Rationalising Rahul Dravid's record in South Africa: a case study in Base Rate Fallacy © Getty Images
Rationalising Rahul Dravid’s record in South Africa: a case study in Base Rate Fallacy © Getty Images

Cricket fans battle Cognitive Dissonance caused by unpalatable data in a number of ways. In this article, Arunabha Sengupta looks at the common Cognitive Bias known as Base Rate Fallacy.

Sharing articles over social media comes with plenty of perks.

Yes, an article that ruffles feathers and rubs the hero-worshipping cricket fans in the wrong way makes one prone to relentless abuse and ad-hominem that masquerade as argumentative devices in the fan-space. However, it also allows one an excellent platform to study and analyse the different reactions, especially the full cycle of cognitive dissonance.

In a recent article where we demonstrated that Rahul Dravid, champion batsman that he was, did not quite perform with anything approaching brilliance against the most difficult opponents of his days. Indeed, his record against South Africa and Australia is less than impressive.

As expected this created a lot of heartburn. The figures revealed were devastating to a lot of beliefs and convictions. And as is normal in such cases, there were Cognitive Dissonance and rationalisation in various ways. Some of them are listed below.

Rationalisation Method

Technical Name

However …

The writer is a &*ӣ$%#

He should write comic books.

Ad Hominem

The character of the writer notwithstanding, Dravid’s record against the toughest opponents of his era remain less than impressive.

It is agenda-based.

Fundamental Attribution Error

Again, agenda or no agenda, Dravid’s record against the toughest opponents of his era remain less than impressive.

It is selective data, biased data …

Semmelweis reflex

All the Tests Dravid played against the two toughest opponents of his time, Australia and South Africa, have been considered. If that is selective, one has to relook at the definition of the term.

Why are England and New Zealand not considered? They were difficult conditions.

Anecdotal rather than statistical data

The conditions were rather horrendous in the two Tests of 2002 in New Zealand. That perhaps sticks to the memory because it helps battle cognitive dissonance created by the article. However, the other two series during Dravid’s career saw high scores and the average runs per wicket for India during the three tours was 34.66. Similarly in England, while sometimes the conditions were indeed demanding, the average runs for India was 35.77. Contrast these with 26.79 in South Africa and 30.91 in Australia

Tagging like-minded fans and arriving at consensus that the numbers notwithstanding the conclusions are not valid

Groupthink

Mostly this takes recourse to anecdotal rather than statistical analysis. We will focus on this aspect in the article.

Note:The analysis also included the figures in Sri Lanka, which was the third most difficult land for visiting batsmen during Dravid’s career. And once again Dravid’s numbers are rather ordinary in that land where he struggled against spin. However, some readers have pointed out that Sri Lanka was not really a difficult land for Indian batsmen. Perhaps the record in Sri Lanka can be ignored in the analysis.

However, in this article we will focus on the phenomenon of Groupthink-based rationalisation and the cognitive illusions that it entails.

Base Rate Fallacy

It was Dravid’s average of 29.71 in South Africa that really put the cat among the pigeons. It was indeed devastating to the image of the man synonymous with The Wall.

One way that this was handled was to reach a consensus among like-minded fans. In spite of the statistics, there were plenty of innings of value. Everything cannot be explained by numbers, after all. So on and so forth.

Hence, there were examples: Dravid scored 27 not out in a total of 66 in 1996-97. In 2006-07, his innings of 32 at Johannesburg was incredibly vital to the team’s cause.

Along with that there were claims of some esoteric essence of these innings that went beyond statistics. After all, cricket is never only statistics, right?

So, having underlined that Dravid did play innings of value in South Africa the discomfort due to data was overcome.

There are problems with this type of argument. Depending on our convictions, these innings can be interpreted in various ways. Our beliefs can generate their own confirmation. That is why there is no substitute for runs.

If the 32 at Johannesburg is as good as a hundred, as many do claim, what is the corresponding value of Sachin Tendulkar’s 169 at Cape Town 1996-97, when he came in at 25 for 3 and battled through 58 for 5 and launched one of the most phenomenal counterattacks with Mohammad Azharuddin?

Or what about the Tendulkar-Virender Sehwag mayhem at Bloemfontein in 2001, when they joined forces at 68 for 4 and carried the team to 288.

And while the 32 by Dravid and 44 by Tendulkar at Johannesburg, 2006-07, indeed negotiated a difficult period and laid the foundation for the famous comeback 51 by Sourav Ganguly, it was the same pair of batsmen who added 24 in 15.1 overs in Cape Town in the third Test of the series and effectively dug the side into a hole. Not always is a slow 30 or 40 useful.

