Tag Archives: Statistics

Indian Test Team Rises to Highest Ever Rating

UPDATE: On 14th August 2017, after Test #2269, India defeated Sri Lanka by an innings and 171 runs to reach its highest ever team rating of 60.37 – past the very difficult barrier of 60 points. 

On 12th December 2016,  after Test # 2239,  India defeated England by an innings and 36 runs to reach its highest ever team rating of 57.47.

Sachin Tendulkar retired in Nov 2013 after a hastily arranged 2 test farewell series against West Indies. India’s Team Rating was 55.98 after that test, the highest since Bangladesh joined as the 10th nation to play test cricket. The next test was a thrilling draw against South Africa at Johannesburg. Chasing a target of 458 on a tricky pitch, South Africa came within eight runs of breaking the world record, thanks to du Plessis and de Villiers. It was a good performance by India setting a stiff target of over 450 runs in an away match. The team rating value dropped slightly after this match to 55.71. India was ranked 2nd behind South Africa at the time. In the next year and half, team performances dipped. India was ranked 7th, with 42.37 points, after losing the opening test at Galle against Sri Lanka in August 2015. This was the last test featuring Harbhajan Singh.

India has played 17 more test matches in 5 test series since that loss. Recovering after that early loss, India won next 2 matches to beat Sri Lanka 2-1. South Africa visited in Nov-Dec 2015 for a 4 test series. Excluding a rain affected draw, India won remaining 3 matches with 108, 124 and 337 runs. A tour to Carribean, after a prolonged gap, in Jul-Aug 2016 for a 4 test series followed. India won 1st and 3rd test easily and the other two were drawn. This was the time when India, England, Australia and Pakistan were neck to neck in team ratings. England, Australia and India exchanged a place at the top of the rankings within a space of 15 days. India climbed upto 54.39 points after a win in 3rd test to reach #1 spot.

Black Caps toured for a 3-test series in Oct-Nov 2016. Batting first in all 3 tests, India registered big wins by 197, 178 & 321 runs. There was a further marginal improvement to 55.41 points mainly due to size of victory since India was expected to beat New Zealand at home. Team Ratings were fairly close to all time high but a tough opponent was waiting.

India not only lost to England in earlier two away visits but also lost a home series despite winning first. Not unexpectedly, honours went to England at Rajkot in the opening test. England was ahead 59-34 in the drawn test. This was the first reversal for Indian Team since the lost test against Sri Lanka. After that loss, India had won 10 test matches and enjoyed the upper hand in 3 draws. A tense finish was on the cards in this 5 test series.

3 comprehensive wins on the trot followed. In an anti-climax the series has been decided with 5th test yet to play. This is the 5th consecutive series win. India is unbeaten for 17 test matches with 13 wins. This is the best streak ever especially when we account for the margin separating two teams. India has now reached its highest ever team rating of 57.47 (since Jan 2002).

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Axis on right hand side shows the steady increase from about 42 points to recent rise reaching nearly 58. Each of the 13 wins took India a step higher with occasional breaks applied after each of the 4 draws.

Cricket is a team game and this is a fantastic team. 18 test matches are covered in this post. Only 2 players – Ashwin and Kohli – have featured in all these tests. 21 other players were involved for anything between 1 to 17 tests. 7-8 or even more players start regularly when a team is on a streak. It is evident that there were hardly any passengers in this squad. The bench strength ensured that replacement openers, wicket keeper and bowlers operated at more or less the same level as first choice players.

6 players are featured in above chart as the top contributors for India. Without any doubt, R Ashwin is the most valuable player for India. Mukul Kesavan in The Telegraph:

There is an immortal in the making in the Indian Test side and it isn’t Virat Kohli. If Ravichandran Ashwin was to retire tomorrow, he would, arguably, be the best all-rounder in India’s Test history. Better than Vinoo Mankad, better even than Kapil Dev. We think of Ashwin as a young man making his way in the world. He isn’t. He is 30 years old and he has played 41 Test matches. He isn’t a veteran yet, but he’s an experienced player in his cricketing prime.

In these 18 tests, Ashwin has bagged an astonishing 123 wickets while scoring 740 runs. Every finished test is assigned a total of 100 points to be shared by 22 players. Ashwin averages over 11 points in each test. He was not only the best bowler in 8 of those 18 tests, he once managed to be the best batsman too. On the opening day of 3rd test against West Indies, he joined Rahane as #6 with India struggling at 4-87. It soon became 5-126 when wicket keeper Saha joined Ashwin. Both of them scored centuries while adding over 200 runs for the 6th wicket. India eventually won that test by 237 runs.

In the same period Herath has bagged 88 wickets in 15 matches also scoring 424 runs averaging 8.8 points. Jadeja, despite playing only 12 matches, is 3rd in that list with 56 wickets and 433 runs. Moeen Ali featured in 21 tests scoring 1053 runs and taking 55 tests. All-rounders tend to lead such lists. Kohli, a specialist batsman, scoring 1633 runs in 18 tests is ahead of Bairsow(1713) and Root(1784) who played 3 more tests. Broad, Stokes and Cook complete the top 11. Barring Herath, this list features players from India and England only. To the credit of this Indian Team, they have reached an all time high by beating an in-form team comprehensively.

Ashwin, Jadeja and Kohli are the architects with able support from Pujara, Rahane and Murli Vijay who played in 15, 17 & 14 tests respectively. 4 specialist batsmen followed by Ashwin and Saha have done the job for India while batting. Ashwin and Jadeja were primarily supported by Mishra/Shami and Umesh Yadav to form the bowling unit.One opening spot and fitness of pace bowlers are the causes of concern.

All 23 players who have played for India appear in the next illustration. Those who scored the most points over 18 tests appear at the top. Plenty of players did not get a chance to play in all the tests.Some may have missed tests due to fitness, others for lack of form and a few warmed the bench for a regular player. Amit Mishra will feel bad for being left out despite solid performances. Bhuvaneshwar Kumar and Jayant Yadav have stepped up when they got a chance.

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Above illustration does not clearly show relative peaks attained by each player. It can be seen as a visual aid to composition of Indian team. Harbhajan made a solitary appearance in the lost test against Sri Lanka. Ojha was a replacement for Saha in Sri Lanka. Recently this role went to recalled Parthiv Patel who has done well as keeper/batsman. Gambhir was also recalled briefly for the opening slot. Nair and Rahul have filled in for specialist batsmen. Aaron was a replacement bowler in the Caribbean. Binny was dropped. Ishant and Rohit Sharma were given extended runs. Dhawan has partnered Vijay most often. Umesh Yadav, Bhuvaneshwar Kumar and Mohammad Shami have shouldered responsibility in the pace department. Disappointment for Mishra as Jayant appears to replace him with an added advantage of wonderful footwork. His 100 from #9 position was vital in winning the most recent test.

Finally, we take a look at percentage contribution. Let us first understand what is meant by Par value. Every completed match is assigned 100 points. Par value for each team is 50 points or half the total points from incomplete matches. These 50 points per team are then further divided amongst 11 players. Thus par value for each player is about 4.5 points. Par for the opponents is 50 points but India won most of the matches comprehensively reducing the actual value to only 36.5%. This was the key to India’s assent to all time high ratings.

perc

6 players are featured in above chart. Only 2 of these played in all 18 matches. Hence rest of Indian team varies between 5 and 8 players. Ashwin alone has secured 1/8th of total available points vis-a-vis a par value of 1/22 that is nearly 3 times the expected value. Jadeja is the surprise in second position. He earned 7.3% of gross points despite appearing in only 12 of the 18 matches.

Kohli is the in-form batsman. In 2016, he has outperformed everyone else in all formats – not limited to test cricket alone. Pujara and Rahane are hovering just around the par values followed by Vijay who is a little under. Points assigned by Relative Value model are a zero-sum game. Absolute values such as 100s, 200s or 5-for, 10-for do not matter as much as the context of the game. If 3 players score over 100 runs, then the value of the tallest score will not be as high in the zero-sum world. Ashwin is on a miracle run. Assuming his extra points are counting towards the winning margin, the rest of the team is doing admirably well by performing around near-par or just above. Pujara and Rahane as the 4th and 5th player have done an excellent job to return figures just above par. Vijay appears slightly under-par but his figures must be read in the context of 5 other players ahead of him.

How the rest of the team performed is the most impressive aspect revealed by this chart. Collectively they have risen above the average. This macro figure can be understood by taking into account all the tricky situations which the team found itself in and how different players shouldered the responsibility to carry the team to safety. Cricket is a team game and this team has done an admirable job in winning 5 back-to-back series. We have to keep in mind that the best this team has achieved for India is far from the best. Australian team of 2003 is the gold standard who reached an astounding 68 points out of 100. South Africa around the same time scaled over 62 points despite playing with the most dominant side ever. England went one better with 63 points in 2012. Sri Lanka has never reached the top spot but managed to reach over 60 points in 2007. This Indian team should set itself new targets to first reach 60 points out of 100.

Is Kohli better than Tendulkar? The simple answer to that question is Yes – in T20 cricket. Kohli is not only better than Tendulkar, he is the best ever batsman. In ODIs, Tendulkar is second behind Viv Richards. Kohli is a top-20 batsman in the all time ODI list. To rise in relative terms, he has to outperform as a batsman even more significantly because runs have become cheaper. Tendulkar is merely a very good test match batsman and should not be the yardstick to judge upcoming talent. In any case, I recently compiled the Fantasy Indian XI where Kohli failed to make the cut. He needs to carry his current form into a sustained run before we can include him as a first choice middle order batsman.

Absolute numbers are important but these have a limited usage. Every tall score requires above average support from the team. In Relative Value terms, a lower score may fetch more points when you run out of partners. Looking for individual brilliance in a team game is the key attraction of this sport. We still have to remember that a player will earn more points for the same contribution if the team fares better. A good batting knock needs support from the bowling unit to translate it into a win. Being part of a winning unit helps a player raise his relative score. Good collective performances, not individual brilliance in a mediocre pool, helps the team to earn more points. Each one has to play well for the team to excel. An excellent team will help individuals earn more relative points. It is a virtuous cycle where better individual performances result into greater team success which in turn earns more value for the individual.

If this Indian team continues its glorious run, the individual members will start replacing the members of Fantasy XI selected soon after 500th test. Here is  wishing them all great success!


UPDATE:

India won the 3 test series against Sri Lanka in Aug 2017 to break the 60-point barrier. This feat was already achieved by Australia, South Africa, Sri Lanka and England indicating a sustained period of dominance over its rivals.

Since the last update, India managed to beat England by an innings in the last test of the series. After that India hosted Bangladesh for a solitary test. Despite scoring 687/6d and restricting the tigers to 388, follow on was not imposed. India won the test by 208 runs but the margin of victory was diminished. India reached a career high rating of 59.12 after that test.

Continuing the upward run was going to be difficult in the 4-test home series against Australia. Winnin in itself is not sufficient – the margin of victory must remain high to add more rating points when the base is already close to 60. Australia began the series with a comprehensive 333 run win. India lost 2.22 rating points due to the unexpected home loss against the run of successive wins.

India won the next test, drew the third and won by 8 wickets in the last one to marginally improve the rating points by 11 basis points.

Playing away after a long home season, India faced Sri Lanka. 2 years earlier, India lost the first test at Galle descending to a low value of 42.57. In the opening test, India earned a sizeable first innings lead of over 300 runs but chose to bat again. A comprehensive win by 304 runs was measured as a roughly 65-35 win. An innings defeat is worth at least 75 points but often many teams like to give the bowlers some break. Indian team gained a few tens of basis points after this comprehensive win.

Yet crossing the barrier of 60 appeared remote. The margins of victory had to be even more comprehensive. India scored over 600 runs in the second test and bundled Sri Lanka for 183. This time follow-on was imposed. India won the test by an innings and 53 runs after Sri Lanka batted much better in the second innings. This win was rated around 76-24 taking team rating points to a round 59.

In the last test, India scored 487 runs batting first. Sri Lanka collapsed twice for 135 and 181 handing India a victory by an innings and 171 runs. This was a massive 82-18 win. For the first time, India went past the 60-point barrier with 60.37 points.

The three charts explained earlier in this post regenerated below:

Rating

KL Rahul appears in this updated chart who now outperforms the injured Murali Vijay in the combined performances over 2 years.

Perc

Jadeja has contributed more than Ashwin in recent tests. Similarly Pujara was better with the bat compared to Kohli.

Team

And finally, the team composition chart shows that Hardik Pandya had a very good debut series. Also Shikhar Dhawan did well as a returning opener in place of Murali Vijay.

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India XI

India defeated New Zealand by 197 runs in Kanpur while playing its 500th test match. To mark this occasion BCCI asked fans to vote for their all-time dream team. The results were announced during the closing stages of the win on 26 Sep:

The above team includes 11 who justify their selection through weight of their achievements. Only 12th man Yuvraj Singh is out of place in a TEST team because he enjoyed his success in limited overs format. Sunil Gavaskar is the oldest to play in this team who made his debut in 1971, about 40 years after India started playing Test Cricket. There could be a recall bias in this selection and hence another attempt to select India’s Best Test XI based on objective data. The numbers used are updated at the end of second test between India and New Zealand at Eden Gardens celebrating India’s 250th test at home.

Here we first set a few guidelines on selection, then identify multiple players for each role and eventually get to the toughest part of elimination. Elimination over selection highlights achievements of those that failed to make the final cut. Those who are eliminated are deserving and we get a chance to talk about their accomplishments too.

