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Anantha Narayanan

Pitch quality analysis across all Tests

A detailed analysis of pitches using Runs-per-wicket and Balls-per-wicket values

This is the second of three very important and significant articles on batting performances against differing conditions and players. The first did a revised take on the Bowling Quality Index. This one covers the Pitch Quality and the third one would combine both and do an analysis of runs scored by batsmen.

Before I get into the article I have to report a very significant move forward in my database contents. Most readers would know that I had the ball data for only around 740 matches, a meagre 37%. In order to redress this situation, I had approached a few readers and five of them, Raghav, Boll, Rameshkumar, Ranga and Anshu, responded magnificently.

Over the past two weeks, the six of us have shared the work and downloaded over 600 scorecards. I have incorporated the balls played information for all these and also took the opportunity to post the 4s/6s information also. Now my database is looking wonderful with 1374 scorecards (68% - a far cry from 37%) containing balls played and 4s/6s data. From match no 1070 (1987), I have an unbroken sequence of 957 scorecards with complete data. This opens up many new avenues of analysis, especially in the analysis of boundaries hit.

Once again my heartfelt thanks to Raghav, Boll, Rameshkumar, Ranga and Anshu, who spent hours during the holiday season. May their tribe flourish.

There is nothing to be gained by looking at history to determine the quality of pitch. The following example will convince anyone on the futility of such a view. Let us look at happenings in the same ground, Hamilton, in two matches played within 12 months of each other.

Tale of two Tests at Hamilton

2003: Ind 99 ao & 154 ao. Nzl 94 ao and 160 for 6. 36 wkts at 14.1.
2003: Nzl 563 ao & 96/8. Pak 463 ao. 28 wkts at 40.1, despite the last innings.
Let us move north for a few thousand kilometres from the Waikato river to Sabarmathi river and into dusty Ahmedabad. Again two matches within an year of each other.

India at Ahmedabad within a 18-month period

2008: India 76 ao against South Africa. RpW: 33.2.
2009: India 760/7 against Sri Lanka. RpW: 76.1.
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Bowling Quality Index re-visited: incorporating home/away and recent form

Analysing Bowling quality using career-to-date home/away performances and recent form

This is the first of three very important and significant articles on batting performances against differing conditions and players.

About six months back I had come out with an article on Batting performances against different Bowling groups based on BQI (Bowling Quality Index). Notwithstanding the fact that it was a rough unpolished stone, it was one of the best received of all my articles and I came out with a follow-up article after doing some amount of polishing. However there were so many valid suggestions and great ideas that there is a need for me to re-visit that theme, this time incorporating improvements and new ideas. These tweaks would define this very important theme once and for all.

I have summarized below the ideas and suggestions. This is the extract from hundreds of comments.

1. The Bowling quality was determined based on Ctd (Career-To-Date) figures. That was very essential. However there is a clear need to do this work based on Ctd-Home and Ctd-Away figures depending on where the Test was played. As has been shown later, bowlers are poor travellers and these changes will make a significant difference.

2. The initial phase of the bowlers, during the period when the bowler is yet to take the first 50 wickets, has to be done correctly with no ambiguity. Most bowlers who had captured quite a few wickets in their Test career were nearly as good from day 1 and this fact has to be recognized.

3. Almost all bowlers go through widely varying form swings in their career. This important factor of Recent Form has to be recognized, based on their performance during their last 10 Tests, usually an year or so.

4. Bowling quality is not enough to determine the value of batting. The type of pitch plays a very important fact. Scoring a 200 at Lahore during 2006 is equivalent to a 100 while scoring a 100 at Hobart last week is the equivalent to scoring a 200. It is also essential that this should not be considered as a stand-alone measure. It is necessary to combine the two measures. Facing Marshall and Ambrose at Faisalabad on a batting wicket is quite different to facing Prabhakar and Prasad on the same pitch.

All this means that this coverage cannot be completed in one article. It would require three articles. In this one, the first, I will talk about the revised Bowling Quality Index based on Ctd-H/Ctd-A values and adjusted by Recent Form values. In the second one I will cover in depth how the Pitch Index will be calculated, using both Top-7 RpW (Runs-per-wicket) and BpW (Balls-per-wicket) values. Once the stage is set, the third article will revert to the Batting performances against a combination of these two measures. Thus there will be opportunity to come with your comments on the whole process. All three articles will follow in one unbroken sequence so as not to lose the threads of discussion.

Streamlining of Bowling Quality Index:

First, the handling of the first 50 wickets has been streamlined. Until a bowler, who has captured 87 or more wickets in his career, reaches 50 wickets, he is protected to the level of his career average. If he has done better than his career average, like Brett Lee, that is considered. This is very fair to established bowlers. Of course the other bowlers will have notional figures during their first 50 wicket-period. Why 87, why not 100 ? The number 87 has been considered to get world-class bowlers like Mailey, Spofforth, Richardson, Patterson, Hawke, Bond, de Villiers et al into this group. If this is termed as arbitrary it is no more arbitrary than setting the cut-off at 100 wickets. What is the sanctity about 100 wickets anyhow?

Most of the top batsmen travel well. In other words their home and away batting averages do not show very high degree of variation, as described below. I have selected 6 batsmen who represent the best in Test batting from different angles.

Average comparison for selected batsmen

BatsmanCareer AvgeHome AvgeAway Avge
Bradman99.9498.23102.85
Tendulkar56.0356.3855.75
Ponting52.2856.9347.48
Lara52.8958.6547.80
Dravid53.2351.3654.72
Richards50.2449.7850.50


Even for Lara and Ponting their variation away from career average seems to be only around 10%. Bradman and Dravid have in fact performed better away to a significant extent.