Again, in such cases, depending on points of view our interpretations will vary. We tend to be overconfident about our accuracy of judgement.  If we ignore statistics and go by our opinion, it boils down to the claim “my opinion overrides statistics, scientific analysis and all other opinions”. In my book, that is not a very strong argument.

Yet, let us be accommodating and play along with this idea. Let us look at the 32, the 27*, or any score where Dravid has not been dismissed under 30, and consider them significant innings.

In South Africa, Dravid crossed 50 once in every 7.14 innings as opposed to 3.67 of Tendulkar and 4 of Laxman and Ganguly during the same tours. Tendulkar had 4 hundreds and 2 fifties in the tours alongside Dravid, while Dravid did not manage to cross 50 in his last two tours to the land. That is to say, when Tendulkar or Laxman settled they went on to play a more substantial innings more often than Dravid. But we will ignore that.

We will give the same weight to any innings over 30, or undefeated under 30. Hence, we won’t be looking at batting average at all. We will go with the assumption that while 169, 105 and 111 are substantial innings, so are 32, 31 and 47.

Is Dravid indeed reinstated as The Wall with this curious reasoning?

Unfortunately, there is a cognitive illusion that plagues this sort of thinking.

What we are falling prey to is base rate fallacy. We are looking at anecdotal data based on availability heuristic that brings useful innings to our recall, because it helps us battle cognitive dissonance. We pick and choose the innings that suits our groupthink based consensus, but ignore the huge space of failures.

Here is a list of Dravid’s innings in South Africa. It is the complete list and hence in no way selective.

7, 27*, 2, 12, 148, 81, 2, 11, 2, 87, 32, 1, 11, 5, 29, 47, 14, 43, 25, 2, 5, 31

All the innings in which he has not been dismissed for less than 30 have been considered as success. I think for a No. 3 dismissal for less than 30 can be justifiably considered failures.

It underlines that Dravid failed in 14 of the 22 innings, which gives him a failure rate of 63.63%.

During the same tours, here are the numbers for the rest of the Indian batting.

Indian batsmen in South Africa (1996-97 to 2010-11, 10 or more innings)

Batsman

Innings

Dismissed for < 30

Failure rate

Average

Rahul Dravid

22

14

63.6%

29.71

Sachin Tendulkar

22

11

50.0%

50.47

VVS Laxman

20

9

45.0%

40.42

Sourav Ganguly

16

8

50.0%

36.14

Virender Sehwag

16

9

56.7%

25.46

Yes, Dravid failed way more than the rest of the top-order Indian batsmen in South Africa.

Hence, when we look at conforming evidence of ‘useful 30s and 40s’ to arrive at a consensus about Dravid’s performance in South Africa, we ignore the enormous 63.63% failure rate.

Base Rate Fallacy is a well-known Cognitive Bias: our propensity to ignore the generic base rate information and dwell on special causes.

Other examples of Base Rate Fallacy in cricket

We tend to attach labels of ‘crisis player’ to some cricketers because of two fundamental reasons:

A) His demeanour makes us believe he is good in crisis, and

B) There are some innings that stick to our memory when he actually performed in a crisis situation.

While A) is a different illusion altogether, B) often succumbs to Base Rate Neglect. We overlook the many situations of crisis when the cricketer did not quite perform.

We often hear this about Sunil Gavaskar. The knock at Feroz Shah Kotla against the West Indians showed what he was capable of if he wanted to score fast. However, because of the weakness of the Indian batting he curbed his attacking instincts.

This is wrong at several levels.

The attacking innings at Kotla was mainly an effect of continuous failures against the West Indian pace during the tour of 1982-83 and at Kanpur. Gavaskar had perhaps realised that the strategy of biding away time against the good bowlers and waiting for the bad ones was not going to succeed against the mighty West Indian attack. Hence he went hammer and tongs.

He followed it up with the superb 90 at Ahmedabad where he again started striking the ball from the word go. However, that was followed by four back-to-back low scores and in the rain-washed Test at Madras he was back to his circumspect self.

The proof of ability to play in a certain way is in doing it continuously. Gavaskar was not that sort of a batsman as a Viv Richards or a Greg Chappell. Else, how does one explain the 36 not out in the 1975 World Cup against England, and the 8 off 54 balls at Melbourne 1985-86 as India crawled to 60 in a session before rains came down, and thus the 120 required to win remained a tale of so near yet so far? It robbed the side of the golden opportunity of a series victory in Australia.

Once again we see the example of base rate fallacy. We go by the anecdotal evidence of the Kotla knock, and perhaps the century against the Kiwis in the second-last ODI of his career. However, we neglect the several situations when the team would have been helped by fast scoring when Gavaskar could not quite accelerate.