Benford’s Law states that in many real-life sources of data, the leading digit is not distributed uniformly. Instead the digit 1 tends to occur with a probability of 30.1%, 2 with a probability of 17.6% but 9 has a probability of just 4.6%. In an uniform distribution, you would expect the digits to occur with a probability of 11.1% (1 out of 9). Physicist Frank Benford stumbled upon the phenomenon when he noticed that the first few pages of his logarithmic tables were more worn than the last few.

Media reports indicate that the Canada Revenue Agency employs Benford’s Law to flag tax cheats for further scrutiny. Unlike, made-up numbers that are picked to give the appearance of randomness (you can find an example here), real-life data in tax returns tend to follow Benford’s law. With so many Canadians choosing to file their taxes electronically, it must be a snap for the CRA to check for non-compliance in child-care receipts, charitable donations and medical expenses.

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