Saturday, April 9, 2011

Was Sachin right in praising Dhoni? - A Statistical Analysis

In the late nineteenth century, English artist Frank Barraud inherited a lovable fox terrier called Nipper from his late brother Mark. This dog, now immortal through the painting made by his new master, started and heart wrenchingly moved towards the newly invented gramophone whenever Mark’s voice rang out of it. After Frank committed this touching scene on canvas, it became the logo of The Gramophone Company, and the popularity of the image made them change the company’s name to His Master’s Voice.

 Times have changed. In a pathetic, pitiable parallel following the World Cup, The Master voiced an opinion in public and all the modern nippers – the media mongrels –turned their stink-whiffing noses and poison tipped pens in his direction.

The statement was simple enough. Sachin Tendulkar went on record saying that Dhoni was the best captain he had played under.  About someone who has led India to triumph in the limited overs World Cup, the Twenty-twenty World Cup and to the top of the World Test ranking, the pronouncement should not be very debatable.

But, India is a different type of nation altogether. With a billion eyeballs on the sport, there are a million opinions about everything. A view aired by someone respected the world over as a statesman of the game is sure to be splashed on tabloids and comedy shows masquerading as sports channels and analysed with the most grotesque arguments ever. 

The reaction was predictable, with every major, minor and insignificant personality in obscurest connection with the game voicing his opinion about it. The most ridiculous perhaps was the stance of the glorified tabloids of Bengal which also call themselves newspapers.

Lokendra Pratap Sahi, a veteran, experienced journalist, hastened to produce an article on the front page comparing success statistics of captains Sachin played under, while harping on the fact that Sourav still remained the most successful test captain and had started the trend of winning overseas with regularity.  In his laughable analysis, he manipulated the data with the crudeness of a one year old fiddling with play-dough. Win-Loss ratio, till a while back the only statistic used since it showed Sourav in the best possible light was dispensed with. Understandably so, since Dhoni’s W/L ratio now reads 4.67 compared to Sourav’s
1.61. Instead, a football league type of scoring was used which awarded one point to draws, thus bringing down the difference between captaincy records.
Additionally, rather shrewdly, only matches featuring Sachin were considered, since that took away one win each from Dhoni and Dravid while taking 3 wins and 3 losses away from Sourav, making him look better in the percentage figures.

In the One Day Internationals, the Bengali journalists have never used the Win Loss ratio, although it makes even more sense. This is simply because Mohammed Azharuddin has been ahead of Ganguly in that aspect, regardless of the virtual reality we are fed by the media.

It was a desperate attempt to fit the USP built around the local icon in the overhauled landscape of Dhoni’s exploits along with The Master’s pronouncements. It is quite evident from the article that the newspaper would have been happier if India had failed to reach the finals after 2003, so that the regional halo could be polished to sparkling glory at the expense of the success of the cricket team.

The public responded by agreeing that Dhoni was at best a lucky captain, wins coming by no merit other than strokes of good fortune.

Unfortunately, that is what irrational cricket fanaticism has turned into.

Sourav Ganguly himself was the first to admit of Dhoni’s remarkable feats, acknowledging him as the best skipper in an interview to the Times of India. However, Lokendra Pratap Sahi brought his immense experience into the field, salvaging the situation by taking another interview on the eve of the IPL, coaxing the southpaw to say that it was not possible to compare eras.

It is quite obnoxious, but Indian journalism finds it more lucrative to feed on the public fascination for larger than life icons and personality cults rather than steady improvement of the team.
In simple terms, Sourav started the transformation into a winning side, his work was carried forward by Dravid and Kumble, and now has been taken to an unprecedented level of excellence under Dhoni. But, truth is hardly likely to sell papers.

Now, coming back to the Master’s remarks, the statement has been criticised by the media and public alike. When Sachin walked out to bat for the first time as a fifteen year old against Imran Khan and Wasim Akram, no one in the cricketing or journalistic or fan world could contemplate even halfway towards 33000 runs and 99 centuries in international cricket. A mind that believes such feats are possible and actually makes them happen is not bound by the parameters of the normal. It is difficult to gauge it with the yardsticks used to judge politicians and corporate clowns.

However, many deduced the supposed motivations for Sachin to make the statement.  There are again multiple opinions, and some of them range from ingratiating himself to the current skipper to mutual back scratching.

