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February 26, 2009
Okay, Bradman is at No.1... but who is last?
Posted by Ananth Narayanan at
in Trivia - batting
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Chris Martin does everything right except make contact with the ball
© Getty Images
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| A lot of analysis has been done on the best batsmen in Test cricket. Whatever be the methodology used, all analysis lead to the incomparable Don Bradman at the top. The arguments start when some one is anointed the second best, any one of 5 batsmen could fill this place.
Let us leave that topic aside. I have always felt that the other end of batting table presents a fascinating possibility. Who is the worst batsman who ever carried a bat and walked in. Is it Chris Martin, is it one of the Indian spinners, is it a West Indian fast bowler or an unexpected batsman out side this lot? Without further ado, let us delve in.
First a few criteria to be fixed.
The first is that the batsman (okay, I know I am stretching the point) has to have played 25 Test innings, which, for a tail-ender, represents nearly 20 Tests. The next is that the career batting average should be below 10.00. These twin criteria have enabled 70 tail-end batsmen to be selected.
Let me also mention that I would not do just a simple table based on, say, Batting Average. That is something which anyone could get using the excellent Cricinfo Statsguru. I will do a composite but not complex analysis of these 70 batsmen.
I have considered three measures for analysis. These are explained below.
1. Batting Average. This is the simplest and most acceptable of all batting measures. Readers can easily identify with this measure and it reflects the batting ability very realistically, notwithstanding the "not outs" conundrum. In this particular analysis even the "not outs" do not matter since most of these batsmen remain not out on quite a few occasions. This measure will carry a weight of 20 points.
2. Dismissed Zeroes. The emphasis here is on both the words. An innings which ends at 0 means that, barring a few exceptional circumstances, very little has been contributed and another batsman, almost always a better one, has been left in the limbo. I have determined the number of dismissed zeros and determined a frequency of innings in which this has occured. The lower this figure is, the worse the batsman is. This measure will carry a weight of 15 points.
3. Average partnership runs added. This is a useful measure since it tests another facet of the tail-end batsman's skills, which is the support he provides to the senior batsmen. Basically I have computed the number of runs added while the tail end batsman was at the crease, mostly at no.10 or no.11, and determined the measure of average partnership runs per innings. This measure will carry a weight of 15 points.
I have considered (and ignored) the batsman's highest score since that does not convey any additional information. I have also not considered the "Balls played" information since that is available only for about a third of Tests. And extrapolating based on team scoring rate will not work since these batsmen are likely to take a lot more balls to score the runs.
Let us take a look at tables, first the support table.
Cty Batsman Ins No Runs Avge HS Dis Runs Avge
0s Added Bpa
Zim Mbangwa M 25 8 34 2.00 8 9 171 11.0
Nzl Martin C.S 65 30 76 2.17 12 25 663 10.9
Win King R.D 27 8 66 3.47 12 7 275 10.2
Bng Manjural Islam(Sr) 33 11 81 3.68 21 10 351 10.6
Ind Chandrasekhar B.S 80 39 167 4.07 22 23 760 10.9
Ind Maninder Singh 38 12 99 3.81 15 11 396 10.8
Ind Doshi D.R 38 10 129 4.61 20 14 384 10.9
Aus Reid B.A 34 14 93 4.65 13 6 262 10.8
Ind Nehra A 25 11 77 5.50 19 10 221 10.6
Win Valentine A.L 51 21 141 4.70 14 12 502 10.9
Now the final table.
Cty Batsman Batting Avge Dis 0s Freq Avge Ptship Total
(20) (15) (15) (50)
Zim Mbangwa M 4.00 (2.00) 2.08 ( 2.78) 5.13 ( 6.84) 11.21
Nzl Martin C.S 4.34 (2.17) 1.95 ( 2.60) 7.65 (10.20) 13.94
Win King R.D 6.95 (3.47) 2.89 ( 3.86) 7.64 (10.19) 17.48
Bng Manjural Islam(Sr) 7.36 (3.68) 2.48 ( 3.30) 7.98 (10.64) 17.82
Ind Chandrasekhar B.S 8.15 (4.07) 2.61 ( 3.48) 7.12 ( 9.50) 17.88
Ind Maninder Singh 7.62 (3.81) 2.59 ( 3.45) 7.82 (10.42) 18.02
Ind Doshi D.R 9.21 (4.61) 2.04 ( 2.71) 7.58 (10.11) 18.83
Aus Reid B.A 9.30 (4.65) 4.25 ( 5.67) 5.78 ( 7.71) 19.33
Ind Nehra A 11.00 (5.50) 1.88 ( 2.50) 6.63 ( 8.84) 19.50
Win Valentine A.L 9.40 (4.70) 3.19 ( 4.25) 7.38 ( 9.84) 19.97
As foreseen, a dark horse has emerged. Who would have thought of a batsman who could come ahead of Chris Martin. (Mpumelelo) Pommy Mbangwa's batting is for the Gods to view. 25 innings, 8 not outs and 34 runs gives him an unbelievable average of 2.00. He has been dismissed at 0 for nearly 40% of his crease visits. He has a highest score of 8, the only one in this elite group not to have crossed 9 runs. He has always batted at no.11. His average partnership is an unbelievably low 6.8. What more do you want. I would have paid money to see Pommy bat. Note his batting sequence: 0, 2, 0, 4, 0*, 0, 0, 0, 0, 2*, 3, 2, 0, 1*, 2, 0*, 0*, 1*, 3, 0, 0, 1*, 8, 0*, 5. One fascinating string of scores.