Till 3rd October 2016, India has played 250 tests at home and 251 away. The first ever test was a 3 day match against England in June 1932 played at Lord’s. First home test was played 18 months later at Gymkhana Ground in Mumbai against the same team in a 4-day affair. India lost both matches. India’s first encounter against a non-English side was a tour down under, soon after gaining independence, in late 1947 for a 5 test series. Don Bradman made merry with 715 runs in 4-0 series win supported by Lindsay Hassett who scored 332 runs. Bowling honours went to Johnston (16-182) and Lindwall (18-304). Top contributors for India were Dattu Phadkar (314 runs, 8-254), Vijay Hazare (429 runs, 7-382) and Vinoo Mankad (306 runs, 12-630).

The only drawn test of the series was played at Sydney where less than 10 hours of cricket was possible over 6 days. Phadkar, who did not play the first test, contributed on debut with both bat and ball. He was part of a 70 run stand after India lost 6 wickets for 95 to reach a team total of 188. He claimed 3-14 with the ball as Australia was bundled for 107. The match is now remembered widely for the run out of Bill Brown by Vinoo Mankad when non-striker Brown moved down the pitch and Mankad whipped off the bails. In an earlier tour match, Mankad warned Brown first and then ran him out. There was no warning during the test and this form of dismissal which is completely legal yet controversial continues to be called ‘Mankading’.

Next year India hosted West Indies for another 5 match series losing it 1-0. Subsequent 5 match home series against England in 1951-52 was drawn 1-1 where India recorded first test win at Chennai inflicting an innings defeat. India hosted Pakistan in 1952. The 5 match series ended 2-1 to hand first series win for India. New Zealand visited in 1955 to lose 2-0. Vinoo Mankad was the top performer scoring 526 runs and picking 12 wickets. Subhash Gupte was the wrecker-in-chief who took 34 wickets. He earlier took 21 wickets in a drawn series against Pakistan.

India’s first away series win was against West Indies in 1971 with Ajit Wadekar at helm. Sunil Gavaskar made his debut scoring 774 runs. The established quartet of Bedi, Chandrasekhar, Prasanna & Venkataraghavan then carried that form further to record a home and away series win against England.

In 1986, Kapil Dev led India to another away series win against England. Dilip Vengsarkar was in great form supported by Mohinder Amarnath.

Sachin Tendulkar and Anil Kumble were individually brilliant in 1990s. The team enjoyed sustained success in 2000s with Rahul Dravid, Sourav Ganguly, Virender Sehwag, VVS Laxman and Harbhajan Singh peaking together. Dhoni took over from Ganguly with the same core and Zaheer Khan as the prominent pace bowler to become the most successful Indian captain.

This brief history gives us an idea about the names likely to appear in the selectorial basket. Some of the players will select themselves. There will be competition for other spots. We need to define some parameters to assess players across era for a fairer comparison.

285 players have represented India in test matches. Senior Pataudi played for England before representing India. After the partition, Abdul Hafeez Kardar, Gul Mohammad and Amir Elahi played for Pakistan too. Virender Sehwag and Rahul Dravid played the one-off super test against Australia as part of the ICC team.

The first step is to find a shorter list of players who have played sufficient tests representing India. 48 players earned a solitary cap. Shute Banerjee and Mantu Banerjee both took 5 wickets in the only test played. Incidentally both took 1 and 4 wickets in the two innings bowled. 5 wickets per match is a good return but one swallow does not a summer make. Hence we will not consider 17% players who did not get another chance to play second test.

Another 119 played between 2 to 10 tests. Vijay Merchant and CK Nayudu are notable in this group. CK led India in the inaugural test. A player still remembered by his initials, he was the first Indian cricketer to endorse a brand as far back as 1941. A stroke maker known for his sixes – he once hit a six crossing the River Rea which was the boundary between Warwickshire and Worcestershire while batting in a tour match at Edgbaston. Despite an exceptional first class span between 1916 and 1964, he featured in only 7 test matches.

Vijay Merchant with a first class average of 71 finds a place between White George Headley and Black Don Bradman but he too played in only 10 test matches, all against England, over a period of 18 years. He recorded his highest test score at the age of 40 in his last appearance. His test match batting averages were covered in this post to understand G and µ, the preferred averages of this blogspace.  As a Test selector, he was responsible in opting for Ajit Wadekar as captain of India over Mansur Ali Khan Pataudi. His radio show on Sundays was keenly followed by cricket fans. Merchant was a great philanthropist working for the blind and the handicapped. He will be remembered forever for his achievements on and off the field but his short test career makes it difficult to objectively judge his cricketing achievements vis-a-vis others. A further 42% players, including these two, will not be considered for lack of sufficient data.

Vinod Kambli, another flashy stroke player, was a precocious talent. In a school match he put on an unbroken 644 run partnership with Sachin Tendulkar. He scored two centuries and two back-to-back double hundreds in his first 7 tests reaching the milestone of 1000 runs in 14 innings – a feat bettered only by Sutcliffe, Weekes, Bradman and Harvey. Fantastic against spinners at home, he was found out against the short ball in a less than favourable away career. He signed off with 1084 runs in 17 tests.

Narendra Hirwani played 17 tests too. His career started off even more spectacularly. Against the mighty West Indies, albeit at the tailormade Chepauk, he claimed 16 wickets for 136 on debut breaking the record of Bob Massie. He followed it by taking 8 and 7 wickets in next two tests. He discovered that away games were not played on his favourite surface and the wickets dried. After 31 wickets in first 3 tests, he added 35 more in remaining 14. His career ended with the arrival of Anil Kumble.

Other than Kambli and Hirwani, 30 more players played between 11 and 20 tests. Very few manage to start on a scintillating note but it is evident that sustaining an above average performance for a period of 20 tests is very difficult.  No player with career spanning 20 or fewer tests will be considered for selection.

27 more players in the next slab of 21 to 30 tests. This list includes active players like Dhawan and Rahane who may eventually enjoy a very long career. Lala Amarnath and Vijay Hazare are notable performers from an era when test matches were infrequent. Likely that each one would have played far more tests had they plied their trade when the rewards became better? Not easy to discard these names but in the absence of objective data for fair comparison, it is best to leave them out too. Salim Durani, Rusi Surti, Syed Abid Ali, Roger Binny, Dilip Sardesai, Eknath Solkar and Sandeep Patil also served India with distinction before the 1990s. Pragyan Ojha, Venkatpathy Raju and Rajesh Chauhan have decent home record as slow bowlers. India does not include 3 spinners away from subcontinent where faster bowlers are preferred. Sreesanth & Ajit Agarkar bowled faster and played their part in scripting rare away wins. None of these bowlers appeared in more than 30 tests though.

Some players were outstanding but did not play enough tests for lack of opportunities. Some started on a brilliant note but could not sustain in alien conditions. And then we have the case of Irfan Pathan. He made his debut at 19 in 2003. A talented left arm bowler with brisk pace AND a sensible batsman who could bail his team out – he seemed like the allrounder India missed. Alas… Injuries played their part, his pace dropped significantly and eventually he did not reach the heights expected. Irfan played only 29 tests! So we can make it a condition that maintaining fitness over a sufficient period is a key criterion for selection.

It means 226 out of 285 players are ineligble because they participated in 30 or fewer tests. On the other hand 59 is still a very high number to study individual careers in detail. So the second step is to pool candidates for specific roles – Openers, Middle order batsmen, Allrounders, Wicketkeeper, Captain, pace bowlers and slow bowlers (legbreak, offbreak and orthodox). There will be additional quantitative criterion to ensure that those with very long careers do not trump others by virtue of gross figures alone.

Let us commence with allrounders. Who qualifies as an allrounder? An allrounder could be a bits and pieces player who can bat a little and bowl a little. A quality allrounder joins the team as a specialist batsman or a specialist bowler who also provides decent support in bowling or batting. A remarkable allrounder is one who can win a match with both his bat and the ball. A unicorn allrounder is one who does this match after match. Here we will consider any player with an average of more than 2 batting points AND 2 bowling points. For every completed test match, Relative Value Model assigns points out of 100 to each player. Fewer points are allocated for draws depending on the progress towards result. These are normalised values to ensure comparison between runs scored in a high scoring match with wickets taken in a low scoring one.

Name Tests Runs Wickets Avg Bat Pts Avg Bowl Pts MVP (Win)
R Ashwin 38 1510 207 2.39 6.63 8
MH Mankad 44 2109 162 2.88 4.45 5
Kapil Dev 131 5248 434 2.06 3.81 3
M Prabhakar 39 1600 96 2.28 2.88 1
RJ Shastri 80 3830 151 2.49 2.68 1
DG Phadkar 31 1229 62 2.03 2.54 0

MVP (Win) indicates the number of tests where the team won when player was the top performer – sort of total Man of the Match awards in an Indian test win.

Phadkar bowled right-arm offbreak as well as Fast-Medium. Kapil Dev & Manoj Prabhakar were pace bowlers and Ashwin, Shastri and Mankad are slow. Vinoo Mankad was an opener. Ravi Shastri selected for his bowling started as a #11. With time he eventually moved up the order to become an opener scoring a double hundred in Australia but then he was used more as a stock bowler. It shows that roles change over a long period. Career figures need not capture the essence of any player. Besides Phadkar played just enough to warrant selection while Kapil Dev played in a 100 more tests. For a fairer comparison, we now look at the peak performance measured over 30 tests.

Name Avg Total Pts Start Test Year Started
R Ashwin 9.47 6 2012
Vinoo Mankad 8.72 10 1948
Kapil Dev 7.13 13 1979
Ravi Shastri 6.17 20 1983
Manoj Prabhakar 5.84 3 1989
Dattu Phadkar 4.71 1 1947

Ashwin is in a remarkable form. In fact his current streak makes it to the top 10 ever recorded. Mankad got in his stride by 10th test and hung his boots soon after the peak. Kapil Dev managed to put in 3 different streaks due to a lengthy career. His best streak was fairly early in his career listed above at 7.13 starting in 1979. Second one started in 1985 (averaging 6.01) and last one in 1989 (avg 5.14). These three players will figure in our final selection. Eventually we will select the best allrounders that offer the right team balance in the company of our chosen specialists.

Next we need a wicketkeeper. Before Adam Gilchrist this was a specialist fielding position and keepers were not judged by their ability to bat. These days keeper is someone who can bat aggressively or defend based on match situation as a link between middle order and the tail. Now it is rare to see a wicketkeeper bat below a specialist bowler. There is no quantitative measure that captures chances created (through quick stumpings or difficult catches), chances missed, runs saved or conceded etc. Wicketkeeping skills are judged subjectively and this is a predominantly objective exercise. Hence we will choose one or two wicketkeepers based on available data such as dismissals per test and batting averages.

Name Tests Runs Catches Stumpings Avg Bat Pts MVP (Win)
MS Dhoni 90 4876 256 38 2.85 1
Kiran More 49 1285 110 20 1.50 0
Nayan Mongia 44 1442 99 8 1.94 1
Syed Kirmani 88 2759 160 38 1.70 0
Farokh Engineer 46 2611 66 16 3.06 0

Farokh Engineer and Mongia batted in middle order. Kirmani and More were specialist keepers batting in late order. Dhoni is the modern keeper-batsman typically playing #7 role behind specialist batsmen. Engineer was the best batsman but he has the worst rate of under 2 dismissals per match. This is not a reliable measure though as the dismissals depend on the bowling standard of the team too. Dhoni is the only keeper averaging over 3 dismissals per test and he is second in batting behind Farokh. There should not be any doubt in choosing Dhoni as the sole candidate once we disregard the achievements of Kirmani and More on the post-Gilchrist standards.

Now we move to another subjective role – that of a Captain. It is possible to look at the number of times a player led his team or the win percentage but that does not reveal how weak or strong the team was and how the skills of the captain lifted the performance of his team. Mike Brearley was a skilled captain but an average batsman. The circumstances under which he took over from Ian Botham to stage a remarkable Ashes recovery marks him as an exception – not a yardstick. Typically the best or the seniormost willing player becomes the captain. Two Indian captains are worth a mention though. Ajit Wadekar won only 4 matches for India but those included important series wins including captaincy mind games played against the strong West Indian outfit led by Sobers. Sourav Ganguly too stands tall for improving the record of an inherited team. Yet none of these attributes can be quantified. So we will take a look at those who led India more than 30 times along with their win percentage.

Name Matches Won Win %
MS Dhoni 60 27 45.00
Sourav Ganguly 49 21 42.85
M Azharuddin 47 14 29.78
Sunil Gavaskar 47 9 19.14
MAK Pataudi 40 9 22.50
Kapil Dev 34 4 11.76

Dhoni and Ganguly have the best record. The stability of their reign and the success rate means only these two will be evaluated in final selection to lead India.

Now we move to the bowling unit. Initially we will separate slow bowlers from the fast ones. Back in 1932 at Lord’s, India opened bowling with fast bowlers Mohammad Nissar and Amar Singh. The backup was offered by medium pace as quality spinners were not easy to find. This changed with the arrival of Vinoo Mankad and until 1970s spinners were the best bowlers with a stock bowler employed to take the shine off the new ball. Dattu Phadkar and Karsan Ghavri were the exceptions to this tradition until Kapil Dev stamped his authority as the strike bowler. Srinath and Zaheer Khan carried his tradition forward. Here we look at the record of all medium pacers with at least 50 wickets.

