A didactic note on the use of Benford's Law in public works auditing, with an application to the construction of Brazilian Amazon Arena 2014 World Cup soccer stadium

Globalization requires developing countries' governments to invest heavily in expensive large-scale infrastructure projects in order to keep on the map of an ever more competitive world. In a context of capital constraint, it is essential to keep public procurement works at their lowest possible cost while assuring a high quality output. This paper introduces Benford's Law as a tool to detect overpricing in worksheets of public works. That law suggests that the frequency of the first digit in a multitude of non-manipulated numerical databases decreases successively from digit 1 (about 30%) to digit 9 (less than 5%). The paper describes a few relevant statistical tests of Benford's Law and applies them to the construction work of Brazil's Amazon Arena 2014 World Cup soccer stadium. Then, it compares Benford's Law results with those obtained from the analysis of prices conducted by the Brazilian Court of Accounts (TCU). The tests identified items in the worksheet that did not comply with the Law and corresponded to over 80% of the total overprice uncovered by TCU. That identification required auditing only 65% of total procurement costs, whereas the methodology used by TCU audited about 80% of total costs. Finally, we propose an alternative algorithm for selection of the sample to be audited while still auditing the conventional 80% of total costs.