Saturday, March 01, 2014

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
Sadiq Mohammad (Pak)             74       2     166    35.8   167.4    35.5
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
AD Gaekwad (India)               70       4     201    30.1   138.9    43.5
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

Thursday, January 16, 2014

Some women's T20 record lists

The other day, Avi Singh tweeted:

As best I can tell, McGlashan's score is a women's T20 record, but the team total is definitely not a world record.

I am not aware of any site that compiles record lists of women's List A or T20 cricket, so I have filled a small part of that gap with some tables at the end of this post. The stats are in some cases not complete. There are many gaps in CricketArchive's database – preliminary rounds of at least one tournament in India are completely missing; I ran into matches in both England and South Africa where only very partial scores were available, and in these cases I did not add them to my own database; I ran into matches in Australia and England where some players' names were not recorded (one might have taken five wickets in an innings!); there are as far as I can see no West Indies domestic games classified as WT20 ("wtt") by CricketArchive – for reasons unknown to me (design? accident? they are slowly systematising their classifications and haven't reached the West Indies yet?), the WI domestic tournaments have their matches classified as miscellaneous.

The above paragraph is not intended to be an exhaustive list of the gaps in the data – they just happen to be the cases I consciously noticed, and in some cases I just tweaked my code that was parsing the scorecards, so that I was blissfully unaware of any subsequent gaps of that type.

On a much more minor note, while most of the matches played by the batsmen in the tables below have the balls-faced recorded, there are a couple (literally 2 for Charlotte Edwards) where this isn't the case, and such innings are ignored when calculating the strike rate.

The 'wtt' columns in some tables below refer to the CricketArchive match ID's. I don't have the scorecard URL's handy, but you can go to CA's scorecard Oracle, and enter, e.g., wtt1264 as the match ID, and that will bring up the scorecard showing McGlashan's 131 not out. My hope is that the values I give in the tables below will become obsolete as West Indies (and other?) domestic games are re-classified by CA as wtt.

CA doesn't present record lists for women's domestic matches, but they do show the stats for individual players (useful for me since it allowed me to check my results). In light of this, I think that it shouldn't be too hard for CA to add women's T20 and List A to the list of their stats options, and I would encourage anyone interested to lobby CA on that front. I don't intend to maintain my own database regularly, nor to update the tables in this post. I am willing to compile record lists for women's List A if there is demand for it.

