Look at the logarithmic scale. This law has to do with number sets in the wild, so apparently the scaling is flat over the set of data they examined. If you look at the distribution of the number sets over the logarithmic scale, they are evenly distributed. If you looked at the same numbers on a linear scale, they would become more and more sparse as they grow in size.
In real life distributions you are always going to have situations where you fill up the bigger digits last, so it becomes less likely they show up. The best example of this is the population of cities. For cities between 100k and 999k you’ll have a larger number of cities with 100k-300k because cities of those sizes are smaller and more common.
So if you have a small amount of something, you’ll have maybe 2, maybe 3, or 4, or 5, or 6, 7, 8, 9, 10, 11, 12, 13, 14 or so. If you have a medium amount of something, the numbers might be 20, or 30 ish, or 40 ish, 50s, 60s, 70s, 80s, 90s, 100ish, 110ish, 120 or so, around 130. Larger amounts of stuff end up being 200ish, 300, 400, 500, 600, 700, 800, 900, 1000ish, around 1100, 1200 something, 1300
All the numbers I’ve mentioned are about evenly spaced on this logarithmic scale. You can see that a bunch of them start with 1 just because of how big we think they are! It turns out there is a math reason for this, instead of just being about the weird way humans think.
but… why?
https://en.m.wikipedia.org/wiki/Benford's_law
Look at the logarithmic scale. This law has to do with number sets in the wild, so apparently the scaling is flat over the set of data they examined. If you look at the distribution of the number sets over the logarithmic scale, they are evenly distributed. If you looked at the same numbers on a linear scale, they would become more and more sparse as they grow in size.
Cool! Now imagine I’ve got severe brain damage… can you explain that again?
The further left you are in a number, the more likely it is that the digit will be small
What a great explanation! Thanks for dumbing it down.
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In real life distributions you are always going to have situations where you fill up the bigger digits last, so it becomes less likely they show up. The best example of this is the population of cities. For cities between 100k and 999k you’ll have a larger number of cities with 100k-300k because cities of those sizes are smaller and more common.
Benford’s law is about the leading digit, so it doesn’t matter if the numbers are rounded or not.
No problem!
So if you have a small amount of something, you’ll have maybe 2, maybe 3, or 4, or 5, or 6, 7, 8, 9, 10, 11, 12, 13, 14 or so. If you have a medium amount of something, the numbers might be 20, or 30 ish, or 40 ish, 50s, 60s, 70s, 80s, 90s, 100ish, 110ish, 120 or so, around 130. Larger amounts of stuff end up being 200ish, 300, 400, 500, 600, 700, 800, 900, 1000ish, around 1100, 1200 something, 1300
All the numbers I’ve mentioned are about evenly spaced on this logarithmic scale. You can see that a bunch of them start with 1 just because of how big we think they are! It turns out there is a math reason for this, instead of just being about the weird way humans think.
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