Benford’s Law – 2 Superb Examples Of Nature Being Awesome
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Benford’s Law
There are examples of patterns in nature, most people will have heard of the golden ratio, and other examples like sunflower seeds and the way they grow. There are even honeycombs, one of the strongest structures known to man.
Fun fact, another honeycomb structure on a subatomic level, Graphene has been announced as one of the strongest materials we have created as humans.
But I’m not here to talk to you today about Graphene or how bees became the inspiration to making things super tough.
Today is about Benford’s law.
The American-born Physicist worked on a theory that showed the distribution of numbers has a pattern. He built on the idea and is also known sometimes as Newton-Benford’s law, but more commonly as Benford’s law as the title suggests.
The Juicy Bit
Okay, so… The theory goes that you take the leading digit in any number. A list such as 34,12,99,1010, 400 etc would have the rest of the digits stripped so only the first one remained. Our list would now look like 3,1,9,1,4 and so on and so on.
Benford stated that human nature isn’t quite as random as we thought it was. He said that the distribution of numbers was actually pretty specific when it comes to natural things.
He said that the number 1 would appear 30.1% of the time, number 2 would appear 17.6% of the time and he has percentages all the way up to number 9. Because 0 can’t be a leading number it isn’t counted.
| Leading Digit | Percentage appearance |
| 1 | 30.10% |
| 2 | 17.60% |
| 3 | 12.50% |
| 4 | 9.70% |
| 5 | 7.90% |
| 6 | 6.70% |
| 7 | 5.80% |
| 8 | 5.10% |
| 9 | 4.60% |
It goes on and like the table laid out above. Because I love a good graph it would be nice to plot the percentages to give a visually pleasing aspect because looking at a table of numbers does nothing for most people. Can you see a pattern from the table?
You wanted your graph, have it.
This is the curve that Benford’s law is supposed to take. I’ve only plotted the percentages as numbers.
The fact that you may have sold your house and moved to a different area would strike you as your choice, right? Right?
What about video game sales? Let’s even narrow it down to one specific area. Let’s say North America. Maybe you’re not even making your own choices there either.
House Price Benford’s Law
I stumbled across a dataset about house sales in the UK for 2020. If you like the data is here. It takes a while to load if you’re going to try to replicate it.
I think it goes without saying that it’s not an exact science, but the distribution of numbers usually closely resembles the curve above.
As mentioned I grabbed a dataset, loaded it into a jupyter notebook and turned every sale price into a string so I could extract the leading digit and proceeded to count them. And here is what it looks like plotted..
I was wondering how this was actually going to turn out when I checked on the leading digit count in a tabular format, part of me was hoping I’d found an anomaly and it could be disproved. I actually sat down with a couple of the office guys and plotted it blind to see how it would look. It was quite unnerving, to say the least when the graph came out almost exactly as predicted.
Another test
As any good scientist would do they’d keep testing a theory to see if it fits before declaring the theory as a rip-roaring success. Besides that this has been around for ages, I’d just never heard of it. So I did another test. This time I found a dataset about videogame sales and did the same process, loaded, processed, converted and stripped until I had a new table ready to load up.
The same curve appears again in a completely different industry, on a completely different continent.
Nature has a funny way of creating patterns in our lives, down from the subatomic level complexities of graphene, all the way up a brick-by-brick house being sold in the UK. Doing some recent research for a client of ours it also appears in bra sales!
Think everything you do is your own choice? Here’s evidence to prove that maybe you’re not as in control as you think.
Check out some of the other sweet posts I’ve written…
