The expected amount of what can happen


I am working on that customer forecast thing for my EneFinproject. I want to hit as accurate a forecast, regarding the volume and value of sales, as well as the number of customers, as possible. In my last three updates – Le modèle d’un marché relativement conformiste, Safely narrow down the apparent chaos, and La valeur espérée– I sort of kept turning around that forecast, testing and discussing various angles of approach. So far, I have been sticking to one, central, and somehow an implicit assumption, namely that the EneFinproject – that transactional platform for trading complex contracts, combining futures on energy with participatory deeds – will tap into patterns observable in the market of energy. Still, EneFinis essentially a FinTech concept, which just explores those large disparities between the retail prices of electricity in Europe. Essentially, the concept is applicable in any market with noticeable variance in prices, at the same tier of the value chain. Thus, I could look for good patterns and assumptions in the market of financial services, even very straightforwardly in the FinTech sector.

Good, time to work up to the desired synaptic tension. I open up calmly, with the financial results of Square Inc., a big, US – based FinTech company. I am rummaging in their SEC filings, and more specifically in their 10-K annual report for 2017. I am spotting that nice history of revenues, which I present here below, first as a table with values given in millions of dollars, then as two consecutive graphs, just to give you an idea of proportions.


Table 1

  Revenue of Square Inc., USD mln
Year Transaction-based revenue Subscription-based revenue Hardware revenue Total net revenue
2013  433,74  –  4,24  552,43
2014  707,80  12,05  7,32  850,19
2015  1 050,45  58,01  16,38  1 267,12
2016  1 456,16  129,35  44,31  1 708,72
2017  1 920,17  252,66  41,42  2 214,25


Graph 1

Square Inc Revenue 2017


Graph 2

Square Inc Revenue 2013 2017

The revenues of Square Inc., in terms of sheer size, are a bit out of reach for any startup in the FinTech industry. What I am interested in are mostly proportions. Here, in this update, I am going to apply one particular path of thinking to studying those sizes and proportions. Mind you: this is basic science in action. ‘Basic’ means that I take the very basic analytical tools of logic and mathematics, and I am sort of counting my way through that data. In educational terms it is good example of how you can use the most fundamental logical structures you have in your personal toolbox and invent a method of discovering reality.

And so I discover. I start with the category ‘Subscription-based revenue’, as it looks very much like a startup inside an established business, i.e. it starts from scratch. Intrapreneurship, it is called, I believe. My goal is to find benchmarks for my EneFinproject, and, more specifically, to form some understanding about the way a FinTech project can build its customer base. The specific history of subscription-based revenue with Square Inc. is a process I want to squeeze as much information out as possible. So I start squeezing. A process is an account of happening. It is like a space made of phenomena, carved out of a larger space where, where, technically, anyone can do anything. I take each year of that time series, from 2013 through 2017, as a space, and in a space, distance matters. So I measure distances, the Euclidean ones. In a unidimensional space, as it is the case here, the Euclidean distancebetween two points is very much akin local deviation. I subtract the value at point B from the value at point A, and, just to be sure of getting rid of that impertinent minus that could possibly poke its head out of the computation, I take the so-obtained difference to its square power, so I do (A – B)2, just to take a square root of that square power immediately afterwards: [(A – B)2]1/2.

The logic of the Euclidean distance is basically made for planes, i.e. for two-dimensional spaces. In that natural environment of its own, the Euclidean distance looks very much the I-hope-really-familiar-to-you Pythagorean theorem. C’mon, you know that: a2+ b2= c2, in a right triangle. Now, if you place your right triangle in a manifold with numerical coordinates, your line segments a,b, and cbecome like a = x2– x1, b = y2– y1, and c = [(x2– x1)2+ (y2– y1)2]1/2. If you have more than two dimensions, i.e. when your space truly becomes a space, you need to reduce them down to two dimensions, precisely by taking those multiple dimensions two by two and converting the complex coordinates of a point into Euclidean distances. Complicated? I hope so, honestly. If it wasn’t, I couldn’t play the smart guy here.

Right, my Square Inc. case study. I am coming back to it. I take that history of growing revenues in the ‘Subscription-based’ category and I consider it as a specific, local unfolding of events in a space. I calculate distances, in millions of dollars, in between each pair of years.  I take the value of revenues in a given year and I subtract it from the value of revenues in any given other year. I treat the so-obtained difference with that anti-minus, square-root-of-square-power therapy. The picture below summarizes that part of the analytical process, and Table 2, further below the picture, gives the numerical results, i.e. the Euclidean distances in between each given pair of years, in millions of dollars in revenue, and corrected for the temporal distance in that given pair of years.

