Fig 3. The frequency of lowest-leading-digits among an ensemble of uniformly-distributed-fist-digit distractors N for 3-, 4-, and 5-option multiple choice questions, and the expectation of success using a Benford’s attack on such a test.

For a Benford’s Law-based attack on a testbank the predominance of low-value leading digits in the answers must be maintained in the presence of a group of distracotrs. Despite the fact that for 4- and 5-option questions the distractors are collectively more likely to have the lowest leading digit, a Benford attack on such a group is nonetheless expected to yield an advantage over a random-guessing strategy (inset). In the case of a test with 3-option questions—where the answers are Benford distributed and the two distractors are uniformly distributed—a Benford attack is expected to yield a passing score of 53% (inset).