Now let us look at a similar tables for bowlers. They seem to be poor travellers. I have selected the top four wicket-takers and two recent bowlers of different types and from different countries.

Average comparison for selected bowlers

BowlerCareer AvgeHome AvgeAway Avge
Muralitharan22.7320.1527.02
Warne25.4225.5525.27
Kumble29.6524.937.36
McGrath21.6421.9721.23
Harbhajan Singh32.2228.3639.65
Ntini28.8324.4337.71


Warne and McGrath have bowled with the same level of effectiveness home and away. For Muralitharan there is significant variation. Kumble, Harbhajan and Ntini have very significant variations. Please note that I have selected Harbhajan and Ntini only to show the type of variation which can exist.

It took me quite some time to compile the CTD Home and Away values. Determining the values on a continuous basis and storing them in the match data base presented its own problems. Once I completed that I have re-done the BQI and this has come out very well now. I am not going to show the BQI tables now since more work has to be done.

I would give an example. In match no 1820, played at Christchurch between New Zealand and Sri Lanka, the BQI group was 5 for both teams since Murali's Ctd-figures were 657 at 21.96 and they also had Malinga and Vaas, very good bowlers. However Murali's figures comprised of 406 home wickets at 19.65 and 251 away wickets at 25.71. Once the Ctd-Away average was applied Sri Lanka went to Bowling group 4. New Zealand firmly stayed in group 5 since Bond had done reasonably well both home and away while Martin had a 15% variation between home and career. Only Vettori had done better away but he bowled very little in the match.

Now for Recent Form. This was again very tough work. I tried doing some short cuts, in flight, as I processed the match database. However that was not effective and fool-proof. Finally I bit the bullet and took the major step of incorporating the career details, match-by-match, into the Player database. This doubled the database size at one shot since I had to provide space for 220 matches. Ha! what is this 220. Well, Tendulkar has played 184 as on date and I have estimated that it would take him over 3 years to play more than 36 Tests and THAT is very very unlikely. Well, if that happened or Kallis played another 73 Tests, I will gladly go through another re-vamp. The advantage is that I have, for the first time, the player's entire career in a single record and can come out with many different types of analysis.

The Recent form work has come out very well. It is going to be very significant also since the form swings are widely varying. There is nothing gained by looking at absolute values. A 10-Test average of 20 for Sangakkara is a disaster, 35% of his career average, while the same for Vettori is around 65% of his career average. The following tables show the extreme values in Recent forms for batsmen.

Please note that the Recent form work is for the last 10 Tests, irrespective of location. I cannot very well do it separately for Home and Away since it might take players even 5 years to play 10 away Tests and that is too long a period. However I have done a minor adjustment, based on a suggestion from Sriram. Within these 10 Tests, I have done a minor tweak of 95% for home and 105% for away performances. Also remember that the recent form work has started after the players play 10 Tests or more.

In great batting form

MtIdYearForBatsmanCareer AvgeRF-InnsRF-AvgRF-Idx%
10671987IndVengsarkar D.B42.138127.38302.3
10221985EngGatting M.W35.561197.09278.5
16032002SlkTillakaratne H.P42.886114.83267.8
09621983PakMudassar Nazar38.091093.10244.4
15721990PakImran Khan37.69891.75243.4


Probably it looks as if I should do a separate article on Recent form. Vengsarkar had the best form anyone has ever had. During a 10-Test period during 1987, he scored at 302% of his average. His scores were 37*, 126*, 33, 61, 102*, 38, 0, 22*, 164*, 57, 153, 166, 96. Gatting's golden period was during England's golden period, 1985. Tillakaratne performed at 267.8%. Incidentally during this period, both Vengsarkar and Tillakaratne performed for more than 10 Tests at only slightly lower levels. Note the wonderful batting form exhibited by Mudassar Nazar during 1983 and Imran Khan during 1990. Imran was averaging better than many a specialist batsman at his peak.

It can also be seen that it is not exactly possible for the top batsmen who average above 50 to achieve these RF-Idx % figures since they would then have to have recent 10-Tests average of over 150 or so, not very easy.

In awful batting form

MtIdYearForBatsmanCareer AvgeRF-InnsRF-AvgRF-Idx%
15212000EngNasser Hussain 37.191511.6031.2
12051992AusWaugh S.R51.061416.0031.3
14631999AusHealy I.A27.4178.6531.6
09051981EngBotham I.T33.551810.8932.5
19012008IndDravid R 53.231418.1134.0


Let us take the other end. Nasser Hussain had the worst streak anyone has ever had. Ponting can take heart. His current run is far better than Hussain's whose scores ran 15, 16, 25, 10, 21, 0, 15, 8, 10, 6*, 22, 0, 0, 7, 0 retd, 23 and 5. Steve Waugh had a similar nightmare at the early part of his career in 1992. It is amazing that Botham carried a run of 8, 35, 9, 4, 37, 7, 0, 0, 16, 26, 1, 1, 13, 16, 1, 33, 0, 0 into the Headingley Test. And how he broke this barren spell, with knocks of 50 and 149*. Everyone knows about Dravid's recent barren spell. Here it is in black and white.

Thus it can be seen that the range of RF-Idx is ten-fold, 31.2 to 302.3, that too for established batsmen who have scored 3000 or more runs.

Now for the bowlers, the more important segment of Recent form analysis since these are the ones used in adjusting the BQI. The extreme values are given below.

