## Highest scores

Recently I got thinking about Flappy Bird scores, and noted that they should be similar to cricket scores in the way they're distributed.

Translating the problem to cricket, the question is, "What is the relationship between a batsman's highest score, his average, and the number of innings he's batted in?" A follow-up question is how well such a formula predicts, say, the average based on the innings and highest score. I expected there to be quite a lot of scatter (assessing a batsman on just one innings!), but the correlation ended up being pretty decent. This isn't a particularly useful correlation, but I found it fun to play with.

Given the average, the probability that a batsman makes a score less than x is roughly (1 - exp(-x/avg)). Treating each innings as independent of the others, the probability that all N of a batsman's innings are less than x is therefore (1 - exp(-x/avg))N.

A natural "expected" highest score, given the batsman's average, would be the value x such that the probability that all innings are less than x is 1/2. Calling this value HS, we have

(1 - exp(-HS/avg))N = 1/2,

which is the basic relation between highest score, average, and number of innings batted.

Solving for HS (i.e., what highest score do we expect, given average and innings batted?):

HS = -avg * ln(1 - 0.51/N).

Solving for avg (given only highest score and innings batted, what do we think the batsman's average is?):

avg = -HS / ln(1 - 0.51/N).

Using the latter formula as a predictor works surprisingly (to me) well:

The weird qualification of 50 dismissals rather than innings is because I began by including all abtsmen with at least 2 dismissals, and at sample sizes this small, I figured dismissals would be useful to avoid not-out irregularities. (The R-squared is actually a bit higher, about 0.78, in that expanded sample.)

I doubt I'll ever use this formula, but Perhaps the most amusing individual result is Shane Warne: based on his average and innings batted, his "predicted" high score is... 98! So he didn't quite deserve that hundred after all.

Full table, straight off Statsguru – I was so lazy that I didn't even turn off the ICC game.