Leading run-scorers

name                 mat    inns      no    hs      runs     avg      sr
CM Edwards           109     105      15    88      3043    33.8   112.7
LJ Poulton           101     100       9   103*     2692    29.6   117.7
SJ Taylor            101      95      18    77      2592    33.7   110.3
SW Bates             102     102      10    78*     2513    27.3   101.2
MM Lanning            88      88      12    79      2455    32.3   116.9
AJ Blackwell         113     101      25    99*     2356    31.0   106.7
SJ McGlashan          92      89      18   131*     1979    27.9   113.4
JE Cameron           101      91      17    68*     1960    26.5   111.8
AE Satterthwaite      97      88      15    80*     1754    24.0    95.6
M Raj                 70      63      25    85*     1729    45.5    99.2
Highest averages (qual. 20 innings)
name                  mat    inns      no    hs      runs     avg      sr
KL Rolton              36      33      10    96*     1153    50.1   104.9
M Raj                  70      63      25    85*     1729    45.5    99.2
MD Thirush Kamini      24      23       5    63       783    43.5    85.7
FC Wilson              24      23       5    99       739    41.1   120.4
SR Taylor              58      56      11    90      1612    35.8   100.4
KV Jain                28      28      12    53*      569    35.6    79.2
M Kanojia              43      39      14    57*      849    34.0    80.6
CM Edwards            109     105      15    88      3043    33.8   112.7
SJ Taylor             101      95      18    77      2592    33.7   110.3
SFM Devine             63      61      14    99*     1571    33.4   121.0
Highest strike rates (qual. 20 innings with balls-faced recorded)
name            mat    inns      no    hs      runs     avg      sr
DJS Dottin       61      60      13   112*     1120    23.8   136.1
AC Smith         49      49       4    89      1049    23.3   127.1
SC Taylor        49      46      10    76*     1196    33.2   124.8
SFM Devine       63      61      14    99*     1571    33.4   121.0
FC Wilson        24      23       5    99       739    41.1   120.4
SE Rowe          47      32      12    67       647    32.4   119.0
LJ Poulton      101     100       9   103*     2692    29.6   117.7
MM Lanning       88      88      12    79      2455    32.3   116.9
SC King          52      48      11    81       672    18.2   116.6
AJ Healy         92      84      13    90      1554    21.9   116.5
Centuries
name          score for               against                             year     wtt
SJ McGlashan   131* Auckland          Northern Districts                  2014    1264
SA Fritz       116* South Africa      Netherlands                         2010     437
RA Birch       113* Devon             Dorset                              2013    1139
DJS Dottin     112* West Indies       South Africa                        2010     356
HC Knight      111  Berkshire         Devon                               2012     913
EL Marriott    109* Leicestershire    Oxfordshire                         2011     629
A Shrubsole    109* Somerset          Wales                               2013    1175
RH Priest      106* Central Districts Otago                               2012     812
HC Knight      106* Berkshire         Wales                               2012     891
MJ Bulow       103  Queensland        Tasmania                            2011     698
LJ Poulton     103* New South Wales   Australian Capital Territory        2011     720
DN Wyatt       102  Nottinghamshire   Yorkshire                           2013    1189
LM Keightley   101* Wiltshire         Buckinghamshire                     2010     375
DN Wyatt       100* Staffordshire     Lancashire                          2012     886
Leading wicket-takers
name            mat   balls    runs    wkts     bb      avg    econ
LC Sthalekar     99    2106    1908     110   5/11     17.3    5.44
HL Colvin        82    1771    1513      93    4/9     16.3    5.13
SEA Ruck        102    2121    1885      87    3/9     21.7    5.33
EA Perry         90    1869    1707      85   4/20     20.1    5.48
D Hazell         72    1647    1423      81   4/12     17.6    5.18
LR Doolan        91    1768    1732      80   4/10     21.7    5.88
S Nitschke       68    1450    1329      79   4/21     16.8    5.50
NJ Browne        91    1757    1544      77   4/15     20.1    5.27
SJ Coyte         71    1423    1430      74    4/5     19.3    6.03
EA Osborne       81    1627    1484      71   4/13     20.9    5.47
Lowest averages (qual. 20 wickets)
name                     mat   balls    runs    wkts     bb      avg    econ
J Turner                  18     373     246      27    4/8      9.1    3.96
A Maitra                  17     378     214      20    3/6     10.7    3.40
A Upendran                35     618     432      40   4/12     10.8    4.19
N Buley                   16     328     274      25   4/11     11.0    5.01
S Dabir                   32     680     527      46   4/13     11.5    4.65
S Asha                    24     540     394      34    4/7     11.6    4.38
A Kaur                    31     525     342      28    5/6     12.2    3.91
AN Davidson-Richards      26     408     378      30   4/13     12.6    5.56
P Jagtap                  24     505     346      27   3/11     12.8    4.11
M Chaudhary               23     486     310      24   3/11     12.9    3.83
Lowest economy rates (qual. 80 overs)
name                mat   balls    runs    wkts     bb      avg    econ
Shivangiraj Sin      25     550     349      18    2/1     19.4    3.81
M Chaudhary          23     486     310      24   3/11     12.9    3.83
A Kaur               31     525     342      28    5/6     12.2    3.91
SN Pradhan           32     535     357      20   3/30     17.9    4.00
P Jagtap             24     505     346      27   3/11     12.8    4.11
N David              33     696     477      27    4/8     17.7    4.11
P Dimri              25     570     392      30    3/9     13.1    4.13
J Goswami            60    1246     862      59   5/11     14.6    4.15
A Upendran           35     618     432      40   4/12     10.8    4.19
M Shalini            34     530     381      23    3/7     16.6    4.31
Five wickets in an innings
name              figures        for                           against                              year      wtt
DH Kaur           6/3            Punjab                        Jammu and Kashmir                     2009     281
NM Vijeylakshmi   6/7            Tamil Nadu                    Kerala                                2011     500
AE Satterthwaite  6/17           New Zealand                   England                               2007      25
H Swan            5/6            Hertfordshire                 Cambridgeshire and Huntingdonshire    2011     677
APC Kilowan       5/8            West Coast                    Central                               2008      58
Asmavia Iqbal     5/8            Pakistan                      Nottinghamshire                       2009     168
A Mohammed        5/10           West Indies                   South Africa                          2009     224
LC Sthalekar      5/11           New South Wales               Australian Capital Territory          2011     573
?                 5/14           Durham                        Cumbria                               2011     621
SW Bates          5/15           Otago                         Canterbury                            2011     560
P Roy             5/16           India                         Pakistan                              2009     177
KA Levick         5/16           Yorkshire                     Staffordshire                         2011     648
EAJ Richardson    5/17           Central Districts             Canterbury                            2011     502
CA Anneveld       5/22           Australian Capital Territory  South Australia                       2011     700
Highest team totals
team          opponent        total     year       wtt
Somerset      Wales           3/255     2013      1175
Ireland       Bedfordshire    1/218     2012       876
Derbyshire    Oxfordshire     0/207     2011       658
South Africa  Netherlands     1/205     2010       437
Staffordshire Lancashire      0/202     2012       886
Kent          Essex           8/199     2011       642
Berkshire     Wales           2/199     2013      1162
Kent          Surrey          3/198     2010       386
Maharashtra   Mumbai          3/194     2013      1084
Berkshire     Devon           5/192     2012       913