In great bowling form

MtIdYearForBowlerCareer AvgeRF-WktsRF-AvgRF-Idx%
04601958EngLock G.A.R25.58549.96256.8
00351892EngBriggs J17.75557.84226.6
08341978EngEdmonds P.H34.183415.24224.4
14071998WinHooper C.L49.432024.30203.4
04551958EngBailey T.E29.213516.09181.6


Lock's 10-Test period saw him performing at around 2.5 times his career average. His Test performances were 3/66, 2/38, 3/86, 1/29, 11/48, 3/25, 9/29, 11/55, 8/96, 3/39. Briggs was about 225% better. However see how quickly we go below 200%. This also gives a few not-so-great bowlers like Hooper and Edmonds chances to have their golden runs and move to the top of the Recent form table. Hooper, for a period, bowled like Muralitharan and Edmonds, for a while, bowled like CTB Turner. And Bailey was giving SF Barnes a run for his money !!!

Same as for batsmen. Tough for top bowlers to have a very low % since their averages are already low. For instance Muralitharan's best period has been during 2007 when he captured 89 wickets at an average of 14.62, still giving a RF-Idx % of only around 150%, not enough to even come in the top-10.

In awful bowling form

MtIdYearForBowlerCareer AvgeRF-WktsRF-AvgRF-Idx%
11801991IndShastri R.J40.965113.836.0
5771965PakIntikhab Alam35.95996.3337.3
15932002SafNtini M28.831273.5039.2
04631958WinSobers G.St.A34.04984.5640.3
07401974EngUnderwood D.L25.841561.2742.2

On the other side, Shastri had a horror run. He performed nearly three times worse. Intikhab had a similar disaster run. Look at Ntini's barren period recently. Sobers was bowling like a millionaire and Underwood like an out-of-form Sobers.

The Recent form adjustment is briefly explained below. The adjustments are done based on averages since that is the most stable and proven of all measures.

For good form, ignore if the RF-Idx is within 20% above the career batting average. If the RF-Idx is above 120% of career bowling average, then apply the adjustment factor which will vary from 0.80 to 1.00. The Ctd-x bowling average of the bowler will be multiplied by this adjustment factor.

For Lock, the adjustment factor is likely to be around 0.82.

For poor form, ignore if the RF-Idx is within 10% below the career batting average. If the RF-Idx is below 90% of career bowling average, then apply the the adjustment factor which will vary from 1.00 to 1.20. The Ctd-x bowling average of the bowler will be multiplied by this adjustment factor.

For Shastri, the Adjustment factor is likely to be around 1.18.

Thus the RF related adjustment factor for individual players varies between about 0.8 and 1.2. Let me recapitulate that we are looking at a player's recent form. It does not matter whether he achieves this at home or away. Also remember that these are extreme values.

Let us keep in sight that these are individual bowlers' recent form indicators. When the BQI is determined, first the individual bowler's values are adjusted and then the final BQI compiled. Thus a single BQI is a composite of 4/5/6 bowlers, some in good and some in indifferent form. This leads to a lot of evening out. The team itself will carry a significant adjustment value on either side of 1.00 only if it happens that most of the bowlers are in good form or most of the bowlers are in poor form. This does not happen often. The final innings level adjustment, for the first innings, varies between 0.86 and 1.11. Second innings has a similar range. These innings, which are very illustrative and illuminating examples, are summarized below.

Two innings with extreme Recent form adjustment values


Match Id: 0834
Year: 1978
England vs Australia.
England RF-Idx for innings was 0.86.
Botham-55%,
Miller-121%,
Edmonds-44%,
Old-83%,
Willis-73%.
4 out of 5 bowlers were in great form.
Match No: 0774 Year: 1976 India vs West Indies. India RF-Idx for India was 1.11. Venkataraghavan-120%, Bedi-137%, Chandrasekhar-128%, Madan Lal/Amarnath-100% (They had not even played 10 Tests). All 3 main bowlers were in poor form.
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Part two of five-wicket hauls in Test cricket: a look across and deep

The second part of an in-depth statistical analysis of five-wicket hauls in Tests

This is the follow-up to the previous articles. Another 13 tables have found their place. This is probably a more interesting set of tables since some of the analysis is by innings and relate to result. The comments are given at the end of each tables.

12. Great defensive winning bowling performances in fourth innings

MtId Year For Vs  Score HA Bowler          BT I <--Analysis--> R WonBy
0073 1902 Aus Eng-120/10 A Trumble H S 4 25.0- 9- 53- 6 W 3 0943 1982 Eng Aus-288/10 A Cowans N.G 4 26.0- 6- 77- 6 W 3 1243 1994 Saf Aus-111/10 A de Villiers P.S 4 23.3- 8- 43- 6 W 5 0019 1885 Aus Eng-207/10 H Spofforth F.R 4 32.1-22- 90- 6 W 6 0009 1882 Aus Eng- 77/10 A Spofforth F.R 4 18.4-15- 44- 7 W 7 0042 1894 Eng Aus-166/10 A Peel R S 4 30.0- 9- 67- 6 W 10 0179 1929 Eng Aus-336/10 A White J.C S 4 64.5-21-126- 8 W 12 1436 1998 Eng Aus-162/10 A Headley D.W 4 17.0- 5- 60- 6 W 12 1442 1999 Pak Ind-258/10 A Saqlain Mushtaq S 4 32.2- 8- 93- 5 W 12 0025 1887 Eng Aus- 97/10 A Barnes W 4 30.4-29- 28- 6 W 13 1720 2004 Ind Aus- 93/10 H Harbhajan Singh S 4 10.5- 2- 29- 5 W 13 0437 1957 Saf Eng-214/10 H Tayfield H.J S 4 49.2-11-113- 9 W 17 0905 1981 Eng Aus-111/10 H Willis R.G.D 4 15.1- 3- 43- 8 W 18 1377 1997 Eng Aus-104/10 H Caddick A.R 4 12.0- 2- 42- 5 W 19 0106 1910 Saf Eng-224/10 H Vogler A.E.E S 4 22.0- 2- 94- 7 W 19 2021 2011 Nzl Aus-233/10 A Bracewell D.A.J 4 16.4- 4- 40- 6 W 7 1422 1998 Eng Saf-195/10 H Gough D 4 23.0- 6- 42- 6 W 23 0390 1954 Pak Eng-143/10 A Fazal Mahmood 4 30.0-11- 46- 6 W 24


This is ordered by the margin of wins. All wins by fewer than 25 runs are considered. Norman Cowans's and Fanie de Villiers's performances are of recent vintage. Fred Spofforth has been responsible for two sub-10 run wins. Bob Willis's mind-blower effort of eight for 43 followed Ian Botham's from-the-edge innings of 149. Saqlain Mushtaq's was after the nearly-innings of Sachin Tendulkar.