Name Tests Wickets Avg S/R Avg Bowl Pts MVP (Win)
Zaheer Khan 92 311 32.95 60.40 3.90 2
Kapil Dev 131 434 29.65 63.92 3.81 3
J Srinath 67 236 30.49 64.00 3.74 2
Ishant Sharma 72 209 36.72 66.62 3.54 1
Karsan Ghavri 39 109 33.54 64.55 3.20 0
Venkatesh Prasad 33 96 35.00 73.34 3.09 0
Manoj Prabhakar 39 96 37.30 77.86 2.88 1
Dattu Phadkar 31 62 36.85 96.68 2.54 0
Madan Lal 39 71 40.08 84.46 2.24 0

Unlike batting average which does not treat not out situations properly, bowling average is a very good indicator of the quality of a bowler. Kapil Dev leads in longevity (no injuries), number of wickets and an average below 30 with only Zaheer Khan ahead in strike rate. Average Bowling Points is a propreitary measure that normalises bowling performances across test matches. Zaheer leads on this metric narrowly edging out Kapil. Srinath is not far behind these two. These 3 have also won matches for India as MVP multiple times and are undoubtedly the best candidates. Let us also look at their peak performances too.

Name Avg Total Pts Start Test Year Started
Zaheer Khan 5.06 47 2007
Kapil Dev 4.87 10 1979
J Srinath 4.70 22 1996
Ishant Sharma 4.31 6 2008
Kapil Dev 4.22 47 1983
Kapil Dev 3.80 88 1987
Zaheer Khan 3.55 16 2002
Manoj Prabhakar 3.52 3 1989
Karsan Ghavri 3.35 7 1977
Ishant Sharma 3.21 42 2011
Venkatesh Prasad 2.96 1 1996
Dattu Phadkar 2.62 1 1947
Madan Lal 2.55 3 1974

The same three appear at the top when we evaluate them for peak performance over 30 tests. Zaheer Khan started slowly at the beginning of his career but peaked after 2007. On a subjective note, his contribution goes beyond his bowling efforts as he nurtured his pace partners once he matured into his role. Kapil gave his best at the start of his career starting from 1979. He declined as a bowler while improving as a batsman but even his second and third best is ahead of other bowlers including early Zaheer. Srinath’s best is not far behind Kapil. So the same trio get our approval for selection in list of probables.

A cliche calls India as the land of snake charmers and spin bowlers. Before Kapil Dev, matches were won by spin bowlers – Vinoo Mankad and Subhash Gupte got a mention here already. Ghulam Ahmed, Chandu Border and Salim Durrani were key performers until the golden era of Bedi, Prasanna, Chandrasekhar and Venkatraghavan. With that rich tradition, it is better to categorise our probables by style. There are four types in spin bowling based on arm used (left or right) and technique (wrist or finger). Since we do not have any chinaman bowlers (left-arm unorthodox) in our probables we will look at the remaining three styles separately. Let us begin with left-arm orthodox bowlers i.e. finger spinners.

Name Tests Wickets Avg S/R Avg Bowl Pts MVP (Win)
Bishan Bedi 67 266 28.71 80.32 4.95 6
Dilip Doshi 33 114 30.72 81.77 4.90 2
Vinoo Mankad 44 162 32.32 90.65 4.45 5
Maninder Singh 35 88 37.36 93.39 3.56 0
Bapu Nadkarni 41 88 29.08 104.15 3.10 0
Ravi Shastri 80 151 40.96 104.31 2.68 1

Bishan Bedi is the obvious choice being the most successful bowler and the best average. Vinoo Mankad is already included as an allrounder. These two have won matches for India most often. Bapu Nadkarni will be remembered for his accurate bowling to stifle a batsman but the under-30 average is primarily for leaking fewer runs when we need wickets to force a win. Peak performance list below confirms Bedi and Mankad as probables.

Name Avg Bowl Pts Start Test Year Started
Bishan Bedi 6.00 28 1972
Vinoo Mankad 5.27 10 1948
Dilip Doshi 5.26 1 1979
Maninder Singh 3.96 6 1983
Ravi Shastri 3.52 20 1983
Bapu Nadkarni 3.36 12 1960

Indian spin quartet is the collective name given to Bedi, Prasanna, Chandrasekhar and Venkatraghavan. All four started against England at Edgbaston in 1967. Collectively they played 231 test matches claiming 853 wickets. This quartet was instrumental in producing many Indian Test victories against West Indies, England, Australia and New Zealand. Yet barring the aforementioned test, one of the off spinners, Prasanna or Venkataraghavan was always left out. A right handed finger spinner is also called an offbreak bowler. We take a look at the leading exponents below:

Name Tests Wickets Avg S/R Avg Bowl Pts MVP (Win)
R Ashwin 38 207 25.14 51.41 6.63 8
Harbhajan Singh 103 417 32.46 68.54 5.23 11
Erapalli Prasanna 49 189 30.38 75.94 4.37 2
Shivlal Yadav 35 102 35.10 81.96 3.65 0
Venkataraghavan 57 156 36.12 95.37 3.54 1

Harbhajan Singh is the second highest wicket taking off-spinner behind Muttiah Muralitharan. He established himself by taking 32 wickets in a memorable series victory against Australia in 2001 when no other Indian bowler scalped more than 3 wickets in a 3 match series. He partnered Kumble regularly while playing on the subcontinental surfaces but was left out when a sole spinner was used abroad. Ashwin has enjoyed tremendous success in the subcontinent racing to 100 wickets in 18th match and later the second fastest to 200 when India defeated New Zealand by 197 runs in Kanpur. His rate of 8 MVPs in 38 tests is exceptional. Only Don Bradman and Lohmann enjoy a better success rate. Let us check the peak 30 year performances to determine whether anyone else got closer to him.

Name Avg Bowl Pts Start Test Year Started
R Ashwin 6.89 6 2012
Harbhajan Singh 6.35 64 2008
Harbhajan Singh 5.95 10 2001
Erapalli Prasanna 5.20 7 1967
Venkataraghavan 4.09 14 1969
Shivlal Yadav 3.79 1 1979

Only Harbhajan has played sufficient tests to have 2 separate 30-test streaks. His best streak in the middle of his career is a little behind Ashwin’s phenomenal start. Ashwin, already selected as allrounder, oins Bedi as the specialist offspinner in our list of probables.

A legspinner is a right arm bowler using wrist spin. Sometimes spin bowling is used interchangeably to mean leg spin bowling. Flight and turn generated by a legspinner is harder to read compared to an offspinner. Skilled bowlers make the ball behave unexpectedly such as a googly which is an offbreak bowled with a legbreak action.

All bowlers get to bat but a specialist batsman does not bowl. So who will be called a specialist bowler? Someone who cannot bat, at all! There are a few bowlers who simply do not score enough runs and typically play as #11 or Jack in the pack. Bhagwat Chandrasekhar belongs to that unique club. He has scored only 167 runs, fewer than the 242 wickets taken. A consistent performer for India, he carried forward the tradition of Charlie Grimmett. There was a time during 1980s when the West Indian pace battery was so successful that pace bowlers were used exclusively. At that time Abdel Qadir kept the tradition of legspin bowling alive. Success enjoyed by Shane Warne and Anil Kumble signal that the concerns about death of spin bowling were greatly exaggerated.

Name Tests Wickets Avg S/R Avg Bowl Pts MVP (Win)
A Kumble 132 619 29.65 65.99 5.78 13
Subhash Gupte 36 149 29.55 75.73 4.45 0
Chandrasekhar 58 242 29.75 65.96 4.29 2
CG Borde 55 52 46.48 109.52 1.07 0

Subhash Gupte was India’s first great spinner known to possess two different googlies. He took 9 wickets at Kanpur against West Indies and the tenth batsman was dropped by the keeper off his bowling. Anil Kumble managed to get all 10 against Pakistan at Delhi when teammates from both side assisted once the rare feat seemed likely and the result of the match was certain. Any one of Kumble, Gupte and Chandra will be an excellent fit in India’s dream XI based on their bowling average but we can see that on relative value measure Anil Kumble contributed more to his team. Both his 30-test streaks are significantly better than the other two too.

Name Avg Bowl Pts Start Test Year Started
Anil Kumble 6.98 65 2001
Anil Kumble 6.03 27 1996
Subhash Gupte 4.90 4 1953
Chandrasekhar 4.72 19 1971

Kumble is the only legspinner to captain any side and the gentleman is the next player to join our list of probables.

For the choice for openers we take a look at the list of qualifying bastmen who sport an average µ > 35 & G > 20. Read this for details about µ & G which represent the Arithmetic and Geometric Average of scores adjusted for not outs. µ is similar to traditional batting average whereas G is used to unmask the effect of few very high scores on arithmetic average that hide a string of low scores.

Name Tests Runs Avg Bat Pts µ G MVP (Win)
Virender Sehwag 104 8586 4.26 48.36 26.86 5
Sunil Gavaskar 125 10122 4.21 48.19 25.23 1
Murali Vijay 41 2794 3.83 40.09 22.44 0
Gautam Gambhir 56 4046 3.72 41.78 21.90 2
Navjot Sidhu 51 3202 3.57 41.05 24.14 0

Sehwag, Lara and Bradman are the only three batsmen who have scored over 275 runs thrice with two triple hundreds. He is another player in the mould of Gilchrist who transformed the traditional expectations. As an aggressive opening batsman, who holds several records for scoring big and quick, he scored his last 11 centuries by going past 150. He has an enviable record in first innings but the returns are modest in second. Gavaskar is the traditional opener admired for his technique especially against fast bowlers. In 1977-78 he scored three consecutive Test centuries in the second innings touring Australia. His record is impressive especially in the fourth innings when India was battling to win or save the match. Gavaskar and Sehwag complement each other and should be everyone’s choice to open in the dream team. Incidentally Gavaskar has the better 30 match streak averaging 5.62. Sehwag is at second position slightly behind at 5.24.

And now we take a look at the most difficult choice – selecting Indian middle order. In the golden age of Indian middle order batting, Sachin Tendulkar, Rahul Dravid, Sourav Ganguly and VVS Laxman came together like the famed spin quartet. No one will bat an eyelid if these 4 are selected in the dream team. But our selection pool reveals plenty of candidates that meet the tough criterion of an average µ > 35 & G > 20.

Name Tests Runs Avg Bat Pts µ G MVP (Win)
C Pujara 37 2713 4.74 44.33 25.21 2
Rahul Dravid 164 13288 4.40 47.76 26.47 7
Sachin Tendulkar 200 15921 4.21 49.50 27.24 6
Virat Kohli 47 3326 3.81 41.92 22.68 0
G Viswanath 91 6080 3.50 39.75 22.33 4
M Azharuddin 99 6215 3.40 42.55 23.49 2
Sourav Ganguly 113 7212 3.33 39.23 23.46 1
VVS Laxman 134 8781 3.29 40.27 23.49 2
Dilip Vengsarkar 116 6868 3.25 38.21 21.10 4
Polly Umrigar 59 3631 3.23 39.26 20.99 0
M Amarnath 69 4378 3.03 39.61 24.64 0
Vijay Manjrekar 55 3208 2.88 35.77 21.42 0

The list above reveals that those batting at #3 & #4 tend to have higher average batting points than those at #5 & #6. It is fairly obvious that the best batsmen should bat higher in the middle order where they score in the company of openers above them and specialist batsmen below. This maximises team chances to set up a total, defend or chase as the case maybe. Hence Dravid and Tendulkar fare high but it is important to balance average batting points by the batting position too. Pujara and Kohli are active players likely to remain the backbone of Indian middle order and there stats will change over time. Umrigar, Amarnath and Manjrekar had relatively shorter careers. Measuring peak performances over the sufficiently long 30 test span allows comparison between personal high of each player.

Name Avg Bat Pts Start Test Year Started
Rahul Dravid 5.85 62 2002
Sachin Tendulkar 5.70 61 1998
Dilip Vengsarkar 5.10 72 1984
C Pujara 5.10 4 2012
Rahul Dravid 5.03 18 1997
Sachin Tendulkar 4.86 153 2008
G Viswanath 4.80 21 1974
Rahul Dravid 4.67 131 2008
Sachin Tendulkar 4.64 14 1992
Sachin Tendulkar 4.57 96 2002
Virat Kohli 4.38 14 2012
Rahul Dravid 4.23 93 2005
M Azharuddin 4.23 48 1992
VVS Laxman 3.97 100 2008
Sourav Ganguly 3.94 77 2004
VVS Laxman 3.86 21 2001
Polly Umrigar 3.83 6 1952
Sourav Ganguly 3.67 1 1996
M Amarnath 3.57 31 1983
M Azharuddin 3.51 12 1986
Dilip Vengsarkar 3.46 7 1977
VVS Laxman 3.44 64 2005
Vijay Manjrekar 3.40 13 1953
G Viswanath 3.18 52 1979
Sourav Ganguly 3.09 45 2001
M Amarnath 2.85 1 1969
Dilip Vengsarkar 2.71 38 1981

Rahul Dravid and Sachin Tendulkar are simply the best. The incredibly long career is a testimony in itself but the consistency over that period is astounding. Both have 4 streaks listed and even their worst sequence is better than the best of others. Rahul Dravid (2002) and Sachin Tendulkar (1998) should be on every list but a quick glance at the fan poll shows that while practically everyone chose Dravid, 1 in 4 does not select Tendulkar.

