Benford vs. Bash usage

I was on IRC today listening (reading) to some people complaign about stored procedures, reading between the lines they were falling into the keep in simple camp of SQL/RDBMS. Wanting to find saner pastures I googled to see if Joe Celko had a blog, I couldn't find one but I did find a collection of his articles.

The first reminded me of a phenomenon known as Benford's Law, quickly explained it states that if you examine any set of data, the digit one will be the leading digit approximately 30% of the time (out of the 9 possible leading digits for values > 1). In fact P(d) where d is the digit is approximately,

 

P(d) = log10 (1 + 1/d)

It's the sort of thing you can't really believe until you test it, so I ran the data on bash usage from yesterday against it. Here are the results (and in my opinion they are pretty darn close) ...

 

Digit	Bedford Probability	bash Data
1	0.301029995663981	0.347826086956522
2	0.176091259055681	0.217391304347826
3	0.1249387366083	0.0869565217391304
4	0.0969100130080564	0.0434782608695652
5	0.0791812460476248	0.0652173913043478
6	0.0669467896306132	0.0434782608695652
7	0.0579919469776867	0.0652173913043478
8	0.0511525224473813	0.0869565217391304
9	0.0457574905606751	0.0434782608695652