Customer Lifetime Value Modeling and Its Use for Customer Retention Planning

Transcription

1 Customer Lfetme Value Modelng and Its Use for Customer Retenton Plannng Saharon Rosset Enat Neumann Ur Eck Nurt Vatnk Yzhak Idan Amdocs Ltd. 8 Hapnna St. Ra anana 43, Israel {saharonr, enatn, ureck, nurtv, yzhak}@amdocs.com ABSTRACT We present and dscuss the mportant busness problem of estmatng the effect of retenton efforts on the Lfetme Value of a customer n the Telecommuncatons ndustry. We dscuss the components of ths problem, n partcular customer value and length of servce (or tenure) modelng, and present a novel segment-based approach, motvated by the segment-level vew marketng analysts usually employ. We then descrbe how we buld on ths approach to estmate the effects of retenton on Lfetme Value. Our soluton has been successfully mplemented n Amdocs Busness Insght (BI) platform, and we llustrate ts usefulness n real-world scenaros. Keywords Lfetme Value, Length of Servce, Churn Modelng, Retenton Campagn, Incentve Allocaton. 1. INTRODUCTION Customer Lfetme Value s usually defned as the total net ncome a company can expect from a customer (Novo 21). The exact mathematcal defnton and ts calculaton method depend on many factors, such as whether customers are subscrbers (as n most telecommuncatons products) or vstors (as n drect marketng or e-busness). In ths paper we dscuss the calculaton and busness uses of Customer Lfetme Value (LTV) n the communcaton ndustry, n partcular n cellular telephony. The Busness Intellgence unt of the CRM dvson at Amdocs talors analytcal solutons to busness problems, whch are a hgh prorty of Amdocs customers n the communcaton ndustry: Churn and retenton analyss, Fraud analyss (Murad and Pnkas 1999, Rosset et al 1999), Campagn management (Rosset et al 21), Credt and Collecton Rsk management and more. LTV plays a maor role n several of these applcatons, n partcular Churn analyss and retenton campagn management. In the context of churn analyss, the LTV of a customer or a segment s mportant complementary nformaton to ther churn probablty, Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. SIGKDD 2, July 23-26, 22, Edmonton, Alberta, Canada. Copyrght 22 ACM X/2/7 $5.. as t gves a sense of how much s really beng lost due to churn and how much effort should be concentrated on ths segment. In the context of retenton campagns, the man busness ssue s the relaton between the resources nvested n retenton and the correspondng change n LTV of the target segments. In general, an LTV model has three components: customer s value over tme, customer s length of servce and a dscountng factor. Each component can be calculated or estmated separately or ther modelng can be combned. When modelng LTV n the context of a retenton campagn, there s an addtonal ssue, whch s the need to calculate a customer s LTV before and after the retenton effort. In other words, we would need to calculate several LTV s for each customer or segment, correspondng to each possble retenton campagn we may want to run (.e. the dfferent ncentves we may want to suggest). Beng able to estmate these dfferent LTV s s the key to a successful and useful LTV applcaton. The structure of ths paper s as follows: - In secton 2 we ntroduce the general mathematcal formulaton of the LTV calculaton problem. - Secton 3 dscusses practcal approaches to LTV calculatons from the lterature, and presents our preferred approach. - The practcal mplementaton of our LTV calculaton, wth some examples, s presented n secton 4. - In secton 5 we turn to the busness problem of estmatng LTV gven ncentves and usng these calculatons to gude retenton campagns. - Secton 6 presents our LTV-based soluton to the ncentve allocaton challenge and llustrates ts use for real-lfe applcatons. 2. THEORETICAL LTV CALCULATIONS Gven a customer, there are three factors we have to determne n order to calculate LTV: 1. The customer s value over tme: v(t) for t, where t s tme and t s the present. In practce, the customer s future value has to be estmated from current data, usng busness knowledge and analytcal tools. 2. A length of servce (LOS) model, descrbng the customer s churn probablty over tme. Ths s usually descrbed by a survval functon S(t) for t, whch descrbes the probablty that the customer wll stll be actve at tme t. We can then defne f(t) as the customer s nstantaneous probablty of churn at tme t: f(t) -ds/dt The quantty most commonly modeled, however s the hazard functon h(t) f(t)/s(t). Helsen and Schmttlen (1993) dscuss why h(t) s a more approprate quantty to estmate than f(t). The LOS

