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# Benford's Law

Submitted By jla6x7
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Mark Nigrini – Benford’s Law

After attending Mark’s presentation, I feel as though I have a better understanding of Benford’s

law. Mark talked about the history of Benford’s law and how Frank had tested it and first used it as

physicist. He showed us several graphs of data where Benford’s law applied. Not only did it apply to

financial data, but it also applies to many other sets of data. I was extremely fascinated when he showed

us a graph that compared the speed of river currents to Benford’s law. It truly made me believe and

understand that sets of data, when compared on a large scale, should follow Benford’s law. If they don’t

follow Benford’s law, then it is highly likely that something isn’t being allowed to happen naturally.

Mark explained to us that the first digit is the only digit that should be affected by the higher

probability of it being 1, 2, or 3. The possibility that the first digit of a set of numbers that should follow

Benford’s law is 1, 2, or 3 is approximately 60%. 30% of the 60% is just for the probability of the first

number being 1. Because only the first number should be affected by a higher percentage of 1, 2 or 3,

this means that the ending numbers should be evenly spread percentage wide. You should be alarmed if

you see any significant spikes in data for the ending digits. This may mean that the numbers are being

Spikes in graphs may be explained by artificial alterations or things like rounded numbers. There

may be fixed numbers that always turn out to be rounded numbers. Let’s say for example that you

receive a bill every month from your internet provider. It is highly unlikely that your bill would vary from

month to month. You would more than likely have a fixed cost that is set at a rounded number. It

wouldn’t be a red flag to see a cost for \$2,500 every month for your business to pay for its internet. This

may cause a set of data to not obey Benford’s law. You may be looking at a set of data and thinking,

“Wow, something is seriously wrong here.” As soon as you dig into the data, you should be able to

identify the things that make the graph not obey Benford’s Law.

It isn’t uncommon for fraudsters to hang around specific thresholds that they fear may trigger

extra attention to the crimes they are committing. After fraud has been committed over a long period of

time, if Benford’s law is applied to the data, you will notice that the 9’s and 0’s may appear far more

often than other numbers. This is because fraudsters may be trying to stay under or over a specific

number that may grab someone’s attention to what is happening. If you notice huge spikes in these

threshold numbers, it may be a good sign that there is a fraudster amongst your company.

He also spoke with us about the irony of how we are taught accounting as students. There have

been tests through a large variety of accounting text books. The top numbers used in the books are all

rounded numbers. He talked with us about the irony on how we are constantly being shown rounded

numbers in our textbooks but how we are supposed to label them as red flags in the professional world.

It would be alarming if we constantly saw rounded number’s in our company’s accounting books, then

why are we being constantly fed those numbers in our text books?

Mark also told us about a couple crimes that had occurred recently. He explained that if

Benford’s law would’ve been applied they may have been caught sooner. It also appeared that there

was an extremely severe lack in controls in general. Both crimes’ involved persons who had to create

their unique number to receive as payment. This means the numbers they were generating were not

Darlene Wooten and Charlene Corley were twin sisters that owned a hardware company. They

would get contracts with the department of defense and sell them small amounts of goods. However,

they noticed something very strange. No matter the amount, the department of defense would almost

always pay for whatever the shipping cost turned out to be. At first, the sisters would set a shipping cost

that matched the price of the invoice. Then, they would slowly start to double the cost. After years

passed, they were charging \$30,000 shipping for a \$30 product. They would continue to receive

approvals and payments for the invoices that they sent. They continued to increase the shipping costs to

an amazing amount of money. At one point, they were charging over \$900,000 in shipping for an item

that was under \$5. The sisters had racked up over \$20 million in revenue from the department of

defense. They had bought and excessive amount of cars, houses, and others goods. The eventually got

caught when they mistakenly created two invoices using the same number. Mark seems to think the

only reason they were caught was because after this duplicate number, the invoice was actually

physically placed on someone’s desk rather than being sent through their automatic system. Anyone

would notice an issue with a \$1 invoice that included a \$900,000 shipping cost. After getting caught, one

of the sisters committed suicide. The other sister blamed all the wrongdoing on the deceased. She was

sentenced to 6 years in jail and owed \$15 million in restitution. The joke of the whole story is that she

only has to pay back the \$15 million in amounts of \$300 a month. AKFJHSKJFHKSSDHGKJSDHGKJSDH!!!!

Is that what you were thinking too? That means after 50,000 months of \$300 payments, her restitution

would finally be paid off. If you guessed that that was equivalent to 4,166 years, you were right.

Mark also talked with us about Harriette Walters. She fraudulently gave away over \$31 million in

tax refunds to family and friends. In doing so, she was most definitely able to get a significant portion for

herself for the amount given away. If the tax refunds were properly audited, someone would have been

able to spot the errors in the amounts allotted for the refunds. Some of the amounts refunded were

perfectly rounded numbers. Since there is a specific calculation used to calculate tax refunds, this makes

perfectly rounded numbers impossible. She was clearly just making up her own numbers to reward

friends and family. She eventually got caught when she forged an official’s signature and sent it in the

mail in attempt to convince a bank that a refund given to a family member of hers was legitimate.

However, they were already concerned because the \$400,000 check was attempting to be cashed at a

bank that was located inside a convenient store. They don’t often see deposits for that amount, and

when they do, you can be assured that will be asking questions.

After listening to Mark, I feel as though I am a lot more in tune with Benford’s Law. He was able

to provide his own examples of different sets of data that he tested against Benford’s Law. It was

amazing to see the graph line up perfectly with the statistics and probabilities that are stated in

Benford’s Law. I am more than interested in doing my own research and tests using Benford’s Law and

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