Let me devote some space to one specific performance. That is Hugh Tayfield's nine for 113. This was analyzed and concluded as the best ever Test bowling performance in the famous Wisden-100 lists which I had prepared for Wisden. If I do the lists today, I have no doubt that this would be on top. England, trailing by 89 runs in first innings, dismissed South Africa for 142 and England had to score 232 for a win on a turf wicket. Tayfield bowled unchanged for 35 8-ball overs on the last day and never flagged even when England were 147 for 2. He captured the next 8 wickets for nothing and England fell short by 17 runs. This performance had everything. Low total to defend, close margin of win, top order wickets, against a good batting side and the result.

Bracewell's heroics this week were missed out and thanks to Yash, this entry has been added.

12a. Great defensive winning bowling performances in fourth innings - 2

MtId Year For Vs  Score HA Bowler          BT I <--Analysis--> R
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Five-wicket hauls in Tests: a look across and deep - part one

Part one of a detailed statistical analysis of five-wicket hauls in Tests

There is a tendency to ignore the bowlers in Test cricket. I myself am guilty of this and do not allocate equal time and effort for these forgotten species. This time I have decided to make amends by doing the article on fifers in Test cricket immediately after I finished the one on Test hundreds.

First, the term used. Let me reproduce the Wikipedia entry below.

Five-wicket haul (also Five-for, five-fer, fifer, or shortened to 5WI or FWI)


Five or more wickets taken by a bowler in an innings, considered a very good performance. The term fifer is an abbreviation of the usual form of writing bowling statistics, e.g. a bowler who takes 5 wickets and concedes 117 runs is said to have figures of "5 for 117" or "5-117". Sometimes called a "Michelle", after actress Michelle Pfeiffer.

I like the term "Fifer". However since that also refers to the foot-soldier who plays the "Fife", the Scottish flute, I am somewhat reluctant. "Pfeiffer" would be injudicious. I am not too comfortable with "Five-for", being slightly contrived and seemingly incomplete. So I will stick with "fifer", a single non-hyphenated (!!!) word and my favourite. Much better than "DLF maximum" or "Karbonn Kamaal Katch".

Some maxims have to be repeated in EVERY article since quite a few readers have a one-track mind and see what only they want to see. This is not a Bowling Ratings article. The ordering is based on an indicated measure and is visible to the reader clearly. Do not draw any unintended inferences and come out with comments based on those. There is no personal discretion involved other than setting up the parameters. In view of the size of the articles and number of tables, I have kept my narratives to a minimum.

Test Bowling is a fascinating subject. It is far more nuanced that Batting when it comes to analysis.

- The number of wickets in an innings is strictly limited to 10.
- Bowling successes are very clearly defined and measurable in terms of wickets (who and when) and accuracy.
- Bowling is three-dimensional: balls, runs and wickets. These three dimension-related values are available for all bowling spells. (Batting is also three-dimensional: runs, time, balls. Unfortunately only runs information is available for all matches.)
- Batsmen win and save matches. Bowlers, almost always, win matches. They rarely draw matches, a la Atherton, Hanif et al. But you will be surprised: wait for the next article !!! A great ODI team can be founded on top-class batting and average bowling, not a great Test team.
- 5 batsmen can score hundreds in an innings, and have done so. Only two bowlers can capture 5 wickets each in an innings.

All these nuances lead to a more exciting analysis of fifers.

It took me nearly a week to think of all possibilities, write the program, prepare the tables and then weave the article around the tables. I did so much work on the keyboard that my legs (yes, you read it correctly) started aching. This turned out to be the longest article I had ever done, barring none. So I decided to release this in two parts. This will also enable me to do some specialized requests and add those tables. At the end of the article, I have indicated the types of analysis which have been included in Part 2. Even now, the current article has been exceeded in size by only one article, the one published last, on Special hundreds.

A note on the tables. I have standardized the presentation to have the first 14 columns common. These are self-explanatory. I have shown Home/Away (H/A), Bowling Type (S for spinners), innings bowled in and Result (W for Win, = for draw and * for loss).

First the basic table. I did not do this for the hundreds. However it is necessary to start with this table in the bowling analysis since many readers may not be familiar with all these performances.

