GuerrillaMaths 1#

The Cambridge Dictionary state that "Guerrilla Marketing" is defined as unusual methods of getting attention for a product or service, usually ones that cost little money and involve giving or showing things to people in public places and by extension any form of marketing that is original, unusual, and not expensive.

I think that in math there exist the same counter-part in terms of "Guerrilla Maths" or "Guerrilla statistics" that in my mind indicates the easy formulas (ie not involving higher level maths or statistics) that can be used to analyze datasets and numbers to perform easy forecasting. Unfortunately considering the combination of hyperspecialized math and the fact that mathematician seems to love to create language symbols and overstructured constructs, it is very difficult to find such formulas but there are some gems that I would like to share here.

Being that #sharingiscaring I think that they can be valuable even for people that do not have great math skills.

So let us begin with an empirical law that although unproven in the traditional sense of the term can be seen in many numerical sets whether described by a mathematical rule or by datasets with a number of data.

The observation starts with any sufficiently large numerical set (typically above one million but also applies in smaller cases). If we consider the first digit of each number (doesn't matter if with or without decimals), we would be led to think that the distribution occurs randomly, so that all numbers from 1 to 9 appear more or less at the same frequency. Surprisingly, however, it has been observed that the distribution of the first digit of the numbers follows a rather simple mathematical pattern:

where d is the first digit of the number. Using the formula it is easy to calculate the following table where d=1,2,...,9:

In other words, if we take a large enough set of numbers, the formula above tells us that the number 1 will appear as the first digit in 30% of the numbers present, while 9 only appears in 4.6% of the cases.

This formula is known as Benford's laws also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law (https://en.wikipedia.org/wiki/Benford%27s_law).

Quite apart from the fact that this seems nonsensical, since one would expect numbers 1 to 9 to be equally distributed, Benford's Law has been observed in a great many number sets, both artificial and real, provided, as I said before, that they are sufficiently large. In some sets the law is so precise that the error in prediction is almost zero. However, the real question is what this has to do with everyday work beyond being able to use this topic as entertainment at a dinner party or over an aperitif.

Well, the interesting fact about this rule is that it allows an easy verification to understand whether a numerical set has been manipulated or not. For example if we have a numerical dataset it is easy (even with Excel) to calculate the first digit of every number then if for example we get that the frequency of 1 as first digit is for example 20% (ie the number with 1 as first digit are the 20% of the total) we are with a great probability looking at a fake dataset.

Benford's law has already been used on the macroeconomic data the Greek government reported to the European Union before entering the eurozone to shown that their were probably fraudulent. https://www.theguardian.com/commentisfree/2011/sep/16/bad-science-dodgy-stats

Benford's law has also been applied for forensic auditing and fraud detection on data from the 2003 California gubernatorial election,[https://www.wiley.com/en-us/Benford%27s+Law%3A+Applications+for+Forensic+Accounting%2C+Auditing%2C+and+Fraud+Detection-p-9781118152850] the 2000 and 2004 United States presidential elections,[https://www-personal.umich.edu/~wmebane/fraud06.pdf] and the 2009 German federal election[https://www.degruyter.com/document/doi/10.1515/jbnst-2011-5-610/html].