The 3rd name in above list, Dilip Vengsarkar, also makes it to the very bottom. He would have been rated #1 batsman in mid 80s but just like Ravi Shastri we have a case where career figures are deceptive. In the early 80s, selectorial judgement could be questioned but in a few years he reached the summit justifying the faith in him.

What is the utility of a dream team? I guess it is to compete with the very best of other nations. And when you are selecting the best, it is worth selecting them when they were at their respective personal best. Vengsarkar around 1981 was not a match to the world beating Vengsarkar around 1984. Tendulkar around 2002 was a shadow of his best around 1998. To his credit he rediscovered his form to get closer to his former glory days. That is why Vengsarkar is selected in out list of probables. There is a toss-up between Pujara and Viswanath – Pujara has played his relatively short career in a much stronger Indian team vis-a-vis Viswanath. A look at his average µ & G reveal much better consistency. Hence Pujara gets in the list of probables. All four players typically batted at #3 & #4. VVS Laxman gets in to the list of probables for batting lower down the order and shepherding the tail. Sourav Ganguly is already in the list as a captain.

We have largely relied on career figures to find a team of probables. The next step is to compare them over a respective best ever 30 test period. Let us compare the batsmen first with an honourable mention to allrounders.

Name Inns NO Runs 100 50 HS µ G Points
Dravid 48 7 3029 10 11 270 65.89 37.12 175.52
Tendulkar 54 6 3251 13 11 217 61.55 37.40 170.86
Gavaskar 50 3 3216 14 11 221 66.20 37.81 168.57
Sehwag 52 2 2774 8 7 309 54.96 30.25 157.01
Vengsarkar 46 12 2344 9 9 166 54.56 32.95 153.04
Pujara 53 6 2474 8 6 206* 47.39 27.45 152.84
Laxman 52 10 2250 4 19 176* 44.09 25.69 119.20
Ganguly 52 6 2156 4 12 239 44.29 31.49 118.07
Mankad 46 5 1550 3 5 231 35.50 15.55 101.75
Dhoni 50 7 1667 2 10 224 35.28 18.34 97.74
Ashwin 44 9 1175 3 5 124 28.57 13.75 76.26
Kapil Dev 45 4 1110 1 5 116 25.31 14.84 64.29

This table is sorted by gross batting points earned by each player over a 30 test period. Gavaskar at his best produced a 50+ score in 25 out of his 50 outings over a 30 test period. Although he trails in total batting points, by scoring over 3200 runs at an arithmetic average of over 66 and a very high geometric mean above 37 mark him as the best Indian batsman ever. Scoring 4 fewer hundreds yet matching him very closely in µ, G & total runs scored is the ever dependable Rahul Dravid. Actually there is very little to separate these two despite playing in very different teams. Gavaskar had to bat at the top of the innings more or less trying to save a match or avoid defeat. Dravid batted in the middle order in a settled team where wins were not that rare. Tendulkar’s peak was between these two. Although he scores 5 fewer runs per innings in terms of arithmetic average, the geometric mean is almost same. A higher value of G despite lower µ point to fewest absolute batting failures. On the other hand, when he got going he did not post huge totals either. His best batting period does not coincide with relative team success and that may explain why 1 in 4 who voted were comfortable in excluding him out despite his monumental batting. Sehwag at #4 in this list is a little behind these 3 illustrious stalwarts. His strength was converting his start into a match winning score more regularly than anyone else. Tendulkar, Sehwag and Dravid played a lot of matches together and fortunately for India, Sehwag and Dravid peaked around the same time beginning 2002. Tendulkar peaked a little earlier around 1998 and suffered a relative slump when the other two were going great guns. India has never won a test series in Australia. If, and that is big one, Tendulkar too peaked at the same time, the 2003 farewell series of Steve Waugh could have ended in India’s favour.

There is no doubt that Indian XI must feature Gavaskar, Sehwag, Dravid and Tendulkar at the top. It is a coincidence that the 4 top performers played at opening, #3 and #4 position too which makes their selection even easier.

Next we have two eliminations. Vengsarkar and Pujara essentially go head to head with Dravid for the one-down spot. Both have scored less than 2500 runs with middling average relative to top-3. Indian team has enjoyed greater success when these two peaked so there contributions in terms of gross score need not be high yet it was sufficient in terms of match context. Pujara and Vengsarkar could very well have been part of another middle order but the stellar figures of Dravid means they will not be able to make it in this team.

Dhoni is the sole wicketkeeper and thus an automatic inclusion. His position in the table below specialist batsmen and just above bowlers, who can bat a bit, confirm his role as the link between specialists and tail.

Kapil and Ashwin pitch in with sufficient 50+ scores and occasional 100s from the lower order to merit their selection as allrounders. Mankad was the third allrounder in the list of probables. Unfortunately his low averages despite playing as a top order batsman work against him. A very low geometric average of around 16 for an opener indicates that his batting successes overlap with frequent failures. Mankad is the 3rd player after Pujara and Vengsarkar to be excluded.

Laxman and Ganguly will both be selected if we choose 6 specialist batsmen. We must single out one if the team needs 5 specialist bowlers though. So let us review our bowlers to help us make that decision.

Name Wickets Average S/R Bowl Points
Kumble 171 27.27 58.30 209.31
Ashwin 166 24.34 50.54 206.83
Bedi 145 25.21 71.66 180.01
Mankad 122 29.20 88.43 157.98
Zaheer Khan 126 28.03 51.45 151.68
Kapil Dev 131 25.66 53.56 146.15
Srinath 132 27.23 54.63 141.09

Ashwin has made a frenetic start to his career. Kumble hit his stride circa 2001 around the middle of his career. The figures at the peak are very similar and there is very little to choose one over the other. One of them is a legspinner and the other bowls offbreak. Without any doubt these two should be the first choices offering variety.

In the pace department – Srinath took most wickets, Kapil has the lowest average and Zaheer has the best strike rate. Zaheer leads in the normalised bowling points adjusted for match context. Kapil edges other two due to his allround skill. Zaheer takes the second spot due to higher match points earned for the team. Srinath will be the third choice seamer if we pick all three especially for matches outside subcontinent.

That leaves Bedi and Mankad. Despite the lowest number of wickets, poorest average and a very high strike rate we have to remember Mankad for his total contribution to the team adjusted for era. As an offspinner he misses out behind Ashwin. As an opener he was not a match to Gavaskar and Sehwag. Yet he is the best allrounder produced by India. With a very heart, he is excluded in the interest of team balance.

On the subcontinental wickets, India should play to its strength with 3 spinners. Bedi is the ideal choice as a slow left arm bowler complimenting the right armers. His strike rate and wicket haul is inferior to Kumble and Ashwin but much better than seamers. Of course it does not make sense to compare across discipline because this team will always start with 2 seamers and 2 spinners.

We started with 16 probables. So far we have excluded 3 players – Vengsarkar and Pujara as middle order batsmen and Mankad as allrounder. That leaves us with 13 players. Laxman/Ganguly as batsmen and Bedi/Srinath as bowlers are still in the probables list.

Objectivity gets us this far. Subjective choices are required to prune this team further. 9 players selected so far make India a formidable batting and potent bowling unit at home. The away record especially outside the subcontinent should be kept in mind to choose the remaining squad. Do we need 6 specialist batsmen? Will two seamers suffice? How good is the line-up with 5 specialists, a keeper batsman and 2 bowling allrounders?

We must play 3 pace bowlers for away matches. One of them is surplus in familiar conditions so the 3rd seamer becomes the 12th man. This cements inclusion of Srinath in dream team. Laxman is chosen over Ganguly as the specialist batsman to join the XI.

The remaining spot is to be decided between Bedi and Ganguly. On spin friendly pitches, should we play a 3rd specialist spinner or use Sehwag and Tendulkar as third choice to include Ganguly as the 6th batsman? 

After deliberating the decision is to play 3 specialist spinners at home. Indian batting is stronger than bowling so 5 specialists must do the job while 3 seamers or 3 spinners will always play depending on the surface. The last spot goes to Bedi.

On review, we find the same XI as selected by the fans, except Bedi replacing Yuvraj as the 12th man. Yuvraj has solid credentials in limited overs cricket but his selection to Dream Test Team was highly questionable. We can infer that that crowdsourcing, soliciting data from a large online community, is very effective as long as the choices offered (or the end results) are curated.

Finally, we see the peak period of each player plotted against time to understand how many of them peaked simultaneously.

Dream Team - India XI

In-form batsman does not get dropped. Gavaskar, Dravid, Sehwag and Laxman did not miss any tests at their summit. Tendulkar missed one series against Sri Lanka due to injury.

Bowlers are played according to surface. A top bowler may get overlooked either due to injury or selectors’ view that the surface may not suit the him. Bedi, Srinath, Kumble, Zaheer and Ashwin have all missed tests. Kapil Dev is an exception and his injury free longevity is rare for a pace bowler.

Gavaskar’s success as a batsman coincided with Bedi and Kapil as bowlers but not at the same time. During late 1970s Gavaskar and Bedi were key to India’s fortune then Kapil Dev took over from Bedi during early 80s. After a lull, Tendulkar reached his zenith along with Srinath who was not an automatic choice on all surfaces. Kumble started peaking towards the end of Tendulkar’s reign. Fortunately for India, both Dravid and Sehwag hit top form at the same time as Kumble. Later Zaheer and Laxman enjoyed a period of superiority together. It can be seen that though a number of core players played in the same XI for a long period, there wasn’t any time when 4-5 of them were at pinnacle of their career. Indian team is currently ranked #1 in Tests but it must be underlined that its success coincides patchy performances from others. We still wait for a time when an Indian outfit enjoys sustained success both home and away beating strong opponents. Hope it will be soon!

The Paramount Utility of the 10th Wicket

We observe. We measure. We try to be accurate. Assuming we have enough reliable observations we measure centrality of the data. The central value (or average) can be computed in a number of ways so we choose the most appropriate method. The central value need not be the most frequent observation. In fact it need not match any observation. Still it offers a benchmark which can be used beneficially.

Representing a whole set by a single value is bare bones modelling. Models are used to reduce an object. The object may or may not be complex. Complexity is stripped by focussing on essentials to understand what lies beneath. Earth is not a perfect sphere but its model will be spherical.

Of course we need more than a basic model. We observe a system; we understand its guiding principles; we try to find the chief causes that affect its core behaviour. And then we try to build a model that mimics most of whatever happens.

George Box said:

Now it would be very remarkable if any system existing in the real world could be exactly represented by any simple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations. For example, the law PV = RT relating pressure P, volume V and temperature T of an “ideal” gas via a constant R is not exactly true for any real gas, but it frequently provides a useful approximation and furthermore its structure is informative since it springs from a physical view of the behavior of gas molecules.

For such a model there is no need to ask the question “Is the model true?”. If “truth” is to be the “whole truth” the answer must be “No”. The only question of interest is “Is the model illuminating and useful?”.

The Relative Value Model to determine player contributions in a limited overs match is wrong. But is it useful?

The model is driven by:

  • Actual values only. No predictive element.
  • Most of the matches are equal. A select few are more equal. A bilateral between any two teams is equal. The same encounter in a World Cup tournament is more equal.
  • Total points for a match will be same irrespective of who played whom in an uniterrupted match. Fewer match points when matches interrupted.
  • A uniform margin of victory will determine the share for each team. Points will be shared equally in tied matches.
  • The difference in scoring rate of two teams and ‘averaged‘ scores from earlier matches determine whether batting unit contributed more towards margin of victory (or defeat) or bowling. This ‘advantage’ will be used to calculate the share of total team batting points out of total team points. In tight matches, whether low scoring or not, this advantage will be close to zero as both sides found it equally easy(or difficult) to score. In one sided matches, the entire credit may go to bowling or batting unit but usually it will be shared proportionately.
  • Team batting points will be divided amongst all batsmen based on runs scored and scoring rate when the team bats through an innings. Otherwise it will be based on runs scored.
  • Team bowling points will be determined using number of overs bowled, runs conceded, wickets taken and when the wickets were taken by each bowler. The value for wickets is higher if opposition is bowled out and even higher when it is bowled out early. Wickets are valued less when the top order bats till the end but a bit more when the lower order batsmen are facing the final delivery.

The current Relative Value model relies solely on information recorded in scorecards. The model is called Relative because Value of every performance is measured against remaining 21. It does not scan the scorecard against a set of tests to create an index by allocating weights to each measure. In future ball by ball data will also be used to determine Relative Value. This is required to measure runs scored or conceded based on match situation. When plenty of wickets fall too soon, the absolute number of runs added will matter and not the rate of scoring those runs. Which brings us to the topic of this post. The value of taking the 10th wicket vis-a-vis the price paid for not taking all ten.

The longer version played in two innings format is won by bowling out the opposition twice and scoring an extra run. It does not matter whether runs were scored quickly or not. Margin of victory is determined by extra runs scored or innings/wickets saved. A limited overs match, on the other hand, is won by scoring an extra run in fewest possible deliveries. It does not matter how many wickets were lost. For example a bonus point is awarded when a side batting second wins by more than 10 overs. Teams are willing to sacrifice wickets to achieve this objective.

A specialist batsman does not bowl but every bowler must bat. In the longer format bowlers do not have a choice because an innings will not come to an end until the 10th wicket falls (or the captain forfeits remaining wickets) but in the limited overs edition a typical tailender often does not have to face bowling when batsmen do their job well. McGrath had to face a delivery in about 25% ODI matches only.