predict one based
real        on the other
Player                         Inns      NO      HS     avg      HS     avg
DG Bradman (Aus)                 80      10     334    99.9   475.0    70.3
H Sutcliffe (Eng)                84       9     194    60.7   291.6    40.4
KF Barrington (Eng)             131      15     256    58.7   307.7    48.8
ED Weekes (WI)                   81       5     207    58.6   279.3    43.4
WR Hammond (Eng)                140      16     336    58.5   310.4    63.3
KC Sangakkara (SL)              209      17     319    58.1   331.6    55.9
GS Sobers (WI)                  160      21     365    57.8   314.5    67.0
JB Hobbs (Eng)                  102       7     211    56.9   284.4    42.2
CL Walcott (WI)                  74       7     220    56.7   265.0    47.1
L Hutton (Eng)                  138      15     364    56.7   300.1    68.7
JH Kallis (ICC/SA)              280      40     224    55.4   332.4    37.3
GS Chappell (Aus)               151      19     247    53.9   290.1    45.9
AD Nourse (SA)                   62       7     231    53.8   242.1    51.3
SR Tendulkar (India)            329      33     248    53.8   331.5    40.2
BC Lara (ICC/WI)                232       6     400    52.9   307.5    68.8
Javed Miandad (Pak)             189      21     280    52.6   294.9    49.9
R Dravid (ICC/India)            286      32     270    52.3   315.1    44.8
Mohammad Yousuf (Pak)           156      12     223    52.3   283.3    41.2
AB de Villiers (SA)             152      16     278    52.3   281.9    51.6
S Chanderpaul (WI)              261      45     203    51.9   308.1    34.2
RT Ponting (Aus)                287      29     257    51.9   312.5    42.6
HM Amla (SA)                    130      11     311    51.6   270.0    59.4
A Flower (Zim)                  112      19     232    51.5   262.2    45.6
MEK Hussey (Aus)                137      16     195    51.5   272.5    36.9
Younis Khan (Pak)               158      14     313    51.4   279.1    57.6
SM Gavaskar (India)             214      16     236    51.1   293.1    41.2
SR Waugh (Aus)                  260      46     200    51.1   302.7    33.7
MJ Clarke (Aus)                 178      19     329    50.8   282.0    59.3
ML Hayden (Aus)                 184      14     380    50.7   283.2    68.1
AR Border (Aus)                 265      44     205    50.6   300.7    34.5
DPMD Jayawardene (SL)           240      15     374    50.3   294.2    63.9
IVA Richards (WI)               182      12     291    50.2   279.9    52.2
DCS Compton (Eng)               131      15     278    50.1   262.5    53.0
Inzamam-ul-Haq (ICC/Pak)        200      22     329    49.6   281.1    58.1
FMM Worrell (WI)                 87       9     261    49.5   239.3    54.0
V Sehwag (ICC/India)            180       6     319    49.3   274.4    57.4
B Mitchell (SA)                  80       9     189    48.9   232.3    39.8
TT Samaraweera (SL)             132      20     231    48.8   256.1    44.0
Misbah-ul-Haq (Pak)              80      14     161    48.8   231.7    33.9
GC Smith (ICC/SA)               203      13     277    48.7   276.8    48.8
RN Harvey (Aus)                 137      10     205    48.4   256.0    38.8
KD Walters (Aus)                125      14     250    48.3   250.8    48.1
SJ McCabe (Aus)                  62       5     232    48.2   216.9    51.6
ER Dexter (Eng)                 102       8     205    47.9   239.2    41.0
G Boycott (Eng)                 193      23     246    47.7   268.7    43.7
VS Hazare (India)                52       6     164    47.7   206.1    37.9
EH Hendren (Eng)                 83       9     205    47.6   228.1    42.8
AC Gilchrist (Aus)              137      20     204    47.6   251.8    38.6
SM Nurse (WI)                    54       1     258    47.6   207.6    59.1
RB Kanhai (WI)                  137       6     256    47.5   251.4    48.4
KP Pietersen (Eng)              181       8     227    47.3   263.2    40.8
WM Lawry (Aus)                  123      12     210    47.2   244.3    40.5
LRPL Taylor (NZ)                 98       9     217    46.9   232.6    43.8
RB Simpson (Aus)                111       7     311    46.8   237.8    61.2
PBH May (Eng)                   106       9     285    46.8   235.4    56.6
CH Lloyd (WI)                   175      14     242    46.7   258.2    43.7
AL Hassett (Aus)                 69       3     198    46.6   214.4    43.0
DM Jones (Aus)                   89      11     216    46.6   226.2    44.5
AN Cook (Eng)                   183      10     294    46.5   259.4    52.7
AR Morris (Aus)                  79       3     206    46.5   220.3    43.5
IJL Trott (Eng)                  87       6     226    46.5   224.7    46.7
DR Martyn (Aus)                 109      14     165    46.4   234.7    32.6
DL Amiss (Eng)                   88      10     262    46.3   224.5    54.0
AD Mathews (SL)                  62      12     157    46.2   207.7    34.9
M Leyland (Eng)                  65       5     187    46.1   209.4    41.1
