Spoiler Alert: If you’re a Biden supporter, find your favorite safe space/cry room. Trump supporters, read on, I’m about to explain how the bean counters beat Biden.
So, what’s all this hub bub about Benford Analysis? And does it provide compelling evidence that Joseph R. Biden received fraudulent votes in the 2020 presidential election? Well, I’m about to explain the answer to the first question in plain English, and the answer to the second question is: “You’re damn right it does!”
Benford Analysis is based on Benford’s Law. Simply put, this theory states when you have a natural collection numbers, the leading digit is likely to be a small number. Smaller numbers appear as leading numbers more frequently than larger numbers. The graph below shows a “perfect” distribution of the frequency of leading digits under Benford’s Law:
So, if we had 1,000 numbers in a data set, 301 of them would start with a 1, 176 would start with a 2, 125 would start with a 3, and so on, until you get down to the last 46 numbers, which would start with a 9. The red line with the red diamonds show the perfect frequency distribution under Benford’s Law, and the blue bars show the actual distributions for the data set we are analyzing.
In the real world, would a data set of 1,000 numbers always have 301 numbers that started with a 1? No. Of course not. So, let’s come up with a hypothetical example for an area of the real world where Benford’s Law is frequently used to detect fraud – fake invoices! Yes, believe it or not, there are fraudsters out there that actually create fake companies and submit fake invoices to businesses, and the businesses pay them, and the fraudsters pocket the money. True story.
Let’s say we have a law firm that usually receives about 1,000 invoices from vendors that they have to pay each month. Everybody’s got bills, right? So, the law firm’s invoices for the month of October might look this:
Remember, the red line with the red diamonds shows what Benford’s Law says the distribution of leading digits should be. But again, now we’re dealing in reality. So, the blue bars represent the actual distribution of the 1,000 invoices that the law firm received in October. Let’s assume that the law firm only receives invoices in $1,000 increments. This means they received 281 invoices from vendors for $1,000 each, totaling $280,000 dollars. Benford’s Law says that normally, the firm would receive 301 invoices for $1,000 each.
Remember, the leading digit for a $1,000 invoice is 1. So, you can see that the blue bar representing the number of $1,000 invoices received falls just short of the red diamond for that column. The red diamond is Benford’s Law, the blue bar is the law firm’s actual number. By the time we get to the $9,000 invoices received, Benford’s Law was expecting only 46 invoices, but the firm actually received 66. Again, no biggie. What really matters is that the slope of the red line representing Benford’s Law matches the slope of the blue bars representing the actual number of invoices.
So, in our little law firm example here, nothing jumps out at the fraud auditors. The slopes in the graph are very consistence, with reasonable variances. Now, let’s take a look at the month of November. The law firm as just hired a brand-new lawyer. His name has been changed to protect the innocent. Let’s call him “Hunter.” In addition to his legal duties, Hunter is also going to handle the payment of the firm’s bills.
In the month of November, the firm once again receives 1,000 invoices. And again, all the invoices are in $1,000 increments, ranging from $1,000 to $9,000. Remember, under Benford’s Law, there are going to be more invoices with lower amounts than invoices with higher amounts. This just makes sense during the normal course of business, right? You deal with more small vendors than you do large vendors. It’s just how things are.
Now, Hunter is pretty sharp. Well, actually, Hunter’s dad is a big honcho for an international company that does a lot of business overseas. Let’s just say, China. So, Hunter convinces the managing partner at the law firm to change several vendor relationships from US based companies to Chinese companies. Uh oh, now look at the distribution of invoice amounts:
What happened?! The slope of the red Benford’s Law line doesn’t match the slope of the actual blue bar results anymore! Well, Hunter didn’t actually have relationships with legitimate vendors in China. He made them up. Yep. He fabricated invoices. Hunter did away with American vendors that submitted smaller invoices each month for $1,000 – $3,000 each and replaced them with fictitious Chinese vendors that submitted fake invoices for $7,000 – $9,000. Hunter also replaced high invoice American vendors with bogus high invoice Chinese vendors. And Hunter had the checks mailed to his dad’s business address in China and deposited the checks payable to the fraudulent vendors into a bogus checking account that he controlled.
So, let’s take a look at Hunter’s payday. By messing with the expected normal frequency distribution of invoice amounts under Benford’s Law, Hunter pocketed a cool million. Take a look:
Simply put, Hunter fraudulently replaced bona fide smaller invoices with bigger bogus invoices. Now, in our example, that was a million-dollar money grab in just one month, and the drastic change alone would have probably detected this. But the Benford Analysis graph DEFINITELY does!
In the 2016 movie “The Accountant,” Ben Affleck’s character uses Benford’s Law to expose the theft of funds from a robotics company. The US State Department used Benford Analysis to expose election fraud in the 2009 Iranian elections.
So, let’s take a look at some Benford Analysis graphs from the 2020 presidential election, shall we? Yes, that’s right, Benford’s Law is just as applicable to vote counts as it is in detecting financial fraud. Fasten your seatbelts.
Gee, what happened to your vote counts with a leading digit of 1 in Chicago, Joe?
Darnit! Those vote counts with a leading digit of 1 disappeared in Alleghany County, Pennsylvania too, Joe!
President Trump’s slope looks pretty darn awesome, Joe!
Benford’s Law can be a tough concept to grasp. I hope this example helped. I just wanted you to see a real-life application, and the power behind Benford Analysis. And we’re supposed to follow the science, right?! Well here ya go . . . how ‘bout some bean counter science!
See ya in the Supreme Court, fraudsters!