Openers have an advantage. A bowler is restricted by the maximum overs allowed in a match. An opening batsman can bat through the innings without any restriction on number of balls faced. In general, the top 4 batsmen will get a chance to bat and it is their job to bat for bulk of the innings. Others may not get a chance and when they do, it should be for fewer overs. Best to send your best early.

Of course some teams choose to play their best batsman much lower. Think Brian Lara. Misbah-ul-Haq is a more recent case. I think Shaiman Anwar should bat higher for UAE. Does the team’s best batsman need protection? The answer is NO if it is understood that failure is certain but the odds of a longer innings are higher. In any case a team needs more than one good batsman. Anything may happen but playing the strongest quartet at the top means they are more likely to survive collectively as a unit despite individual failures.

The lower order batsmen usually bat towards the end of an innings and are expected to score quickly. It is a different responsibility when a lot of overs remain. An in-form bowler (or a pair) may have done bulk of the damage. The primary task at hand is to see off that spell even if scoring remains attritional for an extended period. When wickets remain in hand then lesser bowlers will have to bowl.

If a team gets bowled out for 120 it does not matter whether they got there in 40, 30 or 20 overs scoring at 3, 4 or 6 Runs Per Over. The effective run rate will be 2.4 in all these cases. On a difficult surface both sides will struggle when the contest is between near equals. Then there are times when bowlers earn bagful of wickets. This is about the times when wickets are gifted while trying to unnecessarily attack.

There is no value in re-iterating common knowledge. Here is a handy guide for a team keen on giving its entire XI a chance to demonstrate its batting prowess. If you are in a situation similar to Pakistan (4 wickets down after 3.1 overs) then the task for 5th wicket is to bat until 34th over. If a wicket falls earlier then the task in hand for 6th wicket partnership is to last until 39th over.

Pakistan scored 160 despite losing 4 wickets for 1 run. Bunch of wickets can fall at any point. England scored 123 after losing 4 wickets for 104 runs. Relative Value model does not use predictive element in allocating points at present. It will continue to use actual match data in future. Pulse, WARR & FIPS  map current match status with projections based on past data. These models are getting tested during CWC 2015 to understand whether match situation is read properly. The next step involves deriving raw data for the Relative Value model after each delivery to replace the current macro model with its micro version.

What is a good first innings total? A team may win after scoring 150 and lose even after scoring 300. FIPS projects team score after each delivery against an ‘average’ score based on past first innings data. It makes 3 projections after each delivery out of which 2 are shown in the chart: one favouring batting side and another favouring bowling team. The model projects that batting team will initially aim to score 300 and bowling side will try to restrict them under 200. Model will reveal revised projections as we fill in the actual runs scored and wickets fallen after each delivery. The projections do not assume uniform scoring rate throughout the innings.

England lost 3 wickets before 15th over and the run rate was slightly below par. At 57-3, we can assume that bowling side had an advantage. Model projects restricting England to 175 after 13.1 overs. At half way stage the 4th wicket partnership has made a mini recovery lifting projected score to about 200. Two more quick wickets reduce England to 104-5 after 26.2 overs. projected score is down to 175. The main difference between 13.1 & 26.2 is that we have double the actual data and lost 5 of Top 7 batsmen. 70 more runs in about 24 more overs is possible and a decent partnership may take England further.

The next 8 overs witnessed an exceptional collapse. An exception means it is an uncommon event. It is unlikely to happen often.

Oooo fiesty one #cricket #billboard #australia #england #LOL 😂😂

A post shared by Jodie Sharp (@jodiesharp) on

Aussie fans wondered how England got in that tangle. A run fest making use of smaller boundaries was expected. There is no need to play a game if we can anticipate what happens next.

Australia started briskly. Lost an early wicket. Kept scoring at a rate healthier than par. Yet found themselves at 80-3 after 13.1 overs. Not much unlike England then. They continued to aim for batsman favoured ~300 instead of less than 200 favouring New Zealand. No 4th wicket partnership this time and soon it became 97-6 after 17.4 overs. Plenty of overs remain with Clarke and Haddin at crease. No doubts now that the match situation favoured bowling side. The projected score was under 150. A good partnership would certainly left Australia above 150 with 32 overs remaining. There was a partnership. It was for 10th wicket. Australia eventually bowled out for 151 with about 18 overs remaining.

There have been games where 10th wicket partnership rescued a side. There will be more such games in future. We can make very good projections about how a team will fare after losing bulk of the wickets. Projections get better once we have more data. Extra data comes in two forms: plenty of balls played without losing equivalent wickets OR plenty of wickets lost irrespective of balls played.

To differentiate between actuals and projections the very obvious rule must be kept in mind. Losing 9 wickets does not reduce the balls available resource. The fall of 10th wicket is the key event where remaining balls are forfeited. Try not to lose the first 9.

If the game halts suddenly then victorious team will be decided based on the match situation at the end of that delivery. The chasing team is expected to stay ahead of the par curve throughout the match. A typical successful above average score chase comprises of saving wickets in the middle overs and scoring just around or below required scoring rate and upping the tempo in the last lap. If sufficient wickets are in hand, it is expected that the team batting second will significantly increase the run rate once the target is in sight. It means the winning team stayed below the par curve for most of the match as part of a plan. A last ball six is sometimes sufficient to win the game even if scoring remains below par curve throughout the match.

McCullum scored 50 in 24 balls and took New Zealand to 78-2 after 7.4 overs, way above the par score. Fall of two more immediate wickets put them behind par. If the match stopped at that point, the game will be declared no result because 20 overs were not bowled. Since this is a low scoring game where more than 50% of target has been chased it is possible to call a winner within this blogspace. At 79-4 after 8.2 overs, Australia is ahead based on WARR and will be declared victorious if the game stops. This is based on the actual state of the match. The Pulse projection puts New Zealand firmly in command. With 6 wickets in hand, overs taken out of the equation and less than 75 runs remaining – an easy win with lots of balls to spare is projected. That is the projected state of the match.

PULSE allocates points out of 100 for both team after each delivery relying on projected scores. No projections required at the end of the match where points allocated by PULSE based on ball-by-ball data match the scorecard determined result values of Relative Value model.

I created the Pulse model based on my understanding of the game relying on fewest assumptions and recent historical data. One of my checks for the model is calling who is ahead during the game. I have my biases and I try not to conquer them. I rely on who is batting, who has overs left, recent form etc. The model does not care. It relies on runs remaining, wickets remaining, balls remaining and the recent historical trend. At 79-4 I told myself that the game will get interesting if Williamson departs. In other words I agree with the model even though we use different data.

5th wicket partnership secured the game. There was a wobble not unlike the Scotland match but it was too close to the target. Vettori departed at 145-7 and it still does not matter with only 7 runs needed. Model predicts a win for New Zealand with plenty of balls to spare and so did I.

Malinga fails to make it 5-in-5

Malinga fails to make it 5-in-5

World Cup 2007. Sri Lanka v South Africa. Chasing 210, South Africa sitting pretty at 206/5 after 44.4 overs. Malinga took 4-in-4 to leave them at 207-9 after 46.2 overs. Despite those 4 wickets, South Africa was ahead because WARR Par was 204. Sri Lanka needed the 10th wicket as Malinga tried to make if 5-in-5.

 46.3 Malinga to Langeveldt,no run,beaten Just kissed past the off stump. Tremendous nerves out there. Full and just outside off, yorker-length, Langeveldt pokes at it and gets beaten 

It did not happen. Eventually South Africa edged past Sri Lanka with 10 balls to spare. It was a tense finish to what should have been an easy one. Something similar although less dramatic happened in 23rd over bowled by Starc.

Williamson took a single on the second delivery. 146-7 with 6 needed. Next we get 2-in-2, both bowled by Starc making it 146-9. What if he made it 3-in-3?

A narrow 50.5-49.5 win for Australia, 7/28 by Starc would have fetched over 200 points relegating Boult’s 5/27 below 150 points. It is the magic of taking the 10th wicket. No need to guess what could have happened. The model was predicting a win for New Zealand until the hat trick delivery but updates values in favour of Australia once the improbable win is secured.

But the 10th wicket did not fall. Scoring a few runs is easier than taking a wicket. Wickets need to fall regularly while defending a low target. McCullum’s innings made the job easier for Williamson. New Zealand has stumbled twice while chasing an easy total. In these two cases the late clutter made the job tense without putting the chase in serious jeopardy. There will be other cases where a lot of wickets fall early and a late partnership secures a win with plenty of overs to spare.

A limited overs match is won by scoring an extra run in fewest possible deliveries. It does not matter how many wickets were lost. For example a bonus point is awarded when a side batting second wins by more than 10 overs. Teams are willing to sacrifice wickets to achieve this objective. Wickets play an important role during the match. The primary objective is reducing the run rate. Taking wickets is a good way to achieve that. Bowling out the opposition will limit the target. Bowling them out as early as possible is the best way to restrict runs. A side may not get bowled out. In general a team will score more runs if less than 5 wickets fall. Getting into the tail without getting the side out is helpful too. In a hypothetical scenario one team may set the target without losing any wicket. Side batting second can win the match while losing as many as 9 wickets. Wickets are secondary. It helps to take the 10th wicket which will happen only if the first 9 have fallen. Wickets are important. But it is extremely important to get the 10th wicket. It may decide whether a team wins or loses. Failing to do that and margin of victory gets decided by balls saved.

Relative Value model awards points by the size of victory. A narrow win or a loss conveys good performances by other team. The Relative Value of a very good performance can’t be significantly better than the rest in such matches.

How does one compare Starc’s figures with those by Boult?  Relative Value model evaluates these on the basis that it is a team game. The bowling performance that helps in bundling the opposition is more valuable. The bowling performance that sets up a win is more valuable. The bowling performance that sets up a very big win is even more valuable. Boult’s 5 wickets helped his team to bundle Australia in less than 32 overs. Starc’c 6 didn’t. His performance would have fetched far more points if he took the 7th or his team took the 10th.

This is about the Paramount Utility of the 10th Wicket!

ICC Cricket World Cup 2015

The home page of Relative Value Model’s ICC Cricket World Cup 2015. This page provides links to corresponding Tweet/YouTube video. A tweet will contain one or more charts. A YouTube video displays a chart updated after each ball. Tournament summary below the links.

Pool A

 Aus Bat Bowl

 Nzl Bat Bowl

 Slk Bat Bowl

 Bng Bat Bowl

 Eng Bat Bowl

 Afg Bat Bowl

 Sco Bat Bowl

Pool B

 Ind Bat Bowl

 Saf Bat Bowl

 Pak Bat Bowl

 Win Bat Bowl

 Ire Bat Bowl

 Zim Bat Bowl

 Uae

 

Match by Match Links

Final – Nzl 183(45); AUS 186/3(33.1)
2nd Semi-Final – AUS 328/7(50); Ind 233(46.5)
1st Semi-Final – Saf 281/5(43); NZL 299/6(42.5)                          Pulse Video
4th Quarter final – NZL 393/6(50); Win 250(30.3)                       Guptill 237*
3rd Quarter-Final – Pak 213(49.5); AUS 216/4(33.5)
2nd Quarter final – IND 302/6(50); Bng 193(45)
1st Quarter final – Slk 133(37.2); SAF 134/1(18)
42nd match, Pool B – Ire 237(50); PAK 241/3(46.1)
41st match, Pool B – Uae 175(47.4); WIN 176/4(30.3)
40th match, Pool A – Sco 130(25.4); AUS 133/3(15.2)
39th match, Pool B – Zim 287(48.5); IND 288/4(48.4)                Pulse Video
38th match, Pool A – Afg 111/7(36.2); ENG 101/1(18.1)
37th match, Pool A – Bng 288/7(50); NZL 290/7(48.5)               Pulse Video
36th match, Pool B – SAF 341/6(50); Uae 195(47.3)
35th match, Pool A – SLK 363/9(50); Sco 215(43.1)
34th match, Pool B – Ire 259(49); IND 260/2(36.5)
33rd match, Pool A – BNG 275/7(50); Eng 260(48.3)
32nd match, Pool A – AUS 376/9(50); Slk 312(46.2)
31st match, Pool A – Afg 186(47.4); NZL 188/4(36.1)
30th match, Pool B – IRE 331/8(50); Zim 326(49.3)
29th match, Pool B – PAK 222(46.4); Saf 202(33.3)
28th match, Pool B – Win 182(44.2); IND 185/6(39.1)
27th match, Pool A – Sco 318/8(50); BNG 322/4(48.1)
26th match, Pool A – AUS 417/6(50); Afg 142(37.3)
25th match, Pool B – PAK 339/6(50); Uae 210/8(50)
24th match, Pool B – SAF 411/4(50); Ire 210(45)
23rd match, Pool B – PAK 235/7(50); Zim 215(49.4)
22nd match, Pool A – Eng 309/6(50); SLK 312/1(47.2)
21st match, Pool B – Uae 102(31.3); IND 104/1(18.5)
20th match, Pool A – Aus 151(32.2); NZL 152/9(23.1)               Pulse Video
19th match, Pool B – SAF 408/5(50); Win 151(33.1)
18th match, Pool A – SLK 332/1(50); Bng 240(47)
17th match, Pool A – Sco 210(50); AFG 211/9(49.3)                  Pulse Video
16th match, Pool B – Uae 278/9(50); IRE 279/8(49.2)
15th match, Pool B – WIN 372/2(50); Zim 289(44.3)                  Gayle 215
14th match, Pool A – ENG 303/8(50); Sco 184(42.2)
13th match, Pool B – IND 307/7(50); Saf 177(40.2)
12th match, Pool A – Afg 232(49.4); SLK 236/6(48.2)
10th match, Pool B – WIN 310/6(50); Pak 160(39)
9th match, Pool A – Eng 123(33.2); NZL 125/2(12.2)
8th match, Pool B – Uae 285/7(50); ZIM 286/6(48)
7th match, Pool A – BNG 267(50); Afg 162(42.5)
6th match, Pool A – Sco 142(36.2); NZL 146/7(24.5)
5th match, Pool B – Win 304/7(50); IRE 307/6(45.5)
4th match, Pool B – IND 300/7(50); Pak 224(47)
3rd match, Pool B – SAF 339/4(50); Zim 277(48.2)
2nd match, Pool A – AUS 342/9(50); Eng 231(41.5)
1st match, Pool A – NZL 331/6(50); Slk 233(46.1)

* * *

The end of a World Cup marks the beginning of a new cycle. Seniors retire indicating no further appetite for plenty of bi-laterals until the next marquee event. Some of the established stars and the promising talent will get 4 more years to hone their skills for the next big stage. On the other hand, an exception like Tharindu Kaushal will make a debut at the quarterfinal stage. A veteran like Vettori may get recalled for one last hurrah despite lack of games leading into the tournament. A non-veteran like Grant Elliott gets another chance years after making the debut. Players like Boult and Mohit Sharma get selected on the basis of recent form instead of experience. In general, a team is likely to field a settled core of experienced players with depth in each department while incorporating a few talented inexperienced players to represent the nation at the World Cup.