Saturday, April 14, 2012

Balls faced errors

Charles Davis, in his blog post titled "Balls Faced Blues" (31 March 2012), reports on errors in the previously published scorecards to this Test between the West Indies and Australia in 1983/4. He writes:

A full re-score confirms Border’s runs and the sequence of strokes, yet the balls faced figures as published seem to be quite wrong. Border is given 314 balls for his 98* and 269 for the 100*. The figures I get are 283 and 285 balls, respectively. Viv Richards’ figures for his 76 are also very doubtful: I get 130 balls not 188. There are other discrepancies. Using the revised figures, the balls faced now reconcile with the bowling figures.

I had never thought to compare the balls faced with the total overs in an innings. I was surprised to find that substantial disagreements are quite common. Some discrepancies are to be expected – a single off a no-ball used to be an extra ball but not a sundry; many wides can come from one ball; a wide used to be counted as a ball faced in Australia; there have been plenty of 5- and 7-ball overs which won't show up in the team totals.

But still. Below is a list of innings where the discrepancy is at least 20 balls. It's enormous. I've defined "discrepancy" as the sum of the balls faced, minus the total number of balls in the innings, minus the extras. I had originally planned to manually check all of these anomalies, but I couldn't be bothered. I've made notes on a few of the more egregious cases.

I didn't output the dates of the Tests when making this table. The quickest way to pull up the scorecard is probably via CricketArchive's Scorecard Oracle. To bring up Test 104, enter t104 as the 'match id'. The Test that Davis talked about is t983 – you can see that all three innings of that match are on the list, as are two innings from the fourth Test of that series.

The following list is based on the CricketArchive scorecards as they were a few years ago. Probably some errors have been ironed out since. (I've also omitted one scorecard which had obviously flipped the balls-faced and minutes; hopefully it will be corrected in the coming days.)