WM Woodfull (Aus)                54       4     161    46.0   200.6    36.9
VVS Laxman (India)              225      34     281    46.0   265.9    48.6
EJ Barlow (SA)                   57       2     201    45.7   202.0    45.5
NC O'Neill (Aus)                 69       8     181    45.6   209.8    39.3
Saeed Anwar (Pak)                91       2     188    45.5   222.2    38.5
IR Bell (Eng)                   170      22     235    45.4   250.0    42.7
MD Crowe (NZ)                   131      11     299    45.4   237.9    57.0
JL Langer (Aus)                 182      12     250    45.3   252.3    44.9
G Kirsten (SA)                  176      15     275    45.3   250.7    49.6
CC Hunte (WI)                    78       6     260    45.1   213.0    55.0
SM Katich (Aus)                  99       6     157    45.0   223.6    31.6
M Azharuddin (India)            147       9     199    45.0   241.3    37.1
Zaheer Abbas (Pak)              124      11     274    44.8   232.4    52.8
MH Richardson (NZ)               65       3     145    44.8   203.5    31.9
CG Greenidge (WI)               185      16     226    44.7   249.9    40.4
GP Thorpe (Eng)                 179      28     200    44.7   248.1    36.0
GM Turner (NZ)                   73       6     259    44.6   208.1    55.6
AI Kallicharran (WI)            109      10     187    44.4   224.9    36.9
RB Richardson (WI)              146      12     194    44.4   237.6    36.2
TW Graveney (Eng)               123      13     258    44.4   230.0    49.8
Shoaib Mohammad (Pak)            68       7     203    44.3   203.6    44.2
AH Jones (NZ)                    74       8     186    44.3   207.0    39.8
DI Gower (Eng)                  204      18     215    44.3   251.6    37.8
DJ Cullinan (SA)                115      12     275    44.2   226.1    53.8
G Gambhir (India)                96       5     206    44.2   218.0    41.7
MC Cowdrey (Eng)                188      15     182    44.1   246.9    32.5
Hanif Mohammad (Pak)             97       8     337    44.0   217.5    68.2
ME Trescothick (Eng)            143      10     219    43.8   233.5    41.1
Saleem Malik (Pak)              154      22     237    43.7   236.2    43.8
RA Smith (Eng)                  112      15     175    43.7   222.2    34.4
EAB Rowan (SA)                   50       5     236    43.7   187.1    55.1
DC Boon (Aus)                   190      20     200    43.7   245.1    35.6
JH Edrich (Eng)                 127       9     310    43.5   227.0    59.5
MA Taylor (Aus)                 186      13     334    43.5   243.3    59.7
IR Redpath (Aus)                120      11     171    43.5   224.1    33.2
BF Butcher (WI)                  78       6     209    43.1   203.8    44.2
PA de Silva (SL)                159      11     267    43.0   233.7    49.1
DA Warner (Aus)                  54       3     180    42.9   187.0    41.3
HP Tillakaratne (SL)            131      25     204    42.9   224.8    38.9
MJ Slater (Aus)                 131       7     219    42.8   224.6    41.8
C Washbrook (Eng)                66       6     195    42.8   195.3    42.7
GA Gooch (Eng)                  215       6     333    42.6   244.4    58.0
M Amarnath (India)              113      10     138    42.5   216.6    27.1
RC Fredericks (WI)              109       7     169    42.5   215.0    33.4
IM Chappell (Aus)               136      10     196    42.4   224.1    37.1
JB Stollmeyer (WI)               56       5     160    42.3   186.2    36.4
DL Haynes (WI)                  202      25     184    42.3   240.1    32.4
PR Umrigar (India)               94       8     223    42.2   207.4    45.4
SC Ganguly (India)              188      17     239    42.2   236.4    42.6
DB Vengsarkar (India)           185      22     166    42.1   235.5    29.7
NS Sidhu (India)                 78       2     201    42.1   199.2    42.5
DJ McGlew (SA)                   64       6     255    42.1   190.6    56.3
CH Gayle (WI)                   174       9     333    42.0   232.2    60.2
HH Gibbs (SA)                   154       7     228    42.0   226.8    42.2
GR Viswanath (India)            155      10     222    41.9   226.9    41.0
ME Waugh (Aus)                  209      17     153    41.8   238.8    26.8
CG Macartney (Aus)               55       4     170    41.8   183.0    38.8
AG Prince (SA)                  104      16     162    41.6   208.8    32.3
MP Vaughan (Eng)                147       9     197    41.4   222.1    36.8
JC Adams (WI)                    90      17     208    41.3   200.9    42.7
GN Yallop (Aus)                  70       3     268    41.1   190.0    58.0
GRJ Matthews (Aus)               53       8     130    41.1   178.4    29.9
KC Wessels (Aus/SA)              71       3     179    41.0   190.0    38.6
TM Dilshan (SL)                 145      11     193    41.0   219.1    36.1
AJ Strauss (Eng)                178       6     177    40.9   227.1    31.9
PH Parfitt (Eng)                 52       6     131    40.9   176.9    30.3
MJ Prior (Eng)                  116      20     131    40.8   209.2    25.6
