Benford's Law is a tool that can help detect possible fraudulent transactions by analyzing patterns in leading digits. It states that in random data, lower digits like 1 and 2 will occur more frequently as the first digit compared to higher digits like 7-9. Two examples are described where Benford's Law identified suspicious transactions - a $2M check fraud case where digit patterns trended higher and a $4.8M procurement fraud case where duplicate invoices were found. The document provides background on Benford's Law and how it can be used to focus fraud investigations by examining first digit or first two digit patterns in accounting data.

1. It’s All in the Numbers -Benford’s Law Ed Tobias, CISA, CIA May 12, 2010

2. Expectations Background Why it works Real-world examples How do I use it? Questions Topics

3. How many have heard of it? Useful tool to quickly discover possible fraudulent transactions Spend more time analyzing data instead of searching for it Expectations

4. As of 2004, over 150 articles have been written about Benford’s Law Expectations

5. Expectations

6. All over the professional journals J. of Accountancy – 2003, 2007 J. of Forensic Accounting – 2004 Internal Auditor – 2008 ISACA Journal – 2010 Fraud Magazine - 2010 Expectations

7. 1881 – Simon Newcomb, astronomer / mathematician Noticed that front part of logarithm books was more used Inferred that scientists were multiplying more #s that started with lower digits (1, 2, 3, etc.) Background

8. 1938 – Frank Benford, Physicist at GE Research labs Front part of the log book was more worn out than the back Analyzed 20 sets of “random numbers” – 20,299 #s in all Background

9. Tested random #s and random categories Areas of rivers Baseball stats #s in magazine articles Street addresses - first 342 people listed in “American Men of Science” Utility Bills in Solomon Islands Background

10. Benford’s Law: Random #s are not random Lower #s (1-3) occur more frequently as a first digit than higher numbers (7-9) In a sample of random numbers: #1 occurs 33% #9 occurs 5% Background

11. What are “random numbers”? Non-manipulated numbers Population stats, utility bills, Areas of rivers NOT human-selected #s Zip codes, SSN, Employee ID Background

12. What’s the practical use? 1990s – Dr. Mark Nigrini, college professor Tested insurance costs (reim. claims), sales figures Performed studies detecting under/overstmts of financial figures Published results in J. of Accountancy (1990) and ACFE’s The White Paper (1994) Useful for CFEs and auditors Background

13. What about financial txns? “Random data” = non-manipulated numbers AP txns, company purchases NOT human-selected #s Expense limits (< $25) Approval limits (No sig < $500) Hourly wage rates Background

14. How will it help me with non-random data? Aid in detection of unusual patterns Circumventing controls Potential fraud Background

15. You won the lottery – invest $100M in a mutual fund compounding at 10% annually First digit is “1” Takes 7.3 yr to double your $ Why it works

16. Why it works First digit is 1 for 7+ years First digit is 2 in the 8th year

17. At $500M … First digit is “5” Takes 1.9 yr to increase $100M Why it works

20. Seems reasonable that the lower digits (1-3) occur more frequently These 3 digits make up approx. 60% of naturally-occurring digits Why it works

21. Scale invariant 1961-Roger Pinkham If you multiply the numbers by the same non-zero constant (i.e., 22.04 or 0.323) New set of #s still follows Benford’s Law Works with different currencies Why it works

22. $2M Check Fraud in AZ $4.8M Procurement fraud in NC Examples

23. Check fraud in AZ #s appear random to untrained eyes Suspicious under Benford’s Law Counter-intuitive to human nature Example #1

24. State of Arizona v. Wayne James Nelson (1993) Wrote 23 checks (approx. $2M) Check amounts < $100K Tried to circumvent a control that required a human signature Mgr tried to conceal fraud Claimed to be testing the system controls against a bogus vendor Example #1

25. Avoided common indicators: No duplicate amounts No round #s – all included cents Example #1

27. Lots of 7, 8, and 9s

28. Counter-intuitive

30. Example #1

31. Benford’s Law can be extended to first 2 digits Allow examiner to focus on specific areas High-level test of data authenticity Example #2

