BENFORD’S LAW ANALYSIS

WHAT IS BENFORD’S LAW?

• Frank Benford was a physicist at GE Research Laboratories in

the 1920s

• He found that numbers with low first digits occurred more

frequently in sets of numbers and calculated the expected

frequencies of the first digits in tabulated data

• In 1999, Mark Nigrini proposed using Benford’s Law as an

analysis method to alert users to possible errors, fraud, costly

processing inefficiencies or other irregularities

BENFORD’S LAW

WHAT IS IT?

• Benford's law states that if there is a set of non-manipulated,

“naturally occurring” numbers, the occurrence frequency of

digits one through nine as the first digit should be expected

• 30 percent of such numbers have one as a leading digit, and

nine occurs as a leading digit only one time in twenty

• Because most financial and accounting data are “naturally

occurring” numbers, by comparing the occurrence frequency

of these first digits to Benford's pattern, auditors should be

able to determine irregularities and possible manipulations

BENFORD’S LAW

WHAT IS IT?

ANALYZING CITY DATA WITH BENFORD’S LAW

• Data that has a wide variety in the number of figures - data

with plenty of values in the hundreds, thousands, tens of

thousands

• A data set that is fairly large

• Data that has no predefined maximum or minimum value

• Accounts payable data are a favorite target for digital analysis

• City has two main data “avenues” for accounts payable:

ProCard transactions and Workday vendor payments

ANALYZING CITY DATA

WHAT DATA IS SUITABLE?

• Auditing reviewed the expense data available through

Workday reports

• Found a useful Workday report: Finance - Supplier Payments

• Prepared reports for FY 2014-5 and FY 2015-6 transactions –

2015 had 39,889 transactions and 2016 had 42,649

transactions

• Accounting has a dedicated staff member for ProCard

oversight and she was consulted and provided two reports of

monthly ProCard transactions

• October 2016 had 2,998 transactions and November 2016 had

3,407 – combined data from both months since transactions in

each month are similar

ANALYZING CITY DATA

WHAT DATA IS SUITABLE?

FIRST DIGIT ANALYSIS

FIRST DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 8 9

Rate

First Digit

FY 2014-15 Supplier Payments*

Benford Rate

Sample Data Rate

FIRST DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 8 9

Rate

First Digit

FY 2015-16 Supplier Payments*

Benford Rate

Sample Data Rate

FIRST DIGIT ANALYSIS

Procard Transactions

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 2 3 4 5 6 7 8 9

Rate

First Digit

Oct/Nov 2016 Procard Transactions

Benford Rate

Sample Data Rate

SECOND DIGIT ANALYSIS

SECOND DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9

Rate

Second Digit

FY 2014-15 Supplier Payments*

Benford Rate

Sample Data Rate

SECOND DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.05

0.1

0.15

0.2

0.25

0 1 2 3 4 5 6 7 8 9

Rate

Second Digit

FY 2015-16 Supplier Payments*

Benford Rate

Sample Data Rate

SECOND DIGIT ANALYSIS

Procard Transactions

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5 6 7 8 9

Rate

Second Digit

Oct/Nov 2016 Procard Transactions

Benford Rate

Sample Data Rate

FIRST AND SECOND DIGIT ANALYSIS

1st and 2nd DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98

Rate

Two-Digit Pair

FY 2014-15 Supplier Payments*

Benfords

Sample Rate

1st and 2nd DIGIT ANALYSIS

Workday Transactions

* - Payments include the ACH, Check, ePayables, Manual and Separate Check Payment Types.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98

Rate

Two-Digit Pair

FY 2015-16 Supplier Payments*

Benfords

Sample Rate

1st and 2nd DIGIT ANALYSIS

Procard Transactions

0

0.01

0.02

0.03

0.04

0.05

0.06

10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98

Rate

Two-Digit Pair

Oct/Nov 2016 Procard Transactions

Benfords

Sample Rate

CONCLUSIONS

• No major deviations from Benford Law expectation for payments selected

• Procard transactions have noticeable “spike” at dollar values close to card spending limits – this “spike” is not indicative of fraud but should continue to be monitored

• Workday transactions for both fiscal years are very similar and analysis should be repeated each year to see if any changes occur

• Audit should continue to use Benford to analyze financial transactions and share results with Business Services