2 model has to be estmated from current and hstorcal data as well. 3. A dscountng factor D(t), whch descrbes how much each $1 ganed n some future tme t s worth for us rght now. Ths functon s usually gven based on busness knowledge. Two popular choces are: - Exponental decay: D(t) exp (-αt) for some α (α means no dscountng) - Threshold functon: D(t) I{t T} for some T> (where I s the ndcator functon). Gven these three components, we can wrte the explct formula for a customer s LTV as follows: LTV S(t)v(t)D(t)dt (2.1) In other words, the total value to be ganed whle the customer s stll actve. Whle ths formula s attractve and straght-forward, the essence of the challenge les, of course, n estmatng the v(t) and S(t) components n a reasonable way. We can buld models of varyng structural and computatonal complexty for these two quanttes. For example, for LOS we can use a hghly smplstc model assumng constant churn rate so f we observe 5% churn rate n the current month, we can set S(t).95 t. Ths model gnores the dfferent factors that can affect churn a customer s ndvdual characterstcs, contracts and commtments, etc. On the other hand we can buld a complex proportonal hazards model, usng dozens of customer propertes as predctors. Such a model can turn out to be too complex and elaborate, ether because t s modelng local effects relevant for the present only and not for the future, or because there s not enough data to estmate t properly. So to buld practcal and useful analytcal models we have to fnd the golden path whch makes effectve and relevant use of the data avalable to us. We attempt to answer ths challenge n the next sectons. 3. PRACTICAL LTV APPROACHES In ths secton we revew some of the approaches to modelng the varous components of LTV from the lterature and present the segment-based approach, whch follows naturally from the way analyses and campagns are usually conducted n marketng departments. The segment-based approach helps n smplfyng calculatons and ustfes the use of relatvely smple methods for estmatng the functons. To model LTV we would naturally want to make use of the most recent data avalable. Therefore let us assume that we are only gong to use churn data from the last avalable month for modelng LOS. So for the rest of ths paper we assume we have a set of n customers, wth covarates vectors x 1,,x n representng ther current state and churn ndcators c 1,,c n. The customers tenure wth the company s an mportant churn predctor snce LOS frequently shows a strong dependency on customer age, n partcular when contracts prevent customers from dsconnectng durng a specfc perod. Let us denote these tenures by t 1,,t n.addtonal covarates are customer detals, usage hstory, payment hstory, etc. Some of the covarates may be based on tme-dependent accumulated attrbutes (e.g. averages over tme, trends). Our dscusson s gong to vew tme as dscrete (measured n months), and thus the t s wll be ntegers and f(t) wll be a probablty functon, rather than a dstrbuton functon. 3.1 LOS Modelng Approaches We now present a bref descrpton of common Survval Analyss approaches and ther possble use n LOS modelng. Detaled dscusson of prevalent Survval Analyss approaches can be found n the lterature, e.g. Venables and Rpley 1999, chapter 12. Pure parametrc approaches assume S(t) has a parametrc form (Exponental, Webull etc.) wth the parameters dependng on the covarates, ncludng t. As Man et al (1999) menton, such approaches are generally not approprate for LTV modelng, snce the survval functon tends to be spky and non-smooth, wth spkes at the contract end dates. Sem-parametrc approaches, such as the Cox proportonal hazards (PH) model (Cox 1972), are somewhat more flexble. The Cox PH model assumes a model for the hazard functon h(t) of the form: f () () t h t λ t exp β ' x (3.1) S t or alternatvely: log () () ( ) ( h () t ) log( λ ( t) ) + β ' x (3.2) So there s a fxed parametrc lnear effect (n the exponent) for all covarates, except tme, whch s accounted for n the tmevaryng baselne rsk λ(t). Man et al (1999) buld a Neural Network sem-parametrc model, where each possble tenure t has ts own output node (the tenure s dscretzed to the monthly level). They llustrate that the more elaborate NN model performs better than the PH model on ther data. The data as descrbed above, makes LOS modelng a specal case of survval analyss where each subect s observed only once n tme, and customers who dsconnected before ths month are left censored. Consequently we can approach t ether as a survval analyss problem or a standard supervsed learnng problem where the tme (.e. customer s tenure wth the company) s one of the predctors and churn s the response. To nclude a baselne hazard effect, tme can be treated as beng factoral rather than numercal, thus allowng a dfferent effect for each tenure value. In ths settng, a log-lnear regresson model for churn predcton usng left-censored data would be equvalent n representaton to a Cox proportonal hazards survval analyss model. To see ths pont, consder that a customer s churn rsk s n fact hs h(t) value (snce f the customer already left we would not observe hm). Thus a model of the form: log ( P ( c 1) ) α ( t ) + β ' x (3.3) s obvously equvalent to (3.2). The Kaplan-Meer estmator (Kaplan and Meer 1958) offers a fully non-parametrc estmate for S(t) by averagng over the data: S () t I( t t) I( t t) + Ct (3.4) Where: I t t equals 1 f customer 's tenure s at least t months ( )