Square Euclidean Subscription Revenue


Table 2

Euclidean distance in subscription-based revenues, USD mln over time between years
2013 2014 2015 2016 2017
2013 12,09 58,05 129,39 252,70
2014 12,09 45,98 117,32 240,64
2015 58,05 45,98 71,35 194,66
2016 129,39 117,32 71,35 123,32
2017 252,70 240,64 194,66 123,32


Now, as we have those results, what’s the next step? The next step consists in a bit of intellectual gymnastics. Those Euclidean distances in Table 2, they are happenings. They reflect the amount of sales that happened in between those pairs of years. Each year is a checkpoint: those revenues are measured at the end – or, more exactly, after the closure – of the fiscal year. Between 2014 and 2015, there are 365 days of temporal distance etc.

We have a set of happenings. What is the kind of happening that we can expect the most to happen? Answer: the average. Yes, the average. Why the average? Because the average is the expected value in a set of numerical observations. You can go back to Safely narrow down the apparent chaos if you need to refresh your background. This is the theorem of de Moivre – Laplace: the expected value in a set is the average. I am just reverting the order of ideas. I claim that the average is the expected value.

The average from Table 2 is $124,5 mln. This is the expected amount of what can happen, in one year, to the revenues of Square Inc. from subscription-based sales. It serves me to denominate the actual revenues as reported in Table 1. By denominating, I mean taking the actual, subscription-based revenue from each year, and dividing it by that average Euclidean distance. You can see the result in the picture below. Some kind of cycle seems to emerge: this particular branch of business at Square Inc. needed like 4 years to exceed the expected amount of what can happen in one year, namely the average Euclidean distance.

Square Euclidean Subscription Revenue_2

A good scientist checks his facts. Firstly, it is in order to make sure they are his facts. Sometimes, quite embarrassingly, they turn out to be somebody else’s facts, and that creates awkward situations when it comes to sharing the merit, and the cash, coming with a Nobel award. Secondly, checking facts broadens one’s intellectual horizons, although it might hurt a bit. So I am checking my facts. Good scientist, check!

I repeat the same computational procedure with the two remaining categories of revenues at Square Inc: the transaction-based ones, and those coming from the sales of hardware. Still, what I do is almost the same computational procedure. The ‘almost’ part regards the fact that those two other fields of business had non-null revenues in 2013, when the publicly disclosed financial reporting starts. Subscription-based revenues started from the literal scratch, and those two other had already something in their respective belts in 2013. In order to make my calculations mutually comparable, I need to transform the time series of transaction-based, and hardware-based revenues so as they look as starting from nearly nothing.

This is simple. You want to make people look as if they were starting from scratch? Just take their money from them. Usually works, this one. This is what I do. I take $433,73 mln from each year of transaction-based sales, and $4,23 mln with respect to each year of hardware-based revenues. Instantaneously, both look younger, and, as soon as they do, I make them do the same gymnastics. Bet Eucliean, one! Compute the expected Euclidean, two! Divide reality by the expected Euclidean, three!

Seems to work. In those two other categories of revenues, I can observe slightly shorter a cycle of achieving the expected amount of happening, like 3+ years. Useful for that business plan of mine, for the EneFinproject.

You can see the general drift of those calculations in the pictures and tables that follow below. Now, one thing is to keep in mind. What I am doing here is having fun with science, just as we can have fun with painting, photography, sport or travel: you take some simple tools, and you just see what happens when you use them the way you think could be interesting. This is probably the strongest message I want to deliver in that entire scientific blog of mine: it is fun to have fun with science.

Square Inc transformation of revenue


Table 3

Euclidean distance in transaction-based revenue, USD mln over time between years
2013 2014 2015 2016 2017
2013 274,06 616,71 1 022,43 1 486,44
2014 274,06 342,65 748,36 1 212,38
2015 616,71 342,65 405,72 869,73
2016 1 022,43 748,36 405,72 464,02
2017 1 486,44 1 212,38 869,73 464,02



Table 4

Euclidean distance in hardware-based revenues, USD mln over time between years
2013 2014 2015 2016 2017
2013 12,09 58,05 129,39 252,70
2014 3,24 45,98 117,32 240,64
2015 12,30 9,11 71,35 194,66
2016 40,18 37,04 27,95 123,32
2017 37,39 34,22 25,12 3,06

Square Euclidean Transaction Revenue

Square Euclidean Hardware Revenue


I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French versionas well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon pageand become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

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