HW Taylor (SA)                   76       4     176    40.8   191.7    37.4
LEG Ames (Eng)                   72      12     149    40.6   188.5    32.1
PD Collingwood (Eng)            115      10     206    40.6   207.4    40.3
W Bardsley (Aus)                 66       5     193    40.5   184.6    42.3
AW Greig (Eng)                   93       4     148    40.4   198.2    30.2
Saeed Ahmed (Pak)                78       4     172    40.4   191.0    36.4
B Sutcliffe (NZ)                 76       8     230    40.1   188.5    48.9
ST Jayasuriya (SL)              188      14     340    40.1   224.6    60.7
BL D'Oliveira (Eng)              70       8     158    40.1   185.1    34.2
SP Fleming (NZ)                 189      10     274    40.1   224.7    48.8
RR Sarwan (WI)                  154       8     291    40.0   216.3    53.8
WJ Edrich (Eng)                  63       2     219    40.0   180.6    48.5
KWR Fletcher (Eng)               96      14     216    39.9   196.9    43.8
HA Gomes (WI)                    91      11     143    39.6   193.4    29.3
AJ Stewart (Eng)                235      21     190    39.5   230.4    32.6
BM McMillan (SA)                 62      12     113    39.4   177.1    25.1
CC McDonald (Aus)                83       4     170    39.3   188.3    35.5
DN Sardesai (India)              55       4     212    39.2   171.8    48.4
C Hill (Aus)                     89       2     191    39.2   190.5    39.3
Mushtaq Mohammad (Pak)          100       7     201    39.2   194.9    40.4
Azhar Ali (Pak)                  60       4     157    39.1   174.8    35.1
VL Manjrekar (India)             92      10     189    39.1   191.4    38.6
VT Trumper (Aus)                 89       8     214    39.0   189.7    44.0
MS Atapattu (SL)                156      15     249    39.0   211.4    46.0
AP Gurusinha (SL)                70       7     143    38.9   179.8    31.0
Majid Khan (Pak)                106       5     167    38.9   195.9    33.2
Asif Iqbal (Pak)                 99       7     175    38.9   192.9    35.2
MS Dhoni (India)                130      15     224    38.8   203.0    42.8
Taufeeq Umar (Pak)               81       5     236    38.7   184.5    49.5
WW Armstrong (Aus)               84      10     159    38.7   185.7    33.1
CD McMillan (NZ)                 91      10     142    38.5   187.7    29.1
PJP Burge (Aus)                  68       8     181    38.2   175.2    39.4
Mudassar Nazar (Pak)            116       8     231    38.1   195.1    45.1
BB McCullum (NZ)                145       8     302    38.1   203.6    56.5
Shakib Al Hasan (Ban)            65       5     144    38.0   172.6    31.7
JG Wright (NZ)                  148       7     185    37.8   202.9    34.5
Imran Khan (Pak)                126      25     136    37.7   196.2    26.1
MA Atherton (Eng)               212       7     185    37.7   215.8    32.3
Ijaz Ahmed (Pak)                 92       4     211    37.7   184.3    43.1
JV Coney (NZ)                    85      14     174    37.6   180.8    36.2
PE Richardson (Eng)              56       1     126    37.5   164.8    28.6
KR Stackpole (Aus)               80       5     207    37.4   177.9    43.6
KJ Hughes (Aus)                 124       6     213    37.4   194.1    41.0
ND McKenzie (SA)                 94       7     226    37.4   183.7    46.0
AN Petersen (SA)                 52       3     182    37.3   161.3    42.1
N Hussain (Eng)                 171      16     207    37.2   204.9    37.6
SV Manjrekar (India)             61       6     218    37.1   166.5    48.6
Mohsin Khan (Pak)                79       6     200    37.1   175.9    42.2
NJ Astle (NZ)                   137      10     222    37.0   195.8    42.0
KR Miller (Aus)                  87       7     147    37.0   178.8    30.4
Tamim Iqbal (Ban)                62       0     151    36.6   164.6    33.6
CL Hooper (WI)                  173      15     233    36.5   201.3    42.2
WJ Cronje (SA)                  111       9     135    36.4   184.9    26.6
KS Williamson (NZ)               56       2     135    36.4   160.0    30.7
SR Watson (Aus)                  95       3     176    36.3   178.9    35.7
JDP Oram (NZ)                    59      10     133    36.3   161.6    29.9
Wasim Raja (Pak)                 92      14     125    36.2   176.9    25.6
AJ Lamb (Eng)                   139      10     142    36.1   191.4    26.8
FE Woolley (Eng)                 98       7     154    36.1   178.7    31.1
AL Logie (WI)                    78       9     130    35.8   169.2    27.5
RJ Shastri (India)              121      14     206    35.8   184.9    39.9
A Ranatunga (SL)                155      12     135    35.7   193.2    24.9
JN Rhodes (SA)                   80       9     117    35.7   169.5    24.6
CG Borde (India)                 97      11     177    35.6   176.0    35.8
MW Gatting (Eng)                138      14     207    35.6   188.3    39.1
MN Samuels (WI)                  90       6     260    35.5   172.9    53.4
BJ Haddin (Aus)                  94       9     169    35.5   174.4    34.4