I can see the New Zealand readers having mixed feelings. They would dearly love to have Chris Martin head this table because they love his batting. I can only suggest that if you increase the number of innings to 30, Chris Martin will be at the top. Let us see Martin's exploits. 65 innings, 30 not outs, 76 runs giving Martin a slightly higher average of 2.17 as compared to Pommy. He has crossed single figures once in his career, an unbeaten 12 against Bangladesh when he outscored O'Brien. He has 25 dismissed zeroes, the most frequent amonst all these batsmen. But his partnership average is a healthy 10+. Only twice has Martin batted at no.10 when Shane Bond and Cummings could not bat. Let me add, I would also pay money to see Chris Martin bat.
Reon King is next. Not as great a fast bowler as some of the other greats such as Walsh or Ambrose, but equally inept a batsman.
Then comes Manjual Islam, followed by three Indian spinners. Reid of Australia separates these three from Ashish Nehra, another rabbit of a batsman. Alf Valentine is last in this table.
Fidel Edwards, who is 11th in the table is the only other batsman wiith a sub-5.00 batting average. However he has recently batted very well, saving West Indies twice at Antigua and Napier.
To view the complete list please click here.
Comments (75)
February 16, 2009
Does the tail wag more inTests now?
Posted by Ananth Narayanan at
in Trivia - batting
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Ian Botham was at the forefront of that amazing fightback by England at Headingley against Australia in 1981, when the last three wickets added 221 and helped script a remarkable win
© Getty Images
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| During the last few Tests of 2008 I got the feeling that late order batsmen were playing rear-guard innings far more effectively than they normally do. Look back at
Clarke with tail in Sydney, Duminy with the tail at the MCG, Nash with the tail in Napier, Haddin with the tail in Perth, Dhoni/Harbhajan at Chepauk, Taylor
in Dunedin, McCullum with the tail in Adelaide, Katich with the tail in Brisbane, Dhoni/Harbhajan in Nagpur, Harbhajan/Zaheer in Bangalore et al. All these
and other such instances happened during the last three months of 2008.
I felt that this deserved a detailed look. As normally happens, the scope of the article expanded and I have covered the Test tail-enders' batting in depth.
How do we define late order batting? I have decided to be quite conservative and defined a tail-end batting effort as starting from 7 wickets down. While
theoretically the late order might start from no.8, I am influenced by the fact that a score of xyz for 6 still represents a reasonable position while xyz
for 7 signifies the start of the end. Also, seven down means the two batsmen at the crease are one good batsman with a no.9, or no.8 and no.9 batting
together. Thus any batting effort at this juncture is bound to be extremely valuable.
The other criterion I have is that the late order wickets should have added at least 50% of the score at which the seventh wicket fell. Incidentally this
also translates to more than 33.33% of the final score. To avoid peculiar situations such as a team, tottering at 20 for 7, having a biff or two or three and
trebling the score to 60 all out, I have also excluded the 36 innings which have ended as sub-100 all-out situations.
Let us first do a summary of these situations to determine whether there has been a spurt in late order batting exploits.
Period Tests # of instances Frequency
> 50% of runs (Tests)
added for
last 3 wkts
All: 1906 641 2.97
2000s: 424 157 2.70
2000: 46 14 3.28
2001: 55 21 2.61
2002: 54 9 6.00
2003: 44 13 3.38
2004: 51 31 1.64
2005: 49 22 2.23
2006: 46 19 2.42
2007: 31 6 5.16
2008-9: 50 17 2.94
Overall the late order batsmen have been successful once in 3 Tests. This figure has improved slightly for the 157 Tests played during the current decade.
