      39    3781      38    32.3     9.3    26.9KG Viljoen          27      50       2    1365      22    28.4     9.7    26.8Kamran Akmal        53      92       6    2648      30    30.8     9.8    26.8JDP Oram            33      59      10    1780      24    36.3     9.8    26.7Yashpal Sharma      37      59      11    1606      24    33.5     9.8    26.7RP Arnold           44      69       4    1821      26    28.0     9.8    26.6PJL Dujon           81     115      11    3322      33    31.9     9.5    26.4IA Healy           119     182      23    4356      40    27.4     8.8    26.4GJ Whittall         46      82       7    2207      28    29.4     9.6    26.1RS Mahanama         52      89       1    2576      29    29.3     9.4    25.9MS Sinclair         33      56       5    1635      23    32.1     9.4    25.8DS Smith            32      56       2    1370      23    25.4     9.4    25.8K Srikkanth         43      72       3    2062      26    29.9     9.4    25.5Imtiaz Ahmed        41      72       1    2079      26    29.3     9.4    25.5RS Kaluwitharana    49      78       4    1933      27    26.1     9.3    25.5TE Bailey           61      91      14    2290      29    29.7     9.2    25.4Rashid Latif        37      57       9    1381      23    28.8     9.3    25.3RA McLean           40      73       3    2120      26    30.3     9.3    25.2MR Ramprakash       52      92       6    2350      29    27.3     9.1    25.1GO Jones            34      53       4    1172      22    23.9     9.1    25.0G Giffen            31      53       0    1238      22    23.4     9.1    25.0RC Russell          54      86      16    1897      28    27.1     9.1    25.0SMH Kirmani         88     124      22    2759      33    27.0     8.8    24.9W Jaffer            31      58       1    1944      23    34.1     9.1    24.9L Klusener          49      69      11    1906      25    32.9     9.1    24.6AC Parore           78     128      19    2865      33    26.3     8.5    24.3Moin Khan           69     104       8    2741      30    28.6     8.7    24.1JT Tyldesley        31      55       1    1661      22    30.8     8.8    24.0J Darling           34      60       2    1657      23    28.6     8.8    24.0W Rhodes            58      98      21    2325      29    30.2     8.6    23.8CC Lewis            32      51       3    1105      21    23.0     8.6    23.7G Miller            34      51       4    1213      21    25.8     8.6    23.7KR Rutherford       56      99       8    2465      29    27.1     8.5    23.6SE Gregory          58     100       7    2282      29    24.5     8.4    23.4D Ramdin            42      73       8    1482      25    22.8     8.6    23.3N Boje              43      62      10    1312      23    25.2     8.5    23.2SC Williams         31      52       3    1183      21    24.1     8.5    23.2Javed Omar          40      80       2    1720      26    22.1     8.5    23.1MN Samuels          29      53       4    1408      21    28.7     8.3    22.7GS Ramchand         33      53       5    1180      21    24.6     8.3    22.7R Benaud            63      97       7    2201      28    24.5     8.1    22.5KS More             49      64      14    1285      23    25.7     8.3    22.5R Illingworth       61      90      11    1836      27    23.2     8.1    22.4Abdur Razzaq        46      77       9    1946      25    28.6     8.1    22.2JJ Crowe            39      65       4    1601      23    26.2     8.1    22.1KLT Arthurton       33      50       5    1382      20    30.7     8.0    21.8SA Durani           29      50       2    1202      20    25.0     8.0    21.8D Ganga             48      86       2    2160      26    25.7     7.9    21.7DW Randall          47      79       5    2470      25    33.4     7.9    21.7AK Davidson         44      61       7    1328      22    24.6     7.9    21.6RG Nadkarni         41      67      12    1414      23    25.7     7.9    21.5WAS Oldfield        54      80      17    1427      25    22.7     7.8    21.5RD Jacobs           65     112      21    2577      29    28.3     7.5    21.5BF Hastings         31      56       6    1510      21    30.2     7.9    21.4IDS Smith           63      88      17    1815      26    25.6     7.7    21.3DL Murray           62      96       9    1993      27    22.9     7.6    21.3RJ Hadlee           86     134      19    3124      31    27.2     7.2    21.2Wasim Akram        104     147      19    2898      32    22.6     7.0    21.0JM Parker           36      63       2    1498      22    24.6     7.7    20.9WPUJC Vaas         111     162      35    3089      33    24.3     6.7    20.7DJ Richardson       42      64       8    1359      22    24.3     7.6    20.6S Abid Ali          29      53       3    1018      20    20.4     7.5    20.5V Pollard           32      59       7    1266      21    24.3     7.5    20.3MH Mankad           44      72       5    2109      23    31.5     