The Strange Logic Behind Catching Business Frauds - Benford's Law

1,451 views Wait, is this logic right? • May 16, 2023

Slog Reference: Benford's law

Description

Benford's law easy explanation. There is a really simple law that explains how to detect fraud when there are numbers involved. It can help you detect accounting fraud, and election fraud and help you get an idea of whether the given data has been altered or not. It's called Benford's law, and we're talking about it in this episode of the FutureIQ podcast with Dr. Navin Kabra and RJ. Shrikant.

Let's understand what is Benford's law. How does Benford's law work? What are the examples of Benford's law? What are the real-life applications of Benford's law and everything else that will help you detect auditing, business, accounting and other types of fraud?

Hope you enjoyed FutureIQ by Navin Kabra and Shrikant Joshi. Do hit us up on Twitter:
@ngkabra http://twitter.com/ngkabra
@shrikant https://twitter.com/shrikant

Listen it on the podcast provider of your choice: https://tapthe.link/FutureIQRSS

Learn how the ideal amount of fraud is not zero: https://youtu.be/joF5dHhF3s0
Another interesting law, Goodhart's law: https://youtu.be/OU5W-b_e8a4

Chapters:
00:00 Introduction
00:45 Detecting frauds
03:33 How it works?
04:45 Real life examples
05:18 How to detect frauds?
07:10 Iran's election fraud
09:20 Can you fool it?
11:12 Real life applications

#futureiq #benfordslaw

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Transcript

- okay I see a bump at four that four is much higher than where it should have been yeah see another bump at nine where it is like maybe ten percentages of five yeah what do you think it means it means the manager and the employees have been makhan eating a lot right do you think that a fifth standard kit well seven standard kid would be able to detect election fraud if just given the number of votes in all the different ballot boxes what do you think shrikant no what how wait what yeah so that is today's video it's about a concept called benford's law um let me explain with an example okay a different example okay and now imagine

0m 46s there is an office in which employees are allowed to spend up to five thousand uh on their own with just their manager's approval like most offices there is always some petty cash and then uh there's a next level for uh ten thousand there is um you know managers managers approval is needed I think more than that goes through a much more elaborate process now the CFO of the company believes that there are a lot of fraudulent expenses going on in the company right how would they detect that now the first thing you would imagine is that you have to go through all the receipts and then you have to see which one seems fake and you know just basically

1m 31s bring in Sherlock Holmes right yeah I mean how how do you figure out which of them is is fake otherwise because it's so benefits law is a very interesting statistical law which probably you haven't heard of but it's fun okay okay uh so let me ask this if I just took all the expense receipts and all the payments that were made out okay and let's say I end up with uh like 12 000 different amounts huh okay now here is a very simple thing I'm going to do okay I am going to take the first digit out of every amount okay first digit not the last digit so if it is a reimbursement of 462 I will

2m 24s take four if it's a reimbursement of 1300 I will take one first digit and then I just count them uh now and I uh count all the digits how many ones how many to what percentage over ones what percentage were two What percentages were nines and I plot them what do you think the distribution will be like has to be random like and anybody can reimburse any amount between one and whatever number so you expect like it would be you know an equal number of bars or equal number of things and eleven percent once ten eleven percent twos and so on right yeah actually that's not what happens right in a lot of real world cases the

3m 03s distribution is like a skewed distribution okay one third of the numbers will usually be starting with one about you know a little less than one fifth of the numbers will be starting with uh two and so on and it falls uh down all the way so that the eights and the nines are about like five percent and four percent and why would that be it doesn't how does that make sense so um the thing to realize is that when let's say uh that I took a large number of uh numbers from one to two hundred you realize that half of them will start with one oh yeah right or if it was from 1 to 300 a lot of

3m 52s them will start with one sum with two so because uh it is open-ended uh whenever you cross to the next number of digits for a long time you see only once yeah right so uh I mean in fact let's not get too much into the details of why it happens human mathematicians uh get a little worried it makes sense because when you cross a certain uh order of 10 the next so many numbers are going to start with one and that is where you are going to be one drawing around plus also I think a lot of times what we do is if it's a higher number like say 850 or 900 we round it off to the nearest correct

4m 40s uh correct multiple of 10 right um so even if you do something like you know uh take the first digit of the populations of all the countries and territories in the world right now it's not a very large number 236 only okay so you expect when the numbers are not large it won't follow laws very easily yeah but even then you notice that it's a very similar curve very interesting right so now coming back to our example I want to look at fraud huh okay the office the office fraud I just take all the amounts that were paid out here and I look at the first digits and I do this analysis very easy to do in Excel and then I plot it right and