1. 9+ wicket bowling performances in Tests


MtId Year For Vs  Score HA Bowler          BT I <--Analysis--> R
0428 1956 Eng Aus-205/10 H Laker J.C S 3 51.2-23- 53-10 W 1443 1999 Ind Pak-207/10 H Kumble A S 4 26.3- 9- 74-10 W 0048 1896 Eng Saf-151/10 A Lohmann G.A 2 12.0- 6- 28- 9 W 0428 1956 Eng Aus- 84/10 H Laker J.C S 2 16.4- 4- 37- 9 W 1583 2002 Slk Zim-236/10 H Muralitharan M S 1 40.0-19- 51- 9 W 1029 1985 Nzl Aus-179/10 A Hadlee R.J 1 23.4- 4- 52- 9 W 1081 1987 Pak Eng-175/10 H Abdul Qadir S 1 37.0-13- 56- 9 W 1266 1994 Eng Saf-175/10 H Malcolm D.E 3 16.3- 2- 57- 9 W 1423 1998 Slk Eng-181/10 A Muralitharan M S 3 54.2-27- 65- 9 W 0483 1959 Ind Aus-219/10 H Patel J.M S 2 35.5-16- 69- 9 W 0967 1983 Ind Win-201/10 H Kapil Dev N 3 30.3- 6- 83- 9 * 0849 1979 Pak Aus-310/10 A Sarfraz Nawaz 4 47.2- 7- 86- 9 W 0683 1971 Win Ind-352/10 H Noreiga J.M S 2 49.4-16- 95- 9 * 0461 1958 Ind Win-222/10 H Gupte S.P S 1 34.3-11-102- 9 * 0131 1913 Eng Saf-231/10 A Barnes S.F 3 38.4- 7-103- 9 W 0437 1957 Saf Eng-214/10 H Tayfield H.J S 4 49.2-11-113- 9 W 0138 1921 Aus Eng-315/10 H Mailey A.A S 3 47.0- 8-121- 9 W
I have limited this to bowling spells in which the bowler captured 9 or more wickets. Only twice have bowlers captured all 10 wickets. Jim Laker's feat came 79 years and 427 Tests after Alfred Shaw bowled the first ball to Charles Bannerman. Anil Kumble's feat came a further 1015 Tests and 43 years after Laker dismissed Len Maddocks. I wonder how many years would pass before this happens again: let me say, around 2050.

Laker had another 9-wicket haul, in the same match. Muttiah Muralitharan is the only other bowler to capture 9-wkts in an innings twice. Quite surprisingly, the three spinners, Muralitharan, Abdul Qadir and Subhash Gupte, captured 9 wickets on the first day. Another wonderful spinner, Hugh Tayfield's 9 for 113 was adjudged to be the best ever bowling performance in the Wisden-100 analysis. More of this performance later. Kapil Dev, Gupte and Jack Noreiga all captured 9-wickets in an innings, in vain. Surely let us all agree that no one, I repeat no one, in the next 1000 years, if Test cricket survives that far, would capture all 20 wickets in a match.

Now for something I think is very important, performance away from home.

2. Wonderful performances, away from home


MtId Year For Vs  Score HA Bowler          BT I <--Analysis--> R
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Special Test hundreds: a look across and deep

A detailed analysis of various quantifiable aspects of the best Test centuries scored

I had mentioned in response to one of the comments on the macro-analysis article on Test hundreds that in my follow-up article I would look at special hundreds, selected based on specific selection criteria. I had also made it clear that this would not be my own personal selections, as I normally do but one based on selection criteria in my computer program, with external additions in very very special cases only. Anyone finding fault with the three special additions is probably not a true follower of the game.

To answer the sceptics, I have also shown the actual program statement doing the filtering. Though it is a 'C' program statement, it will be crystal clear to anyone reading this article. So kindly do not come out with statements that this article has been written to specifically include or exclude one specific hundred.

If a nice new selection criterion is suggested I will have no problem doing that and adding the tables at the end. I have also toughened the selection criteria to make sure that there are approximately between 10 and 25 entries in the tables. This has been done to ensure that all the table entries are shown in this article itself. Hence everything is in the open in this article.

My own selections from out of the table entries are spread right through the article. Readers can come with their own selections.

Preliminary program work
score = matchdata[mat]->score[inns]; bqi = matchdata[mat]->weighted_ctd_bow_avge[inns]; mat_rpw = matchdata[mat]->rpw; runs = matchdata[mat]->pldata[inns][pos].batruns; balls = matchdata[mat]->pldata[inns][pos].batballs; score1 = matchdata[mat]->score[0]; score2 = matchdata[mat]->score[1]; score3 = matchdata[mat]->score[2]; score4 = matchdata[mat]->score[3]; if (follow-on) deficit = score1-score2; else deficit = score2-score1; if (follow-on) target = score2+score3-score1+1; else target = score1+score3-score2+1;
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Test hundreds: everything anyone wanted to know ... and more

Evaluating various parameters of Test centuries including frequency, result of match and bowling quality

I write three types of articles. The first, and the most often done, are the hard-core analysis, often sailing on uncharted seas. Examples are the Bowling quality and Series analysis. Then there are anecdotal articles which are normally my selections, with facility for readers to come out with their own. Examples are the the Test opening day performances and the innings bowling efforts. The third type of articles are rare. I take a single facet of the game and analyze it in depth but in a narrow manner, bringing out almost every aspect of that. Examples are the articles on Bradman and Muralitharan. The current article is one such analysis. The subject is Test hundreds. I would be very surprised if, after reading this article, the reader reverts with a possible analysis on Test hundreds I have missed.

1. Number of Test hundreds scored

SNo Batsman          Year Cty Mat 100s
1.Tendulkar S.R 1989 Ind 182 51 2.Kallis J.H 1995 Saf 145 40 3.Ponting R.T 1995 Aus 154 39 4.Dravid R 1996 Ind 158 35 5.Lara B.C 1990 Win 131 34 6.Gavaskar S.M 1971 Ind 125 34 7.Waugh S.R 1985 Aus 168 32 8.Hayden M.L 1994 Aus 103 30 9.Bradman D.G 1928 Aus 52 29 10.Jayawardene M 1997 Slk 125 29


As anyone and their neighbour's cat are aware of, Tendulkar stands head-and-shoulders above all others with 51 Test hundreds, 99 in all. This might be 52 by the time this article is published. Kallis and Ponting would have to play about 50 Tests more to overhaul Tendulkar and it is very unlikely that this would happen. The modern greats are all there, along with the incomparable Bradman, who has 29.

