Sunday, 15 March 2009

Benford's Law

During an idle moment earlier this week, I decided to put Benford’s Law to the test using as the data my daily P&L totals which have been recorded since January 1st, 2006. Over 1,000 individual data items.

For those not into mathematics and statistics, Benford’s Law pertains to the leading significant digit of any collection of real data.

At first thought, it might seem that on any day, the chances of the leading digit being any one specific digit are the same as it being any other number, i.e. 1 in 9, and that if you were offered odds over 8-1, this would be a value bet.

Well, it would indeed be a value bet for some digits, but not for most. Benford’s Law states that the leading digit will be a ‘1’ 30.1% of the time with ‘9’ leading just 4.6% of the time.

The results using my data do bear this out very closely. Remarkably two of my numbers are exactly the percentage predicted, and all are very close. A few less ‘8’s and a few more ‘2’s and they would be an almost perfect fit.

The expected percentages along with my results (bottom line) are shown in the screenshot above.

A completely pointless exercise I know, but I found it interesting!


Anonymous said...

I first came across this in a wonderful piece of easy reading called "freakonomics" written by Steven Levitt and Stephen Dubner. A very interesting topic; perhaps you could use it to analyse some of the posted P/Ls out there to test if they are real or not (assuming that you have nothing better to do sometime again this week, and if you're anything like me, you probably will).


Cassini said...

Actually, one of the uses of this 'law' is to detect fraud so it would indeed be perfect for that! Have you tried this with your figures?

Anonymous said...

In the book that is the example they use (fraud). I did try it with my figures about a year ago after I had read the book. At the time I was going through a phase of trying to win 10% from £1000 so I had a high number of £95.80 entries and it rather skewed the figures. I might have a look at the past 3 months tomorrow, I'll let you know after I have.