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Análisis matemático para la detección de ventas fraudulentas - Blog AffiliRed

A mathematical law discovered in 1881 by Simon Newcomb states that in any real-life set of numbers, for example sale amounts for hotel bookings, the first figure tends to be the number 1 much more often than any other number. At AffiliRed, we use this method as another tool to detect fraudulent sales (see Automatic Fraud Detection).

1. Benford’s law applied to the detection of fraudulent sales

This law, known as Benford’s law or the First-digit law, shows that the specific probability of the first figure of any number being 1 is as follows:

First figure

Probability

1

30.1%

2

17.6 %

3

12.5 %

4

9.7 %

5

7.9 %

6

6.7 %

7

5.8 %

8

5.1 %

9

4.6 %

That is, the probability of a number beginning with 1 is 30%, while the probability of a number beginning with 9 is lower than 5%.

Benford’s law is governed by the following formula: P(d) = Log10(1+1/d)

This does not happen with randomised or falsified data; therefore, this mathematical law can be used to investigate if the data we record at AffiliRed is reliable or not, including data segmented by customer, affiliate, network, country, etc. Specifically, we can see if the sale amounts that we record, by either grouping them together or segmenting them, appear normal or, on the contrary, if they appear to have been intentionally manipulated; in which case, we can suspect that fraud has been committed.

Logically, the extracted data will depend on the data selection criteria and there are a number of factors that must be taken into account:

  • The more data, the better the estimate. A limited data set might not produce the results indicated by Benford’s law.

  • Sale amounts are often static or prefixed amounts and as such are not always ideal for this type of study. For example, a product sold at €9.99 instead of at €10.00 can distort the results as 9 could achieve an unusually higher frequency than 1.

  • By obtaining a subset of the bookings recorded at AffiliRed (grouped by merchant, affiliate or country of origin of the sale) and providing there is a sufficient amount of data, we can review sales and investigate those that appear to be fraudulent.

2. Application of Benford’s law at AffiliRed

Results of the percentage per number of the first figure of sales registered at AffiliRed (non-cancelled sales registered since 2012, not including those under 1 euro). Approximately 360,000 sales were included in the sample data set.

First figure

Percentage

1

31.0%

2

17.4%

3

11.5%

4

9.4%

5

8.2%

6

6.8%

7

5.7%

8

5.2%

9

4.7%

Results displayed on a graph (blue bars on the graph below) and in comparison with the mathematical formula of Benford’s law (red line)

1. Results

  • The results obtained are very close to the theory defined in Benford’s law, leading us to conclude that, in general terms, the active sales (non-cancelled) show a normal pattern; or rather that the sale amounts have not been manipulated (fraudulent sales).
  • This technique does not solve the problem of fraud in the online sale of “travel” products, yet it does serve as another control measure used at AffiliRed to detect potentially fraudulent sales.
  • An analysis of this method at merchant level needs to take into account the type of products they offer and the “typical” amounts of their sales.

1. References

  • http://fraudit.blogspot.com.es/2009/01/peligros-de-la-ley-de-benford.html
  • http://en.wikipedia.org/wiki/Benford’s_law
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ByDavid Rivera

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