2. Average value of hundreds


SNo Batsman          Year Cty Mat 100s  Avge
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ODI batsmen against bowler groups: across ages

Measuring ODI batting performances by the quality of the bowler groups faced

A few months back I had come out with an article on Test batsmen by bowling quality, in groups. This was one of the best received of all my articles since the analysis took Test batting into hitherto unchartered seas. Many new insights were drawn from the analysis. I think it is time I do a similar analysis for ODI batsmen also since the bowling quality varies considerably across teams and years. The average runs scored by batsmen in their careers is also quite high and an analysis like this will let us look at the batsmen with a new perspective.

This analysis has come out partly because a single number indicating the weighted average bowling quality faced by a batsman across the career hides many truths. This is based on the Arjun Hemnani's suggestion. This is a quasi-rating work based on the most important of parameters, viz., the Bowling quality.

I have summarized below all relevant facts related to this analysis. First let me emphasize that this is not a ODI innings Ratings analysis. There are many other relevant factors which would have to be considered in such an analysis. I have not done so in this analysis which is centred on Bowler quality. I would appreciate if the readers do not keep on repeating again and again that other relevant factors such as Pitch type, Innings status at entry, Result, Match importance, Bowler recent form, Innings target et al, have not been included. That would be counter-productive.

1. The Bowling quality index (BQI) is based on Career-to-date values. This is the most dependable and accurate of the bowling measures. There is no situation where the Ctd figure is not the appropriate one. Coupled with the fine-tuned handling of established bowlers described later, this works very well. This takes into account the way a bowler's career shaped up.

2. The BQI is based on the Bowling average. In Test matches the bowling strike rate has greater relevance. However in ODIs, both strike rate and bowling accuracy (RpO) have equal importance and the Bowling Average is a perfect representation of this. Very good averages of say, 25.0, can be reached by a combination of 60 and 0.41 or 50 and 0.5 or 40 and 0.62. All these, patently different, bowlers are considered similar in this analysis. Individual match circumstances might require bowlers with varying attacking and accuracy-related skills, but, in general the average takes care of all conditions.

3. The BQI is based on the actual bowlers who bowled in the particular innings. This is very important. If Imran Khan played as a batsman, to that extent, the bowling attack would be less strong.

4. The BQI is determined using the modified reciprocal method suggested by Arjun Hemnani which irons out the imbalance created by weak fifth bowlers.

5. I have taken care of top bowlers during their initial Initial figures for bowlers with career haul of 100+ wickets. Whatever be the Ctd figures for these qualifying bowlers, their Ctd bowling average will be fixed at their career bowling average levels. This takes care of both situations: Walsh capturing 10 wickets at 50+, nearly 20 more than his career average and Mendis, at one point capturing 25 wickets at 9.83. Of course once any bowler crosses 50 wickets, their Ctd figures will apply.

For the bowlers who have not captured 100 career wickets, their Ctd bowling averages below 50 wickets is pegged at a minimum of 40.0. Makes eminent sense.

6. The computed BQI values will be used only for innings of 10 overs or more. For shorter innings the minimum BQI value is pegged at a minimum of 30.0. This is to prevent situations like Wasim Akram and Waqar Younis bowling 6 overs between them. The BQI would be a very low number.

7. The BQI is reduced by 5% for Home games and increased by 5% for away games. Reader should remember that the lower the BQI, the more potent the attack is. 5% either way is ample and provides some compensation for batsmen playing away. In general this concept is fine and works well in most cases.

It is possible that the visiting team has the right bowlers and can exploit the "away" bowling conditions. However there is no denying that, in most cases, the home bowlers would have the advantage of familiarity with and knowledge of local conditions. Great examples are the recent whitewashes in England and India and the way West Indies are struggling in Bangladesh.

8. No period-based adjustment is done. Such adjustment is relevant only for determining team strength values. If the period was a great one for the bowlers, as the 1971-84 was, it was a tough one for the batsmen and this is taken care of by leaving the relatively lower BQI values as they are. It is obvious that the runs scored during 1971-1984 were more valuable than the runs scored in more batting-friendly conditions later.

Finally the bowling attacks are classified into 5 groups, as described below. The fifth group was necessary to separate the really weak bowling attacks.

There have been 6302 qualifying innings until the fifth ODI between India and England which was played on October 25. The underlying idea is that the middle group should have about a third and the other groups symmetrically lower. In view of the profusion of weak bowling attacks, the first and the last would not necessarily have similar % shares. There may be a subjective element in this part of the exercise but that cannot be avoided. Around 28% for the first two groups means that at any time there are 2-3 really good bowling attacks makes eminent sense. The other cut-offs follow logically. The group cut-off details are given below.

Group     B Q I   # of Inns   %
1 21.30-27.99: 709 11.25 % Very good bowling attack. 2 28.00-30.99: 1070 16.98 % Good bowling attack. 3 32.00-35.99: 2104 33.38 % Average bowling attack. 4 36.00-39.99: 1203 19.09 % Passable bowling attack. 5 40.00-57.98: 1216 19.30 % Poor bowling attack.
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A macro look at ODIs over four decades

A statistical analysis of major batting and bowling trends in ODIs over the years

The last 12 articles have all been on Test cricket and I think it is time I moved over to the ODI space. The first is a re-visit of an earlier article. I will follow this with a look at the ODI batsmen's performance against bowlers, strength of whom is ordered by groups, a la Test cricket. That work will borrow freely from the findings in this article.

