Can someone explain Benford’s Law to me. I get that certain numbers show up more often in large data sets, but why?
In: Mathematics
The simple explanation is that when looking at a randomly occurring number of things the first number is most likely to be small with 1 being the most likely.
Now when counting an amount of things you can see a simple trend regardless of what you are counting. That trend is that changing a small leading number is harder than changing a big leading number. I am going to do some rounding for simplicity sake, but going from a leading digit of 1 to 2 requires a 100% increase in total things, 2 to 3 a 50% , 3 to 4 33%, 4 to 5 25%, 5 to 6 20%, 6 to 7 16%, 7 to 8 14%, 8 to 9 12.5%, and last 9 back to 1 11% increase in total things.
As a real world example imagine you are a youtuber and after years of effort you hit 100,000 subscribers. From now on, all your subscriber number counts will be 1xx,xxx subscribers until you have become so successful that you literally double the amount of subscribers and reach 200,000. This likely means that you would need to repeat the same years long effort to change that leading digit. Meanwhile let’s say after a lot of effort, you reach 900,000 subscribers and your leading digit will be 9xx,xxx until you hit 1 million. However going from 900,000 to 1,000,000 is relatively speaking very easy to do as that is only a 11% increase in subscribers. Then once you reach 1 million and have the number 1 as your leading digit. You will need to once again double your subscribers before 2 is the leading digit again.
Another way to look at it is going from 9 back to 1 is an 11% increase, but going from 9 to 2 is a 222% increase.
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