I am not here to judge the claims, however ridiculously far-fetched they seem even by the lenient, liberal standards of conspiracy theory. I would rather take a fact-based look at things.  Looking at the statistics, Sachin does not need to appease any captain for a place in the team. At this stage of his career, scoring more prolifically than ever even by a Tendulkarian standard, teams are more in dire need to coax him to continue.
To me it seems more believable that Sachin said whatever he did because he thought it was true, something which seems quite radical in the cacophony that echoes around Indian public figures.

 One critic pointed out that Sachin with all his experience should have known that the press would stir this up into a major discussion point, and should have avoided making the statement. Whereas, it baffles me why singling out a particular captain as the best would give rise to controversy, especially when backed by figures, there is some truth in the statement.

In a country of millions of cricket ‘lovers’, any statement by the Master will create a division. Even if he answers in the affirmative when asked whether he has normal bowel movements is likely to break the hearts of thousands of constipated followers of the game. So, it definitely seems that the best solution for the little master is to take a vow of silence for the rest of his life apart from one or two statements about it not having been possible without the fans.

So, let us not try a moral judgement of the master’s words in a country where even morality may be polarised. Instead let us see how correct the master was with statistical verification.

As in a previous article in which I compare  the fab five batsmen of Indian cricket, I will be using hard core statistics. Again, there won’t be a tabular representation of data pretending to be statistical analysis as one is used to from Cricinfo. 

The idea will be to compare the proportions of success and failure of different captains and to judge whether one has a better record than the other in statistically significant terms. What that means is testing the hypothesis that there is no difference between the records of two captains, and finding the probability (p-value) of the results being as they are if the two captains were equal in their achievements. A very low
p-value will indicate that the hypothesis can be rejected and there is indeed statistically significant difference between the success ratios of the two captains. This means that it is very unlikely for such different success ratios to be a result of fluke or chance.

In technical terms, proportions are compared, and a Z-test is carried out to arrive at a test statistic which
corresponds to a p-value. If the p-value is less than a very small value, we reject the claim that the proportions are equal. 

India’s historical record in test cricket still leaves a lot to be desired. The Win-Loss ratio still stands at 109 to
139. The fact that they are ranked one in the world stems obviously from exceptional performance after 2000, the time Sourav took the reins.

So, let us test whether there has been statistically significant change in India’s record since 2000.

From the table it is pretty clear that there has indeed been a significant change in the fortunes of Indian cricket since 2000, and the credit needs to go to all the players and captains who have played the game since the turn of the century. Transformation is a gradual process and I would like to state my opinion that Sourav did start the process that sees fruition now.

However, the scavenging reaction of the scribes makes me go ahead further and compare the records of different captains who have led the sides in this century. Was Sachin Tendulkar statistically correct in his evaluation of Dhoni?

Let us explore the question. The captains we will consider are Sourav, Dravid and Dhoni. We will not talk about Anil Kumble because he led India in just 14 tests and does not satisfy the statistically significant sample size to be evaluated.

First, let us try to see whether there is a significant difference in the results of the team while Sourav was at the helm and thereafter.

From figures, there is no significant difference between the results of Sourav’s captaincy and others in the
post-Sourav era.

Now, let us do the same analysis for Dhoni.

So, at this stage, Dhoni definitely stands head and shoulders above the rest as far as results are concerned. In fact, the probability of his being a lucky captain, as alleged by many ‘fans’, is 2.3%.
In any scientific analysis, it will be considered significant. With the analysis performed only for test matches played after 2000, this is remarkable because it shows Dhoni shines brighter than the rest even in the most luminous period of Indian cricket.

Having done the analysis for the individual captains, let us do a pair-wise comparison of the three major captains of the 2000s to see whether there is a significant difference between their captaincy records or not. 

And the final comparison everyone will be waiting for with anticipation and bated breath.

From these results, it is quite evident that while there is nothing to distinguish between the captaincy records of
Sourav, Dravid from the each other, Dhoni’s success record is currently significantly better than everyone else. The difference is more striking if we remove the minnows  from the equation (outliers in statistical terms). He comes out better than the rest in the most stringent of statistical tests.

These figures do clearly indicate that whatever be the complicated ethical or moral question, from pure factual point of view, Sachin Tendulkar has judged the delivery to a perfection. For someone who has  played more international cricket than anyone in the history of the game, it is natural to be correct in evaluation.