During 2002 the tail did not wag at all and the 8-9-10-11 batsmen just came in and went. During 2004, it was impossible to dislodge the tail. They stuck like
leaches.
During 2007 again the tail has just folded up. However during 2008-09, the frequency has been the same as the all-time Test figure and is in fact slightly
higher than the 2000s decade. However I have also found out why we get the feeling of a strongly wagging tail. Out of the 17 instances, 11 have occured
during the last 3 months (out of 20 Tests). Hence it is true that during the last three months the bowlers found it difficult to disllodge the late order
batsmen.
Let us do one more basic analysis. This is to look at the frequency of such innings by country.
Country Tests # of instances Frequency
> 50% of runs (Tests)
added for
last 3 wkts
Australia 705 118 5.97
Bangladesh 59 22 2.68
England 880 122 7.21
India 427 80 5.33
New Zealand 348 76 4.57
Pakistan 335 56 5.98
Soouth Africa 341 66 5.17
Sri Lanka 182 23 7.91
West Indies 451 56 8.05
Zimbabwe 83 22 3.77
First point to remember is that the two frequency values are not comparable, since the number of Tests played by the countries adds to twice the number of
Tests played. So the frequency numbers have 50% value.
Bangladesh has the best late order batting record with a very low frequency of 2.68 Tests per such innings. Next comes Zimbabwe, the other weak team with
3.77 Tests. That's probably expected with the poor manner in which these two teams' top orders have batted. New Zealand, South Africa, India, Australia and
Pakistan then appear. The other end of the table sees England and Sri Lanka, whose tails have been the poorest of the lot.
Having got a 641-innings database, I have worked on couple of tables, across all 130 odd years of Test cricket.
The first one is a table ordered by the quantum of runs added for the last 3 wickets.
Table of late order batsmen successes: By Runs added
MtNo Year For Final Score Runs % of 7 wkt
Added score
0609 1966 Eng 527 for 10 from 166 for 7 361 217.5% vs Win
0098 1908 Aus 506 for 10 from 180 for 7 326 181.1% vs Eng
1336 1996 Pak 553 for 10 from 237 for 7 316 133.3% vs Zim
1800 2006 Nzl 593 for 8 from 279 for 7 314 112.5% vs Saf
1902 2008 Saf 459 for 10 from 184 for 7 275 149.5% vs Aus
0209 1931 Eng 454 for 10 from 190 for 7 264 138.9% vs Nzl
1139 1990 Nzl 391 for 10 from 131 for 7 260 198.5% vs Ind
0078 1903 Eng 577 for 10 from 318 for 7 259 81.4% vs Aus
1573 2001 Nzl 534 for 9 from 281 for 7 253 90.0% vs Aus
1676 2003 Nzl 563 for 10 from 314 for 7 249 79.3% vs Pak
0160 1925 Aus 489 for 10 from 253 for 7 236 93.3% vs Eng
0914 1981 Ind 487 for 10 from 254 for 7 233 91.7% vs Eng
1380 1997 Pak 456 for 10 from 230 for 7 226 98.3% vs Saf
0066 1902 Aus 353 for 10 from 128 for 7 225 175.8% vs Eng
0905 1981 Eng 356 for 10 from 135 for 7 221 163.7% vs Aus
0136 1921 Aus 499 for 10 from 282 for 7 217 77.0% vs Eng
1681 2004 Saf 532 for 10 from 315 for 7 217 68.9% vs Win
0621 1967 Pak 354 for 10 from 139 for 7 215 154.7% vs Eng
1066 1987 Pak 487 for 9 from 273 for 7 214 78.4% vs Ind
1397 1998 Saf 517 for 10 from 305 for 7 212 69.5% vs Aus
The first is an amazing match. After dismissing a strong West Indian side for 268 and against Hall/Griffith/Sobers/Gibbs, England were 166 for 7, there would
have been very few takers on England saving the match. Then Graveney, who scored a masterly 165, with support from Murray, who scored 112, took the score to
399 for 9. To add insult to injury, Higgs and Snow, both reaching their 50s, added 128 for the last wicket. England reached 527 and the strong but
demoralised West Indies, were all out for 225, losing by an innings.
The 1906 match should not really figure in this list. Australia recovered from 180 for 7 to 506 through Clem Hill's 160. However Hill normally batted at no.3
and by no stretch of imagination a late order batsmen.
