Random the Book

Questions for you:

• When reviewing information, do I look for patterns that are suspiciously regular or “too good to be true”?
• What data or claims do I accept at face value that might benefit from scrutiny about their randomness?
• Am I aware of what natural randomness should look like in the contexts I work in?

Organisational applications:

• Expense and financial fraud detection:
  Apply Benford’s Law analysis to expense reports, invoicing patterns, and financial submissions. Natural datasets exhibit predictable first-digit distributions (1 appears ~30%, 9 appears <5%), whilst fabricated data shows unnaturally even distributions. Implement automated screening that flags submissions with suspicious digit patterns for closer review. This catches fraud that looks reasonable to human reviewers but fails statistical tests.
• Procurement and supplier data validation:
  Analyse vendor invoice patterns and pricing data for statistical anomalies. Fraudulent suppliers often create invoices with numbers that seem varied but lack genuine randomness. Compare digit distributions across suppliers and flag those showing suspiciously uniform patterns. This identifies fictitious vendors and inflated pricing schemes that pass conventional approval processes.
• Quality control and testing data verification:
  When products undergo testing (safety, performance, compliance), fabricated test results typically lack the natural variation present in genuine measurements. Apply statistical randomness tests to identify suspiciously consistent results that suggest data manipulation rather than actual testing. Particularly valuable when testing is outsourced or conducted by third parties with incentives to pass products.
• Automated integrity screening systems:
  Build statistical screening layers into approval workflows that automatically flag submissions requiring human review based on randomness tests. This doesn’t replace human judgment but directs attention efficiently toward submissions most likely to contain fabrication. Particularly valuable for high-volume processes where manual review of everything is impractical.

Further reading

On Benford’s Law:
Benford’s Law: Applications for Forensic Accounting, Auditing, and Fraud Detection by Mark J. Nigrini (Wiley, 2012). Comprehensive guide to applying Benford’s Law in forensic accounting, with practical examples of detecting financial fraud and data manipulation.

Following Benford’s Law, or Looking Out for No. 1 by Malcolm W. Browne (New York Times, 1998). Accessible introduction to Benford’s Law explaining why it works and how it’s applied to detect fraud.

On election fraud detection:
The Fingerprints of Fraud by Bernd Beber and Alexandra Scacco (Washington Post, 2009). Explains how statistical analysis of last-digit patterns can reveal election manipulation, with case studies from authoritative regimes.

Electoral Fraud: Detecting and Deterring Electoral Manipulation edited by R. Michael Alvarez, Thad E. Hall and Susan D. Hyde (Bloomsbury, 2009). Academic examination of various fraud detection methods including statistical analysis of voting patterns.

On data fabrication in research:
Science Fictions: How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth by Stuart Ritchie (Metropolitan Books, 2020). Examines how fabricated research data is detected through statistical anomalies, with case studies of major scientific fraud.

The GRIM Test: A Simple Technique Detects Numerous Anomalies in the Reporting of Results in Psychology by James Heathers et al. (Social Psychological and Personality Science, 2016). Academic paper on detecting impossible statistical summaries in published research.

On human inability to generate randomness:
The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow (Pantheon, 2008). Includes discussion of why humans are terrible at generating random sequences and how this creates detectable patterns in fraud attempts.

Randomness by Deborah J. Bennett (Harvard University Press, 1998). Historical and mathematical examination of randomness including why human attempts to simulate it fail predictably.

On financial fraud and market manipulation:
The Signal and the Noise: Why So Many Predictions Fail—But Some Don’t by Nate Silver (Penguin Press, 2012). Includes discussion of detecting market manipulation through statistical anomalies in trading patterns.

Flash Boys: A Wall Street Revolt by Michael Lewis (W.W. Norton, 2014). Though focused on high-frequency trading, includes examples of how statistical patterns reveal market manipulation invisible to casual observation.

About the image

There was a point between the referendum in 2016 and the pandemic when it felt like we were in a state of permanent election. This signboard would appear regularly at the bottom of our road, directing voters in Teddington to the polling station at the Sea Scouts Hall. This time was at the May 2019 local elections.

Photo montage and photo by Matt Ballantine, 2026 and 2019.