However, we take nothing away from Sourav Ganguly’s achievements. He started India’s re-emergence, with test wins in foreign soils of West Indies, England and Australia. He combined with Rahul Dravid to win a series in Pakistan.

Dravid continued from where he left off by winning a series in England and West Indies and a test match in South Africa. 

Kumble, in his brief tenure, ensured that the legacy continued by battling unsporting Aussies and winning a test in Perth.

After that Dhoni ensured that Indians top the test rankings, square a series in South Africa, win a series in New Zealand  and triumph in the World Cup.

Each one of them sterling contributors to the history of Indian cricket.

And I am sure every one of them wishes that soon either Dhoni himself or his successor will better the record by winning a series in South Africa, conquering new peaks in the cricketing world. These are the people who bring glory to Indian cricket, and do that in spite of the scavenging scribes who crawl beneath their strides, to make a living out of the semblance of dirt that they leave in their wake.

And while on the subject of conquering  peaks, let me end the piece by doing the same analysis with someone who has conquered all conceivable peaks in the history of the game. How did India’s cricketing fortune change when he entered the scene? Let me quickly share the analysis in the same format.

Does he need to ingratiate himself to captains? Sorry, the numbers do not point to any remote possible statistical significance for not rejecting this hypothesis.

 I will allow the figures to demonstrate the importance of the man, his match-winning capability and his contribution. I suffer under no illusion that his critics will be convinced. The usual reactions will be snide remarks with the underlying theme that matches are not won with calculators. They are not, but as in everything else in the world, the figures left in the wake of events tell a major story if one knows how to interpret them without manipulating them like a one year old with play-dough.

However, the Indian ‘fan’ is more obsessed with icons than figures. I do not even dream of convincing ones with tri-colour painted to their bare bosom, intent on shouting themselves hoarse rather than hearing the crisp sound of the willow on the leather, swaying to the blaring music at every boundary, looking with baffled confusion if ever asked the current score. 

Addendum on 22.03.2012 :
There are some who have written to me wondering where MS Dhoni stands now given the 8 overseas losses (7 in Tests led by him) since the article was written - although some comments speak less of curiosity and more of the fanatism that is associated with some Indian cricketing fables . For them I can point to this article I wrote after the Australian tour.... There is no categorical data analysis, but the simple statistics presented may be useful.


  1. Amazed at your passion of putting your views with so much of in-depth analysis of facts and figures!! Could not understand how u arrived at the z statistics. We will discuss

  2. You used tests of equality of binomial proportions correct? Or a normal
    approximation to that given the large numbers?

  3. @Hermes : Tests of Equality of binomial proportions is correct.
    Great to find a question regarding statistics here.

  4. Good analysis Senantix. Both of the people who put up random articles ridiculing someone by reading between the lines as well as for your statistical analysis of the patterns of Indian cricket over the years...


  5. Absolutely magnificent! Good statistics (which is fairly common)backed by, more importantly, an outstanding understanding of the game (which is very rare!).

  6. i am sorry, i am not a mathematician but isn't the sample size of matches for dhoni quite low compared to ganguly or even dravid? p.s. this is a purely mathematical related query.

  7. @Achal : Good question.
    To an extent you are right. The sample size of matches for Dhoni is not a problem, he satisfies the eligibility criteria. The size does not need to be comparable to the other sample sizes for comparison either as long as it satisfies a minimum size.
    However, what matters is that he has had too few losses. If he had lost at least 5 matches, then it would have met all the criteria for scientific comparison. However, I decided to go ahead, because his record is such that even if he had lost two of his drawn tests or loses the two following matches in England, he will still be at the top of the list.
    Hope this clarification helps.

  8. @senantix: definitely helps. dhoni might be the best captain but for some reason i like ganguly more. maybe it was becoz he flurred up a sense of patriotism and passion when he was on the field. watching him fight back against bullies when everyone else just kept quiet. and he passed that on to likes of sehwag and bhajji. neways, happy that india won the wc. hope pune and kkr reach the finals of ipl.

  9. Shouldn't the victory before-after test carried out for other players too ? I guess Sehwag\Gambhir\Dhoni to have the lowest p-value. Not too hard to see why.

    I am also a bit surprised that you neglect Kumble's 14 tests as insignificant while including Dhoni's 17 tests.