Pakistan's recovery from 237 for 7 to 553 was through a massive 257 not out from Wasim Akram and 79 from Saqlain Mushtaq. New Zealand's move from 279 for 7
to 593 for 8 was through Fleming's huge double century and an unlikely 100 from Franklin. South Africa's match and series-winning progression from 184 for 7
to 459 was through Duminy's epic 166 and Steyn's 75.
Botham's once-in-lifetime innings of 149 at Headingley during 1981, which took the post-follow-on score from 135 for 7 to 356 all out also figures late in
this table.
The second is a table ordered by the % of runs added.
Table of late order batsmen successes: By % of score at 7 wkt down
MtNo Year For Final Score Runs % of 7 wkt
Added score
0186 1930 Nzl 112 for 10 from 21 for 7 91 433.3% vs Eng
0623 1967 Pak 255 for 10 from 53 for 7 202 381.1% vs Eng
0168 1927 Saf 170 for 10 from 38 for 7 132 347.4% vs Eng
0003 1879 Eng 113 for 10 from 26 for 7 87 334.6% vs Aus
0111 1910 Saf 174 for 10 from 49 for 7 125 255.1% vs Aus
0063 1899 Aus 196 for 10 from 57 for 7 139 243.9% vs Eng
0761 1975 Aus 268 for 10 from 81 for 7 187 230.9% vs Eng
0609 1966 Eng 527 for 10 from 166 for 7 361 217.5% vs Win
1459 1999 Aus 188 for 10 from 60 for 7 128 213.3% vs Slk
1450 1999 Slk 188 for 10 from 61 for 7 127 208.2% vs Pak
1139 1990 Nzl 391 for 10 from 131 for 7 260 198.5% vs Ind
0883 1980 Eng 209 for 9 from 73 for 7 136 186.3% vs Win
1096 1988 Pak 194 for 10 from 68 for 7 126 185.3% vs Win
0098 1908 Aus 506 for 10 from 180 for 7 326 181.1% vs Eng
1455 1999 Eng 126 for 10 from 45 for 7 81 180.0% vs Nzl
0066 1902 Aus 353 for 10 from 128 for 7 225 175.8% vs Eng
0669 1969 Aus 153 for 10 from 57 for 7 96 168.4% vs Ind
0327 1950 Eng 122 for 10 from 46 for 7 76 165.2% vs Aus
0967 1983 Ind 103 for 10 from 39 for 7 64 164.1% vs Win
0905 1981 Eng 356 for 10 from 135 for 7 221 163.7% vs Aus
I am aware that a 400% improvement in score could be caused by a sub-25 for 7 situation improving to 100+ all out. However let us give credit to those
hapless and less gifted batsmen who have batted bravely. This is their "15 minutes of greatness", at least as far as their batting is concerned.
In the 1930 match New Zealand were 21 for 3 and then lost 4 wickets in one over, including a hat-trick to Maurice Allom, making his debut. They recovered to
a score four times bigger, mainly through Blunt. They still lost the match, though.
Pakistan's recovery was amazing. Trailing by 224 against England at The Oval, 53 for 7 and 65 for 8 before Asif Iqbal who scored a thrilling 146, added 190
in partnership with Intikhab Alam who scored 51. They avoided an innings defeat but lost comfortably.
The next three matches are old ones.
During the 1975 Ashes Test, Australia were 81 for 7 against an England total of 315. Follow-on and a huge loss loomed ahead. Then Ross Edwards added 52 with
Walker but more importantly 66 with Lillee before he was out. Lillee carried on with Mallet and finished unbeaten on 77. Australia scored 268 and saved the
match.
Then we have the England-West Indies Test already described. Then we come to two Tests playing within a month of each other with virtually the same scoring
pattern.
First Sri Lanka, playing against Pakistan and trailing by 360+ runs slumps to 61 for 7. Tillakaratne who scored 55, in the company of the last three batsmen,
added 127 more runs.
Now, six months later, Australia, batting first, slumps to 60 for 7 before Ponting who scored 96 glorious runs, adds 128 for the last three wickets, mainly
with Gillespie. Australia, however, went on to lose the match.
What is the best ever late order recovery? It's impossible to pin-point one innings. However, if there is an imaginary gun pointing at me, I will plump for
England against Australia at Headingley during 1981. Note the order of events. Australia scored 401. England scored 174, followed on and slumped to 135 for
7, against Lillee, Lawson and Alderman. 500 to 1 were very generous odds at this point.