3 ( t t) I s the number of customers whose tenure s at least t months C t s the number of customers who should have been at least t months old at the current date but have already left. The data as descrbed above s left censored and does not nclude C t. However t can often be calculated based on hstorcal nformaton found n customer databases, whch are typcally used for LTV calculatons. 3.2 The Segment-Based LOS Approach When we are consderng the use of analytcal models for marketng applcatons, we should take nto account the way they are gong to be used. An mportant concept n marketng s that of a segment, representng a set of customers who are to be treated as one unt for the purpose of plannng, carryng out and nspectng the results of marketng campagns. A segment s usually mplctly consdered to be homogeneous n the sense that the customers n t are smlar, at least for the property examned (e.g. propensty to churn) or the campagn planned. Amdocs Busness Insght tools assst marketng experts n automatcally dscoverng, examnng, manually defnng and manpulatng segments for specfc busness problems. We assume n our LTV mplementaton that: - the marketng analyst s nterested n examnng segments, not ndvdual customers - these segments have been pre-defned usng Amdocs CMS or some other tool - they are homogeneous n terms of churn (and hence LOS) behavor - they are reasonably large Based upon these assumptons, estmatng LOS for a segment s reasonable and relatvely smple. Under these assumptons we can dspense completely wth the covarate vectors x (snce all customers wthn the segment are smlar) and adopt a nonparametrc approach to estmatng LOS n the segment by averagng over customers n the segment. The Kaplan-Meer approach s reasonable here, but as we dscussed before t requres the use of left-censored data referrng to customers who have churned n the past. Whle ths data s usually avalable t refers to churn events from the (potentally dstant) past, and so may not represent the current tendences n ths segment, whch may well be related to recent trends n the market, offers by compettors etc. So an alternatve approach could be to calculate a non-parametrc estmate of the hazards rate: h () t I( t t) I( c 1) I( t t) (3.5) Where: I t t equals 1 f customer 's current tenure s t months ( ) ( 1) I c equals 1 f customer churned n the current month I t t I c 1 s the number of customers whose ( ) ( ) current tenure s t months and churned n the current month. Ths approach reles heavly on havng a suffcent number of examples for each dscrete tme pont t (usually taken n months), but has the advantage of usng only current data to estmate the functon. We can obtan an estmate for S(t) through the smple calculaton: S () t < S( u + 1) / S( u) u t ( S u) f ( u) )/ S( u) ( 1 h( u) ) u< t u< t ( (3.6) Where S() 1, of course. In secton 4 we descrbe Amdocs LTV platform, whch utlzes ths approach and llustrate t on real data Theoretcal Dscusson of a Segment Approach When examnng the adequacy of a modelng approach, we generally have to consder two statstcal concepts: - Bas / Consstency: f we had nfnte data, would our estmate converge to the correct value? How far would t end up beng? - Varance: how much uncertanty do we have n the estmates we are calculatng for the unknown value? These concepts have concrete mathematcal defntons for the case of squared error loss regresson only (although many suggestons exst for generalzed formulatons for other cases see, for example - Fredman 97). However the prncples they descrbe apply to any problem: - The more flexble and/or adequate the model s, the smaller the bas. - The more data one has, and the more effcently one uses t, the smaller the uncertanty. Under the segment-homogenety assumpton mentoned n the prevous secton, the bas of our segment-based approach should be close to zero. Furthermore, even wthout ths assumpton, f we assume that the marketng expert plannng the campagn s only nterested n the segment as a whole, then the quanttes we want to estmate are ndeed segment averages and not ndvdual values. Hence the segment-based estmates are unbased n ths scenaro as well. As for varance, ths s obvously a functon of segment sze. Parametrc estmators wll tend to have smaller varance. It s an nterestng research queston to nvestgate ths bas-varance tradeoff between non-parametrc and parametrc estmates n ths case. Under the assumpton that segments are large (as are ndeed the segments n most real-lfe segments encountered n the communcaton ndustry), and that there s a reasonable amount of churn n each segment, we can safely assume that the segment based non-parametrc estmates wll also have low varance, and hence that our approach s reasonable. 