I had looked at a summary analysis of ODI matches about three years back. Since then over 400 matches have been played, ODI rules have been changed, more T20 matches have been played introducing new techniques, 5 types of slower deliveries have been invented, slow bowlers are opening and finishing the innings et al. Hence I have re-constructed the periods to be able to look at the current millennium more closely. Out of the 7 periods, 3 are allocated to these 12 years. The last period is 2008-2011 and is really the post-T20 era and the previous one, 2004-2007 is the transition period. It is possible that a minor adjustment here and there will bring major rule changes in sync with the periods. However that would leave the number of matches unbalanced.

I have retained, but brought up-to-date, most of the previous analyses since many current readers might not have viewed the previous article. I have kept my comments to a minimum since I want some lively discussions among the readers.

Let us get into the analysis of the tables. These tables are current upto ODI # 3200, the second ODI between Bangladesh and West Indies.

1. Match analysis (Runs/Wkts per match, RpO, RpW)

Period    Mats  R/M  W/M  RpO  RpW
1971-1984 281 352 14.0 3.88 25.2 1985-1989 317 368 13.7 4.11 26.9 1990-1994 369 366 13.6 4.06 26.8 1995-1999 564 394 14.5 4.36 27.2 2000-2003 543 390 14.1 4.40 27.6 2004-2007 586 400 14.3 4.60 27.9 2008-2011 540 407 14.4 4.72 28.2
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Test teams' stay at the top: a complete re-look

A graphical analysis to measure the series records of top Test teams over the years

A great fall-out of my Test Series analysis has been that it has provided me an alternate and very effective way of looking at the various teams' stay at the top. This has been triggered by a suggestion provided by Raghav Bihani.

I have approached this analysis with the following points in mind.

1. 4-0 wins should carry more weight than 2-1 wins.
2. Big wins (Inns/10-wkts etc) should carry more weight than narrow wins (1-wkt/20 runs etc).
3. Away results should carry more weight than home results.
4. Deciding Tests should carry more weight.
5. If a 4-Test series is pegged at 1.00, 3 & 2 Test series should carry lower weight than this and 5 & 6 Test series should carry more weight.
6. 1-Test contests are not series and have been ignored in this analysis as also the three Triangular tournaments. The reason for not including 1-Test contests is because inclusion would have a significant adverse impact on the calculations. As can be seen later the averaging across multiple series pre-supposes the need to have series performance as the base. Taking single Test performances as series performances, especially as the strength differentials are quite substantial, distorts the numbers. Anyhow there have been about 100 1-Test series and most of these involve teams in their early stages.
7. Win indices should be adjusted by relative team strengths. Stronger teams should get lower weight and weaker teams should get higher weight.

The first four of these were built into the Team analysis for Series and the last two have been rationalized with multiplying factors, suitably limited. Just to recap the series team analysis, the winning of a match gets a SIN (Series Index) value of just above 60 (for a 1-run win), upto a maximum of around 97 (for the innings and 579 run win). The losing team gets the balance, out of 100. The draws get either side of 50, depending on the nature of draw. Assigning 60+ for a win, as against, say, 55+ is to recognize Test wins in a sharp and definable manner. At the same time the team which draws the match but has been in command throughout, will get nearly 60.

In order to evaluate the results of the teams, I also have considered 10 consecutive Test Series, including the series being considered and averaged the SIN values to work out a TSIN (Ten Series Index) value. This means that for any evaluation a minimum of 10 Test series (easily 3 years) is considered. This value is determined for each series for each country and rolling values arrived at. These TSIN figures are then plotted on a graph similar to the one I had done couple of years back on batting and bowling streaks. Some of these points may not be clear now but will get clarified as we move on to the graphs.

Readers should understand that it is quite tough to get a TSIN value of 60.0 for the next 10 series for a team. 60 represents a reasonably comfortable series wins and every loss/draw/narrow-win has to be compensated within the 10 series period. Also the stronger teams are already pegged back because they are stronger and expected to do well. All this means that only four teams, viz., Australia, England, West Indies and South Africa have ever crossed 60.0 as a rolling average. The other 6 teams have never crossed 60.0 once in their history. That should put these values in perspective.

First a summary table of Series information by country.

Team        # of Series   SIN >70   TSIN>60    Mean SIN   High TSIN
Australia 178 22 41 55.74 66.52 England 221 21 12 52.25 62.33 West Indies 121 8 10 50.50 66.06 South Africa 98 6 4 51.32 60.67 Pakistan 116 4 0 48.31 54.56 India 126 6 0 47.88 55.67 Sri Lanka 73 5 0 46.83 53.92 New Zealand 126 4 0 43.03 52.94

First let us look at the graph for the Australian team. Let me repeat that these are not series performances but plotted using the TSIN values. As such the stay at the top or bottom would be clearly visible. There would not be abrupt moves up and down and the trends would be obvious.

Australia's Test-series record over the years
© Anantha Narayanan

What does one say. If you forget the initial few series, Australia have had only one really bad period, between 1982 and 1986. Hughes took over after the Packer era and did not move the world. Greg Chappell could not do much and Border took over a weakened side. The wholly unexpected World Cup 1987 triumph changed everything. Otherwise their TSIN values have almost always been above 50. But the real strength of Australians over the years has been the fact that out of the 178 series being considered in which they have TSIN values of 60 or above in 41 of the series.. They have had two real peaks, one between 1930 and 1951 and the other mind-blowing one between 1998 and 2007. Both these are expanded separately later.

West Indies' Test-series record over the years © Anantha Narayanan

West Indies have had a spectacular Manhattan structure until 2000 and then the poorer shanty towns take over. During the past 10 years, they have barely crossed 40. However their heyday was during the 1980s-90s when they had a run of 27 consecutive unbeaten series. Many teams went into Test series against West Indies during these years, considering a series draw as success. Wins were almost out of question. Maybe this defensive attitude also meant the fair number of draws. The later 25 series of this almost unparalleled period of domination is covered separately.

