Gamma-Gamma Spend Model

The name refers to its two layers of gamma distributions. The first gamma describes how an individual customer's transaction values vary around their own average spend, capturing order-to-order randomness within a customer. The second gamma describes how customers' average-spend levels vary across the population, capturing genuine differences between high-value and low-value customers. By mixing the within-customer gamma over the between-customer gamma, the model produces a marginal distribution of observed average spend that depends only on three population parameters and each customer's transaction count and average. This compound structure is what enables the Bayesian shrinkage estimate of expected spend, and it parallels the gamma-Poisson (NBD) logic used on the frequency side.

The Gamma-Gamma model assumes that a customer's average transaction value is independent of how frequently they transact. This matters because the standard customer-lifetime-value pipeline estimates the spend model and the frequency model separately and then simply multiplies expected spend by expected future transactions. If spend and frequency were strongly correlated, for example if frequent buyers systematically spent less per order, this multiplication would be biased and the separability would break down. Best practice is therefore to compute the correlation between each customer's transaction frequency and their average transaction value before applying the model; a small correlation supports using Gamma-Gamma, while a large one signals that a joint or covariate-augmented model is needed instead.

It handles them through Bayesian shrinkage. The expected-spend estimate is a precision-weighted blend of the customer's own observed average transaction value and the population average spend, with the weight on the customer's own data increasing with the number of transactions they have made. A customer with many orders has a reliable observed average, so the estimate sits close to it; a customer with only one or two orders has a noisy average, so the estimate is pulled strongly toward the population mean. This prevents the model from over-valuing a customer whose single order happened to be large, or under-valuing one whose single order happened to be small, which is exactly the kind of error a naive raw-average approach makes on thin data.