Benford's Law dictates that, in any group of related numbers, whether it's a list of the areas of rivers or the street addresses of the first 342 people listed in the book "American Men of Science," numbers that begin with the digit 1 are found about 30% of the time -- three times more frequently than a naive theory might predict. The probability declines smoothly as the digits rise; the digit 9 is found at the beginning of numbers only 4.5% of the time. This counterintuitive and freaky result can, in theory, be used to help detect fraudulent tax returns, bogus scientific experiments, and other cases of data fabrication, at least until the fabricators catch on to Benford's Law.

Re: Benford's Law

There are 3 messages in this thread, displayed in the order they were posted.

stupidsexyflanders 2/19/2004 6:37:55 AM Pacific

Maybe I'm not understanding it correctly, but I don't get what's so freaky about this. The "disproportionate" appearance of lower first digits seems like simply a reflection of the fact that there are fewer big things in nature than small things. There are more small lakes than big lakes. There are more small streets than big streets. etc., etc. Even when you're talking about a list of numbers that are ginormous -- say, a list of the weight of 2000 different stars, in ounces -- you would still expect to see a higher distribution of stars at the lower end of the scale, with the first digit of the weight more likely to be closer to 1 than 9. As the the link explains, the theory doesn't work for perfectly random numbers, like lottery drawings; it only works for things that are counted. Am I wrong about this?

JM Ferat

5/13/2004 1:55:15 PM Pacific

I think that your analysis of "there are fewer big things in nature than big things" does not address the issue. The number 1,000 is clearly larger than the number 90 yet it begins with the digit 1. Benford's does not address the absolute size of each number, merely the first digit....

Jerry Kindal

5/13/2004 2:22:07 PM Pacific

Indeed, what is super-freaky about it is that it is independent of units. Say a list of measurements was originally in yards and you changed it to feet by multiplying by three. Benford's Law would supposedly still hold! Even though every 1 is now a 3, every 2 a 6, every 3 a 9... assuming a typical distribution. What used to be 4, 5, and 6 will now be 12, 15, and 18, and these will start with 1... but there are now more of them than the other numbers. This is counterintuitive but I'm sure if you do the math with a real set of numbers, it all works out.

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Re: Benford's Law