Friday, May 30, 2008

The Drukard's Walk

A great talk from Authors@Google;
The Drunkard's Walk: How Randomness Rules Our Lives
by Leonard Mlodinow

Numbers Guy Interview: Leonard Mlodinow;
WSJ: If you can pick an index-outperforming stock 51% of the time, how many picks do you need to make to have better than a 99% chance of outperforming the index? (We’ll assume your picks are uncorrelated and that the magnitude of any outperformance or underperformance is the same.)

Mr. Mlodinow: Consider a stock analyst versus an index fund in a kind of stock-picking World Series. The law of large numbers says if you play a best-of-X series you can be confident that the best team will win — if X is large enough. But for small X, say, a best-of-seven series, there is a surprisingly large chance that the lesser team will win. So in sports just because one team is superior doesn’t mean it will win the series.

The same uncertainty applies to the market. For example, suppose the stock picker has a 51/49 edge over the index fund, meaning he or she will outperform it, in the long run, in 51% of the years in which they compete. How long is the long run in this case? The mathematics shows that in order to justify 99% confidence that the stock picker will outperform the index fund more often than it underperforms it, the contest would have to go on for about 13,700 years...

WSJ: After a particular drug is on the market, it will cause a particularly serious adverse effect to happen to one of every 3,000 patients in an epidemiological, i. e., post-hoc analysis. In retrospect, how many patients must be tested in the randomized, double-blinded, placebo-controlled, clinical trial to achieve 95% confidence that the side effect will show up?

Mr. Mlodinow: You need roughly 14,000 patients. Here is how you get that: The process is governed by the binomial distribution, which can be approximated by the normal distribution. The chance of an adverse reaction in any one patient is one in 3,000. Since you want a 95% confidence interval for one (or more) reactions, you want enough patients so that 1.00 is 1.64 standard deviations (or more) below the mean. With 14,000 patients the mean number of adverse reactions will be about 4.6 and the standard deviation is about 2.2, which gives you what you require. (I have rounded my answer to the nearest 1,000).

Correction: To achieve 95% confidence that the side effect will show up, you need 8,985 patients receiving the drug. This blog post misstated the number as 14,000. See the comments of this post for more details.

WSJ: Might we need to proceed irrationally in our lives to succeed? In other words, if we really believed that so much of success was the result of luck, wouldn’t a lot of us just give up trying?

Mr. Mlodinow: Some theorize that this is the evolutionary reason that we like to assume we are in control, even when we clearly aren’t. That may be so, but I don’t mourn the role of luck, I celebrate it. All else equal, it is a lot more fun not knowing how your book will do, or how your life will turn out, than it would be if everything could be determined by a logical calculation. Moreover, the fact that luck matters means you can help yourself by being persistent. A failure doesn’t mean you are unworthy, nor does it preclude success on the next try. As Thomas J. Watson, the highly successful IBM pioneer, said, “If you want to succeed, double your failure rate.”

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