Our weekly explainer on economics using lessons from popular culture. In Installment 27, Shah Rukh Khan misunderstands the Law of Large Numbers.
‘Kabhi kabhi kuchh jeetne ke liye, kuchh haarna bhi padta hai. Aur haar kar jeetne waale ko baazigar kehte hai.’
“Sometimes to win something, you first have to lose. And those who win after losing are called baazigars.’ Shah Rukh’s statement, from the film Baazigar, indicates two things: One, he has no knowledge of statistics; Two, he is so charismatic that he will get the girl anyway. And indeed, look at Kajol in the middle of Shah Rukh’s dialogue and you can see, even in this close-up, that she is already weak in the knees. When a loved one looks at you like that, you can recite Donald Trump tweets and still get action.
So what’s the mistake Shah Rukh made? Well, he showed that he has no understanding of the Law of Large Numbers.
Here’s a definition of the Law of Large Numbers: “In probability and statistics, the Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population.” A simple example: take an evenly weighted coin and flip it 10 times. It’s likely that despite the coin being evenly weighted, you won’t get five heads and five tails, because, well luck. But over a larger sample size of 100 flips, an even distribution is likelier. That’s more so over 1000 spins, even more over 10 million spins, and so on. That’s the Law of Large Numbers: the more you flip, the closer your actual result is to the expected value (EV).
A concept related to this is Regression to the Mean. This is “the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement.” So if you toss a fair coin ten times and get eight heads, Regression to the Mean refers to the likelihood that in the next ten spins, there will be less than eight heads. (That is, the result will be closer to the mean of five heads.) This is a likelihood and not a certainty, and is thus distinct from the Gambler’s Fallacy, which we discussed in an earlier Housefull Economics, which insists that after ten heads in a row, tails is ‘due’. Regression to the Mean ensures that the 11th spin is likely to be closer to the mean than the results so far, and the Law of Large Numbers ensures that the more you spin that coin, the closer your overall results get to the mean.
I think of Regression to the Mean as the mechanism by which the Law of Large Numbers finds expression.
One example of Regression to the Mean is when we expect tall parents to have kids as tall as themselves. Well, the parents are tall due to a combination of genes and luck, and luck tends to even out, so the kids are likely (not certain, mind you) to be shorter than their parents. In other words, the family height regresses to the mean.
Another example: people speak of the Sports Illustrated Jinx. Sportspeople who appear on the cover of Sports Illustrated often experience a downswing in their careers after that. But this is no jinx: sportspeople are likely to appear on the cover of Sports Illustrated when they are at the peak of their career, after outlier performances, so a Regression to the Mean is likely.
A further example (and one I wrote about in an old column along with the SI Jinx) is what I call the Godman’s Blessing. A desperate person goes to a Godman for his blessing when he is at a low point in his life. Then things get better as his life takes a Regression to the Mean, and he attributes it to the Godman.
Regression to the Mean is also a reason people believe in quackery like Homeopathy. As I wrote here, many diseases have a natural life cycle, and patients get worse before they get better. (The common cold is an example.) In other words, they show a Regression to the Mean. If you take medicine towards the bottom of this progression, you might mistake correlation for causation and give credit to the medicine.
What does this have to do with Shah Rukh Khan, though? Well, here’s what he says in a nutshell: One loses, one wins, and those who win after losing are called Baazigars. Duh, no! Assuming that you are not a complete loser whose EV is zero, you will eventually win if you keep trying. Given a large enough sample size, the Law of Large Numbers will ensure that your results match your EV. (With Shah Rukh’s abundant charisma, his EV was probably high to begin with.)
What is the life lesson we can derive from this? Simple. Don’t get disheartened by failure, and don’t let success get to your head. And if a girl looks at you like Kajol looks at Shah Rukh in that clip, don’t sweat the exact words. You’ve already won.