JA Rudolph (SA)                  83       9     222    35.4   169.7    46.4
Aamer Sohail (Pak)               83       3     205    35.3   169.0    42.8
GM Ritchie (Aus)                 53       5     146    35.2   152.9    33.6
MAK Pataudi (India)              83       3     203    34.9   167.2    42.4
JP Crawley (Eng)                 61       9     156    34.6   155.2    34.8
MA Butcher (Eng)                131       7     173    34.6   181.3    33.0
TL Goddard (SA)                  78       5     112    34.5   162.9    23.7
TW Hayward (Eng)                 60       2     137    34.5   153.9    30.7
W Jaffer (India)                 58       1     212    34.1   151.2    47.8
GS Blewett (Aus)                 79       4     214    34.0   161.3    45.1
Mohammad Hafeez (Pak)            70       6     196    34.0   156.9    42.4
WR Endean (SA)                   52       4     162    34.0   146.8    37.5
Yuvraj Singh (India)             62       6     169    33.9   152.6    37.6
AP Sheahan (Aus)                 53       6     127    33.9   147.3    29.2
AC MacLaren (Eng)                61       4     140    33.9   151.8    31.2
IT Botham (Eng)                 161       6     208    33.5   182.8    38.2
CL Cairns (NZ)                  104       5     158    33.5   168.1    31.5
KD Mackay (Aus)                  52       7      89    33.5   144.8    20.6
Yashpal Sharma (India)           59      11     140    33.5   148.8    31.5
Shoaib Malik (Pak)               54       6     148    33.5   145.9    33.9
AC Hudson (SA)                   63       3     163    33.5   151.0    36.1
DW Randall (Eng)                 79       5     174    33.4   158.2    36.7
JR Reid (NZ)                    108       5     142    33.3   168.1    28.1
GR Marsh (Aus)                   93       7     138    33.2   162.7    28.1
WW Hinds (WI)                    80       1     213    33.0   156.9    44.8
L Klusener (SA)                  69      11     174    32.9   151.3    37.8
APE Knott (Eng)                 149      15     135    32.8   176.0    25.1
M Prabhakar (India)              58       9     120    32.7   144.7    27.1
NT Paranavitana (SL)             60       5     111    32.6   145.5    24.9
P Roy (India)                    79       4     173    32.6   154.3    36.5
CJ Tavare (Eng)                  56       2     149    32.5   142.9    33.9
GP Howarth (NZ)                  83       5     147    32.4   155.4    30.7
Mushfiqur Rahim (Ban)            71       4     200    32.4   150.3    43.2
SL Campbell (WI)                 93       4     208    32.4   158.8    42.4
SM Pollock (SA)                 156      39     111    32.3   175.1    20.5
BE Congdon (NZ)                 114       7     176    32.2   164.5    34.5
JM Parks (Eng)                   68       7     108    32.2   147.7    23.5
MS Sinclair (NZ)                 56       5     214    32.1   141.0    48.7
Imran Farhat (Pak)               77       2     128    32.0   150.9    27.1
PJL Dujon (WI)                  115      11     139    31.9   163.4    27.2
Rameez Raja (Pak)                94       5     122    31.8   156.4    24.8
GM Wood (Aus)                   112       6     172    31.8   162.0    33.8
BA Young (NZ)                    68       4     267    31.8   145.9    58.2
A Flintoff (Eng/ICC)            130       9     167    31.8   166.4    31.9
RES Wyatt (Eng)                  64       6     149    31.7   143.6    32.9
MJK Smith (Eng)                  78       6     121    31.6   149.5    25.6
NJ Contractor (India)            52       1     108    31.6   136.6    25.0
CPS Chauhan (India)              68       2      97    31.6   144.9    21.1
MH Mankad (India)                72       5     231    31.5   146.3    49.7
DJ Bravo (WI)                    71       1     113    31.4   145.6    24.4
GA Hick (Eng)                   114       6     178    31.3   159.9    34.9
HAPW Jayawardene (SL)            77      11     154    31.2   147.2    32.7
MG Burgess (NZ)                  92       6     119    31.2   152.6    24.3
GT Dowling (NZ)                  77       3     239    31.2   146.9    50.7
FM Engineer (India)              87       3     121    31.1   150.3    25.0
AL Wadekar (India)               71       3     143    31.1   144.0    30.9
N Kapil Dev (India)             184      15     163    31.1   173.4    29.2
Habibul Bashar (Ban)             99       1     113    30.9   153.3    22.8
Kamran Akmal (Pak)               92       6     158    30.8   150.6    32.3
JT Tyldesley (Eng)               55       1     138    30.8   134.7    31.5
KLT Arthurton (WI)               50       5     157    30.7   131.6    36.6
ML Jaisimha (India)              71       4     129    30.7   142.2    27.8
MJ Greatbatch (NZ)               71       5     146    30.6   141.9    31.5
BA Edgar (NZ)                    68       4     161    30.6   140.4    35.1
Salman Butt (Pak)                62       0     122    30.5   137.0    27.1
JHB Waite (SA)                   86       7     134    30.4   146.9    27.8
T Taibu (Zim)                    54       3     153    30.3   132.2    35.1
