Targeting Customer Groups using Gain and Cost Matrix: a Marketing Application

This paper introduces gain-cost classi…cation matrix for targeting customer groups. A real life application was realized on a customer database of CCF Bank containing more than 400,000 instances. Results shows that scoring is almost insensitive to di¤erent cost-gain hypothesis; on the other hand, the optimal targeted group size and the expected global bene…t rely to cost-gain hypothesis. Keywords: cost-sensitive learning, customer targeting, decision tree, marketing application 1 Cost-Bene…ts Aspects of Targeting in Marketing Introduction. Identifying target groups for marketing purposes is one of the most common applications of Data Mining. It aims at identifying the group of clients most likely to respond positively to a new product. This targeting is often done using classical machine learning techniques such as decision trees. The underlying assumption is that clients contacted in vain (false positive) and those who might have bought had they been contacted (false negative) can be treated in a similar manner. In real life situations, the hypothesis is not veri…ed, as the two cases are not symmetrical. In the …rst case, the company spent resources with no return on its expense; in the second case, there is a potential income loss; moreover, correctly targeted clients represent substantial gains for the company. In this paper, an example of targeting a customer group using decision trees will be examined, using a 400,000 rich customer base of Crédit Commercial de France (CCF). The originality of this paper lies in the introduction of a cost-gain matrix during the construction of the prediction model to identify the group the least expensive to target. In section 2, the determination of costs and bene…ts (gains) in the context of a direct marketing campaign is developed and the maximization of the expected gains is showed. Related works are covered in section 3, concentrating on authors who suggested ways to include costs in the scoring models and on the solution developed here. The CCF case study is detailed in section 4; hypotheses about costs are tested, the sensitivity of the scores (the estimated probabilities of purchase) is studied as well as the optimal target size for a maximized expected bene…t. The proposed decision model is applied to an actual targeting problem with respect to the advertising campaign of CCF Bank …nancial product using a database of more than 400,000 clients. The paper concludes with an evaluation of the strategy and suggested improvements currently under further development. 2 The general problem of targeting in marketing. The question of cost-bene…ts. Usually, error minimization algorithms are used to target a group of clients or prospects for a given commercial campaign [1] and the problem can be reduced to the simplistic case of the campaign cost matrix: Decision Decision Targeted Not Targeted Reality Does (or would) buy No Error, Cost = 0 Error, Cost = 1 Reality Does not (or wouldn’t) buy Error, Cost = 1 No Error, Cost = 0 In reality, the matrix is di¤erent: when a targeted client buys (= true positive), there is a bene…t and some cost if he doesn’t (= false positive); if no targeting is done, there is no bene…t, or gain, nor cost save the absence of a bene…t (= false negative). Working in a business context, it is better to use a ”gain matrix” than a ”cost matrix”. Decision Decision Targeted Not Targeted Reality Does (or would) buy Gain = +a No bene…t, no cost Reality Does not (or wouldn’t) buy Error, Cost = -b No bene…t, no cost 2.1 Accounting for costs and bene…ts in targeting. The following aspects of introducing costs and bene…ts are of interest in this paper : estimating the expected unit cost and unit bene…t; the role these play in determining the optimal target (marginal gain and total gain); and a fresh model for estimating the expected total bene…t with respect to the quality of the estimated probability of purchase and cost/gain hypotheses. Estimating the expected unit cost and unit bene…t The expected unit gain from selling one additional unit must be estimated. For example, with an investment, the discounted gain over the period must be estimated. Now, to estimate expected unit costs, the direct cost of one commercial action and the marginal cost of targeting an additional client are distinguished. Fixed costs comprise the concept, forms and lea‡ets design, sta¤ training, etc. Marginal (or variable) costs comprise what an additional targeted customer costs. For example, printing one more copy of a form letter, stu¢ng the envelope, postage stamp, etc. would be some of the marginal costs of a large scale mailing. In a telephone marketing campaign, the marginal costs would comprise the cost of one phone call, the salary of the phone operator, equipment rental, management of call-backs, etc. If estimating is di¢cult, hypotheses about costs and bene…ts can help. Such hypotheses would be incorporated into the estimated probability of a purchase for each client on the database which are to be used for estimating the expected bene…t from each customer and for drawing marginal and total gain curves (see § 4.1 and …gure 6). Determining the optimal target In order to determine the optimal target, individuals, or homogenous groups of individuals, are sorted by decreasing probability of a purchase P (i), thus P (i) is a decreasing function of i. Then, the expected marginal bene…t can be computed as: Gm(i) = a£ P (i) ¡ b£ (1¡P (i)) This marginal bene…t is equal to ”a” if individual ”i” buys with certainty and equal to ”¡b” if individual ”i” does certainly not buy. Now, an optimal target could be the set of clients for which the expected marginal bene…t is positive, that is: Gm(i) = a£ P (i)¡ b£ (1¡ P (i)) = (a + b)£ P (i)¡ b or P (i) > b a+ b Figure 1, shows the marginal bene…t per targeted client as a function of the proportion targeted on the database, with a false positive cost b = 200 and a true positive bene…t a = 2; 000 euros. Note that P (i) is a decreasing function of i and Gm is a decreasing function of P (i), hence Gm(i) is a decreasing function of i. On this example, the marginal bene…t is zero for P (i) = 200=(2; 000+200) = 0:09 that is to say i=N = 18%. Alternatively, the optimal target corresponds to the point where the total gain curve is maximum. Summing bene…ts of individuals from i = 1 to i = x, the total bene…t is the sum of the marginal bene…ts minus …xed costs: