ExplainSpeaking: Did India lose the World Cup because of the law of averages?

As it turned out, India beat all the teams participating in the tournament to enter the semi-finals with a perfect record of 9 wins out of 9 matches. When India beat New Zealand in the semis to make it 10-0, these worries heightened further.

Even though India had beaten every team quite comprehensively — almost shockingly comprehensively — and even though none of the former players and cricket experts were able to find any real weakness, there was always a nagging suspicion that India might lose the final just because of the law of averages.

So, did India lose the finals because of the law of averages?

The short answer is no. And the simple reason for this is that there is no such thing as the “law” of averages in statistics. If you don’t believe it, pick up any dictionary of statistics and try to look for it.

Had such a “law” existed, perhaps it would have also explained why it was damning India after 10 straight wins while sparing Australia, which entered the finals after winning 8 successive matches. Or indeed, why did it spare Australia from a perfect 11-0 record during their victory in the 2003 World Cup.

Indeed, those who believe in the law of averages determining the fate of cricket matches should also wonder why the law hasn’t provided some relief to Pakistan, which has been losing to India in every World Cup match since 1992. Similarly, one should wonder why some world class batsmen tend to get out to a specific bowler — this is often referred to in cricket as a batsman being someone’s “bunny”.

The recently concluded Ashes (traditional name for a Test match series between England and Australia) provided a very good example of this. When the series started, David Warner, one of Australia’s (and indeed modern era’s) best Test opener, faced his nemesis: Stuart Broad. Everyone knew this was the last Ashes they were playing against each other. Of all the bowlers Warner had faced in the 104 Tests since making his debut in 2011, Broad had dismissed him the most times. And since Broad was England’s opening bowler and Warner Australia’s opening batsman, this meant that Warner had a lousy Test record in England: As against an overall Test batting average of over 44 runs, Warner’s Test average in England languished in the mid-twenties.

If the law of averages was real and applied to cricket, Warner was due to hit Broad out of the park in the 2023 Ashes. Nothing of the sort happened. To Warner’s misery, Broad never forgot to remind Warner who was the boss, often convincing the enthusiastic crowd to chime in as he started his run-up. By the end of the series, Broad got Warner out three more times, with Warner ending the series with an average of 28.5 runs after batting for 10 innings and unsure of his place in the Australian Test side.

Then what explains the deep popular belief in the “law of averages”?

While there is no such thing as the law of averages, the popular belief reflects one of the fundamental laws of statistics, albeit applied incorrectly. It is called the law of large numbers.

The formal definition of this law will most certainly put lay readers to sleep and as such, it is better understood from a real life example.

When Winston Churchill was asked if he had it all to do over, would he change anything, he replied as follows: “Yes, I wish I had played the black instead of the red at Cannes and Monte Carlo.”

Churchill was possibly alluding to an iconic incident that took place in a casino in Monte Carlo on August 18, 1913. It so happened that for several successive turns of the Roulette table, the ball repeatedly landed on “black”. To be sure, the ball could either land on a black spot or a red one. In other words, there was a fifty percent chance of the ball landing on red.

With each passing turn, gamblers around the table grew more restless and certain in equal measure, believing that the ball would land on red at the next spin. As they saw the ball land on black yet another time, they increased their stakes, guided presumably by the non-existent law of averages.

It seemed fairly reasonable to assume that the ball was due to land on red.

In the end, the ball landed on black for a record 26 times in succession. According to Darrell Huff, author of “How to take a chance”, if a player had bet one louis (about $4 at that time) when the run started and pyramided for precisely the length of the run on black, they could have taken away $268 million — a mind-boggling amount of money in 1913. But this also provides a sense of the scale of losses that gamblers racked up that day in Monte Carlo.

It is for this reason that the so-called “law of averages” is more popularly referred to as the Gambler’s Fallacy or Gambler’s Ruin in statistics.

What is the Gambler’s Fallacy?

Where did the gamblers go wrong?

They confused the law of large numbers with what is now commonly referred to as the law of averages. The gamblers thought that since the probability of the ball landing on red was the same as the probability of the ball landing on black, sooner, rather than later, the ball was sure to land on red.

But there is no rule or law in statistics that either predicts or indeed guarantees that the ball will land on red after a certain number of spins. Just like there is no law that bars a coin toss resulting in heads for 10 times on the trot. In fact, the law of large numbers only states that if the Roulette table was spun for a large enough number of times, the average number of times the ball would have landed on either red or black would be close to 50% of the total spins.

The significance of the word “large” is that there is no guarantee that in a “small” sample, the ball will land on red half the time. By the same measure, it is entirely possible for a cricket captain to keep calling heads and winning at coin tosses repeatedly for 20 times on the trot.

But why isn’t there a guarantee that the ball will land on red after it has landed on black for 20 times on the trot?

That’s because every spin of the Roulette table (and every coin toss) is “statistically independent” of the previous spins (and tosses). In other words, when it is being spun for the 21st time, the ball doesn’t know that it has already landed on black on the past 20 spins. The ball or the coin don’t feel compelled — especially by the fabled law of averages — to change their behaviour. Every spin and every coin toss is “statistically” independent of all the previous ones.

Between misinterpreting the law of large numbers — that is, by presuming that it must apply to every small sample — and not understanding the salience of statistical independence, the gamblers met their ruin.

Why India lost and why it shouldn’t have

There cannot be a definitive answer to why India lost, even though everyone who watched the final would be certain that at least they know the real reason. These reasons can range from the choice of stadium to India losing the toss and from the absence of Hardik Pandya to Travis Head’s catch of Rohit Sharma.

Only one thing is certain: India did not lose because of the law of averages.

On the contrary, India’s unbroken streak should have helped them win. That’s because, unlike coin tosses, a series of cricket matches (and the performance of the players both individually and as a team) are not statistically independent of each other.

The fact that India entered the final after having beaten every team (including Australia) in the competition would have given India an added advantage. The same kind of psychological and/or skill advantage that Broad had over Warner during the Ashes. Winning teams often place a lot of emphasis on such momentum — be it how one ends a batting innings or how they get into the habit of finding ways to win matches.

Losing teams/players also have momentum, albeit an unwanted one.

Cast your mind back to that over in the inaugural T-20 World Cup when Yuvraj Singh hit the same Stuart Broad for six sixes in an over. Some of those who were watching that match live and who knew about Yuvraj Singh’s temperament might have predicted the first six because Singh had been involved in an animated exchange of ideas with England’s Andrew Flintoff.

But by the time four more deliveries were smacked into the stands, almost everyone watching (including perhaps Broad himself) expected Yuvraj to hit the sixth six. That’s momentum and it is built up because each delivery (and its outcome) affects the next one. There was no law of averages that came to Broad’s rescue.

Lastly, even though South Africa has done little to get rid of the “chokers” tag, is India more deserving of it now that it has faltered at the final and semi-final stages of the ICC events with an alarming regularity since 2014? Share you views and queries at udit.misra@expressindia.com

Until next time,

Udit