# Customer Life Time Value (CLTV)

**Even before a customer makes their first purchase with a company, much of their potential value is already there. In this article, I will discuss the ways to reveal this potential value.**

This is the second and the final part of the article series about **Customer Value**. In the first part, I discussed about the core of customer value calculation : RFM metrics and scores. This final part will be about Customer Life Time Value prediction using BG/NBD and Gamma Gamma Models.

With RFM Analysis, a company can have a vision of its customers’ current behaviour by scoring and segmenting them based on their purchasing habits and therefore be able maintain an effective CRM. In order to look forward and to have a projection of what will be coming next, a company or a brand equity must be calculated for a longer period of time. A brand equity is nothing more than the sum of its **customer equity**. So we will focus on the customers.

Companies should be aware of the customer heterogeneity in order to be **customer-centric**. Not all customers are the same, they have different purchasing patterns, they react differently to campaigns, their tendency to be loyal varies, so they shouldn’t be treated the same way. In order to use company’s limited resources (budget and man-hour) wisely, these patterns should be revealed and strategies should be developed according to these patterns.

CLTV, alias for Customer Life Time Value is the ultimate metric that is used to understand and to influence the customer’s behaviour by predicting each customer’s equity covering the period where he/she is alive. Being alive is a metaphor for “a customer who still purchases from the company”. The existing customers’ purchasing habits will be of great help for creating different patterns and measuring the CLTV of a new customer as well as the existing ones.

Online Retail II dataset will be used for this approach. The first five observations are as follows. The link for the dataset is here.

CLTV is based on 4 metrics, let’s examine them one by one:

**Recency** : The period between the first and the last purchase date, that is the duration where we can observe the behaviour of this customer,

**T** : The age of the customer within the company, that is the period starting from the first purchase date until today,

**Frequency** : Number of purchases the customer has, that is how often he/she purchases,

**Monetary** : The average of the total prices among all the purchases.

The Customer ID’s Recency, T, Frequency and Monetary values are calculated.

With the aforementioned metrics, it is possible to create a pattern for each customer and use this pattern to calculate the value of that specific customer. CLTV is a powerful tool to retain the customers and to reveal the purchasing potential that is hidden inside the customers. It also gives solid information on whether it is worth the effort to acquire this specific customer. The relationship between the company and the customers are non-contractual, so the date for the customers to be inactive is vague. Changes in the purchasing behaviour of the customer and the risk for the customer to become inactive can be predicted via CLTV using BG/NBD and Gamma Gamma Models. Let’s briefly explain the models:

# BG/NBD Model (Transaction Flow Model)

Given the Frequency, T and Recency values of a customer it is possible to predict the expected number of purchase that he/she would make within a specified time period.

This model is based on Pareto/NBD model, but offers an easy way to implement on business cases thanks to the following assumptions:

- While active, customer’s purchasing behaviour follows a pattern (the time between transactions is distributed exponential with transaction rate)
- After any transaction, there is a possibility of p that the customer will be inactive.
- The transaction rate and the dropout (being inactive) rate vary independently across customers.

With BG/NBD Model, the company can have a vision of “who is still alive”. But being alive is a term that should be considered differently for every customer due to their different purchasing habits, especially their frequency values. Imagine there is a customer that used to purchase once in every week and didn’t purchase for four weeks, it’s probably because this customer is no longer alive. But for another customer who purchases once in every two months, not purchasing for four weeks is not a sign of being no longer alive.

It is possible to visualize this relationship using **Frequency-Recency matrix **which computes the expected number of transactions an artificial customer is to make in the next time period, given his/her recency and frequency.

In the below Recency-Frequency Matrix, a customer who has a frequency of 200 and the last purchase that he/she made was 50 weeks ago has a 80% probability of being alive.

# Gamma Gamma Model (Spend Model)

It is used to estimate the average monetary value of customer transactions. Given the Frequency and Monetary values of a customer it is possible to predict the expected average profit of a customer. The model of spend per transaction is based on the following general assumptions:

- The monetary value of a customer’s given transaction varies randomly around their average transaction value.
- Average transaction values vary across customers but do not vary over time for any given individual.
- The distribution of average transaction values across customers is independent of the transaction process.
- There is no relationship between the monetary value and the purchase frequency.

# CLTV Calculation

There are different approaches for calculating CLTV and I will share the most common one:

*CLTV = (Customer Value / Churn Rate) * Profit Margin*

*Customer Value = Average Order Value * Purchase Frequency*

*Churn Rate = 1 — Repeat Rate*

It is possible to degrade the above equations and simply reach this one:

*CLTV = Expected Number of Transactions * Expected Average Profit*

So how would these values be calculated?

Expected Number of Transactions : Calculated using BG/NBD Model

Expected Average Profit : Calculated using Gamma Gamma Model

This is the final output of our dataset:

# Conclusion

In order to be customer-centric, a company should be aware of its customer’s CLTV. The realistic distribution of the customer CLTV of a company is visualized in the below graph.

In reality, the customers with lower value make up the larger proportion. As CLTV increases there are fewer customers left. This should be taken as a proof of **Pareto Principle** stating that “80% of the total profit is brought by 20% of the customers”.

This means that the modal customers can be found toward the lower end of the CLTV scale and acquiring them, having the best CRM with them is worth the effort.

## References:

- Data Science and Machine Learning Bootcamp Lectures https://www.veribilimiokulu.com/bootcamp-programlari/veri-bilimci-yetistirme-programi/
- Fader P.&Toms S. (2018). The Customer Centricity Playbook: Implement a Winning Strategy Driven by Customer Lifetime Value. Wharton School Press
- Fader, Peter & Hardie, Bruce & Lee, Ka. (2005). “Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model. Marketing Science.
- Fader, P. S., & Hardie, B. G. S. (2013). The Gamma-Gamma model of monetary value.
- https://mathchi.medium.com/why-is-customer-lifetime-value-so-important-f6f78999a85e
- https://lifetimes.readthedocs.io/en/latest/index.html
- https://pinard.medium.com/how-to-calculate-and-predict-the-value-of-your-customers-rfm-27ace29f0b1e