3.3 Practcal Value Calculatons Calculatng a customer s current value s usually a straght forward calculaton based on the customer s current or recent nformaton: usage, prce plan, payments, collecton efforts, call center contacts, etc. In secton 4 we gve llustrated examples. The statstcal technques for modelng customer value along tme nclude forecastng, trend analyss and tme seres modelng. However the complexty of modelng and predctng the varous factors that affect future value: seasonalty, busness cycles, economc stuaton, compettors, personal profles and more, make future value predcton a hghly complex problem. The soluton n LTV applcatons s usually to concentrate on modelng LOS, whle ether leavng the whole value ssue to the experts (Man et

4 al 1999), or consderng customers current value as ther future value (Novo 21). Workng at the segment level also makes the value calculaton task easer, snce t mples we do not need to have an exact estmate of ndvdual customers future value, but can rather average the estmates over all customers n the segment. Ths does not solve the fundamental problem of predctng future value, but t allows us to get a relable average current value estmate at the segment level. 4. LTV WITHIN THE CMS One of the Amdocs BI platform systems s the Churn Management System (CMS). The key outputs of the system are churn and loyal segments, as well as scores for each ndvdual n the target populaton, whch represent the ndvdual s lkelhood to churn. The frst step we take n the process of churn analyss s defnng and creatng a customer data mart that provdes a sngle consoldated vew of the customer data to be analyzed. It ncludes varous attrbutes that reflect customers profle and behavor changes: customer data, usage summares, bllng data, accounts recevable nformaton, and socal demographc data. Relevant, trends and movng averages are calculated, to account for tmevarablty n the data and explot ts predctve power. The preparaton of the data for the exact needs of the data mnng process ncludes Extractng Transformng and Loadng (ETL) the necessary data. The churn analyss process wthn the CMS combnes automatc knowledge dscovery and nteractve analyst sessons. The automatc algorthm s a decson tree algorthm followed by a rule extracton mechansm. The analyst can then vew and manpulate the automatcally generated predctve segments (or patterns), and add to them based on hs marketng expertse. The automatc and nteractve tools whch the CMS utlzes to dscover and analyse patterns, and to perform predctve modellng, have proven themselves as hghly successful when compared to the state of the art data-mnng technques (Rosset and Inger 2, Inger et al 2, Neumann et al 2). The analyss tool ncludes an easy-to-use graphcal user nterface. Fgure 1 s a capture of one of the system analyss tool s screens whch provdes the analyst wth nsght nto varous customer populaton segments automatcally dentfed by ther attrbutes, churn lkelhood and related value. These segments (or rules) are characterzed by several attrbutes accompaned by statstcal measures that descrbe the sgnfcance of the segments and ther coverage. Addtonal graphcal capabltes of the CMS nclude analyzng the dstrbuton of each varable per churn/loyal groups or n comparson to the entre populaton and an nteractve vsual data analyss, whch provdes the ablty to further nvestgate attrbutes to provde addtonal nsght and support the desgn of retenton actons. The data s extracted on a monthly bass and accordngly the scorng process s performed once a month. The churn score s one of the man components of the LOS; thus each customer wll have a new LTV every month. As shown n Fgure 1 the system produces segments that characterze churn and loyal populatons. Thus, the segment level and not the customer level s the bass for the nteracton wth the analyst. That s the level on whch retenton campagns are planned and therefore the level on whch the analyst s nterested n vewng LTV. The LOS soluton mplemented n Amdocs CMS s the segmentbased calculaton