I am going to compare the performance of a player during these 6-9 games (that have a higher recall value) against his own performances between CWC11 and CWC15 with a cut-off of 20 ODIs. A chart for batting and bowling per team where all-rounders get included in both.

Let us begin with UAE. This Associate team did not feature a single player with an experience of 20 ODIs between 2011 and 2015. I am in favour of more ODIs for plenty of lower ranked teams throughout the cricket season and not limited to the festive season. In an earlier post about 28 team World Cup, I recommended that top 8 test nations, in groups of 2, should separately host 5 teams each alternately over two home seasons. Associates to feature in a few official ODIs while participating in host nation’s domestic tournaments. Back to UAE. Well no comparative charts for UAE because we do not have a decent sample to compare their performances. Is it a co-incidence that they not only failed to win any match but also earned the wooden spoon in performance measures?

Scotland was the other team with no wins. At least they had a core of 4 experienced players. We begin with Majid Haq and Berrington in their bowling hat. Note: Click on the tweet to view a larger image.

All World Cup matches are given higher weight. Hence a player performing at par will appear to have put in an above average performance at CWC. Majid Haq bowled in 21 matches before the World Cup with good consistency indicated by a very thin blue box. Not unexpectedly, against stronger opposition, he was not consistent. But overall in the 4 matches where he got an opportunity, he has improved. If you are keen to find out how Josh Davey, Alastair Evans, Iain Wardlaw and Rob Taylor performed, you need to click on ‘Sco’ link under Pool A in the table at the top of this post.

Preston Mommsen improved on all four averages: Q1, Q3, Arithmetic Average and Geometric Average. His consistency improved too evident by a much thinner blue box. On other hand Calum Macleod, expected to be the lead batsmen, had a very bad series: 48 runs in 63 balls over 6 innings. Majid Haq also improved with the bat but from a very low base.

Captain Mohammad Nabi performed below expectations. Dawlat Zadran improved considerably. Mirwais Ashraf improved well in the two matches he played but his presence on the right hand side of chart indicates that he was not an automatic choice despite the 20+ ODIs played. Again, if you are interested in the performances of Shapoor Zadran and Hamid Hassan then click on the ‘Afg’ link under Pool A above.

Samiullah Shenwari had a very good series with the bat and was the top performer for Afghanistan along with bowler Shapoor Zadran. Mohammad Nabi was expected to be the leader with both bat and ball but disappointed. Mirwais Ashraf improved well in the two matches he played.

Zimbabwe also won a solitary game against the lowest performing team in its pool. They feature at the bottom on all performance measures as a collective bowling unit. Individually, Chatara and Sean Williams improved well from a low base. Even less was expected off Chigumbura and Masakadza. They ended up performing even worse at the World Cup or in other words they were taken apart by top nations.

Brendan Taylor was one of the top performers at the group stage justifying his place as the top batsman for Zimbabwe. Sean Williams was expected to give him good support and he did so admirably and makes the Top 5 in the Relative Value Model’s list of all-rounders.

Ireland beat 2 test playing nations to finish fifth in Pool B above Zimbabwe. None of the experienced bowlers performed above expectation during the six group matches. All-rounder Kevin O’Brien was the best amongst 3 bowlers with 20+ ODI games before the World Cup. Alex Cusack, John Mooney & Andy McBrine are not featured here due to insufficient games.

Kevin O’Brien and Paul Stirling were expected to be the best with bat for Ireland. Both scored at run a ball but either side of 150 runs in 6 Innings is not sufficient. Ed Joyce scored an 80 and a 100 in wins over West Indies and Zimbabwe but completely failed against South Africa and India. Porterfield’s best was against losses to Pakistan and India. He scored in double digits but 4 of these were under 40. These two could have been more consistent. Batting primarily at #6, Gary Wilson’s best knock was in the win against UAE. Also a cameo in the high scoring thriller with Zimbabwe. Collectively it was a mixed bag. They did well to win 3 matches but would have backed themselves to do better in the other 3 at least to minimise the margin of loss.

England failed to qualify for knockouts. Enough has appeared in print and online. Suffice to say Relative Value Model ranked Finn, Jordan and Tredwell higher than Broad but he was the only automatic selection. Anderson was expected to be the pick of the bowlers but he had a series to forget.

One would expect more than 4 batsmen to have played over 20 ODIs before the major tournament but England’s selection policy is not under discussion here. Let us move on to the quarter-finalists.

Bangladesh qualified at the expense of England. The top 3 bowlers expected to do well lifted their performance especially Mortaza followed by Rubel Hossain. Shakib consistently ranks amongst the top players in the Relative Value Model’s unpublished measures. He maintained his level but the expectations were higher.

Shakib was expected to be the best batsman too. He raised his level a bit but not as much as Mushfiqur. Most notable mention goes to Mahmudullah who was the least ranked batsman for Bangladesh which is evident from his right most appearance in the chart. Tamim was expected to do much more at the top of the innings. Anamul & Nasir Hossain did not make much of the two chances they got.

Jerome Taylor did not play enough ODIs to qualify for these comparisons. Kemar Roach was the top performer in CWC 2011 for West Indies and expected to lead the attack based on his performances before the World Cup. He seriously underperformed in the three matches he bowled. Jason Holder did extremely well. Andre Russell too was good as an all-rounder. Chris Gayle, the bowler, was a surprise.

Chris Gayle, the batsman, was ranked very low. Barring the double hundred, he performed along those limited expectations. None of the batsmen raised the performance levels at this event but managed to win big when they could to ensure that Ireland did not take their place in the knockouts.

Tharindu Kaushal was handed a debut at the quarterfinal stage which shows that Sri Lanka could not field a settled core for a variety of reasons. None of the bowlers had an outstanding series and relatively Malinga and Angelo Mathews were better than others.

On the other hand, Kunar Sangakkara had an OUTSTANDING series with the bat. Dilshan did well but not as well as he did in the previous World Cup. Angelo Mathews was decent in his supporting role. Jayawardene would have liked to match Kumar especially against the stronger opposition. Thirimanne  was inconsistent. Tharanga and Chandimal got a chance to bat only once each.

Pakistan was handicapped. Only three bowlers had played over 20 ODIs and their case was very different from England. Shahid Afridi was outstanding in the 2011 World Cup but failed this time. Irfan justified his place as top bowler for Pakistan but it was Wahab Riaz who contributed at a high level consistently in all the matches.

Misbah-ul-Haq scored 350 runs in 466 balls. Any Absolute Value Model will mark down such slow batting efforts. Relative Value Model evaluates each innings in the context of the match. Such performance in high scoring games will not get many points but it is different when both teams struggle to reach 250 in completed innings. According to Relative Value Model, Misbah-ul-Haq raised his game during the tournament and was the star batsman for Pakistan. Sarfraz Ahmed did very well in the 3 matches he got a chance to play unlike Nasir Jamshed who had the worst series. Afridi disappointed with the bat too and Shehzad could have done better.

Before the tournament I had expected a semi-final lineup of Aus vs Ind and SA vs NZ. It turned out that way by accident. I expected Australia and South Africa to top their respective pools. Neither did. In fact, South Africa lost thrice in the tournament.

Dale Steyn was expected to be the top bowler for South Africa. He will still be the go to bowler for defending 12 runs in the last over. It was disappointing that he had an ordinary series in the light of this strong performances between the two world cups. Morkel raised his game. imran Tahir was the pick of the bowlers.

de Villiers had an outstanding series. Hashim Amla had a very ordinary series. de Kock was inconsistent. du Plessis and Miller performed above expectations perhaps due to failure at the top giving them more chances to bat. Hashim Amla is the top performer in an ODI once every 5 times. de Villiers is the top performer in an ODI once every 5 times. When one outperforms, generally the other is not too far behind. The underperforming duo of Amla & Steyn could be the reason why South Africa lost 3 of the 8 matches played.

India won 7 games in a row dismissing the opposition every time. Shami and Yadav exceeded themselves. Shami was the most consistent bowler picking wickets at either end of the innings. Ashwin did the same role that Tahif performed for South Africa. Mohit Sharma is not listed due to insufficient games but he too excelled in his role of the first change bowler. Compared to these 4, Jadeja was the weak link. But he too on an average performed near his par.

Shikhar Dhawan, Dhoni, Rohit Sharma and Raina performed above expectation with bat. Kohli was expected to be the top batsman for India. He had a disappointing series like Amla. He kept getting the starts but it was unlike him to not convert some of them to become the top performer in the match. Just like Amla and de Villiers he too finishes as the top player once every 5 games. Before the tournament, I expected India to win one of the 2 opening games, finish second in the group and win the quarter-final. The odds of beating the hosts were low but a semi-final finish gave a good account of the team. That India performed very well as a unit, without heroics from an individual, was a pleasant surprise. The semi-final finish after that performance was underwhelming.

New Zealand won 8 out of 8 at home. Boult and Vettori did not play enough games hence they are not part of the comparison. Southee had an outstanding tournament in 2011. He had a relatively quiet series this time. Corey Anderson was admirable as fourth bowler after the first three had done sufficient damage.

Brendan McCullum can get a very good start. But he fails often. He was not expected to the top performer for New Zealand. Kane Williamson, Corey Anderson and Ross Taylor were the best batsmen coming into the tournament. None of them had an outstanding series. It was compensated by McCullum, Guptill and Elliott. While Indians performed as a unit without outstanding effort from any player, the Kiwis won their matches on the back of 3 exceptional bowlers and 3 outstanding batsmen.

Doherty featured in a single match not picking any wickets. Starc was expected to be the top performer for Australia. He improved beyond expectation during this series. Johnson was expected to the consistent performer just behind Starc. He was consistent and very very good. Faulkner was expected to put in solid efforts maintaining consistency at a lower level. He was inconsistent but excellent in the games where he performed. Watson was below par but it did not matter. Maxwell was OK with the ball in his role as an all-rounder.

Watson, Clarke and Warner were expected to lead the batting. Stability was found only after moving Watson down the order to make way for the star performer Steven Smith. Clarke was not consistent but Warner had a good series. Finch was alright compared to his par but Maxwell made hay when the sun shone. Australia was clinical in the knock out games to take the title.

Relative Value Model relies on aggregate performances. It is difficult to separate performance from luck in a single match but as the sample size increases one can get a better understanding of the relative performance levels of an individual. Just as change is the only constant, failure is the only certainty. Hence performances are evaluated using 4 different averages accounting for abject failures. Which brings us to the summary for this World Cup:

👍 Steven Smith, Mitchell Starc (Australia)
👍 Brendan McCullum, Trent Boult (New Zealand)
👎 Virat Kohli (India)
👍 Mohammad Shami (India)
👎 Hashim Amla, Dale Steyn (South Africa)
👍 Misbah-ul-Haq, Wahab Riaz (Pakistan)
👍 Kumar Sangakkara (Sri Lanka)
👍 Jason Holder (West Indies)
👍 Mahmadullah, Mashrafe Mortaza (Bangladesh)
👎 James Anderson (England)
👍 Brendan Taylor, Sean Williams (Zimbabwe)

In other words, England and South Africa should be disappointed. India may rue the missed opportunity. All other teams should be elated/satisfied depending on the stage they reached.

ODI Pulse Chart: Tracking team points during a match

In a Pulse chart, Team batting first is depicted in red and other team is plotted in blue. A worm tracks the progress of a match by plotting the team score after each delivery against a black PAR value. Worm is shaded red or blue based on the team deemed ahead of the Par value after that delivery. PAR value for first innings is determined from the average scoring rate for a 50 over match. The second innings PAR is determined by the TARGET set by team batting first, overs played and wickets lost (see Wicket Adjusted Run Rate Chart for details).

