## What Motivates a Customer

The Holy Grail of every marketing system is to **understand how the mind of the customers works**. For example answering the question: “**From how far can I attract customers?**” To do so means to **increase profits**. You can deploy your communication and products more efficiently and maximize your returns. Clearly, **there is no silver bullet for this task**. There is no way that one single aspect is so predominant in a person’s mind at the point of empowering a seller to have perfect control over who will buy her product, where and when. If that would be true, there would be no space left for marketing specialists, demand segmentation and so on. Many little tricks can be deployed in the market.

I am by no means an expert on the field, so my way to frame this problem may sound trivial. In any case, I can list three obvious parameters that affect a customer’s decision in buying or not buying a product. The first is **price**. Few people want to throw their money senselessly, most of them want to literally maximize the bang for their buck (okay, maybe not **that** literally). The second is the **quantities needed**: if I need to buy product X everyday in large bulks and product Y once in a blue moon, then it’s only fair to assume that I’ll consider different parameters to evaluate X and Y.

The third is the **level of sophistication** of a given product. There are things that fewer and fewer people need: birdseed, piña colada flavored lip balm. Narrower customer base means less widespread offer, thus the need of travel more to specialized shops. Intuitively, sophistication is more powerful than price and quantity: a Lamborghini **is still a car **– also quite useless when doing groceries – like a Panda, but it satisfies very different and much more sophisticated needs. Sophistication is powerful because you can **play with it**, increasing the perceived sophistication of a product, thus your market: like Jonah Berger‘s “thee types of ice” bar, that looked more fancy just by inventing a way to make ice sound more sophisticated than it is.

So let’s play and try to use these concepts **operatively**. Say we want to predict the **distance** a customer is willing to travel to buy a product. Then, we try to **predict** such a distance using different variables. The one leading to better predictions of these distances wins as the best variable describing what motivates a customer to travel. We decided to test the three variables I presented before: price, quantity and sophistication. In this theory, **higher prices mean longer distances to travel**, as if I have to buy an expensive TV I’ll probably go around and check where is the best quality-price ratio. **Higher quantities mean shorter distances**, as if I have to buy bread everyday I don’t care where the best bakery of the city is if that means traveling ten kilometers everyday. Finally, **higher sophistication means longer distances:** if I have sophisticated needs I need to travel a lot to satisfy them.

Price and quantity are easy to deal with: they are just numbers. So we can put them on the X axis of a plot and put the distance traveled on the Y axis. And that’s what we did, for price:

and for quantity:

Here, each dot is a customer buying a product. If the dots had the same distance and the same price/quantity then we merged them together (brighter color = more dots here). We see that our theory, while not perfect, is **correct**: higher prices means longer distances traveled, higher quantities means shorter distances. Time to test for the level of sophistication! But now we hit a brick wall. How on earth am I suppose to measure the level of sophistication of a person and of a product? Should I split the brain of that person in half? How can I do this for thousands or millions of customers? We need to invent a brain splitting machine.

That’s more or less what we did. In a joint work with Diego Pennacchioli, Salvo Rinzivillo, Fosca Giannotti and Dino Pedreschi, that will appear in the BigData 2013 conference (you can download the paper, if you are interested), we proposed such a brain slice device. Of course I am somewhat scared by all the blood that would result in literally cutting open thousands of skulls, so we implemented a **data mining machine** that just quantifies with a number the **level of sophistication** of a customer’s needs and the level of sophistication that a product can satisfy, solving the issue at hand with no bloodshed.

The fundamental question is: **is the level of sophistication a number**? Intuition would tell us “no”: it’s a complex multidimensional space and my needs are unique like a snowflake. Kind of. But with a satisfying level of approximation, surprisingly, **we can describe sophistication with a number**. How is that possible? A couple of facts we discovered: **customers buying the least sold products also buy everything else (the “simpler” stuff), and products bought just by few customers are bought only by those who also buy everything else**. In other words, if you draw a matrix connecting the customers with the products they buy, this matrix is **nested**, meaning that all purchases are in the **top left corner**:

A-ha! Then it’s fair to make this assumption: **customers are adding an extra product bought only if they already buy (almost) everything else “before” it**. This implies two things: first, is that they add the extra product if all their previous products already satisfied their more basic needs (then, **they are more sophisticated**); second, is that they are moving on a monodimensional space, adding stuff incrementally. Then, **they can be quantified by a number**! I won’t go in the boring details about how to calculate this number. Suffice to say that they are very similar to how you calculate a country’s complexity, about which I wrote months ago; and that this number is not the total amount of money they spend, nor the quantity of products they buy.

So, how does this number relate to the distance traveled by customers?

The words you are looking for is “astonishingly well”.

So our quantification of the sophistication level has a number of practical applications. In the paper we explore the task of **predicting in which shop a customers will go to buy a given product**. We are not claiming that this is the only important factor. But it gives a nice boost. Over a base accuracy of around **53%**, using the price or the quantity gives you a **+6-7%** accuracy. Adding the sophistication level gives an additional **+6-8%** accuracy (plots would suggest more, but they are about continuous numbers, while in reality shop position is fixed and therefore a mistake of a few hundreds meters is less important). Not bad!