descrbed n secton For value defnton the CMS allows flexblty and t calculates the value ndvdually per customer. It can be a constant value, an exstng attrbute wthn the data-mart, or a functon of several exstng attrbutes. An example for the customer value can be The fnancal value of a customer to the organzaton. Ths value can be calculated from receved payments mnus the cost of supplyng products and servces to the customer. To effectvely use the data mnng algorthms n the CMS, the nput s usually a based sample of the populaton. Often the churn rate n the populaton s very small but n the sample the two classes (churn and loyal) are much more balanced. The dfference n churn rate between the sample and the populaton s accounted Fgure 1. Churn and loyal patterns dscovered automatcally by the CMS

5 for n the LOS model, as we descrbe below. Rosset et. al. 21 provde a detaled explanaton about the relevant nverse transformaton. LOS s calculated on the segment level. It s calculated for each age group t wthn the segment,.e. for each group of customers wth the same tenure n the segment, there wll be the same LOS. Ths calculaton s based on a large amount of data (customers wth the same tenure n the segment). The base for ths value s the proporton of churners for each age t - p t as defned n the followng formula (ths s an extended verson of the calculaton from equaton (3.5) n secton 3.3) LOS s the Expected Length of Servce for the customer rato s the populaton to sample rato of loyal customers pt factor Where: I ( t t) I( c 1) I( t t) I ( c ) + I( t t) I ( c 1) (4.1) c s the number of churners at tenure t I t t I c s the number loyal customers at tenure t I ( t t) I( 1) ( ) ( ) factor (churn to loyal sample rato) / (churn to loyal populaton rato) Ths quantty s calculated for each tenure t n the segment. There are several assumptons underlyng ths calculaton. Frst, that the current churn probabltes for customers at tenure t represent the future ones at tenure t; second, that the customers come from a homogeneous populaton and thrd, that both I( t t) I( c 1 ) and I ( t t) I( c ) are large enough to gve relable estmates of p t. Now, gven a customer who s currently at tenure t, we can use (4.1) to get the Probablty of a customer to reach age t S(t) S () t ( p ) ( 1 p ) ( 1 p ) 1 t 1 t 2 t L (4.2) And then we can get the expected LOS as follows- LOS h t S () t (4.3) Where h s the horzon,.e. the number of months untl the end of the nterest perod. If we are nterested n a horzon of two years then the sum wll be over 24 months. Implementng other dscountng functons, n addton to ths threshold approach s planned for the future, and poses no conceptual problems. Fnally, LTV wthn a segment wll be the followng sum over all customers n the segment s LTV rato LOS v c (4.4) where s the ndex of customers n the segment v s the value of the -th customer c s an ndcaton for the -th customer. f he s a churner, 1 f he s loyal Fgure 2. LTV calculaton CMS screen Fgure 2 s a screen capture of the CMS wndow for calculatng LTV. It s necessary to select the customer s age (tenure), enter the horzon and enter the full populaton churn rate (the sample churn rate s already derved). It s also necessary to select/defne the value, whch may be one of three optons: an equal value for all customers, a feld that was prevously selected as the value (n ths case the average bll was prevously selected), or a new value functon. The result of the LTV calculaton can also be seen n Fgure 1. The statstc measures (ncludng LTV) of the dentfed segments are already transformed to the full populaton. In general, Loyal segments ( Class: Stay ) have hgher LTVs than Churn segments, snce the LOS of churners s. The am s to try to ncrease the LTV of relevant segments by proper retenton efforts, whch am manly at ncreasng the LOS (a secondary purpose s ncreasng the value). 5. ESTIMATING THE EFFECT OF RETENTION EFFORTS ON LTV We now turn to the most useful and challengng applcaton of LTV calculaton: modelng and predctng the effects of a company s actons on ts customer s LTV. An example of a desrable scenaro for a LTV applcaton would be: Company A has dentfed a segment of Cty dwellng professonals, whch s of hgh value and hgh churn rate. It wants to know the effect of each one of fve possble ncentves suggestons (e.g. free battery, 2 free nght mnutes, reduced prce handset upgrade etc.), on the segment s value over tme and LOS, and hence LTV. Each ncentve may have a dfferent cost, dfferent acceptance rate by customers, and dfferent effect f t gets accepted. The goal of the LTV applcaton s to supply useful nformaton about the effects of the dfferent ncentves, and help analysts to choose among them.