5m 32s if I notice that there is it instead of it being a very simple curve with a high at one at around one third and going all the way down to nine at around five percent okay I see a bump at four that four is much higher than where it should have been yeah see another bump at nine where it is like maybe ten percentage of five yeah what do you think it means it means the manager and the employees have been makhan eating a lot right basically what it means is that instead of the expenses being random right there is extra expenses being squeezed into the below 5000 so that's why there is a bump at

6m 15s four and there is some being squeezed into the below ten thousand so there is a bump at nine right since the manager can only approve a maximum expense of 5000 or rather under five thousand so a lot of 499 expenses are going to come into the list yeah I again you know this might not be fraud but yeah at the very least you know that there is some Distortion happening in the data yeah but if you took all the number of votes in all the ballot boxes individually in an election and then you plotted them you better see a benford's law curve like this if you see a bump hmm at unappropriate places or if you see a shape

7m 00s that is different that means there is high chance that there was something funny going on in this election yeah in fact uh in Iran in the 2009 election okay there were widespread uh allegations that Amazon won the election terribly sorry to any Iranians who might be watching this video uh we try to make sure that we get the pronunciations right but just are a little weak with the language so again apologies I think it's um extremely sorry don't mean to laugh the laughter is about us not being able to do it rather than the name itself there you go so there were widespread allegations of Fraud and statisticians have gone and looked at uh the numbers and found that benford's law was

8m 00s violated in fact you can go one step further if you look at the votes received by his opponent there there is a nice benefits lock curve but if you look at the words for ahmadin ijad then you see the benford's law curve being violated now the entire question about the seventh standard student and election fraud makes sense because even a seven standard student can count those numbers and plot that on a graph so in fact one of the interesting things there is that usually if the numbers haven't come naturally if they come naturally then they follow the benefits Locker if they didn't come naturally if somebody sat and typed in just came up with a bunch of numbers then usually

8m 46s what you find is that the curve is like low on the sides and high in the middle because humans don't want to do anything extreme and you will see four five six High and the others don't right so there are certain curves where you know this was manually generated this was generated by a computer using a uniform distribution that would be like a flat curve and so on like in life mathematics is also dictated by a lot of Curves I said that I did all right so um this basically tells me that now that I know benford's law I can fool it all I have to do is make sure that everything in that I'm trying to manipulate

9m 30s follows the benefits Locker well uh maybe right maybe well one thing to keep in mind is that benford's law even if you make sure that the first digits follow the curve there is a different benefits Locker for the second digits and if you did look at that you will still get caught and third digit and so on right that is one thing to keep in mind the other thing to keep in mind is that criminals are not very smart actually right they get caught in fact some of the greatest scientists in the world have been caught by simple statistical checks like this there is a book called predictably irrational by a scientist whose name I won't take but

10m 16s one of his papers somebody analyzed the numbers in there and found that the distribution was wrong and that is pretty clear that the paper was fake right the numbers in the paper were made up right so this is a world famous scientist the book predictably irrational is there in my house and I'm sure srikant has also heard of it I have heard of the book and I'm sure you guys are going to search for the book uh so go ahead uh check it out but I am still trying to figure out whether Naveen complimented me or insulted me when he said said criminals are not smart when I when I actually asked him about criminal but uh anyway so uh there

10m 58s are multiple benford's law that I will have to take into account so it kind of makes sense to not attempt any fraud in that sense but uh can I apply benford's law in my daily life is there anything well I mean you know if you are a fraud detector or an auditor of accounts then of course you should be applying it in your daily life in fact I have not handbooks that are uh given out to uh the uh you know it Auditors for example in fact they have a nice explanation of benford's Law and how to apply it okay similarly uh isaka is a Association for uh cyber security okay and they also explain nicely how to apply binford's law uh

11m 54s to keep your company uh secure but you know maybe not something you can apply in daily life right uh you don't want to check your son's numbers like this uh but you know what I want to say is that not everything needs to be applicable in real life right I think you should be curious about out interesting things just generally even if it doesn't apply in real life you never know when it will start applying that is true especially if you are called in to verify the results of an election and declare it a fraud or not on that day you will rule not knowing benford's law if you didn't reach this point in the video but since

12m 36s you reach this point in the video you now know benford's law so congratulations and if you've spotted examples of benford's law do tell us about it in the comments my name is srikanth this is Naveen this is future IQ thank you thank you