At this stage Botham plays his epic 149, is well supported by Dilley (56) and Old (29) and England reach 356. Still Australia needs only 119 to win. Then
Willis steps in. His best bowling effort ever, 8 for 43, makes sure Botham's stupendous effort is not wasted. It is my personal opinion that, Calcutta 2001
notwithstanding, that was the greatest recovery in Test cricket. It also happens to be the best in this current analysis. Again my personal view.
Comments (9)
February 7, 2009
19 grounds, 19 years - an in-depth study
Posted by Ananth Narayanan at
in Grounds
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The National Stadium in Dhaka has the lowest mean, but that's also because Bangladesh has batted there so often
© Cricinfo
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| A few readers had made comments in response to my article on "Test Openers" that the pitch/ground conditions should be taken into account while determining the value of an opener's innings. I had responded with a short message on the difficulties of determining the true nature of any pitch/ground. I have been thinking over these comments and have felt that it is essential to explore this point in depth. Thanks to Tushar, and others before, for raising queries in this regard.
The most comical situation in an ODI telecast are the pitch specialist's comments. They are as reliable as a weather forecaster's. When Ravi Shastri pontificates "it is a belter", one can be rest assured that one in two innings would have floundered to 201 for 7 in 50 overs. Alternately when David Lloyd says with his "Roses" twang that "250 should be a winning score", I alwasys look for the situation 7 hours later when the batting team has successfully chased a 300+ total. I wish the broadcasters show a split image of the pitch specialist's comments and the innings scores.
Test matches are different. Normally the specialists comment on the first session and make overall comments. One thing I am sure. No pitch specialist, no analyst or for that matter no curator can, with confidence, forecast how the pitch would behave.
This analysis covers 19 premier Test grounds across 9 countries. MCG, SCG, WACA, Lord's, Oval and Headingley lead the field. These are the major Test playing grounds, with most of these grounds clocking in at over 100 Tests. Then I have taken two grounds from each of the other six major Test playing countries. One ground from Bangladesh completes the selection. This brings up the 19 grounds.
I have taken matches played in these grounds during the last 19 years (from 1.1.1990 onwards) for consideration. Barring Calcutta and Chennai where only 9 Tests have been played during these 19 years (because of BCCI's rotation policies), the other grounds have completed 10 or more Test matches, with 32 Tests at Lord's, London leading the field. A total of 338 Tests are analysed.
Anticipating the readers' comments, I looked at excluding the Test matches played against Bangladesh and Zimbabwe. However that is fundamentally wrong since this is a statistical analysis and I cannot take casual liberties with my selection methodology. Also one of the grounds is in Bangladesh. One should also not forget the fact that a strong team like India was dismissed for 75 on the opening day by South Africa in India and the same team, a few months back, scored 705 against a strong Australia at Sydney. So all the Tests are considered.
In order to have uniform conditions I have taken the completed (all out or delaration) first innings. This is to avoid a Test abandoned with the first innings standing at 24 for 3 or 150 for 5. Later innings vary a lot and will distort the figures considerably.
Readers should remember that this is a departure from my usual analysis insofar as it is a purely statistical analysis. I have tried to make the analysis simple and understandable and explained the statistical terms. With this background, let us look at the tables.
The first is a simple table listed in order of the Mean. The mean is an alternate term for Average. It is worked out by the following formula.
Sum of all values
Mean = -----------------
No. of values
Mean is a very useful value for analysis. One can make a generalised observation on a possible score at the ground. However Mean is strongly affected by very high and very low values. As such, a pinch of salt should be available nearby. I have also got the mean of the most recent 5 Tests played on the ground and presented this and compared with the mean. That shows a recent trend.
Table of Mean scores (in order of Mean)
Ground Num Total Mean Last Ratio
Tests Runs 5 mat
National Stadium, Dhaka 10 2229 222.9 238 1.07
Asgiriya Stadium, Kandy 16 4098 256.1 173 0.68
Kingsmead, Durban 16 4333 270.8 247 0.91
Basin Reserve, Wellington 24 6752 281.3 231 0.82
National Stadium, Karachi 12 3446 287.2 299 1.04
Sabina Park, Kingston 15 4373 291.5 320 1.10
Eden Park, Auckland 16 4706 294.1 282 0.96
S.S.C Ground, Colombo 29 8966 309.2 278 0.90
M.A.C Stadium, Chennai 9 2871 319.0 285 0.89
Kensington, Bridgetown 19 6115 321.8 344 1.07
Wanderers, Johannesburg 19 6118 322.0 261 0.81
Gaddafi Stadium, Lahore 16 5204 325.2 363 1.12
Melbourne Cricket Ground 20 6707 335.4 318 0.95
Sydney Cricket Ground 22 7900 359.1 399 1.11
Lord's, London 32 11665 364.5 449 1.23
Headingley, Leeds 16 5860 366.2 407 1.11
Eden Gardens, Calcutta 9 3348 372.0 426 1.15
W.A.C.A. Ground, Perth 19 7090 373.2 431 1.16
Kennington Oval, London 19 7380 388.4 374 0.96
National Stadium, Dhaka has the lowest mean. Understandable since that involves 7 innings by Bangladesh, 6 of these below 204. Asgiriya Stadium, Kandy also has a fairly low mean value. Here different teams have been dismissed for low scores. Surprisingly Kingsmead, Durban has also showed a penchant for low scores.
