Title: Managing churn to maximize profits
Description: Customer defection or churn is a widespread phenomenon that threatens firms across a variety of industries with dramatic financial consequences. To tackle this problem, companies are developing sophisticated churn management strategies. These strategies typically involve two steps--ranking customers based on their estimated propensity to churn, and then offering retention incentives to a subset of customers at the top of the churn ranking. The implicit assumption is that this process would maximize a firm's profits by targeting customers who are most likely to churn. However, current marketing research and practice aims at maximizing the correct classification of churners and non-churners. Profit from targeting a customer depends on not only a customer's propensity to churn, but also on her spend or value, her probability of responding to retention offers, as well as the cost of these offers. Overall profit of the firm also depends on the number of customers the firm decides to target for its retention campaign. We propose a predictive model that accounts for all these elements. Our optimization algorithm uses stochastic gradient boosting, a state-of-the-art numerical algorithm based on stage-wise gradient descent. It also determines the optimal number of customers to target. The resulting optimal customer ranking and target size selection leads to, on average, a 115% improvement in profit compared to current methods. Remarkably, the improvement in profit comes along with more prediction errors in terms of which customers will churn. However, the new loss function leads to better predictions where it matters the most for the company's profits. For a company like Verizon Wireless, this translates into a profit increase of at least $28 million from a single retention campaign, without any additional implementation cost.