England's Test-series record over the years © Anantha Narayanan

England has had a fairly steady performance graph. They peaked for a spell of 12 series during 1950s and this has been covered separately. Hutton, May, Cowdrey, Compton formed an immense batting lineup. Tyson, Statham, Laker, Appleyard and Lock were formidable on any surface. Other than this they had a brief spell of 60+ TSIN values during 2002-03, with the series ending around 2005. The 1980s were the lowest point for them. Note the spike in the last series. This has been caused by their 4-0 whitewash of the Indians, which fetched them a SIN value of 79. This about 25 above their average and has given a lift-up of 2.5 or so in the TSIN value.

South Africa's Test-series record over the years © Anantha Narayanan

South Africa has had quite a few peaks and near-peaks. Look at the period just after 1962. And as soon as they returned to international cricket during 1998 they had a peak of 10 Tests during which they averaged just above 60. Then they dropped off getting to a fairly low period around 2003, probably prompted by the World Cup debacle. They have since then picked up.

India's Test-series record over the years © Anantha Narayanan

India has been just around average for over 70 years until around the turn of the century. Even then they have been averaging only around the 50-55 mark, never once putting in a sequence of 10 good series level performances. Not once have they reached a TSIN value of 60. Note the fall in the last series. This has been caused by their 4-0 loss to the Englishman, which fetched them a SIN value of only 21. This about 30 below their average and has dropped the TSIN value by around 3.0.

Pakistan's Test-series record over the years © Anantha Narayanan

Pakistan has had a similar graph to India. They had reasonably good periods between 1975 and 1995, the Imran Khan years. They were pretty badly off around 1998, then picked up but have fallen off recently. Again no steady streak. No single TSIN figure exceeding 60.0.

New Zealand's Test-series record over the years © Anantha Narayanan

New Zealand have had alternating good and bad periods. Other than for a short while during early-1980s, their best period has been either side of 1990. This period was orchestrated by Hadlee and Martin Crowe. They are badly dropping off recently.

Sri Lanka's Test-series record over the years © Anantha Narayanan

Barring the first 15 years, Sri Lanka have been fairly steady around the 50+ mark. For a fairly young team, this has been a very good level of consistency.

I have given below the four truly outstanding streaks at top of teams. The criteria is that the concerned team should have secured an average TSIN value of over 60.0 in a minimum of 10 consecutive series. I have taken trouble to find as long a streak as possible. I have also not included the 10-series streaks which have only around 60% value. The bar is higher for these minimal streaks. Looks easy and simple to get in. Let me assure you that it is a very tough criteria and only four streaks have qualified. Australia have two such streaks, West Indies has one and England had a wonderful streak during the 1950s. South Africa had 4 series with TSIN over 60, that is all. The other four teams never even had a single TSIN value of 60.0.

These four streaks have been represented in the following graph. This time the graph has been posted on the actual SIN value since we need to look the details of these series streaks.

Test-series record of top four teams © Anantha Narayanan

Australia played 28 series during 1999-2007. They won 24 of these, often by comfortable margins. The four series outside these successful ones are the 2-1 loss to India during 2001, Ashes loss by 2-1 to England during 2005, the 0-0 draw with New Zealand during 2001 and 1-1 home draw with India during 2003. It can be seen that in these four series Australia have ended with value below 50, but above 40. Australia's average SIN value during these 28 series was 64.57, an achievement which can only be understood after understanding the nuances of numbers used in this article.

West Indies' streak is the only unbeaten one in this elite group. However their 25 series average is not very high since they drew 8 of the 25 series. They also had the two white-washes against England during this streak. This 10-0 record also indicates that their other wins have been closer.

The Bradman-led Australian teams between 1930 and 1951, had a streak of 14 series during which they had an amazing average of 64.82. The only loss was the bodyline series to England and then the 1938 draw.

England had a nice 12-series streak during 1950s when they did very well. A single exception being the Ashes series of 1958-59 when they did very poorly.

Now for a numerical summary of these four streaks.

Team        Streak Period Series Won Drawn Lost SIN avge Tests Won Drawn Lost
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Test-series performances: the top allrounders

A detailed stats analysis of the greatest Test-series performances by allrounders

Last month I had embarked on a major project. This had been triggered by a few comments on performance of allrounders in series. Finally after covering the batsmen, bowlers and teams, I have covered the allrounders in Test series, the idea I started with. This concludes the current series of articles but there are some very good follow-up ideas, especially relating to the teams analysis which will be done later.

I am aware that Cricinfo statistics section gives you an insight into the runs scored and wickets captured in Test series. However those are raw numbers and also do not show the results by series types. Even Statsguru might not provide that. What I intend to do is to weight the individual player performances in series with various relevant parameters. It is necessary to recognize where players performed (home or away), how did the performance measure against those of the other bowlers, what were the quality of wickets captured, what was the quality of bowlers, what was the pitch condition, was there a critical series situation et al. That would let us judge performances at their true worth.

The weight basis is the same as has been done in the batting and bowling analyses. The relevant factors considered is given below in summary form. I do not want to repeat the details here.

Batting - Runs scored
1. Where the series was played
2. Series situation
3. Quality of bowling
4. Pitch type
5. Support provided / % of score
Bowling - Wickets captured 1. Where the series was played 2. Series situation 3. Quality of wickets captured 4. Pitch type 5. Bowler's average vs Teams' series average
The key to the all-rounder analysis is in setting the criteria for selection as an all-round performance. Independent bars have to be set up for batting and bowling. These bars cannot be too high: Very few performances would come in. These bars cannot be too close to the ground: Batsmen who can bowl and bowlers who can bat would sneak in. I have arrived at the following criteria after a few trials.
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