6 From the defnton of the problem t s clear that there s some nformaton about the ncentves whch we must know (or estmate) before we can calculate ts effect on LTV: 1. The cost of the effort nvolved n suggestng the ncentve. Ths fgure s usually known and depends for example on the channel utlzed (e.g. proactve phone contact, letter, comment on wrtten bll). Denote the suggeston (or contact channel) cost by C. 2. The cost to the company f the customer accepts the ncentve (e.g. the cost of the battery offered). Agan ths fgure s ether known or can be relably estmated based on busness knowledge. Denote the offer cost by G 3. The probablty that a customer n the approached segment wll agree to accept the ncentve (whch can be around 1% f the ncentve s completely free, but that s rarely the case). Ths s a more problematc quantty to fgure out and t has to be estmated from past experence, or smply guessed (n whch case many dfferent values for t can be tred, to see how each would affect the outcome). Denote the acceptance probablty by P 4. Change n the value functon f the ncentve s accepted. For example, f the ncentve s free vocemal, the customer s calls to the voce-mal can stll generate addtonal revenue. Smlarly to P, the change n value has to be assumed or approxmated from past data. Denote the new value functon by v () (t). 5. The effect on customer s LOS f the ncentve s accepted. The most obvous way for the ncentve to affect LOS s f t ncludes a commtment by the customer (.e. the customer commts not to leave the company n the next X months). Denote the new survval functon by S () (t). Gven all of the above, calculatng the change n LTV of a customer from a retenton campagn, n whch a gven ncentve s suggested s a straght forward ROI calculaton: LTV new LTV P ( old ( ) ( ) S (t)v (t)d(t)dt S(t)v(t)D(t)dt G) C (5.1) As for the basc LTV calculaton descrbed n secton 2, and even more so, the man challenge s n obtanng reasonable and usable estmates for the above quanttes, n partcular the functons v (), S (). We now descrbe two approaches to ths problem: one that bulds on our segment-level LTV calculaton approach presented above, and another that makes further smplfyng assumptons, negatng the need to predct the future. 5.1 Segment-level calculaton As was mentoned before, workng at the segment level allows us to average our nformaton over the whole segment and avod parametrc assumptons, at the prce of assumng that the segment populaton s homogeneous. To expand the segment-level approach descrbed n secton 3.2 to estmate the effect of ncentves on a segment s LTV, we need to descrbe how we change the LOS model per segment, and how we adust customer value for the ncentve effects. We defne two possble effects of an ncentve on LOS: commtment and percentage decrease. If an ncentve ncludes a commtment perod of X months (usually wth a penalty for commtment volaton that makes t unproftable to leave durng ths perod), then obvously any customer who accepts the ncentve wll not leave durng ths perod. On the other hand, ncentves that do not nclude a commtment also cause the churn probablty to decrease. Our model allows a percentage decrease n the monthly churn rate. Ths percentage s presumed to be constant n all months and for all customers wthn the segment. Thus, to estmate post-ncentve LOS for a specfc segment and a specfc ncentve, we need to know: - Commtment perod ncluded n ncentve, denote by cmt () - Reducton n churn probablty from ncentve, denote by rc () Whch gves us for a specfc customer: S () ( t) ( ) ( ) ( ) I{ t < cmt } + I{ t cmt } (1 c( a + u) rc ) (5.2) t ( ) u cmt where a s the customer s current age, and c(a+u) s the churn probablty estmate for age a+u as estmated for the whole segment. Then a smlar calculaton to the expected LOS calculaton n equatons (4.2) and (4.3) now gves us a post-ncentve expected LOS estmate of: () ELOS cmt ( ) 1 n h t ( (1 c( a ) ) + u rc n 1 ( ) ( ) t cmt u cmt + ) (5.3) where the ndex runs over the customers n the segment. So we are usng the homogenety assumpton to average the effect of the ncentve on LOS over all customers n the segment, and we are assumng agan that the age effect s the only dfferentatng factor of ndvdual behavor wthn the sample. We also assume that the probablty of acceptng the ncentve s constant across the segment and ndependent of all customer propertes (ncludng age), not used for the segment defnton. We also assume that once the commtment perod s over, customers wll on average return to the churn behavor that would characterze them at ther age have they not churned for other reasons (rather than the commtment from the ncentve). The ncentve s effect on customer value s assumed to be as a percentage change n the customer value. Ths change should reflect both the reduced value to the company due to the ncentve cost and the ncreased value due to the ncrease n the relevant customer s usage. For example, when offerng a free vocemal ncentve the reduced value would be the vocemal cost and the ncreased valued would be derved from the ncrease n blled ncomng calls and the ncrease n outgong calls due to the customer s calls to the vocemal box. Thus, we get that for every customer: v () v (1+change () ), where change () s the change n value due to the ncentve, assumed constant for all customers. We can now combne all of the above nto an estmate of the average change n LTV n the segment due to the ncentve:

7 avltv () avltv n 1 ( ) ( ) P ( [ ELOS v ( ) ELOS v( )] G) C (5.4) n 1 Where avltv () s the estmated average LTV per customer n the segment after the retenton campagn and avltv s the estmated current average LTV per customer n the segment. If ths dfference s postve t means we expect the retenton campagn to be benefcal to the company. 5.2 Smplfed Calculaton Based on Constant Churn Assumptons Let us now assume the followng: 1. D(t) s a threshold functon wth horzon h. 2. The churn rsk s constant for each customer n the segment for any horzon. Ths would translate to assumng that for each customer, S(t) 1- p t, where p s the churn probablty of the customer for the next month. 3. p s small 4. The ncentve ncludes a commtment for h months at least. 5. Customer value s constant over tme, v(t) v, and s not affected by the ncentve s acceptance. Then we get the followng value for customer LTV wthout retenton: h 1 LTVold v (1 p) t v h t 1 1 t pt vh(1 p( h 1)) (5.5) 6. RETENTION LTV IMPLEMENTATION IN THE CMS We now llustrate how the concepts of the prevous secton drve the ncentve LTV mplementaton wthn the CMS, by followng the detals of the steps n the applcaton and the calculaton for a couple of real-lfe examples. Fgure 3. Churn segment Fgure 3 demonstrates one of the churn segments selected for a retenton campagn. The segment conssts of young customers who don t have a caller-d feature, whose handset was not upgraded n the past year and who have recently changed ther payment method (for example from drect debt to check). A marketng analyst came up wth two possble ncentves for ths segment: an upgrade at a dscounted prce (lets assume for smplcty that all wll be offered the same new handset) or a free caller-d feature. Both ncentves wll nvolve a 12 months commtment perod. where the approxmaton reles on p and h beng reasonably small. And addng retenton we get: LTV P( hv G) + (1 P) LTV C (5.6) new old Snce f we succeed n gvng the ncentve we are guaranteed loyalty for the full relevant perod of h months. So the dfference n LTV due to retenton s: LTVnew - LTVold P h( h 1) v p P G C (5.7) whch, gven P,G and C and gnorng the naccuracy n our calculaton gves us the elegant result that: LTVnew - LTVold > p > ( P G C) /( P h( h 1)) v (5.8) In other words, we get the ntutve concluson, that f we have a reasonable model for v and p, we should suggest the ncentve only to customers whose value weghted rsk v p s bg enough. Fgure 4. Incentve defnton CMS Screen The frst step s to calculate the current LTV of ths segment. As dsplayed n secton 4 we defned the LTV parameters. Recall, that the feld selected as value was the monthly average bll, the selected horzon s 12 months and the populaton churn rate s 5% (n the sample t s about 5%). The LTV of ths segment, whch s already dsplayed n Fgure 3 s $4,967,22. The next step s to defne the possble ncentves. An example of how ths s done n the CMS s llustrated n Fgures 4 & 5. In Fgure 4 the ncentve s defned and n Fgure 5 the ncentve s attached to a specfc segment. At ths stage t s also possble to refne the segment defnton. Note that the same ncentve may be allocated to dfferent segments.

8 Suppose we wanted to examne the same two ncentves for a dfferent segment, as shown n Fgure 7. Ths s a segment wth many loyal customers, comprsed of older customers wth stable usage and medum bll average amounts. Fgure 7. Loyal segment Fgure 5. Incentve allocaton CMS screen Fnally, we compare the change n LTV related to each of the ncentves. The cost of gvng a dscounted handset upgrade s much hgher than the cost of a free caller d (n ths example we used $1 and $1 correspondngly). On the other hand, the acceptance rate wll be hgher snce t s a more attractve offer (caller-d - 1% of the churners and 2% of the loyals, upgrade - 2% of the churners and 3% of the loyals). Actually, churners often swtch provders n order to receve an mproved handset promsed by the compettor. So, the result of the upgrade ncentve wll be a hgher retenton rate than the caller-d ncentve. Addtonally, a more sophstcated handset wll probably ncrease the usage and thus the added value, whle addng a caller-d wll have very lttle or no mpact on