MV Boucher (ICC/SA)             206      24     125    30.3   172.6    21.9
RA McLean (SA)                   73       3     142    30.3   141.2    30.5
MA Noble (Aus)                   73       7     133    30.3   141.0    28.5
BF Hastings (NZ)                 56       6     117    30.2   132.8    26.6
W Rhodes (Eng)                   98      21     179    30.2   149.6    36.1
HH Dippenaar (SA)                62       5     177    30.1   135.6    39.3
DL Vettori (ICC/NZ)             173      23     140    30.1   166.2    25.4
K Srikkanth (India)              72       3     123    29.9   138.9    26.5
AW Nourse (SA)                   83       8     111    29.8   142.6    23.2
TE Bailey (Eng)                  91      14     134    29.7   145.2    27.5
MJ Guptill (NZ)                  59       1     189    29.6   131.8    42.5
GW Flower (Zim)                 123       6     201    29.5   153.1    38.8
GJ Whittall (Zim)                82       7     203    29.4   140.6    42.5
Imtiaz Ahmed (Pak)               72       1     209    29.3   136.1    45.0
RS Mahanama (SL)                 89       1     225    29.3   142.2    46.3
Rashid Latif (Pak)               57       9     150    28.8   127.0    34.0
Abdul Razzaq (Pak)               77       9     134    28.6   134.9    28.4
J Darling (Aus)                  60       2     178    28.6   127.6    39.9
Moin Khan (Pak)                 104       8     137    28.6   143.2    27.3
KG Viljoen (SA)                  50       2     124    28.4   121.8    28.9
MJ Horne (NZ)                    65       2     157    28.4   129.0    34.5
RD Jacobs (WI)                  112      21     118    28.3   144.0    23.2
RP Arnold (SL)                   69       4     123    28.0   129.0    26.7
IA Healy (Aus)                  182      23     161    27.4   152.6    28.9
MR Ramprakash (Eng)              92       6     154    27.3   133.7    31.5
D Ramdin (WI)                    95      13     166    27.3   134.2    33.7
ADR Campbell (Zim)              109       4     103    27.2   137.7    20.4
Sir RJ Hadlee (NZ)              134      19     151    27.2   143.1    28.7
RC Russell (Eng)                 86      16     128    27.1   130.8    26.5
KR Rutherford (NZ)               99       8     107    27.1   134.5    21.6
SMH Kirmani (India)             124      22     102    27.0   140.3    19.7
SV Carlisle (Zim)                66       6     118    26.9   122.7    25.9
H Masakadza (Zim)                50       2     119    26.9   115.3    27.8
P Willey (Eng)                   50       6     102    26.9   115.3    23.8
J Dyson (Aus)                    58       7     127    26.6   118.1    28.6
PR Reiffel (Aus)                 50      14      79    26.5   113.7    18.4
RW Marsh (Aus)                  150      13     132    26.5   142.6    24.5
AC Parore (NZ)                  128      19     110    26.3   137.2    21.1
JJ Crowe (NZ)                    65       4     128    26.2   119.3    28.2
RS Kaluwitharana (SL)            78       4     132    26.1   123.5    27.9
G Miller (Eng)                   51       4      98    25.8   111.1    22.8
D Ganga (WI)                     86       2     135    25.7   124.0    28.0
KS More (India)                  64      14      73    25.7   116.4    16.1
RG Nadkarni (India)              67      12     122    25.7   117.6    26.7
IDS Smith (NZ)                   88      17     173    25.6   123.9    35.7
DA Allen (Eng)                   51      15      88    25.5   109.8    20.4
MW Tate (Eng)                    52       5     100    25.5   110.2    23.1
N Boje (SA)                      62      10      85    25.2   113.5    18.9
SA Durani (India)                50       2     104    25.0   107.3    24.3
DS Smith (WI)                    58       2     108    24.7   109.5    24.4
AK Davidson (Aus)                61       7      80    24.6   110.2    17.8
GS Ramchand (India)              53       5     109    24.6   106.8    25.1
JM Parker (NZ)                   63       2     121    24.6   110.8    26.8
SE Gregory (Aus)                100       7     201    24.5   122.0    40.4
C White (Eng)                    50       7     121    24.5   104.8    28.2
R Benaud (Aus)                   97       7     122    24.5   120.9    24.7
V Pollard (NZ)                   59       7     116    24.3   108.3    26.1
WPUJC Vaas (SL)                 162      35     100    24.3   132.7    18.3
DJ Richardson (SA)               64       8     109    24.3   109.9    24.1
SCJ Broad (Eng)                  95      12     169    24.2   119.2    34.3
SC Williams (WI)                 52       3     128    24.1   104.4    29.6
NR Mongia (India)                68       8     152    24.0   110.3    33.1
Mohammad Ashraful (Ban)         119       5     190    24.0   123.6    36.9
GO Jones (Eng)                   53       4     100    23.9   103.8    23.0
G Giffen (Aus)                   53       0     161    23.4   101.4    37.1
R Illingworth (Eng)              90      11     113    23.2   113.2    23.2
AC Bannerman (Aus)               50       2      94    23.1    98.9    21.9
