How Much is Your Customer Worth? A Gamma-Poisson Model to Assess Customer Profitability

Assessing the profitability of a customer is very important to a firm from the standpoint of planning retention (and even acquisition) initiatives. Customer profitability is also the defining concept of customer relationship management (CRM). In this paper we propose a framework to quantify the expected profitability of a customer. This is done by first postulating that a customer's probability of responding to a marketing solicitation follows a discrete hazard process (specifically, the customer's inter-purchase times are distributed Poisson), whose parameters are allowed to vary across customers on account of both observed heterogeneity and unobserved heterogeneity (specifically, we assume the heterogeneity distribution to be Gamma). This yields an unconditional model of customers' inter-purchase times, with the "memory" property, that we call the Gamma-Poisson Model (not to be confused with the NBD model, which compounds "memoryless" Exponential inter-purchase times with Gamma heterogeneity). We then show how to use the estimated parameters to score the firm's customers in terms of their expected profitability to the firm at any point of time. These profitability scores are customer-specific and generated by (1) Bayesian updating of the estimated population-level parameters using the observed customer purchases, as well as (2) the time elapsed since the customer's last purchase with the firm. Our proposed procedure enables the firm to track the time-varying profitability of its customers, and also facilitates the elimination of unprofitable customers as and when appropriate. Lastly, we discuss possible ways of dealing with optimal customer prospecting based on our analyses. We illustrate our proposed technique using individual-level purchasing data from 529 customers of a catalog firm. First, we estimate the parameters of our proposed Gamma-Poisson Model. As an empirical benchmark, we also estimate the Beta-Binomial Model, which can be interpreted as a discrete-time analogue of the widely used NBD Model. Our proposed model shows superior empirical performance - in terms of both (1) in-sample calibration fit, and (2) holdout validation fit - over the benchmark. We then demonstrate, using a variety of segmentation analyses, the substantive benefits of employing our proposed Gamma-Poisson Model in terms of how one could effectively segment customers based on their predicted profitability scores. We believe that our proposed technique will greatly assist marketing efforts of firms that possess customer databases