the usage (the relatve value ncrease for the upgrade s 1% n ths example and none for the caller-d). Note that the added value affects both potental churners who accept the offer and loyal customer who wll accept the offer. Furthermore, loyal customers wll also be commtted to 12 more months, so even though they weren t about to churn n the next month the ncentve may lengthen ther LOS. The new LTV calculaton takes nto account all these parameters and the result as can be seen n Fgure 6 s that the estmated ncrease n LTV due to offerng a dscounted upgrade s $2,413,338 and due to offerng a free caller-d s $1,982,294. Fgure 6. Estmated LTV change due to a free caller-d and due to a dscounted upgrade offer In addton to the purpose of retanng the churners n ths segment, offerng an ncentve to ths segment s done also to ncrease the usage / value of the loyal customers and lengthen ther LOS. The orgnal LTV as dsplayed on Fgure 6.5 s $29,91,321. The same cost and acceptance rates were appled for the caller-d and upgrade ncentves. Note that snce the acceptance rate s hgher for loyal customers the overall acceptance rate of ths segment wll be hgher then n the prevous churn segment. The result was that the ncrease n value and LOS wasn t large enough to cover the hgh cost of the upgrade offers. Thus, the estmated change n LTV due to that ncentve s negatve: - $485,45. On the other hand, the caller-d ncentve yelded an estmated LTV ncrease of $1,422,54 (Fgure 8). Fgure 8. Estmated LTV change due to a free caller-d and due to a dscounted upgrade offer The examples llustrate that dfferent ncentves may have dfferent mpacts on LTV of the same segment, and the same ncentve may have dfferent mpacts on LTV of dfferent segments. The calculatons nvolved are complex enough that the dfferental effect of dfferent ncentves on dfferent segments cannot be easly guessed even when all the ncentve s parameters are known. Usng the applcaton s mechansm for estmatng that mpact, t s possble to ft the approprate ncentve (out of the gven optons) to selected segments. 7. SUMMARY AND FUTURE WORK In ths paper we have tackled the practcal use of analytcal models for estmatng the effect of retenton measures on customers lfetme value. Ths ssue has been somewhat gnored n the data mnng and marketng lterature. We have descrbed our approach and llustrated ts usefulness n practcal stuatons. The approach presented here to LTV calculaton s not necessarly the best approach. However our emphass s on practcal and usable solutons, whch wll enable us to reach our ultmate goal -

9 to get useful and actonable nformaton about the effects of dfferent ncentves. As our approach s modular, addtonal LOS and value models can certanly be ntegrated nto the soluton we presented. We beleve that ths problem, lke many others that arse from the nteracton between the busness communty and data mners, present an mportant and sgnfcant data mnng challenge and deserve more attenton than t usually gets n the data mnng communty. In ths paper we have tred to llustrate the usefulness of combnng busness knowledge and analytcal expertse to buld practcal solutons to practcal problems. 8. REFERENCES [1] Cox, D.R. (1972), Regresson Models and Lfe Tables, Journal of the Royal Statstcal Socety, B34, [2] Fredman, J.H. (1997), On Bas, Varance, /1-Loss and the Curse-of-Dmensonalty, Data Mnng and Knowledge Dscovery 1(1), [3] Helsen, K. and Schmttlen, D.C. (1993), Analyzng Duraton Tmes n Marketng: Evdence for the Effectveness of Hazard Rate Models, Marketng Scence, 11, [4] Inger, A., Vatnk, N., Rosset, S. and Neumann, E. (2), KDD-Cup 2 Queston 1 Wnner's Report, SIGKDD Exploratons, 2(2), 94. [5] Kaplan, E.L. and Meer, R. (1958), Non-parametrc Estmaton from Incomplete Observatons, Journal of the Amercan Statstcal Assocaton, 53, [6] Man, D.R., Drew, J., Betz, A. and Datta, P. (1999), Statstcs and Data Mnng Technques for Lfetme Value Modelng, Proceedngs of KDD-99, [7] Murad, U. and Pnkas, G. (1999), Unsupervsed Proflng for Identfyng Supermposed Fraud, PKDD-99, [8] Neumann, E., Vatnk, N., Rosset, S., Duenas, M., Sassoon, I. and Inger, A. (2), KDD-Cup 2 Queston 5 Wnner's Report, SIGKDD Exploratons, 2(2), 98. [9] Novo, J. (21), Maxmzng Marketng ROI wth Customer Behavor Analyss, [1] Rosset, S. and Inger, A. (2), KDD-Cup 99: Knowledge Dscovery In a Chartable Organzaton's Donor Database, SIGKDD Exploratons, 1(2), [11] Rosset, S., Murad, U., Neumann, E., Idan, I. and Pnkas, G.(1999), Dscovery of Fraud Rules for Telecommuncatons - Challenges and Solutons, Proceedngs of KDD-99, [12] Rosset, S., Neumann, E., Eck, U., Vatnk, N. and Idan, I.(21), Evaluaton of predcton models for marketng campagns, Proceedngs of KDD-21, [13] Venables, W.N. and Rpley, B.D. (1999), Modern Appled Statstcs wth S-PLUS, 3 rd edton. Sprnger-Verlag.