Logic, Murderous Maths, Notes on everyday life

Benford’s Law

Simon is looking at his subscribers count on YouTube. We speculate if he gets to 1000 before the end of the academic year. Simon tells me that’s because subscriber count is just another example of Benford’s law in action. What is Benford’s law? – I ask.

“If you take some data that spans a few orders of magnitude and take the leading digits of all numbers, then you’re most likely not going to get a uniform distribution. Instead, 30% of the time, the numbers will start with a 1, a little bit less of the time – with a 2, even less – with a 3, and so on all the way to 9 (which has a low chance of occurring). For example, the populations of countries would follow that law. If something is not random enough, though (like human height in meters), then it wouldn’t follow that law. If something is too random, it also wouldn’t follow that law.”

Simon explains further: “Consider YouTube subscriber count over time. If you have 100 subscribers, then to get up to 200 is an increase of 100% (which is pretty big). But to get from 200 to 300 is only a 50% increase. From 900 to 1000 is just 11 %.”.

Then his dad asks: “What about going from 1000 subscribers to 1100 subscribers?”

“Well, Benford’s law only cares about the leading digit (and that’s what you want to increase as well). So you don’t want to increase from 1000 to 1100, you want to increase from 1000 to 2000! In other words, start a new Benford’s law ‘Epoch’.”

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