I first came across the name of Mr Kaprekar in the mid-70s, when the door of a room in a remote corner of our hostel had a chalked handwritten inscription of Mr D R Kaprekar. My classmates briefly mentioned that it was occupied by an elderly gentleman who was a guest of our Mathematics department.
It is interesting that a mathematics teacher in a small town came up with various sets of numbers, long before computers or calculators existed. He lived in obscurity until Martin Gardner discovered his work and wrote about it in the “Scientific American” in the 1975. Today his work is better known.
In particular, he is known for the Kaprekar constant 6174 (see explanation in above link)
Then there are the Kaprekar numbers.
The Devlali numbers or self numbers (as he was living in Devlali, near Nasik).
The Harshad numbers (based on a Sanskrit word, not Mehtaji).
The Demlo numbers.
Devlali also got itself into the English language because it was a rest camp for British soldiers before they returned home. Thus the phrase “Gone doolally” meant someone who had a mental problem.
As for Demlo, it appears to be a contraction of Dombivili (which meets the stipulation of being 30 miles from Bombay VT).
To keep things simple, these are the teams and their respective groups
Qualifier A1: probably Sri Lanka
Qualifier B2: Bangladesh
Qualifier A2: probably Ireland
Qualifier B1: Scotland
Papua New Guinea
Predicting the winners of the qualifiers is fairly easy, with the help of the latest T20I ranking tables:
T20I cricket being what it is, this ranking table is not likely to predict the winner. But we can be reasonably sure that the last 4 will be England, India, Pakistan and South Africa (not New Zealand as they have India and Pakistan in the same group).
If you take this ranking table very seriously, the results will be
We now look at the other side of the coin-those who have failed to make enough hundreds to match their fifties. And of course we have to consider those who made enough fifties and runs but never a century.
First we look at those who scored at least one century and had the lowest conversion rate:
Headed by the all-rounders Goddard, Jadeja and Noble. Most in this list are not in the side primarily for their batting. But we do have specialist batsmen in Bavuma, Nourse, Wadekar, Contractor, Ramiz Raja and others.
Jadeja, Wadekar, Contractor and Prabhakar represent India.
Current players include Jadeja, Bavuma, Broad and Buttler.
Those who failed to make any century after numerous attempts are covered here:
The ability to convert fifties into hundreds is useful in Tests, even more than converting centuries into double centuries. The “conversion rate” has not received much attention in statistical studies in the past.
If your career includes a score between 50 and 99 but no century, your conversion rate is 0%
If you have no score between 50 and 99 but one or more centuries, your conversion rate is 100%
Most Test batsmen will fall between these extremes (unless they never crossed 50).
Take Virat Kohli. He has 27 Test innings between 50 and 99. Oddly enough he also has 27 centuries.
So he has crossed 50 a total of 27+27 = 54 times, and has gone past 100 on 27 occasions. This is a conversion rate of (27/54)*100 = 50%.
One more example: Sachin Tendulkar has 68 innings between 50 and 99, besides 51 centuries.
So he crossed 50 a total of 68 + 51 = 119 times. His conversion rate is (51/119)*100 is 42.86%
Similarly, we can find Don Bradman’s conversion rate to be (29/(29+13)*100 = 69.05%
Let us now look at studies of all Test players up to Sep 30, 2021.
There are 56 players who have a 100% conversion rate, who have no score between 50-99 plus one or more centuries. The first few are:
RS Bopara is the only one with 3 centuries without any score between 50 and 99.
The next 5 have made 2 centuries, including Wasti who made both his centuries in the same Test.
And then there are 50 others who crossed 50 only once but went on to make a century, ranging from A Lyth to Yasir Shah. KK Nair has a triple century, while D Lloyd and B Kuruppu have doubles. There are a surprisingly high number of players who scored a century on debut and failed to cross 50 afterwards.
For a short time, Fawad Alam had made 4 centuries without a fifty. The record is by GA Headley of long ago, who made 6 centuries before making a fifty.
After crossing the 56 who have a 100% conversion rate with the help of one century, we get:
(This has a cutoff of 55%)
Fawad Alam leads with 5/6 or 83.33%, followed by JF Reid (of the 1980s) and Azhar Mahmood with 75%.
Current players here are Fawad Alam, Najmul Hussain Shanto, Abid Ali and SC Williams (Zimbabwe).
From India there is only S Dhawan and VG Kambli.
If you take those who have scored 10 or more centuries, only Bradman (69.05%) and Headley (66.67) have crossed 55%. The next few are Walcott (51.72), Azharuddin (51.16) and MJ Clarke (50.91)
Here is a complete list of those who scored 10 or more centuries at a conversion rate of 45% or more:
The only current players in this elite group are Kohli and SPD Smith (and M Hafeez from the recent past).
India is represented by Azharuddin, Kohli, Shastri (!) and Umrigar.
(Note that Hayden’s century and other scores in the ICC XI v Aus Test in 2005 have not been counted).