7.3    20.2B Yardley           33      54       4     978      20    19.6     7.4    20.1MG Johnson          39      54       8    1030      20    22.4     7.4    20.1JM Brearley         39      66       3    1442      22    22.9     7.3    20.0JE Emburey          64      96      20    1713      26    22.5     7.0    19.9DD Ebrahim          29      55       1    1226      20    22.7     7.3    19.8AF Giles            54      81      13    1421      24    20.9     7.1    19.7P Willey            26      50       6    1184      19    26.9     7.2    19.6PR Reiffel          35      50      14     955      19    26.5     7.2    19.6C White             30      50       7    1052      19    24.5     7.2    19.6CB Wishart          27      50       1    1098      19    22.4     7.2    19.6NR Mongia           44      68       8    1442      22    24.0     7.1    19.5DG Cork             37      56       8     864      20    18.0     7.1    19.4HDPK Dharmasena     31      51       7     868      19    19.7     7.1    19.2KJ Wadsworth        33      51       4    1010      19    21.5     7.1    19.2AFA Lilley          35      52       8     903      19    20.5     6.9    18.9SK Warne           144     197      17    3142      33    17.5     5.5    18.5Mohammad Ashraful   55     107       4    2306      26    22.4     6.3    18.4JG Bracewell        41      60      11    1001      20    20.4     6.7    18.2TG Evans            91     133      14    2439      28    20.5     5.9    18.0Khaled Mashud       44      84      10    1409      23    19.0     6.3    17.8RR Lindwall         61      84      13    1502      23    21.2     6.3    17.8Madan Lal           39      62      16    1042      20    22.7     6.5    17.7BR Taylor           30      50       6     898      18    20.4     6.5    17.6MG Hughes           53      70       8    1032      21    16.6     6.3    17.4MD Marshall         81     107      11    1810      25    18.9     5.8    17.2HH Streak           65     107      18    1990      25    22.4     5.8    17.2B Lee               75      88      18    1447      23    20.7     6.0    17.1DN Patel            37      66       8    1200      20    20.7     6.1    16.8HJ Tayfield         37      60       9     862      19    16.9     6.0    16.5FJ Titmus           53      76      11    1449      21    22.3     5.8    16.3Intikhab Alam       47      77      10    1493      21    22.3     5.7    16.2Mohammad Rafique    33      63       6    1059      19    18.6     5.7    15.9AC Bannerman        28      50       2    1108      17    23.1     5.8    15.8J Briggs            33      50       5     815      17    18.1     5.8    15.8KD Ghavri           39      57      14     913      18    21.2     5.7    15.6Sarfraz Nawaz       55      72      13    1045      20    17.7     5.6    15.6Harbhajan Singh     90     124      21    1915      25    18.6     5.0    15.6DA Allen            39      51      15     918      17    25.5     5.7    15.5BL Cairns           43      65       8     928      19    16.3     5.6    15.4A Kumble           132     173      32    2506      28    17.8     4.5    15.4RW Taylor           57      83      12    1156      21    16.3     5.3    15.3WW Hall             48      66      14     818      19    15.7     5.5    15.3H Trumble           32      57      14     851      17    19.8     5.1    14.1SB Doull            32      50      11     570      16    14.6     5.1    14.0PH Edmonds          51      65      15     875      18    17.5     5.0    14.0IWG Johnson         45      66      12    1000      18    18.5     4.9    13.9FS Trueman          67      85      14     981      20    13.8     4.7    13.8ATW Grout           51      67       8     890      18    15.1     4.8    13.7JM Blackham         35      62      11     800      17    15.7     4.7    13.1AME Roberts         47      62      11     762      17    14.9     4.7    13.1JN Gillespie        71      93      28    1218      20    18.7     4.3    13.0GAR Lock            49      63       9     742      17    13.7     4.6    13.0JJ Kelly            36      56      17     664      16    17.0     4.6    12.8Wasim Bari          81     112      26    1366      21    15.9     3.9    12.5CM Old              46      66       9     845      17    14.8     4.4    12.5DR Pringle          30      50       4     695      15    15.1     4.5    12.5Fazal Mahmood       34      50       6     620      15    14.1     4.5    12.5Nasim-ul-Ghani      29      50       5     747      15    16.6     4.5    12.5Abdul Qadir         67      77      11    1029      18    15.6     4.2    12.4PAJ DeFreitas       44      68       5     934      17    14.8     4.3    12.3VA Holder           40      59      11     682      16    14.2     4.3    12.3CJ McDermott        71      90      13     940      19    12.2     4.0    12.2J Srinath           67      92      21    1009      19    14.2     3.9    12.0AV Bedser           