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Thursday, November 17, 2005

Don't get fooled by success

Consider this experiment: you are a punter, and you get a letter from me saying that I have the ability to forecast the result of all cricket matches, and if you pay me Rs. 10,000, I shall tell you what will happen in the next game so that you can make a killing -- perhaps in crores -- by betting on it. I invite you to pay me Rs 10,000 for the results of the next game. I promise you that I shall return the money if my prediction turns out to be incorrect. We work out an online mechanism by which you can cancel the payment right after the game if you wish to.

I get it right. I make the same offer regarding the next game. You pay me Rs 10,000 more, and this time make a modest bet with your bookie on the result I predict. I get it right again. You pay me my fee for the third game as well, and bet an even bigger amount with the bookie. I get it right again. You make a killing. I up my fee to Rs 1 lakh per game. You accept, having already made far more than that.

So are you a schmuck for having done all this?


See, you don't know what I did in the meantime. Here's what I did: I wrote to 1000 punters making the same offer to them. They all accepted. I told 500 of them that Side A would win and 500 of them that Side B would win. Side A won. I returned the money of 500 people.

Then, regarding the next game, I told 250 of the 500 people that Side A would win and the others that Side B would win. Whichever side won, I returned the money of 250 people. That still left 250 people who were beginning to trust me by now.

Regarding the third game, well, you get the drift. 125 this, 125 that. After the game, 125 people, one of whom is you, trust me enough to raise my fees substantially. Not that it matters -- I have already made Rs 8,750,000.

And here's what will happen in future: even if I get my next prediction wrong, you will still look at my record, see that I've got 75% of my results right, and reason that my success rate justifies your continuing with me. By the time enough people see through me, I've made tons of money and can retire and go buy that yacht. Hell, many yachts. And I can even start the jhol all over again.

What I just described above is a typical illustration of the survivorship bias. It is the reason, for example, many mutual funds appear to have impressive records over the past few years: we ignore the possibility that they might just have got lucky, and we do not take the many failed mutual funds into account, just as you didn't take into account -- because you didn't know about them -- the many predictions that I made incorrectly.

That is why we should not be impressed by the 28% of managed funds that outperform the Sensex over a five-year term, as Gautam Chikermane points out in yet other fine article in the Indian Express. I must admit, though, that it doesn't explain Warren Buffet. That man is something else.

Cross-posted on The Indian Economy Blog.

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