Humans vs. Algorithms – Who Follows Newcomb-Benford’s Law Better with Their Order Volume?

  • Martin Haferkorn
Part of the Lecture Notes in Business Information Processing book series (LNBIP, volume 135)


Newcomb-Benford’s Law (NBL) is a well known regularity in the distribution of first significant digits (FSD) and therefore research in this field is manifold. As of 2012 research in the domain of financial markets is quite scarce, especially in the field of algorithmic trading. We pose the question whether order submission volumes of algorithmic traders and human traders follow NBL. Results in this context might help regulators to detect suspicious market activity and market participants to quantify the amount of algorithmic trading. Our findings indicate that the submitted order volumes of both groups follow NBL more than the uniform distribution. Comparing these two groups, we give a proof that algorithmic traders match NBL better than human traders, as human traders tend to overuse the FSD five.


Algorithmic Trading Electronic Trading Financial Markets Newcomb-Benford’s Law 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Newcomb, S.: Note of frequency of use of the different digits in natural numbers. American Journal of Mathematics 4(1), 39–40 (1881)CrossRefGoogle Scholar
  2. 2.
    Benford, F.: The law of anomalous numbers. Proceedings of the American Philosophical Society 78(4), 551–572 (1938)Google Scholar
  3. 3.
    Hürlimann, W.: Benford’s law from (1881-2006) Working Paper,
  4. 4.
    Beebe, N.H.F.: A Bibliography of Publications about Benford’s Law, Heaps’ Law, and Zipf’s Law. Working Paper (2012),
  5. 5.
    Buck, B., Merchant, A.C., Perez, S.M.: An illustration of Benford’s first digit law using alpha decay half lives. European Journal of Physics 14(2), 59–63 (1993)CrossRefGoogle Scholar
  6. 6.
    Bhattacharya, S., Xu, D., Kumar, K.: An ANN-based auditor decision support system using Benford’s law. Decision Support Systems 50(3), 576–584 (2011)CrossRefGoogle Scholar
  7. 7.
    Bolton, R.J., Hand, D.J.: Statistical Fraud Detection: A Review. Statistical Science 17(3), 235–249 (2002)CrossRefGoogle Scholar
  8. 8.
    Durtschi, C., Hillison, W., Pacini, C.: The effective use of Benford’s law to assist in detecting fraud in accounting data. Journal of Forensic Accounting 5(1), 17–34 (2004)Google Scholar
  9. 9.
    Ley, E.: Checking Financial markets via Benford’s law. Working Paper (1996)Google Scholar
  10. 10.
    Corazza, M., Ellero, A., Zorzi, A.: On the Peculiar Distribution of the U.S. Stock Indexes’ Digits. In: Proceedings of the International Conference MAF 2008 – Mathematical and Statistical Methods for Acturial Sciences and Finance, Shanghai (2008)Google Scholar
  11. 11.
    Zdravko, K., Zgela, M.: Evaluation of Benford’s Low Application in Stock Prices and Stock Turnover. Informatologia 42(3), 158–165 (2009)Google Scholar
  12. 12.
    Zhipeng, L., Cong, L., Wang, H.: Discussion on Benford’s Law and its Application. Working Paper,
  13. 13.
    Abrantes-Metz, R.M., Villas-Boas, S.B., Judge, G.: Tracking the Libor rate. Applied Economics Letters 18(10), 893–899 (2011)CrossRefGoogle Scholar
  14. 14.
    Giles, D.E.: Benford’s law and naturally occurring prices in certain ebaY auctions. Applied Economics Letters 14(3), 157–161 (2007)CrossRefGoogle Scholar
  15. 15.
    Burns, B.: Sensitivity to statistical regularities: People (largely) follow Benford’s law. In: Proceedings of the Annual Meeting of the Cognitive Science Society, Amsterdam (2009)Google Scholar
  16. 16.
    Scott, S.K., Barnard, P.J., May, J.: Specifying executive representations and processes in number generation tasks. The Quarterly Journal of Experimental Psychology 54(3), 641–664 (2001)CrossRefGoogle Scholar
  17. 17.
    Harris, L.: Stock price clustering and discreteness. Review of Financial Studies 4(3), 389–415 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Martin Haferkorn
    • 1
  1. 1.Goethe University FrankfurtFrankfurtGermany

Personalised recommendations