51      71      15     714      17    12.8     4.1    11.9JR Thomson          51      73      20     679      17    12.8     4.0    11.7Z Khan              76     100      22     995      19    12.8     3.6    11.4RC Motz             32      56       3     612      15    11.5     4.0    11.4MA Holding          60      76      10     910      17    13.8     3.8    11.4S Venkataraghavan   57      76      12     748      17    11.7     3.8    11.4Iqbal Qasim         50      57      15     549      15    13.1     3.9    11.2DK Lillee           70      90      24     905      18    13.7     3.6    11.2CV Grimmett         37      50      10     557      14    13.9     3.9    11.0CEL Ambrose         98     145      29    1439      21    12.4     3.0    10.9JA Snow             49      71      14     772      16    13.5     3.6    10.7EAS Prasanna        49      84      20     735      17    11.5     3.4    10.6D Gough             58      86      18     855      17    12.6     3.4    10.5JC Laker            46      63      15     676      15    14.1     3.6    10.5GP Wickramasinghe   40      64       5     555      15     9.4     3.5    10.3GD McKenzie         60      89      12     945      17    12.3     3.2    10.3Saqlain Mushtaq     49      78      14     927      16    14.5     3.3    10.1Mashrafe Mortaza    36      67       5     797      15    12.9     3.4    10.0J Garner            58      68      14     672      15    12.4     3.3     9.9GF Lawson           46      68      12     894      15    16.0     3.3     9.9M Dillon            38      68       3     549      15     8.4     3.3     9.9AR Caddick          62      95      12     861      17    10.4     3.0     9.9RO Collinge         35      50      13     533      13    14.4     3.4     9.7SJ Harmison         62      84      23     742      16    12.2     3.0     9.6Mushtaq Ahmed       52      72      16     656      15    11.7     3.1     9.6IR Bishop           43      63      11     632      14    12.2     3.1     9.3MS Kasprowicz       38      54      12     445      13    10.6     3.1     9.1Mohammad Sami       35      54      14     475      13    11.9     3.1     9.1DW Steyn            43      54      13     577      13    14.1     3.1     9.1Shahadat Hossain    29      55      15     394      13     9.9     3.1     9.0Shoaib Akhtar       46      67      13     544      14    10.1     2.9     8.9M Muralitharan     132     162      56    1259      19    11.9     2.2     8.9DBL Powell          37      57       5     407      13     7.8     3.0     8.8Waqar Younis        87     120      21    1010      17    10.2     2.4     8.7GR Dilley           41      58      19     521      13    13.4     2.9     8.7AA Mallett          38      50      13     430      12    11.6     2.9     8.4M Ntini            101     116      45     699      16     9.8     2.2     8.1DL Underwood        86     116      35     937      16    11.6     2.2     8.1PR Adams            45      55      15     360      12     9.0     2.6     7.9JB Statham          70      87      28     675      14    11.4     2.3     7.7S Ramadhin          43      58      14     361      12     8.2     2.5     7.6RM Hogg             38      58      13     439      12     9.8     2.5     7.6JM Anderson         54      72      31     513      13    12.5     2.3     7.6AA Donald           72      94      33     652      14    10.7     2.1     7.4BS Bedi             67     101      28     656      14     9.0     1.9     7.1RGD Willis          90     128      55     840      15    11.5     1.8     7.0DK Morrison         48      71      26     379      12     8.4     2.0     6.8LR Gibbs            79     109      39     488      13     7.0     1.6     6.1MJ Hoggard          67      92      27     473      12     7.3     1.6     5.9DE Malcolm          40      58      19     236      10     6.1     1.7     5.7GD McGrath         123     136      51     639      13     7.5     1.2     5.5CA Walsh           132     185      61     936      14     7.5     1.1     5.4Danish Kaneria      61      84      33     360      11     7.1     1.4     5.4ARC Fraser          46      67      15     388      10     7.5     1.5     5.3FH Edwards          43      69      21     248      10     5.2     1.4     5.2MS Panesar          39      51      17     187       8     5.5     1.3     4.3CD Collymore        30      52      27     197       8     7.9     1.2     4.3TM Alderman         41      53      22     203       8     6.5     1.2     4.2AL Valentine        36      51      21     141       7     4.7     1.0     3.5EJ Chatfield        43      54      33     180       7     8.6     0.9     3.4PCR Tufnell         42      59      29     153       7     5.1     0.8     3.3BS Chandrasekhar    58      80      39     167       6     4.1     0.5     2.3CS Martin           59      85      44      97       5     2.4     0.3     1.8`

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