32. Procurement fraud in NC Years 2002-2005 Wake County School employees submitted at least $3.8M submitted for payment Employees purchased cars, campers, golf carts, plasma TVs Bid limit was only $2,500 Run a sample of 660 txns through Benford’s Law … Example #2

33. Example #2 See any suspicious areas?

34. Example #2 Drilling down in the “51” txns Multiple duplicate amts

35. Example #2 Red flags not noticed: Payments to the vendor increased 342% from 2002-2003 ($3.7M+) Over 60% of invoices under $2,500 limit and did not have a PO For 2 years – 99.95% of invoices were under $2,500 On 24 separate occasions – 50+ invoices with the same invoice date / consecutive invoice #s

36. Example #2 On 24 separate occasions – 50+ invoices with the same invoice date / consecutive invoice #s

37. Example #2 The investigation recovered $4.8M from the vendor and former school employees.

38. Data Analytics software ACL / IDEA Excel Add-Ons Built-in Excel Functions How do I use it?

39. Questions

40. Expectations Background Why it works Real-world examples How do I use it? Summary

41. Ed Tobias ed.tobias@hillsclerk.com LinkedIn http://www.linkedin.com/in/ed3200 Contact Information

42. Benford’s Law Overview. n.d. Retrieved March 10, 2010 from http://www.acl.com/supportcenter/ol/courses/course.aspx?cid=010&ver=9&mod=1&nodeKey=3 Browne, M. Following Benford’s Law, or Looking Out for No. 1.n.d. Retrieved March 10, 2010 from http://www.rexswain.com/benford.html Durtschi, C., Hillison, W., and Pacini, C. The Effective Use of Benford’s Law to Assist in Detecting Fraud in Accounting Data. 2004. Journal of Forensic Accounting. Vol. V. Retrieved March 10, 2010 from http://www.auditnet.org/articles/JFA-V-1-17-34.pdf Managing the Business Risk of Fraud. EZ-R Stats, LLC. 2009. Retrieved March 10, 2010 from http://www.ezrstats.com/CS/Case_Studies.htm Kyd, C. Use Benford’s Law with Excel to Improve Business Planning. 2007. Retrieved March 10, 2010 from http://www.exceluser.com/tools/benford_xl11.htm References

43. Lehman, M., Weidenmeier, M, and Jones, T. Here’s how to pump up the detective power of Benford’s Law. Journal of Accountancy. 2007. Retrieved March 10, 2010 from http://www.journalofaccountancy.com/Issues/2007/Jun/FlexingYourSuperFinancialSleuthPower.htm Lynch, A. and Xiaoyuan, Z. Putting Benford’s Law to Work. 2008. Internal Auditor. Retrieved March 10, 2010 from http://www.theiia.org/intAuditor/itaudit/archives/2008/february/putting-benfords-law-to-work/ Nigrini, M. Adding Value with Digital Analysis. Internal Auditor. 1999. Retrieved March 10, 2010 from http://findarticles.com/p/articles/mi_m4153/is_1_56/ai_54141370/ Nigrini, M. I’ve Got Your Number. Journal of Accountancy. 1999. Retrieved March 10, 2010 from http://www.journalofaccountancy.com/Issues/1999/May/nigrini.htm Rose, A. and Rose, J. Turn Excel Into a Financial Sleuth. 2003.Journal of Accountancy. Retrieved March 10, 2010 from http://www.systrust.us/pubs/jofa/aug2003/rose.htm Simkin, M. Using Spreadsheets and Benford’s Law to Test Accounting Data. ISACA Journal. 2010, Vol. 1. Pp. 47-51. References

44. Stalcup, K. Benford’s Law. Fraud Magazine. 2010, Jan/Feb. Pp 57-58. Summerford Accountancy, PC. Fraud Vulnerability Assessment. 2006. Retrieved May 10, 2010 from http://www.wcpss.net/audit/summerford.pdf References