Predict customer lifetime value

Customer lifetime value (CLV) is the present value of the future profit a customer will generate. It tells you how much you can spend to acquire and retain a customer, which customers deserve special treatment, and what the customer base is worth. Historical spend looks backwards; CLV looks forwards.

Why simple formulas fall short

The classic formula CLV = margin × retention rate ÷ (1 + discount rate − retention rate) assumes that every customer has the same retention rate and that you can observe when customers leave. In subscriptions you can; in retail you cannot. A customer who has not ordered for three months may have left, or may just be between purchases. Probabilistic models solve this by estimating each customer’s purchase rate and chance of having dropped out from their own history.

The BG/NBD model

The beta-geometric/negative binomial distribution model (Fader, Hardie and Lee, 2005) assumes that while active, each customer buys at their own rate (which varies across customers following a gamma distribution), and that after each purchase there is a chance the customer becomes inactive (which varies following a beta distribution). It needs only three numbers per customer: frequency (number of repeat purchases), recency (time of the last purchase) and age T (time since the first purchase).

For the 520 customers of the example shop, the model estimates r = 1.31 and α = 6.24, so active customers buy at an average rate of r/α = 0.21 orders per week, or about 0.92 per month. The dropout parameters a = 0.70 and b = 3.55 imply an average 16.4% chance of becoming inactive after each purchase. The model expects 1,452 orders from these customers over the next 12 months.

P(active): who has really left?

For each customer the model computes the probability of still being active. A customer who used to buy weekly and has been silent for six months has a low P(active); a customer who buys twice a year and last bought two months ago still has a high one. The average P(active) is 45.0%, and 53.3% of customers have less than a 50% chance of still being active: a natural, ranked target list for win-back campaigns.

The Gamma-Gamma spend model

The BG/NBD model predicts the number of purchases. The Gamma-Gamma model predicts the value of each purchase, shrinking each customer’s average order value towards the population mean (73.31) when they have few orders. It assumes that spend per order is independent of purchase frequency; the correlation here is −.011, which supports the assumption.

CLV and what to do with it

Combining both models with a margin (30%) and a discount rate gives each customer’s 12-month CLV. The total is 29,616, a mean of 56.95 per customer, and the top 20% of customers account for 73.6% of it. The top customer by predicted value, C0449, has made 29 repeat purchases, has an 86.7% chance of being active and is expected to place 19.6 orders worth 643 in profit.

• Acquisition budgets: compare CLV with CAC by channel. If paid social customers have half the CLV of search customers, their CAC limit is half as high.
• Service and retention: give high-CLV customers priority service and proactive retention offers.
• Win-back: target high-value customers with falling P(active) first.
• Valuation: the sum of CLV is the value of the existing customer base.

Good practice

• Use at least one to two years of history covering several purchase cycles.
• Validate the model: fit it on the first part of the period and compare predicted with actual purchases in the rest.
• Remember that CLV predicts under current conditions; a new pricing strategy or product line changes it.
• Use margin, not revenue, and discount future profits.

Reporting

A BG/NBD model (r = 1.313, α = 6.238, a = 0.695, b = 3.551) and a Gamma-Gamma spend model were fitted to the purchase histories of 520 customers. The models predicted 1,452 orders and a total 12-month CLV of 29,616 at a 30% margin, with the top 20% of customers accounting for 73.6% of predicted value. More than half of the customers (53.3%) had a probability of being active below 50%.