1. Its All in the Numbers -Benfords 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 analyzingdata instead of searching for it
Expectations
4. As of 2004, over 150 articles have been written about Benfords 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 lowerdigits (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 andrandom 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. Benfords Law:
Random#s are notrandom
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. Whats 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 ACFEs 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
18. Why it works

Time is decreasing between digit changes

19. There are more years that start with lower digits