At the other end, Eden Gardens, WACA and Oval have had a fairly high Mean values. It is surprising that there is almost a 75% difference between the low and high Mean values.
Asgiriya Stadium, Kandy has shown an alarming dip in the first innings scores recently. The ratio is 0.68. Basin Reserve, Wellington has seen its Mean value dip by 20%. At the other end, there is a marked increase in first innings scores at Lord's.
The Mean does not reflect the data distribution truly. A simple example. A batsman scoring 100 and 0 in the two innings of a test has a Mean value of 50, which is the same value of another batsman who has scored 50 and 50. However the two values of the first batsman have a much higher degree of variance. This is determined by the measure Standard Deviation which is probably the most used of all statistical measures.
Table of Standard Deviation and CoV (in order of CoV)
Ground Mean StdDevn CoV
National Stadium, Karachi 287.2 77.2 26.9 %
Melbourne Cricket Ground 335.4 92.0 27.5 %
Sabina Park, Kingston 291.5 85.9 29.5 %
Kingsmead, Durban 270.8 84.0 31.1 %
Eden Gardens, Calcutta 372.0 126.6 34.1 %
W.A.C.A. Ground, Perth 373.2 136.7 36.7 %
Sydney Cricket Ground 359.1 132.2 36.9 %
Eden Park, Auckland 294.1 116.0 39.5 %
Kennington Oval, London 388.4 154.1 39.7 %
Kensington, Bridgetown 321.8 129.1 40.2 %
National Stadium, Dhaka 222.9 92.0 41.3 %
S.S.C Ground, Colombo 309.2 130.6 42.3 %
Wanderers, Johannesburg 322.0 139.1 43.3 %
Lord's, London 364.5 163.4 44.9 %
Asgiriya Stadium, Kandy 256.1 115.3 45.1 %
M.A.C Stadium, Chennai 319.0 148.2 46.5 %
Headingley, Leeds 366.2 172.3 47.1 %
Gaddafi Stadium, Lahore 325.2 161.5 49.7 %
Basin Reserve, Wellington 281.3 147.7 52.5 %
Standard deviation is the measurement of the distribution of data about the Mean value and describes the dispersion of data on either side. A low standard deviation indicates that the data set is clustered around the mean value, whereas a high standard deviation indicates that the data is widely spread with significantly higher/lower figures than the mean. The squaring and taking root option eliminates the problem with negative values.
This calculation is described by the following formula in fig 1, where the two 'x' values represent Mean and individual value (sign immaterial). Instead of n, n-1 is used as the divisor.
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Fig. 1: Standard deviation formula
© Ananth Narayanan
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The three English grounds have a very high value of SD, indicating quite a lot of dispersion. Karachi, Durban and Kingston have low SD values indicating a clustering of values around the Mean value.
Standard Deviation has little interpretable meaning on its own unless the Mean value is also reported alongwith. For a given standard deviation value, it indicates a high or low degree of variability only in relation to the mean value. For this reason, it is easier to get an idea of variability in a distribution by dividing the Standard Deviation with the Mean. If this is then represented as a % of Mean, it is called as Coefficient of Variation (CoV), which is a dimension-less ratio.
In general, a low CoV indicates a lower value of SD w.r.t. Mean and a high ratio indicates vice versa. Where CoV is quite high, such as Basin Reserve and Lahore, it would be next to impossible to do any prediction of expected scores. For these and a few other grounds, the SD is around half the Mean value and there is wide dispersion of scores. On the other hand look at MCG and Karachi. The low CoV indicates a heavy clustering of values around the Mean and one can do a decent attempt at predicting a score or at least a score range.
Now we come to an analysis of the quartile scores and Median. Three measures are important in this analysis. Q1 is the first quartile score, the score which is at 25% position. Q3 is the third quartile score, the score which is at 75% position. But the most important score is Q2, known more as Median which is the score at mid-point. If there are odd number of entries, the Median is the mid-score. If there are even scores, the Median is the average of the two mid-point scores.
Table of Quartile values and QVC (in order of QVC)
Ground SD Q1 Median Q3 QVC
Eden Gardens, Calcutta 119.4 305 371.0 428 0.17
Melbourne Cricket Ground 89.6 270 342.5 394 0.19
Sydney Cricket Ground 129.2 291 317.5 451 0.22
National Stadium, Karachi 73.9 216 270.5 337 0.22
S.S.C Ground, Colombo 128.3 234 285.0 380 0.24
M.A.C Stadium, Chennai 139.8 235 257.0 391 0.25
Sabina Park, Kingston 83.0 225 265.0 374 0.25
Wanderers, Johannesburg 135.4 226 302.0 411 0.29
Eden Park, Auckland 112.3 203 283.5 380 0.30
Kingsmead, Durban 81.3 198 261.5 366 0.30
National Stadium, Dhaka 87.3 160 193.5 298 0.30
Basin Reserve, Wellington 144.6 174 245.0 342 0.33
Kensington, Bridgetown 125.7 224 298.0 446 0.33
W.A.C.A. Ground, Perth 133.1 239 373.0 485 0.34
Asgiriya Stadium, Kandy 111.7 150 263.5 305 0.34
Kennington Oval, London 150.0 236 380.0 484 0.34
Lord's, London 160.8 255 350.5 528 0.35
Gaddafi Stadium, Lahore 156.4 183 291.0 398 0.37
Headingley, Leeds 166.9 198 375.5 515 0.44
The Quartile Variation Coefficient (QVC) which is determined by the formula given below represents a measure of central dispersion. It is also a dimension-less ratio. Even though this takes into account only 50% of data, the QVC is a very valuable measure since the 50% considered is the most important either-side-of-middle areas. This can also be expressed as a % value.
Q3 - Q1
QVC = -------
Q3 + Q1
A low value indicates a very strong clustering of values around the Median. For instance for MCG, the Median is 342 runs, the Q1 value is only 70 runs away and the Q3 is only 52 runs away. So the Q1-Q3 differential is only 146 while the overall range, as seen next, is a whopping 392. Similar situation for Eden Gardens and SCG.
On the other hand, a high QVC indicates a thinning of the central area. Take Headingley. The median is 375, Q1 is 177 away and Q3 is 140 away. Q1-Q3 is a high 317 out of a total Range of 481 runs.
Table of Ranges and SDs (in order of Range-SD ratio)
Ground SD Low High Range Ratio
Score
M.A.C Stadium, Chennai 148.2 167 560 393 2.65
Headingley, Leeds 172.3 172 653 481 2.79
Sabina Park, Kingston 85.9 164 431 267 3.11
National Stadium, Dhaka 92.0 107 400 293 3.18
Kennington Oval, London 154.1 173 664 491 3.19
National Stadium, Karachi 77.2 196 450 254 3.29
Gaddafi Stadium, Lahore 161.5 147 679 532 3.29
Kingsmead, Durban 84.0 139 420 281 3.35
Eden Gardens, Calcutta 126.6 185 616 431 3.40
Asgiriya Stadium, Kandy 115.3 71 469 398 3.45
Lord's, London 163.4 77 653 576 3.52
Basin Reserve, Wellington 147.7 110 660 550 3.72
W.A.C.A. Ground, Perth 136.7 82 602 520 3.80
Wanderers, Johannesburg 139.1 119 652 533 3.83
Kensington, Bridgetown 129.1 102 605 503 3.90
S.S.C Ground, Colombo 130.6 89 600 511 3.91
Eden Park, Auckland 116.0 139 621 482 4.16
Sydney Cricket Ground 132.2 150 705 555 4.20
Melbourne Cricket Ground 92.0 159 551 392 4.26
There is another important measure which is the Range, which is the difference between the low score and high score. In other words this measure indicates the range of scores, as its name indicates. By itself the Range is of no great relevance. It has to be seen in relation to the SD. Hence I have worked out a ratio of Range to SD. The above table is sequenced by this ratio.
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Fig 2: Scores at Lord's (Click here for a bigger image)
© Ananth Narayanan
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Normally the ratio is between 2.0 and 6.0. Anything outside these values indicates a way-out distribution of values, either a completely dispersed distribution or a completely centralized distribution.
A low value, say 2.65 for Chennai indicates a high SD value while a high value, such as 4.26 for MCG, indicates a low SD value. A low ratio indicates a wide dispersion and a high ratio indicates central clustering.