CC Lewis (Eng)                   51       3     117    23.0    99.1    27.2
DL Murray (WI)                   96       9      91    22.9   113.0    18.4
JM Brearley (Eng)                66       3      91    22.9   104.4    19.9
DD Ebrahim (Zim)                 55       1      94    22.7    99.3    21.5
WAS Oldfield (Aus)               80      17      65    22.7   107.7    13.7
S Madan Lal (India)              62      16      74    22.7   101.9    16.4
Wasim Akram (Pak)               147      19     257    22.6   121.3    48.0
JE Emburey (Eng)                 96      20      75    22.5   111.2    15.2
MG Johnson (Aus)                 87      14     123    22.4   108.4    25.4
CB Wishart (Zim)                 50       1     114    22.4    96.0    26.6
HH Streak (Zim)                 107      18     127    22.4   112.7    25.2
FJ Titmus (Eng)                  76      11      84    22.3   104.8    17.9
Intikhab Alam (Pak)              77      10     138    22.3   105.0    29.3
GP Swann (Eng)                   76      14      85    22.1   103.9    18.1
Javed Omar (Ban)                 80       2     119    22.1   104.8    25.0
DJG Sammy (WI)                   63       2     106    21.7    97.9    23.5
KJ Wadsworth (NZ)                51       4      80    21.5    92.5    18.6
KD Ghavri (India)                57      14      86    21.2    93.7    19.5
RR Lindwall (Aus)                84      13     118    21.2   101.6    24.6
AF Giles (Eng)                   81      13      59    20.9    99.5    12.4
DN Patel (NZ)                    66       8      99    20.7    94.3    21.7
AFA Lilley (Eng)                 52       8      84    20.5    88.7    19.4
TG Evans (Eng)                  133      14     104    20.5   107.8    19.8
JG Bracewell (NZ)                60      11     110    20.4    91.2    24.6
BR Taylor (NZ)                   50       6     124    20.4    87.4    28.9
S Abid Ali (India)               53       3      81    20.4    88.4    18.6
B Lee (Aus)                      90      18      64    20.2    98.1    13.1
H Trumble (Aus)                  57      14      70    19.8    87.4    15.9
HDPK Dharmasena (SL)             51       7      62    19.7    84.9    14.4
B Yardley (Aus)                  54       4      74    19.6    85.3    17.0
Khaled Mashud (Ban)              84      10     103    19.0    91.4    21.5
TG Southee (NZ)                  50       5      77    19.0    81.4    18.0
MD Marshall (WI)                107      11      92    18.9    95.1    18.2
JN Gillespie (Aus)               93      28     201    18.7    91.8    41.0
Mohammad Rafique (Ban)           63       6     111    18.6    83.8    24.6
IWG Johnson (Aus)                66      12      77    18.5    84.4    16.9
Harbhajan Singh (India)         142      22     115    18.4    97.7    21.6
J Briggs (Eng)                   50       5     121    18.1    77.6    28.2
DG Cork (Eng)                    56       8      59    18.0    79.2    13.4
A Kumble (India)                173      32     110    17.8    98.1    19.9
Sarfraz Nawaz (Pak)              72      13      90    17.7    82.3    19.4
PH Edmonds (Eng)                 65      15      64    17.5    79.6    14.1
SK Warne (Aus)                  199      17      99    17.3    98.1    17.5
JJ Kelly (Aus)                   56      17      46    17.0    74.9    10.5
HJ Tayfield (SA)                 60       9      75    16.9    75.5    16.8
MG Hughes (Aus)                  70       8      72    16.6    76.9    15.6
Nasim-ul-Ghani (Pak)             50       5     101    16.6    71.1    23.6
BL Cairns (NZ)                   65       8      64    16.3    74.0    14.1
RW Taylor (Eng)                  83      12      97    16.3    78.0    20.3
GF Lawson (Aus)                  68      12      74    16.0    73.3    16.1
Wasim Bari (Pak)                112      26      85    15.9    80.8    16.7
WW Hall (WI)                     66      14      50    15.7    71.8    11.0
JM Blackham (Aus)                62      11      74    15.7    70.5    16.4
Abdul Qadir (Pak)                77      11      61    15.6    73.5    12.9
DR Pringle (Eng)                 50       4      63    15.1    64.7    14.7
ATW Grout (Aus)                  67       8      74    15.1    69.0    16.2
AME Roberts (WI)                 62      11      68    14.9    67.2    15.1
CM Old (Eng)                     66       9      65    14.8    67.6    14.2
PAJ DeFreitas (Eng)              68       5      88    14.8    68.0    19.2
SB Doull (NZ)                    50      11      46    14.6    62.6    10.7
Saqlain Mushtaq (Pak)            78      14     101    14.5    68.5    21.4
RO Collinge (NZ)                 50      13      68    14.4    61.7    15.9
DW Steyn (SA)                    89      21      76    14.3    69.2    15.6
PM Siddle (Aus)                  76      11      51    14.2    67.0    10.8
J Srinath (India)                92      21      76    14.2    69.5    15.5
VA Holder (WI)                   59      11      42    14.2    63.2     9.4
Fazal Mahmood (Pak)              50       6      60    14.1    60.4    14.0
