Breaking down the number of customers

In our post about revenue equations, we found an equation for revenue in terms of the number of customers. In this post, we’ll break down the number of customers, assuming we are working with an online market place where sales mostly come from search traffic. This leads us to a formula in terms of search keyword performance.


In the earlier post, we got the following equation for revenue.

    \[\text{Revenue} = \text{NumCustomers} \cdot \text{AvgCustSales} \cdot \text{AvgSaleVal}\]

This expresses revenue as a product of the number of customers, the average number of sales per customer, and the average value across all sales.

Now, we want to break down this equation some more by exploring \text{NumCustomers}. To do this, we’ll ask ourselves another simple question.

What is a customer?

A customer is someone who purchases something. This answer doesn’t help us much, so we can keep asking questions about customers.

How does someone become a customer?

In our setting, customers mostly come from search traffic. So someone becomes a customer by searching and then purchasing one of our products. Let’s be a bit more clear about the steps involved.

  1. A person enters some search terms (keywords) into a search engine.
  2. The person may or may not see our product among these results.
  3. After seeing our product, the person may or may not decide to purchase our product.

A customer is a person who makes it through all three steps. This is an example of a funnel: people enter the top, and fewer and fewer people make it through the steps to the end, where they buy our product.

There are other ways to break down this process and elaborate on the steps involved. For example, there are likely several steps between seeing the product and actually completing a purchase. But this will be enough for now.

This view lets us express the number of customers in terms of the probabilities of a person passing through each of the steps above.


There is some chance that a person searches a keyword, there is some chance that our product is displayed and seen in the results, and there is some chance that a purchase is made when the product is seen.

We can match the steps steps above to these probabilities.

  1. p(\text{search}_k) : the probability that a person searches for keyword \text{k}.
  2. p(\text{see} \mid \text{search}_k) : the probability that a person sees our product, given that they searched for keyword k.
  3. p(\text{buy} \mid \text{see}) : the probability that a person buys our product, given that they have seen it in search results.

These probabilities can be estimated, for example by computing the ratio of people who pass through that step.

For some context, these probabilities are related to the following things (and others).

  1. Popularity – the popularity of the keyword and of that kind of product.
  2. Competitiveness – our ranking for that keyword, which has to do with our relevance and how we stand relative to other products.
  3. Relevance/Appeal – the appeal of our link and our product for a person making these searches.

The probability that a person buys our product is the probability that they go through step 1 and step 2 and step 3 from above. This means that we can write the number of customers as a proportion of the total population \text{Population} by multiplying the probabilities as below.

Note that we need to somehow combine the information as we vary the keyword k. To simplify things in this discussion, we will just take a sum over all such k. This isn’t exactly right, since this would potentially double-count customers who searched several keywords.

\text{NumCustomers} =\\ \text{Population}\cdot \left( \underset{{k\in\text{Keywords}}}{\sum} p(\text{search}_k) \cdot p(\text{see} \mid \text{search}_k) \cdot p(\text{buy} \mid \text{see}) \right)

This expression suggests some strategic ideas. We could aim to increase the number of customers by focusing on any of these probabilities. For example, choosing more popular keywords, developing awareness of keywords, improving our ranking or the attractiveness of our link, and improving our process or offering when the person lands on our page.

Combined with the understanding of how \text{NumCustomers} fits into revenue, this expression also helps evaluate the trade-offs involved in these strategies. An increase in any of these probabilities on its own leads to an increase in the number of customers. However, it can be difficult to increase one without decreasing the others. Being able to evaluate the combined effect helps address this problem.


Suppose we were hoping to target certain keywords by putting them in descriptions of our product.

It is tempting to target an obvious, popular keyword, with the hopes of finding a larger p(\text{search}_k). But this thought occurs to many other people as well. So, when a user searches that keyword, there are already many established products that appear. As a result, we likely show up lower in the search results. In other words, p(\text{see}\mid\text{search}_k) is decreased.

On the other hand, if we choose an obscure keyword (or less common phrase), we could get a larger p(\text{see}\mid\text{search}_k), but maybe nobody searches this keyword, or the relevance to our product is not clear.

Similar issues arise when targeting the other probabilities. Maybe we make our link more interesting by giving it an attractive click-bait title, but this confuses or frustrates the person searching, making them less likely to buy.

None of these choices is obviously right or wrong, so we need to compare the options we have.

The expression above offers a way to evaluate our choices and compare them. If we can estimate the different probabilities through research or testing, we can compute the effect and compare the opportunities.


We made an observation about the steps that someone has to go through in order to become a customer of our product. We used this observation to write an equation for the number of customers in terms of probabilities related to search keywords. Then we saw how the equation suggests strategies and helps evaluate the effect of strategic choices.

Closing comments

In another post, we’ll talk about how to break down customers based on segments rather than a funnel like in this post.