Let us look more closely at current players with 10+ centuries and conversion rates 35+
V Kohli 50.00
SPD Smith 46.55
DA Warner 44.44
Mominul Haque 44.00
D Elgar 43.33
KS Williamson 42.11
CA Pujara 36.73
LD Chandimal 35.48
TWM Latham 35.48
Azhar Ali 35.29
R Taylor 35.19
Note the absence of JE Root (31.51), BA Stokes (29.41), AM Rahane (33.33) and F du Plessis (32.26)
Certainly this last list has some surprises which contradict common perceptions about the heavy scorers of today.
In Part 2, we will look at the other end of the scale-those with the lowest conversion rates.
After looking at those who scored the highest lone century, we look at those who took only one five-for and see who did the best.
This includes all 7wi and better.
The highest here is by Lance Klusener, who was making his debut. He never scored a five-for in Tests again, but did do so in ODIs. Second is SJ Snooke who had a shorter career. But he did take a ten-for, unlike Klusener. Then there is JJ Krejza who took 12 wickets on debut (which his team lost) and played only one more Test
There are many who do better on debut than in their later matches. Here we have Klusener, Krejza, Kendall (in the very first Test), Zahid, de Lange, Ashley (only one innings in his career).
Among current players there is only KC Brathwaite who bowled occasionally until his “breakthrough”.
From India, there are Agarkar (6/41), Ramchand (6/49) ,Abid Ali (6/55 on debut) and Shinde (6/91).
Now we consider the best innings figures by those who took only one four-for.
The first few names also appear in the first list: Emmett, de Lange, Hornibrook, Ashley and Brathwaite.
Debutants include Ashley (only test and innings), Kirtley and Coldwell.
Current players include Brathwaite and ML Cummings (not Pat !).
From India there are Agarkar, Ramchand and Shinde.
Agarkar’s only score above 50 was a century, along with his only 4+wi was a 6-for.
There are players who score several Test centuries. And some score only one. Here we look at the highest innings by players who scored exactly one century:
Led by KK Nair’s 303*, and followed by RE Foster’s 287 on debut and Z Crawley’s recent 267.
Apart from Foster, Mayers, Kuruppu and Conway have the highest lone centuries on debut.
From India, KK Nair is accompanied by ML Apte and NR Mongia.
What about those who made only one score above fifty?
This list is still headed by KK Nair, with the next being D Lloyd and B Kuruppu.. They all made full use of their opportunities once they crossed fifty.
Nair’s second highest score is only 26. For Lloyd it is 49 and for Kuruppu 46. Lloyd started off with 46 and 214* against India’s weak 1974 team, and thus temporarily had a Test average of 260.00 which dipped sharply during the Ashes tour later that year.
There are a few debutants here: Kuruppu, Bannerman, SC Griffith and Hartigan among others.
In recent years there have been Nair, Patterson and Yasir Shah.
From India, Nair is accompanied by A Ratra, RH Shodhan, Agarkar and Pataudi (Sr)
As we will see, Agarkar made only one score above fifty (and made it a century) and only one four-for (which was a 6-for).
Note that the above list includes relatively few lower-order batters. Most are recognized batsmen who got few opportunities. (Ganteaume’s single Test and a few others who played less than 5 Tests.)
Afterthought: KK Nair may well have the record for the highest ratio of highest and second-highest scores: 303/26 = 11.65
Apart from Nair, Sobers (365*) and RB Simpson (311) made their first century a triple. Unlike him, they scored many more centuries after that.
The fourth-innings chase is often regarded as the ultimate challenge for a batter. Let us see who have done the best in successful chases.
Most runs: (400+):
GC Smith is the clear leader here. He also has the most centuries (4) and most 50+ scores (10, followed by contemporaries Hayden, Ponting and JL Langer with 7). Also note CG Greenidge’s 214*.
Tendulkar, Dravid and Sehwag have the most runs for India.
Williamson and Karunaratne are the only current players here, with Amla, Cook and Younis from recent years.
Bradman is not here (but when he batted, a fourth innings chase was often not needed by Australia).
Highest scores in these cases (115 and above):
A total of 76 centuries have been scored here.
Only two double centuries, with KR Mayers scoring his on debut. The next highest in recent years was 153* by K Perera in 2019. There are Morris and Bradman in the same Test at Leeds in 1948, which was the only successful 400+ chase until India followed in 1976. (Years later, MA Butcher emulated Bradman’s 173* at Leeds).
The highest from India are not in the above list.
Viswanath (112) and Gavaskar (102) made their centuries in the same match in 1976, while Tendulkar and Laxman have made 103*.
Highest averages (Minimum 15 innings):
These 21 entries are the only ones with 15 or more innings. GC Smith leads here as well, with Ponting close behind.
From the recent past there are Cook and Amla. Tendulkar, Dravid and Sehwag represent India.
Kisrsten and Dravid are among those who did not score a century, although Hutton has a 98*.
We will take up bowling in 4th-innings wins in the next part.