In 2013 I wrote the following page … at the end of this updated version of the page, I have included the Benford’s Law analysis of the 2017 Sunday Times Rich List. Again you will see that the data do not conform to Benford’s expectations.

In today’s Sunday Times they published their latest Rich List: the 1,000 richest people in Britain over the last year. I copied and pasted the rich list into an Excel file and analysed it according to Benford’s Law.

Benford’s Law is concerned with the distributions of digits in a number: they follow a logarithmic distribution. The following charts show what the Rich List shows and what Benford’s Law predicts. Take a look at the graphs and then read my conclusions: the graphs relate to the values of wealth shown for each person or family in the Rich List. For example, the richest man on the list is Alisher Usmanov with a reported wealth of £13,300,000,000. In terms of Benford’s Law, this means that digit 1 is 1 … the first digit in the number 13,300 … number 3 is digit 2 … and 13 are digits 1 and 2 …

rich_1

rich_2

rich_3

Discussion

The red and blue lines on every graph should overlay each other: there should be no diversion between them. That would mean that the actual distribution of digits within the numbers is equal to the predicted distribution of digits according to Benford’s Law.

2017 Update

Whilst the following graphs are not exactly the same as they were in 2013, there do appear to be significant differences between the actual data and Benford’s expectations.

times_1000_2017_benford_graphs

Conclusions

For full understanding you need to read more widely about Benford’s Law. However, the main conclusion we can draw from the above graphs is that everything is not as it seems. The sample size in both cases is 1,000 people/companies so that is more than adequate. Any divergence from the Benford predictions or standards suggests that the actual data have been manipulated in some way. Now, I am not saying that The Sunday Times people are crooked or anything but it MIGHT suggest that their methodology might be less than perfect!

I cannot let you have my spreadsheets because they contains data that are not mine to share. if you want help with Benford’s Law, however, feel free to discuss it with me and I will help if I can.

Duncan Williamson

One Response to “ST Rich List: Benford’s Law 2013 and 2017”


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