Buy-Till-You-Die Models

A family of probability models that predict, from purchase history alone, how many purchases a customer will make next and whether they have quietly stopped buying.

Schmittlein, Morrison & Colombo (1987) as Pareto/NBD; simplified as BG/NBD by Fader, Hardie & Lee (2005)

What it does

Removes the arbitrary churn definition. In non-contractual categories nobody cancels, so “churned” is whatever number of days someone picked — ninety, a hundred and eighty. These models replace that guess with a probability that a given customer is still alive, estimated from how often and how recently they bought, and they forecast future transactions well enough to price a customer base.

When it breaks

The models assume a customer's underlying purchase rate is stationary — that it does not change. So they break precisely when you intervene: sustained promotion, a price change, a category shift, a competitor entering. They are a forecast of what happens if nothing is done, which makes them a strong baseline and a poor evaluator of your own campaign. They also explain nothing: a customer with a 4% survival probability comes with no reason and no lever.

Case

Fader, Hardie and Lee introduced the BG/NBD as an easier alternative to the Pareto/NBD, showing it reproduced the original model's fit and forecasting accuracy on the same data with a far simpler estimation procedure — the reason buy-till-you-die modelling became practical outside academia.

Fader, Hardie & Lee — “Counting Your Customers” the Easy Way ↗

Diagram — not yet drawn

One customer's purchase history as ticks on a timeline, with the gap after the last tick shaded and the probability-of-being-alive curve falling across that gap — the same history read as a probability rather than as a ninety-day rule.

In the wild

Unvetted · not part of the tier assessment

What has been written about this tool in the last twelve months. Machine-retrieved and unchecked — everything above this line was checked.

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