Conclusion:
1. Mean scores are a reasonable indicator of the expected score. Prediction based on Mean & SD is a possible task. Let us take Kingston. The mean is 292 and SD is 83. If one takes an empirical formula of Mean + or - 0.5 of SD, one can estimate a first innings score of between 251 to 333. One could even increase by the last 5 Test average factor, 1.10, leading to an educated estimate of 276 to 366. Let me see what happens since I am writing this before even the Kingston toss. (On 6/2/09) Ha! England scored 318, smack mid-point of this projection. Not a bad attempt.
2. Evaluation of an innings and individual score is virtually impossible. Headingley has had scores of 570 for 7 during 2007 vs West Indies and 203 all out during 2008 against South Africa. Let us say that Australia or England score 350 in the first innings at Headingley, a few months later. Compared to 2008, it is a great performance while compared to 2007, it is a poor performance. What does one do with any degree of confidence. One can use the Mean value for such analysis, with no great degree of confidence. However as a single point of measure in a broad frame of analysis, it is worth considering.
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Fig 3: Scores at Headingley (Click here for a bigger image)
© Ananth Narayanan
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3. How does one evaluate an innings at Dhaka. The low Mean value will increase the valuation of most innings. However the low scores have been caused by string of low Bangladeshi scores. If we exclude the Bangladeshi scores, then there will be no data available. Other grounds do not present this difficulty since there are not many Bangladeshi innings. Especially in India, where BCCI, with its infinite arrogance, has never invited Bangladesh.
4. The wide variations in innings scoring patterns between grounds belonging to same country is amazing. Look at the figures for the two Pakistani grounds and two Indian grounds.
5. There is a recent batting domination in England and drop in scores at Kandy and to a lesser extent at Wanderer's and Basin Reserve.
Graphs: I have done no Graphs barring for two grounds, Lord's and Headingley - chronological scores to show the yo-yo nature of scores. A BoxPlot is an excellent means of pictorially depicting the quartile variations but we need to do one for each ground.
Please click here for a chronological list of Tests, for selected grounds.
Please click here for a list of Tests sequenced by runs scored, for selected grounds.
I have given explanations to the best of my knowledge. However since my knowledge of statistics is of an acquired nature, there might be errors and/or alternate explanations. I call upon my fellow columnists and readers to come in with their own suggestions and comments.
Comments (19)
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| The Contributors |
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Y Anantha Narayanan has over 35 years of IT background. Over the past 15 years, he has been concentrating on Cricket analysis and software development. He has been involved with StumpVision, Wisden, Hallmark Software and his own site www.thirdslip.com during this period. |
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David Barry was cricket-starved when teaching English in France, and
study of cricket stats was his only way to stay sane. He is now back
in Brisbane, Australia, and working towards a PhD in Physics. He once
played for the worst team in the G-division of Muscat's cricket
league.
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After doing an MBA in marketing and working in an advertising agency, S Rajesh decided that his skills might be put to better use by number-crunching on cricket. He hasn’t regretted that decision in the last six years, and edits the Numbers Game column on cricinfo.com every Friday. |
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Andrew Samson had his moments with bat and ball, once scoring 43 and taking 3 for 14 with his legbreaks, but he was much better at arithmetic, which explains why he is where he is today. Andrew has been keeping cricket stats since the days when it used to be done with pen and paper, and has been involved in scoring/stats for Radio and TV since 1987. He has been Cricket South Africa's official statistician since1994. |
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A former scientist and occasional TV quiz champion, Charles Davis now works full time at sports statistics in Melbourne.
His only real contribution to the Test record books came at age 4, when he formed part of the record 90,800 crowd
who saw West Indies at the MCG in 1961. He has two books to his credit, and claims to be the only cricket statistician
ever who has been quoted in the New York Times and in Australian Federal Parliament on the same day. Not to be
confused with the West Indian batsman Charlie Davis, especially in terms of ability. |
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Having just taken early retirement as a Mathematics teacher in Hobart, Ric
Finlay now fully devotes his time to recording cricket, both past and
present, for the popular CSW cricket database, along with his colleague
David Fitzgerald (www.tastats.com.au). His interest in the game is
inversely proportional to his ability as a player, but he did once score a
century after being dropped at 3 and running out three of his team-mates.
His first memory of international cricket is the 1962-63 MCC tour of
Australia, described as one of the most boring ever. Totally fascinated, he
was instantly hooked, and has never looked back. Author of three books on
cricket of a historical nature, he has provided statistics and scored for
radio and television cricket coverage since 1983. |
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