Overs played are displayed on X-axis, Runs Scored on the Primary Y-axis (left side) and Total Team Points on the Secondary Y-axis (right side).

Batting first, England lost top order wickets early and regularly and as a result stayed below the average scoring rate throughout the match. Some big spikes in the blue points curve show the Australian dominance. The fifth wicket partnership between Morgan and Buttler reduced the gap between red and blue curves. A sharp increase in Australian Points at the fall of 5th wicket indicates that the partnership was good for England but not long enough. 6th and 7th wicket partnerships just about restored the parity when England reached 224/7 after 46.5 overs. At that point, England could have scored 20-25 more runs in the remaining 19 balls. 3 more wickets in next 6 balls resulted in Australia leading 26.2-23.8 at innings break.

The first innings score against an overall average score is indicative at best. 400+ score may not be enough to win while a below 200 score is more than sufficient sometimes. England needed some early wickets and/or a sedate Australian start but neither happened. England’s best chance was at 71/2 after 12.4 overs when Australia was marginally ahead 33.5-31.6 on points but the 3rd wicket partnership prospered.

Even though Australia lost a few more wickets the scoring remained quick enough to stay well above the Par curve increasing the gap between these two teams. At 165/3 (31 ov), the gap increased to 45.8-39.3 and even after two quick wickets the gap widened to 56.8-40.7 at 219/5 (38 ov). England stalled while Australia accelerated.

61 ball win for Australia

61 ball win for Australia

2 more wickets fell before the finish line which were immaterial because the scoring was very quick. Australia won by 61 balls which amounts to a very comfortable 58.8-41.2 win. The quick wickets that England had to take after first 15 overs of Australian innings did not materialise and the game ended in a thumping victory for Australians.

Player Performance Analysis for 2014 edition of Champions League Twenty 20

CLT2014-16: bt 113(19.4 ovs); HOB 117/4(18.2 ovs)

CLT2014-16: bt 113(19.4 ovs); HOB 117/4(18.2 ovs)

This is a Champions League T20 “Who Did How Much?” post on the lines of the introductory post published during IPL 2014. All the key points about understanding the chart which depicts player batting, bowling & fielding performance in a T20 match are covered in that post.

CLT2014-01 - csk 157/4(20 ovs); KKR 159/7(19 ovs)

CLT2014-01 – csk 157/4(20 ovs); KKR 159/7(19 ovs)

The first match of this tournament was won by KKR with 6 balls in hand. This post will summarise all player contributions through a single image. Successful 160 odd runs chase is deemed as a match won by batting unit. So KKR gets more batting points (27.36) compared to bowling points (24.76). Russell’s 58 in 25 balls is worth 13.8 points which is more than half the batting points available. He also earns nominal 0.5 points (out of the team total of 24.76 points) for his single over that cost his team 12 runs. Sunil Narine was the best bowler and overall the next best performer who kept CSK quiet by conceding only 9 runs. Nehra picked up 3 early wickets and a late one but did not get enough support. Despite appearing on losing side his spell of 4 wkts conceding 21 is worth nearly the same (8.56) as Narine (8.61). That is the purpose of this analysis – an attempt to quantify the contribution in each discipline by all the players such that the total adds up to 100 points for a completed match. Ryan ten Doeschate who kept KKR in the hunt with 51 runs off 41 balls is fourth in the list. Chawla and Dhoni are not too far behind with nearly 8 points apiece. At the other end, Pandey does not get any point for his duck which is fairly obvious. Later we will find out how slow batting and expensive bowing also results in NIL points.

CLT2014-02 - hob 144/6(20 ovs); KXIP 146/5(17.4 ovs)

CLT2014-02 – hob 144/6(20 ovs); KXIP 146/5(17.4 ovs)

This is a comfortable win with 14 balls remaining which results in nearly 56-44 split. Perera is the top performer with nearly the same number of points as Russell (from Match 1). But this is a balanced performance with bat and ball. He picked up 2 wkts for 17 runs in his 3 overs. At 77/5 after 10.5 overs, his team was in trouble but his assured 35 in 20 balls in partnership with Bailey resulted in a comfortable win. He gets about 9 points for his batting compared to 11 by Maxwell (43 in 25). Akshar Patel’s spell of 4-20-1 is worth 6.5 points which is nearly equal to 6.7 points for Bailey who scored 34 runs in 27 balls. This is an example of determining near equal contributions from two independent disciplines.

CLT2014-03 - NK 206/5(20 ovs); cob 44/2(7.2 ovs)

CLT2014-03 – NK 206/5(20 ovs); cob 44/2(7.2 ovs)

Third match was interrupted by rain. Williamson’s 101(49) is worth nearly 57% of the total batting points for his team. Cobra’s needed about 3 runs an over when the tie was resolved using D/L. The loss by 33 runs at that stage results in a big victory for Knights who earned nearly 72 points. Losing team bowled entire quota of overs but faced fewer overs. Hence bulk of the 28 points are allocated to bowling side. A similar split in overs faced vs overs bowled results in far more batting points for the Knights compared to bowling. Proportionally reducing the total number of points for an interrupted match will reduce the anomaly of awarding far too many points to a single player. Only 44 balls were bowled during the chase. Kuggeleijn’s sole over costing 11 runs despite a wicket is worth NOTHING because others restricted the scoring to 32 runs in 38 balls. This is an example of how a bowler is not assured of any points as a result of conceding too many runs.

CLT2014-04 - dol 164/7(20 ovs); PER 165/4(20 ovs)

CLT2014-04 – dol 164/7(20 ovs); PER 165/4(20 ovs)

Fourth match went the distance with the winning stroke scored off the last delivery. It means the Ball Difference is 0 which is the boundary condition. That condition means that, irrespective of scores, the batting and bowling units always get exactly half the nearly 50 points. Scorchers get an extra 0.15 points out of 100 for scoring that extra winning run after facing equal number of deliveries. 3 players earned more than 8 points. Marsh was declared the Man of the Match for scoring 40(26) and above average bowling spell of 3-21-0. Zondo appears on the losing side despite scoring 63(50). Frylinck scored quick 15(6) during death overs and completed his quota of 4 overs conceding about par 32 runs while picking up a wicket.

CLT2014-05 - bt 174/6(20 ovs); KXIP 178/6(19.4 ovs)

CLT2014-05 – bt 174/6(20 ovs); KXIP 178/6(19.4 ovs)

In the fifth match, Punjab posted their second win which was much closer this time with only 2 balls in hand. It means that points are split around 51-49 mark and no player manages to get 10 or more points. Miller was awarded MotM but quantitatively he is only the 5th best performer. Tridents did very well to score 174 on the back of two strong batting performances but their death bowling was poor. Patel did extremely well to score 20 in the penultimate over swinging the match in favour of Kings XI. He also bowled his entire quota which fetches him a nominal 2.5 bowling points. In a match where no single player stands out, his collective batting/bowling figures make him the best performer on the winning side. Unlike Patel, Mendis bowled well to finish his quota but the death bowling undid his effort. Note 0 batting points for Chigumbura 3(5) and Bailey 7(11) – an example of below par above-zero scores that still result in no batting points.

CLT2014-06 - cob 184/6(20 ovs); HOB 186/4(19 ovs)

CLT2014-06 – cob 184/6(20 ovs); HOB 186/4(19 ovs)

Hurricanes won with an over to spare in the sixth match thanks to Blizzard. The match would have been closer had Blizzard departed in 18th over after his 50. But the Philander no-ball which spared him was punished by his SIX on the free-hit that turned the tide. His 78(48) was ably supported by Dunk who scored 54(35). Engelbrecht bowled well and Philander batted well for Cobras. Peterson chipped in with a decent all-round performance for the losing side.

CLT2014-07 - lio 151/7(20 ovs); KKR 153/6(19.3 ovs)

CLT2014-07 – lio 151/7(20 ovs); KKR 153/6(19.3 ovs)

KKR were 100/0 and cruising, were then reduced to 147/6 but hung on to win by 3 balls. Lions did not field well which means the assured knock by Shehzad earning about 12 points was wasted. Gambhir batted well at the top of the chase but it was Narine who followed his 9/1 in the first match with 9/3 in this one. Quantitatively his superb bowling performance is only as good as Gambhir’s batting. In the limited overs format, the best bowler does not have the liberty of bowling more than 20% overs. Hence the total points available to a very good bowler gets shared by 4 others especially if the collective bowling effort is not decisive. A batsman in form can bat until the end with no restriction on number of balls faced. Therefore batsmen score higher number of points with an exceptional performance. The opposite is true in Test matches. Generally 4 bowlers share available bowling points while earning some points for their batting. A very good spell will earn plenty of bowling points if the number of overs bowled is not restricted.

Match 8 : CSK 242/6(20 ovs); dol 188(20 ovs)

CLT2014-08 - CSK 242/6(20 ovs); dol 188(20 ovs)

CLT2014-08 – CSK 242/6(20 ovs); dol 188(20 ovs)

Raina scored 90 in 43 balls in a big 26 ball win which results in a nearly 61-38 match in favour of CSK. Raina’s batting performance is deemed worth 25% of total team contribution which meane he gets 15.38 points. How does it compare with Jadeja’s 40(14) who scored 44.44% of his runs but in 33.33% of deliveries faced by Raina? Well it has to be worth at least 44.44% points of the batting points i.e. 6.83 with a bonus for scoring even quicker. That bonus is worth about 10% resulting in 8.31 batting points for Jadeja. Mohit Sharma’s spell of 4-41-4 is deemed better than McCullum’s 49(29). Mohit outscores Brendon 7.2 – 6.76. Bravo’s all-round effort places him between these two. Delport’s brisk 34(9) at the top of chase is worth 17% of his total team contribution. Since his side fell sufficiently short, Delport’s total batting points (6.69) are lower despiteJadeja contributing a lower 14% towards his team.

Match 9: HOB 178/3(20 ovs); nk 92(16.4 ovs)

CLT2014-09 - HOB 178/3(20 ovs); nk 92(16.4 ovs)

CLT2014-09 – HOB 178/3(20 ovs); nk 92(16.4 ovs)

This is a comprehensive win for Hurricanes where both the batting and bowling units contribute towards the final winning margin – an above par score of 178 batting first followed by an exceptional bowling performance to bowl the opposition for 92. This match provides a nice opportunity to compare player specific values. Styris pipping Hilfenhaus – how can it be explained? Hilfenhaus took 3 wickets (at 2.4, 2.5 & 6.4 ov) and conceded only 14 runs after bowling his full quota. That is worth 20% of team performance resulting in a very high score of 12.9 points. Styris was required to both bat and bowl. With winners outperforming in either discipline, Styris is deemed to have faced better bowling and batting. Only Styris and Southee contributed meaningfully fo Knights. 7 of the 11 batsmen get NIL points as Watling and Mitchell join them in scoring batting points. Paine 43(34) on winning side and Styris 37(27) on losing side are comparable. Paine scored 6 more runs facing 7 more deliveries while facing inferior bowling attack. Quantifying – Styris beats Paine 8.90 – 6.69. On the bowling front, Styris, Sodhi & Southee completed their quota with similar above par figures whereas Kuggeleijn and Boult brothers underperformed. This time we will compare Styris using Bollinger’s figures. Styris did not take any wicket conceding 7 runs an over in a match where winners scored above 8. Bollinger picked three wickets off the last 4 balls of his spell conceding over 8 runs against an inferior batting side. Numerically Bollinger leads Styris 5.37 – 4.23. Effectively 2.4-22-3 is not deemed significantly better than 4-28-0 taking match context into account. Mennie’s 3-10-2 is also rated above Doherty’s 4-17-2 by 8.07 – 7.58.

Match 10: per 151/7(20 ovs); KKR 153/7(19.4 ovs)

CLT2014-10: per 151/7(20 ovs); KKR 153/7(19.4 ovs)

CLT2014-10: per 151/7(20 ovs); KKR 153/7(19.4 ovs)

Man of the Match was awarded to Kuldeep Yadav for his spell of 4-24-3. Narine picked 4 wkts for 31 runs. Conventionally 4 wickets is ranked higher than 3 wickets. But here we rank Yadav(8.55) ahead of Narine(6.88) because his spell was more economical and Narine got bulk of his wickets at the death unlike Yadav who picked his wickets after deliveries 8.6, 11.5 & 16.1 ov.

Match 11 was abandoned.

Match 12: bt 174/8(20 ovs); COB 174/5(20 ovs)

CLT2014-12: bt 174/8(20 ovs); COB 174/5(20 ovs)

CLT2014-12: bt 174/8(20 ovs); COB 174/5(20 ovs)

This tied match was won by Cobras who settled it in superover. Cobras were cruising before digging a hole when Engelbrecht scored 11 of 12 in the last over to tie the match. He followed this by protecting 11 runs in superover. Carter was the top performer with 111(68). Requiring 3 to win off the last ball, Engelbrecht faced Emrit. He failed to hit a boundary. Reifer collected the ball and threw it to keeper’s end who failed to collect and Tridents failed to win the match. Carter would have been the deserving player of the match if Dowrich effected the run out which was awarded to Engelbrecht. Man of the Match is generally, not always, awarded to one of the top performers from the winning team. This analysis identifies the top performer based on numbers alone.

Match 13: KXIP 215/5(20 ovs); nk 95(15.2 ovs)

CLT2014-13: KXIP 215/5(20 ovs); nk 95(15.2 ovs)

CLT2014-13: KXIP 215/5(20 ovs); nk 95(15.2 ovs)

Wins keep getting bigger. Kings XI won the match improving on Hurricanes. Batting first they scored way above par and defended 215 by bowling the opposition for 95. This means they won by nearly 80-20 margin. Sehwag, Miller and Vohra benefit the most. Sehwag’s 52(37) is slowest among these three rated 14%. Miller with 40(18) was the fastest of these three but scored fewest runs for his 16% contribution. Vohra was part of the opening century stand with Viru where Punjab overhauled the eventual Knights score in the 9th over itself. The final margin of 71 balls is largely due to Vohra’s 65(32) for which he earns a huge chunk of team points. This model rates such 65 higher than another 100 when scored in context.

Match 14: LIO 164/5(20 ovs); dol 148/9(20 ovs)

CLT2014-14 - LIO 164/5(20 ovs); dol 148/9(20 ovs)

CLT2014-14 – LIO 164/5(20 ovs); dol 148/9(20 ovs)

Lions should have won this match with plenty to spare when they had restricted Dolphins to 93/9 after 15.4 overs. For the 10th wicket, Subrayen contributed 1 run facing 7 out of remaining 26 balls. If we exclude 3 extras in the partnership, then Frylinck scored 51 in 19 deliveries. His allround contribution with bat and ball is worth 31% of his team points. In other words he earned 21.15 points; higher than Vohra’s contribution with bat alone.

Match 15: CSK 155/6(20 ovs); per 142/7(20 ovs)

CLT2014-15 : CSK 155/6(20 ovs); per 142/7(20 ovs)

CLT2014-15: CSK 155/6(20 ovs); per 142/7(20 ovs)

Batting first Jadeja scored 14 runs off the last 3 deliveries. Chennai Super Kings eventually won by 13 runs. That explains the reason for a Ball Difference of 3 despite the margin of 13 runs. CSK scored 66 off the 155 in the last 4 overs. Since Ball Difference takes into account the actual rate of scoring where ball-by-ball data is available, a late surge after a slow start will result in a lower margin of victory.

Match 16: bt 113(19.4 ovs); HOB 117/4(18.2 ovs)

CLT2014-16: bt 113(19.4 ovs); HOB 117/4(18.2 ovs)

CLT2014-16: bt 113(19.4 ovs); HOB 117/4(18.2 ovs)

This was a low scoring match which means bowlers will get more points for checking the run rate. Shoaib Malik contriutes with bat, ball along with a catch to become the top performer. Carter’s brisk 42(34) knock, in context of a low scoring match, is worth close to 10 points. Hilfenhaus gets more bowling points than Doherty due to better economy and picking both his wickets before all four by Doherty.

Match 17: cob 135(18.3 ovs); KXIP 139/3(18.1 ovs)

CLT2014-17: cob 135(18.3 ovs); KXIP 139/3(18.1 ovs)

CLT2014-17: cob 135(18.3 ovs); KXIP 139/3(18.1 ovs)

Once again bowlers check the scoring and gain more points collectively. Saha contributes with bat and glove to become the top performer. Peterson’e 2/19 in a losing cause is rated above 3/15 by Patel (on winning side) because he took his wickets in first 10 overs unlike Patel.

Match 18: KKR 187/2(20 ovs); dol 151/8(20 ovs)

CLT2014-18: KKR 187/2(20 ovs); dol 151/8(20 ovs)

CLT2014-18: KKR 187/2(20 ovs); dol 151/8(20 ovs)

A tall score by KKR batting first and a relatively high score by Dolphins chasing vis-a-vis lower winning scores in the two earlier matches indicate that batting side should get more points. Uthappa and Pandey scored most of the runs batting first to pick up nearly 30 of the available 31 points for the side. Phehlukwayo’s 37(18) is the best effort on losing side.

Match 19: lio 124/6(20 ovs); PER 130/7(19 ovs)

CLT2014-19: lio 124/6(20 ovs); PER 130/7(19 ovs)

CLT2014-19: lio 124/6(20 ovs); PER 130/7(19 ovs)

Two allround efforts, one from each side, stand out. 63(38) by Marsh and 69(55) by Nasim are on either side of 14 batting points but Marsh raced ahead overall due to better bowling figures.

Match 20: nk 135/8(19 ovs); BT 138/4(18.4 ovs)

CLT2014-20: nk 135/8(19 ovs); BT 138/4(18.4 ovs)

CLT2014-20: nk 135/8(19 ovs); BT 138/4(18.4 ovs)

Last group game was interrupted but both sides played the same number of overs. Target was nominally incremented but Tridents managed to win with 2 balls to spare. Bowlers ahead again but not by much. 47(47) by Devcich is not rated much higher than 29(19) by Watling. Munaweera’s economical bowling in second half is worth more than his batting cameo at the top.

Semi-final 1: hob 140/6(20 ovs); KKR 141/3(19.1 ovs)

CLT2014-SF1: hob 140/6(20 ovs); KKR 141/3(19.1 ovs)

CLT2014-SF1: hob 140/6(20 ovs); KKR 141/3(19.1 ovs)

KKR won another match after restricting the opposition to a manageble score. Kallis and Pandey ensured that the chase did not go wrong. Pathan sneaks between these two by virtue of his decent spell with ball. Shoaib Malik and Gulbis scored plenty of points in defeat.

Semi-final 2: CSK 182/7(20 ovs); kxip 117(18.2 ovs)

CLT2014-SF2: CSK 182/7(20 ovs); kxip 117(18.2 ovs)

CLT2014-SF2: CSK 182/7(20 ovs); kxip 117(18.2 ovs)

In the other semi-final, CSK scored above par while batting and then restricted the scoring below par while bowling. The net contribution is only marginally in favour of batting side. It is a big win with roughly 64-36 split. Bravo picks up plenty of points while batting for 67(39) but his bowling spell of 1-12-0 is worth only 0.005 points.

Don Bradman & Geometric Mean

Let us find the average of a set of values. A rectangle has sides 3 & 5 so its perimeter is 3+5+3+5 = 16. An equivalent square with the same perimeter will have each side equalling 4 which is the Arithmetic Mean of 3 & 5.

AM

Arithmetic Mean

Here we add both the numbers and divide the sum by number of data points which is 2. So (3+5)/2 = 4. Arithmetic mean A is defined via the equation: A:=\frac{1}{n}\sum_{i=1}^{n} a_i

Here Σ is the summation operator and the above notation is shorthand for A = (a1 + a2 + a3+ a4 + … + ai + … +an) /n

Now let us consider another rectangle with sides 2 & 8 which has a total area of 16. We can find an equivalent square of side 4 with the same area.  In this case 4 is the Geometric Mean of 2 & 8.

GM

Geometric Mean

Here we multiply both the numbers and then take the square root of the resulting product. The square root of (2*8)=16 is 4 which is shown as 2√(2 × 8) = 4.

So what is the Geometric Mean of a cuboid with sides 2, 4 & 8? For three values it will be the cube root of the product (2*4*8) which turns out to be 4.

Geometric Mean for a cuboid

Geometric Mean – 3D

We can extend this logic to multiple data points. Geometric mean G is computed by taking the product of all the numbers and finding the nth root of the result. It is defined via the equation:

\bigg(\prod_{i=1}^n a_i \bigg)^{1/n} = \sqrt[n]{a_1 a_2 \cdots a_n}.

Here π is the product operator.

Logarithms are a means to simplify calculations. This common technique involves transforming each number to a new domain, carrying out simpler arithmetic and transform the result back to get required answer. It is often used for product, quotient, power and root (by using addition, subtraction, multiplication and division in the log domain). The above equation for GM using logarithm can also be written as:

\log G = \frac{1}{n}{\sum_{i=1}^n \log x_i}.

A quick comparison with the equation for Arithmetic Mean reveals that ‘log of the Geometric Mean(G) is the Arithmetic Mean(A) of the logs of the numbers.’

AM & GM Relationship

The log of the geometric mean is the arithmetic mean of the logs of the numbers.

We have understood Geometric Mean in terms of Geometry. Since we can’t have a side with negative or zero values, Geometric Mean applies to positive numbers only. Also logarithm of a negative number is not defined and a single zero value in the data set will make the product zero.

Geometric Mean is practically used to determine the average investment returns. Consider a portfolio with 5 annual returns of say 0.1, 0, -0.1, -0.2 & 0.2. The Arithmetic Mean of these values is zero.

But a notional investment of 100 at the end of first year will be 110, no change at the end of year 2, down to 99 in year 3, further down to 79.2 in year 4  and finally up to 95.04 at the end of year 5. This shows that the portfolio will lose .05 in 5 years or 0.01 every year.

Arithmetic Mean of zero is not relevant in this case. Since Geometric Mean applies to positive numbers only, we will add 1 to each value. The product of (1.1*1*0.9*0.8*1.2)=.9504 and its fifth root rounded to 2 decimals is 0.99. The Geometric Mean can be computed as -.01 by subtracting 1 which is the average return for our portfolio.

The 2008 book by Lawrence Weinstein and John A. Adams called ‘Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin‘ suggests that if you have an intuition about the upper and lower bounds for any unknown quantity, then your best guess should be the Geometric Mean instead of commonly used Arithmetic Mean. The book asks, ‘How many clowns can fit in a VW Bug?’ and suggests that the answer could be anything between 1 and 100, so go for 2√(1*100) i.e. 10. If you tried 50 then it would be 50 times the lower bound(1) but only half the upper bound(100) whereas the Geometric Mean of 10 is ten times the lower bound and a tenth of the upper bound.

Geometric Mean tends to dampen the effect of a few very high values. What is the mean value of a house on a street where most of the properties are similarly priced but one of these happens to be a mansion? Suppose there are ten properties in a street valued at 100K, 80K, 50K, 95K, 120K, 70K, 105K, 1 Million, 60K & 90K. The Arithmetic Mean of 177K is higher than the price of remaining 9 properties but Geometric Mean of about 106K represents a fairer average.

Let us take a look at the 80 scores by Don Bradman in four batches of 20:

0,0,0,0,0,0,0,1,1,2,4,7,8,8,12,13,13,13,14,16,
18,18,24,25,25,26,29,30*,30,33,36,37*,38,38,40,43,48,49,51,56*,
57*,58,63,66,71,76,77,79,79,82,89,102*,103*,103,112,112,123,127*,131,132,
138,144*,152,167,169,173*,185,187,201,212,223,226,232,234,244,254,270,299*,304,334

The sum of his 80 scores is 6996. He remained not out in 10 of those innings which are shown as 299* etc. in above list. A cricket average is computed by adding individual scores but dividing by number of completed innings only which is 70 in this case. So Don Bradman’s Cricket Batting Average is the iconic 99.94 but the conventional Arithmetic Mean (or Runs per Inning) is 87.45.

A set of numbers such as heights, weights or property prices are non-zero with plenty of values around the mean and a few extreme values at either end. Such a set of numbers is called normally distributed. But the above 80 scores are not. In 20 of those innings, Bradman failed to reach 18. At the other end he scored more than 132 in his top 20 innings. There are 14 single digit scores which include 7 zeroes and 12 scores of 200 or more. His lower scores are very close to one another e.g. 0,1,2,.., 7,8,.. , 12, 13, .., 24, 25, 26, .., 37, 38, 40, .., 56, 57, 58 etc but top 10 scores 223, 226, 232, 234, 244, 254, 270, 299*,304,334 are wider apart. With relatively few high values, most of the distribution is concentrated on the lower side. Such distribution is said to be right-skewed.

For substantially positive skewness (with zero values), Logarithmic data transformation is used. This handout suggests deriving transformed values using the SPSS command NEWX = LG10(X + C) where C = a constant added to each score so that the smallest score is 1.

It is time to combine the two topics of this post. We would like to calculate GM for batting scores which include zero values. We have established that adding a unit value to all the data points, calculating GM and subtracting the unit from the result is an acceptable compromise. GM is generally used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, not for batting scores. But we have seen the value of dampening the effect of few higher scores in right-skewed distribution. It is interesting to note that this type of data gets logarithmic transformation and GM is based on the AM of the logs of numbers.

A dampened Geometric Average is a fair estimate for the central tendency of batting scores by an individual. By not giving any special treatment to not-outs, the Geometric Mean for 80 scores by Don Bradman is calculated as 38.59. Table below lists GM, Average, RpI, Median and Mode for selected players.

Geometric Mean Cricket Average Mean (RpI) Median Mode
Don Bradman 38.59 99.94 87.45 56.5 0
Herbert Sutcliffe 33.62 60.73 54.23 38.0 3
Jack Hobbs 31.70 56.94 53.04 40.0 0
Sachin Tendulkar 25.18 55.44 49.74 34.0 0
Jacques Kallis 24.79 56.78 48.17 33.0 0
Rahul Dravid 24.68 52.31 46.46 33.0 2
Ricky Ponting 23.67 52.75 47.33 30.5 0
Allan Border 23.29 50.56 42.17 31.0 0
M Jayawardene 23.11 51.17 48.11 30.0 0
IVA Richards 22.91 50.23 46.92 32.5 0
S Chanderpaul 22.78 50.44 42.35 32.0 0
Brian Lara 22.72 52.88 51.52 33.5 0
Sunil Gavaskar 22.30 51.12 47.30 29.0 0
Steve Waugh 19.73 51.06 42.03 25.5 0