JC Laker (Eng)                   63      15      63    14.1    63.6    14.0
CV Grimmett (Aus)                50      10      50    13.9    59.7    11.7
FS Trueman (Eng)                 85      14      39    13.8    66.5     8.1
MA Holding (WI)                  76      10      73    13.8    64.8    15.5
GAR Lock (Eng)                   63       9      89    13.7    62.0    19.7
DK Lillee (Aus)                  90      24      73    13.7    66.8    15.0
JA Snow (Eng)                    71      14      73    13.5    62.7    15.8
GR Dilley (Eng)                  58      19      56    13.4    59.2    12.6
Iqbal Qasim (Pak)                57      15      56    13.1    57.7    12.7
HMRKB Herath (SL)                70      15      80    13.0    59.9    17.3
Mashrafe Mortaza (Ban)           67       5      79    12.9    58.8    17.3
JR Thomson (Aus)                 73      20      49    12.8    59.7    10.5
AV Bedser (Eng)                  71      15      79    12.8    59.1    17.0
D Gough (Eng)                    86      18      65    12.6    60.6    13.5
J Garner (WI)                    68      14      60    12.4    57.1    13.1
CEL Ambrose (WI)                145      29      53    12.4    66.3     9.9
M Morkel (SA)                    65      10      40    12.3    55.8     8.8
GD McKenzie (Aus)                89      12      76    12.3    59.6    15.6
CJ McDermott (Aus)               90      13      42    12.2    59.4     8.6
IR Bishop (WI)                   63      11      48    12.2    54.9    10.6
Z Khan (India)                  127      24      75    12.0    62.3    14.4
SJ Harmison (Eng/ICC)            86      23      49    11.8    56.9    10.2
Mushtaq Ahmed (Pak)              72      16      59    11.7    54.4    12.7
S Venkataraghavan (India)        76      12      64    11.7    54.9    13.6
M Muralitharan (ICC/SL)         164      56      67    11.7    63.8    12.3
AA Mallett (Aus)                 50      13      43    11.6    49.8    10.0
Mohammad Sami (Pak)              56      14      49    11.6    51.0    11.1
DL Underwood (Eng)              116      35      45    11.6    59.2     8.8
RC Motz (NZ)                     56       3      60    11.5    50.8    13.6
RGD Willis (Eng)                128      55      28    11.5    60.0     5.4
EAS Prasanna (India)             84      20      37    11.5    55.1     7.7
JB Statham (Eng)                 87      28      38    11.4    55.3     7.9
AA Donald (SA)                   94      33      37    10.7    52.5     7.5
MS Kasprowicz (Aus)              54      12      25    10.6    46.2     5.7
AR Caddick (Eng)                 95      12      49    10.4    51.1    10.0
JM Anderson (Eng)               127      47      34    10.4    54.0     6.5
Waqar Younis (Pak)              120      21      45    10.2    52.6     8.7
Shahadat Hossain (Ban)           65      17      40    10.2    46.3     8.8
Shoaib Akhtar (Pak)              67      13      47    10.1    46.1    10.3
Umar Gul (Pak)                   67       9      65     9.9    45.5    14.2
M Ntini (SA)                    116      45      32     9.8    50.4     6.2
RM Hogg (Aus)                    58      13      52     9.8    43.2    11.7
GP Wickramasinghe (SL)           64       5      51     9.4    42.6    11.3
I Sharma (India)                 81      28      31     9.2    43.9     6.5
PR Adams (SA)                    55      15      35     9.0    39.4     8.0
BS Bedi (India)                 101      28      50     9.0    44.8    10.0
EJ Chatfield (NZ)                54      33      21     8.6    37.4     4.8
M Dillon (WI)                    68       3      43     8.4    38.7     9.4
DK Morrison (NZ)                 71      26      42     8.4    39.0     9.1
S Ramadhin (WI)                  58      14      44     8.2    36.3     9.9
CD Collymore (WI)                52      27      16     7.9    34.1     3.7
DBL Powell (WI)                  57       5      36     7.8    34.5     8.2
CA Walsh (WI)                   185      61      30     7.5    42.1     5.4
ARC Fraser (Eng)                 67      15      32     7.5    34.1     7.0
GD McGrath (Aus)                138      51      61     7.4    39.0    11.5
MJ Hoggard (Eng)                 92      27      38     7.3    35.6     7.8
Danish Kaneria (Pak)             84      33      29     7.1    33.9     6.0
LR Gibbs (WI)                   109      39      25     7.0    35.3     4.9
FH Edwards (WI)                  88      28      30     6.6    31.8     6.2
TM Alderman (Aus)                53      22      26     6.5    28.4     6.0
DE Malcolm (Eng)                 58      19      29     6.1    26.8     6.5
PCR Tufnell (Eng)                59      29      22     5.1    22.7     4.9
MS Panesar (Eng)                 68      23      26     4.9    22.4     5.7
AL Valentine (WI)                51      21      14     4.7    20.2     3.3
BS Chandrasekhar (India)         80      39      22     4.1    19.3     4.6
CS Martin (NZ)                  104      52      12     2.4    11.8     2.4

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