# Function (mathematically speaking)

## Function (mathematically speaking)

Apologies to the author of this nice photo on Unsplash: I cannot find him/her anymore

Theory is when we know everything, but nothing works. Practice is when everything works but we don’t know why. In any case, we always end up combining theory and practice: nothing works and we don’t know why (Albert Einstein)

Here it seems to me that Albert was a little too pessimistic, especially since, apparently, most of his theories (as a matter of fact, virtually all of them) still work perfectly, also in practice.

I should say that the functions that summarize his theories, like the famous E = mc2, that describes the relationship between mass and energy, always looked to me a little arcane, compared to the supposedly more complex functions that I have been using, together with my colleagues and friends, in the development of our business simulations and decision support systems.

But this is the price we pay when we didn’t have the opportunity (and the ability) to study physics!

Anyway, since narration and storytelling are very fashionable, I’ll take the opportunity of today’s topic to tell you a story that turns around the use of common sense and mathematics, although at a very elementary level. It’s the first episode of a sort of real-life anecdote about “Gianni and his share: a case of marketing presbyopia” (too bad that I can’t play with words like in Italian to make this title more picturesque!).

To say the truth, I had included this story in the chapter on “Effectiveness” of our old book, but it’s also pertinent to introduce it here, since the market share (Gianni’s share in this case) is precisely the product of coverage and penetration: in my own small way, I can therefore summarize the concept with a function that looks a lot, mutatis mutandis, like that of Albert: S = cp!

### Marketing myopia vs. marketing presbyopia

You certainly heard about the famous Theodore Levitt’s article on “marketing myopia”, and therefore I won’t waste your time reminding that, sometimes, marketers tend to be blind beyond their noses.

But this is not the point, on the contrary: today I want to tell you about a case of visual aberration in the opposite sense, that in my view affects an even larger number of marketing people: the tendency to look at a much larger market than necessary or, at any rate, at a market that is not the “pertinent” one, disregarding the fact that their market shares are far from insignificant, and it would be worth to keep an eye on them.

Once upon a time, there was Gianni, a small entrepreneur from the south of Italy who manufactured wedding dresses (I hope he is still around!).

He was the only one, as a participant in a course on strategic management (out of 25 attendants), able to answer (although rather roughly, as we will see) to one of my typical introductory questions (just to see whom I’m talking to): Any of you has a slightest idea about the market share of his or her company, at least in one of its most important market segments?

By the way, can you figure out what Gianni’s colleagues had been thinking in the meantime?

• … what the f… is a market share? … and a segment?
• … imagine if, as small as I am, it makes sense to think about shares …
• … forget about spending money in marketing research to estimate my share …
• … and so on …

To make a long story short, this is Gianni’s answer to the roar of amazement unleashed by his show of hands and to the tacit request for explanations on “how-the-heck” he could know his share :

“Very simple: at the Chamber of Commerce, they told me that in Italy there are about 300,000 weddings per year, I sell about 3,000 dresses, i.e. a share of 1%”.

### The “rough” (approximate) method

Can you guess how much it was, instead, the most likely order of magnitude of his share?

• let’s remove from 300,000 marriages 40% of future brides who carefully abstain from buying a wedding dress, either because they already have it (from their mom or grandmother) or because they make it themselves, or because they rent it, or because they dress differently (estimates made by Gianni, stimulated to “think again” and supported by a direct competitor, participant in the same course and known on the spot)
• from the remaining 60% we remove 80% of future brides who don’t belong to Gianni’s target (you should know that both Gianni and his competitor produce high-end dresses)

we would remain with 12% of 300,000, i.e. 36,000 dresses: let’s round to 40,000, but that’s the best part:

• what do you think would be the portion of the domestic market Gianni could get in touch with, thanks to his relatively small salesforce?
• let’s abound, considering that Gianni is very dynamic, intelligent, and covers an élite market segment, served by a fairly limited number of outlets: what about 50%?

We would therefore have, roughly, a “pertinent” market, i.e. the market that Gianni can actually reach, on which it’s worth to estimate his relative position (in practice, his share), of about 20,000 dresses!

A big difference compared to 300,000 marriages!

In practice, the “true” Gianni’s market share would be around 15%, much larger than 1%!

… but are we sure that it would be so “true”?

### Few (relatively) reasonable objections

I can easily imagine your objections:

• anybody could have a large market share, provided that the related market is sufficiently small!
• this method is very rough, it would take much more than that to estimate market shares in a reasonably accurate way!
• … and more accurate methods are costly, and SMEs cannot afford them!

Counter-objection to the first objection:

so, what? all depends on our analytical objectives:

• one thing is understanding how big is the market we could reach with a larger sales organization: this indicator, although significant, only tells us about the relative size of our company, and not how good we are as competitors: who cares about the northern Italy market, if we don’t even have a single salesman who can visit it? It would be like estimating our market position in a totally unknown region and, more in general, who cares about geographical borders, especially in the internet era?
• another thing is keeping under control our ability to compete, over time, in relation to the market we can get in touch with, and this is a fundamental indicator to suggest adjustments of our strategies, especially if we can identify and distinguish coverage and penetration.

Counter-objection to the second and third objections:

• it’s true that the method described above is crude, but who says that it’s the only available method and, specifically, who says that more accurate methods are costly?

Before addressing this last point in another post, I just reemphasize that market share – i.e. the metric that measures the portion of demand that we can satisfy in a given segment, its components, and its trend, within a specific market and competitive context, is one of the best indicators (obviously, not the only one!) of our ability to compete and create wealth, despite the ravings of some so-called gurus who, in the attempt to sell few more copies of their worthless books, say that “market share is not anymore fashionable”!

#### POST SCRIPTUM

… by the way, this is the second of a series of 8 posts that, in my intention and in those of my friends and colleagues Alfonso Pace and Virgilio Gay (they wrote on the same subjects, and you can find their versions, in Italian, at https://medium.com/marketing-mindset) should have – and still should – anticipate the new edition of the now elderly text, currently out of print, reminded in this photo.