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Using residual heat maps to visualise Benford’s multi-digit law

Hull, Benjamin; Long, Alexander; Hughes, Ifan G

Using residual heat maps to visualise Benford’s multi-digit law Thumbnail


Benjamin Hull

Alexander Long


It has been known for more than a century that, counter to one's intuition, the frequency of occurrence of the first significant digit in a very large number of numerical data sets is nonuniformly distributed. This result is encapsulated in Benford's law, which states that the first (and higher) digits follow a logarithmic distribution. An interesting consequence of the counter intuitive nature of Benford's law is that manipulation of data sets can lead to a change in compliance with the expected distribution—an insight that is exploited in forensic accountancy and financial fraud. In this investigation we have applied a Benford analysis to the distribution of price paid data for house prices in England and Wales pre and post-2014. A residual heat map analysis offers a visually attractive method for identifying interesting features, and two distinct patterns of human intervention are identified: (i) selling property at values just beneath a tax threshold, and (ii) psychological pricing, with a particular bias for the final digit to be 0 or 5. There was a change in legislation in 2014 to soften tax thresholds, and the influence of this change on house price paid data was clearly evident.

Journal Article Type Article
Acceptance Date Nov 4, 2021
Online Publication Date Nov 20, 2021
Publication Date 2022-01
Deposit Date Jan 27, 2022
Publicly Available Date Feb 1, 2022
Journal European Journal of Physics
Print ISSN 0143-0807
Electronic ISSN 1361-6404
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 43
Issue 1
Article Number 015803
Public URL


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Copyright Statement
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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