I’d be willing to bet most of us have no idea who Frank Benford is, but he’s certainly keeping an eye on you. Every year millions of people around the world need to file their taxes and he’s making sure they aren’t fudging their numbers. You might be thinking it’s a pretty impressive feat for one guy to be checking millions and millions of tax returns from around the world each year, and you’d be right. What makes it even more impressive is that he’s been dead for over 70 years.
Who is Frank Benford?
Frank Benford is not known for much as he lived a generally average life. He was an electrical engineer and physicist who mostly worked for General Electric in the Illuminating Engineering Laboratory and the Research Laboratory for about 38 years in the early to mid-20th century. He was an expert in optical measurements, with over 100 published papers in the fields of optics and mathematics and was granted 20 patents on optical devices. Not really exciting stuff to most of us and obviously has nothing to do with taxes.
What is Benford’s Law?
In addition to his work at GE, Benford is credited with essentially rediscovering the work of statistician Simon Newcomb about a mathematical and statistical anomaly surrounding the frequency distribution of leading digits in many real-life sets of numerical data, which is now known as Benford’s Law. Confused about that last sentence, join the club, here it is in layman’s terms.
Start with a sampling of 1000 random numbers from the infinite numbers we have, then from those numbers, take a subset of another 200 random numbers. Then look at only the first digits of those 200 numbers. Using this random number method, you’ll find that there will be a consistent distribution of the first digits, it’s just not what you think.
Most of would think that the first digits would be uniformly distributed, aka more or less be evenly spread across the board. 10% would be a 1, 10% a 2 and so on. Turns out, that’s not the case, not even close. What you’ll find is a distribution curve that looks more like this.
Most numbers will start with a 1, then the second most numbers will start with a 2 and so on down the line. Amazing right? I won’t go into why this works the way it does (mostly because I have no idea), but will let you find out more here.
What does this have to do with my taxes?
Clearly, Benford himself isn’t actually checking your taxes, but Benford’s law certainly is. Basically, tax agencies can use Benford's law to check if the numbers reported on your tax return follow the expect distribution of first digits. If your numbers hold true, so far so good for you. If they don’t, the IRS or other governing agency might get suspicious and know they should dig a little deeper. Now, it’s not to say that it’s a perfect method, but what is? Clearly, its possible that your numbers naturally wind up with a different distribution, but it’s a good first line of defense when you need to sift through millions of returns each year.
What else can this be applied to?
I'm glad you asked! Benford’s Law can be applied to far more than just your tax return. You can find plenty of uses for it in the forensic accounting world, but it can be used in all sorts of other industries. Its been used to detect election fraud or more specifically, lack there-of in presidential elections. It can also be applied to finding deepfake images or videos, finding social media bots, it’s even been found to be applicable to classical music!
Benford may not have been the first to discover this law and your new found knowledge of its existence likely won’t help you achieve your financial goals. In fact, the only way I can think that most of us could use the knowledge would be to actually cheat on our taxes (but we won’t!). None the less, it’s a fascinating phenomenon (at least to me) that I thought was worth sharing. Hopefully, you found it as interesting as I did!