Data Science

The Buy-Til-You-Die Model: CLV On Steroids

Customer lifetime value (CLV) is an easy concept to understand. But that doesn’t mean every business is using it right. 🤨Buy til you die illustration

What Is Customer Lifetime Value?

Essentially it is defined as the profit that one single customer brings to your business over the entire time that they engage with you, which could be a few months or many years.

It is cheaper and easier in some ways to retain customers than spend money and energy recruiting them, so getting high customer lifetime value of a smaller number of customers is often more lucrative than having many customers who spend a low amount, briefly, and then disappear. It’s also a great indicator of loyalty. If someone sticks with you for a while, you’re doing something right.

Customer Lifetime ValueKnowing how much a customer is worth enables us to do a few things. It means we can determine the shared characteristics of the most value customer relationships, and seek out similar customers, knowing how much we should spend to acquire that type of customer. It means it’s clearer which channels and communications we should focus on to reach out to those most valuable customers. It also means we know who is most important, and can ask them questions on product feedback and market research.

Contractual & Non-Contractual Customers

Contractual - non-contractual Customers

There are two types of customers – contractual and non-contractual – and different purchase opportunities, defined as discrete or continuous. Contractual customers are subscription customers and they churn if they choose not renew, whereas in most ecommerce or retail businesses there are non-contractual customers, who purchase with varying frequency and amount. Typically, an ecommerce company has a continuous purchase opportunity, which means they can buy whenever they like.

In this guide, we’re looking at the non-contractual, continuous setting. 

What’s Wrong With The Popular Approach To CLV?

Here’s an example of how CLV is often described:

CLV is calculated by multiplying the Average Order Value by number of Expected Purchases and Time of Engagement.

One of the issues is that CLV is an estimation of an unknown, not a calculation of a known. We can look at the past revenue of a customer, but to estimate the value of a customer over their lifetime, we have to introduce predictive elements to estimate their future purchasing behavior. This popular approach relies to heavily on averages just based on the aggregate of your customers. But the actual order frequencies and order values can vary significantly between each customer.
The approach to CLV

For example, imagine two customers:

🛒 Customer A placed a bunch of orders about a month ago, but then lost interest in our company and disappeared.

🛒 Customer B buys less frequently, but has been a regular customer with strong loyalty.

If we base our CLV estimate solely on average purchase frequency and average order value, we would be misled into thinking that Customer A will be more valuable than Customer B over time. We have not accounted for the fact that Customer A has ‘died’ in our business.

To estimate CLV correctly, we need to consider how to estimate lifetime value for each customer and not only for the average of many. That makes it more difficult than multiplying a few averages together, but means that the end result should be much more accurate.

The Buy-Til-You-Die Model

Back in 1987, a group of researchers from Wharton and Columbia described a model called the Pareto/NBD for estimating the number of future purchases a customer will make. This model went on to become part of a of a larger family of variations known as buy-til-you-die (BTYD) models.

BTYD models estimate the purchasing behavior of a customer through two stochastic (which means having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely) processes. These processes are the likelihood that a customer places a repeat purchase and the probability that a customer “dies”, which means that they permanently cease purchasing from you. You can think of this as two coins that are flipped continuously. The first coin dictates whether or not the customer makes a purchase and the second coin says whether or not the customer stays alive, or keep purchasing.

The two driving factors for this model are recency and frequency. The time since a customer’s last purchase is recency, and number of repeat purchases placed by that customer in the given time period is the frequency.

The BTYD Model

Intuitively this makes sense. We can see that a customer who bought frequently in the past, but hasn’t bought recently is probably dead, whereas one who bought infrequently in the past may not be dead but be potentially ready to buy again.

The goal with the BTYD model is to estimate the expected number of future purchases each customer will place over a defined and specific time period given their recency and frequency.

E[X(t)] = expected number of transactions in specific time period

Now, once we have that expected number of future purchases for each customer, we can combine it by the average order value for that customer. This enables us to get their residual life time value (RLV).

RLV = expected future purchases * expected average order value

Residual lifetime value is the amount of additional value we expect to collect from a customer over a specific and defined time period. So then to get to CLV you just add the sum of each customer’s past purchases to their RLV. The benefit here is that you are able to capture variation in each customer’s purchasing behavior. It allows for the nuances that other calculations do not offer.

Implementing A BTYD Model is one on the few software solutions which implements this advanced calculation. It’s a pioneering market leader that uses analytics and proprietary software to deliver powerful data that can transform your business. It goes beyond mere calculations, and gives you insights where the biggest levers are to improve your real customer lifetime value. Numbers alone don’t cut it – what you need is the insight to drive forward your business, and that’s what RetentionX offers.


Josh Temple, „How to estimate the value of your customers the right way“

Data Science Enthusiast, growing revenues with the power of data – Founder & CEO of RetentionX, the leading Software for Decision Intelligence.