Test no.  Home           Away           inns   sum BF inns balls   nb   wd discrepancy
104 England Australia 4 310 330 0 0 20
180 Australia England 4 832 805 0 0 27
290 Australia India 3 368 399 1 0 32
303 England Australia 1 277 253 0 0 24
470 New Zealand England 2 377 437 0 0 60 Judging by the minutes,
I think Bolton faced ~60
more balls than is given
537 Australia England 1 715 693 0 2 20
598 Australia England 1 883 861 1 0 21
613 South Africa Australia 2 736 763 0 0 27
628 Australia India 4 618 590 0 0 28
673 South Africa Australia 3 779 728 20 0 31
703 India England 1 458 508 0 0 50 Minutes make sense.
Probably Venkat faced more.
708 India England 3 522 636 3 0 117 Minutes make sense.
Probably Denness faced more.
730 Australia New Zealand 3 740 717 2 0 21
731 West Indies England 2 798 736 16 0 46
748 Australia England 3 645 729 11 1 96 Wisden says Titmus batted for
200 minutes, not 108; probably
faced a lot more. Old too?
757 New Zealand England 3 401 461 12 0 72
835 India West Indies 1 812 822 13 0 23
835 India West Indies 2 928 966 8 0 46
855 India Australia 2 831 783 23 0 25
855 India Australia 3 657 682 3 0 28
858 India Australia 1 932 866 24 0 42
858 India Australia 2 628 639 19 0 30
859 India Australia 2 787 754 8 4 21
863 India Pakistan 1 593 551 4 0 38
865 India Pakistan 3 399 419 5 0 25
869 India Pakistan 3 441 400 17 0 24
876 Pakistan Australia 2 664 713 10 0 59
876 Pakistan Australia 3 521 540 2 1 22
878 Pakistan Australia 1 1302 1266 3 0 33
878 Pakistan Australia 2 724 756 15 0 47
889 Australia New Zealand 3 316 289 5 2 20
891 Australia New Zealand 1 799 729 6 3 61
908 England Australia 3 658 626 7 1 24
914 India England 2 955 961 21 4 31
918 India England 2 917 935 12 0 30
922 New Zealand Australia 1 762 696 11 4 51
924 New Zealand Australia 4 138 178 0 0 40
937 Pakistan Australia 3 494 540 8 0 54
970 Australia Pakistan 1 722 734 4 4 20
983 West Indies Australia 1 605 553 17 0 35
983 West Indies Australia 2 815 756 1 2 56
983 West Indies Australia 3 634 673 14 1 54
985 Sri Lanka New Zealand 2 1079 1050 6 2 21
987 West Indies Australia 1 563 581 10 0 28
987 West Indies Australia 2 850 874 1 0 25
993 England West Indies 3 639 579 0 0 60
998 Pakistan New Zealand 1 392 448 0 0 56
998 Pakistan New Zealand 2 530 560 2 0 32
998 Pakistan New Zealand 3 441 498 4 1 62
998 Pakistan New Zealand 4 347 391 0 0 44
1000 Pakistan New Zealand 1 674 651 1 0 22
1000 Pakistan New Zealand 3 378 337 3 0 38
1010 New Zealand Pakistan 2 1002 882 6 0 114 Probably Wright faced a lot less.
1033 Australia India 2 930 890 17 0 23
1045 West Indies England 2 635 646 40 0 51
1052 India Australia 2 600 566 6 0 28
1052 India Australia 3 273 294 1 0 22
1058 Pakistan West Indies 2 566 661 2 1 98 Rameez faced much more.
1065 Australia England 2 598 564 2 2 30
1072 New Zealand West Indies 3 382 423 8 0 49
1087 Australia New Zealand 4 577 552 4 0 21
1097 West Indies Pakistan 3 546 563 14 0 31
1118 West Indies India 1 618 632 22 0 36
1118 West Indies India 2 667 671 22 0 26
1118 West Indies India 3 543 585 13 0 55
1118 West Indies India 4 271 288 3 0 20
1152 Pakistan New Zealand 2 782 750 12 0 20
1163 Australia England 1 509 400 5 1 103 Atherton faced much less.
1170 West Indies Australia 3 584 547 4 0 33
1180 Australia India 2 836 732 11 0 93 Probably Jones faced much less.
1186 Australia India 3 719 681 6 0 32
1195 Sri Lanka Australia 3 715 690 5 0 20
1220 West Indies Pakistan 1 222 230 11 2 21
1232 Sri Lanka South Africa 4 592 672 15 1 96 Probably Rhodes faced much more.
1237 Pakistan Zimbabwe 1 903 930 1 0 28
1238 Australia New Zealand 1 608 633 2 0 27
1239 Sri Lanka West Indies 3 102 133 1 0 32
1247 India Sri Lanka 1 350 383 0 0 33
1247 India Sri Lanka 3 608 627 1 0 20
1262 England New Zealand 1 855 879 2 1 27
1266 England South Africa 1 543 554 18 1 30
1268 Pakistan Australia 2 558 523 4 0 31
1278 India West Indies 1 855 856 14 5 20
1278 India West Indies 2 767 771 17 1 22
1282 South Africa New Zealand 3 643 667 6 1 31
1291 New Zealand South Africa 1 663 633 0 0 30
1293 New Zealand Sri Lanka 2 887 834 15 0 38
1325 West Indies New Zealand 1 369 372 17 1 21
1325 West Indies New Zealand 2 949 987 12 0 50
1415 Sri Lanka New Zealand 1 665 632 9 1 23

Friday, March 30, 2012

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:

y = mx

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:

y does not equal m

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:

Hours of work and I get nothing but a straight line....

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):

Not sure what the deal is with Bradman's relatively low h-average: his century rate is dead on what you'd expect.

With that pesky Ryder outlier out of the way, the title can return to the top of the plot.

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

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