Customer Relationship Management:A Database Approach

MARK 7397Spring 2007

James D. HessC.T. Bauer Professor of Marketing Science

375H Melcher Hall jhess@uh.edu713 743-4175

Class 2

Marketing Metrics

Marketing Metrics

TraditionalPrimary

Customer-based

Market Share Sales GrowthCustomer

AcquisitionCustomerActivity

Popular Customer-based

StrategicCustomer-based

Traditional and Customer BasedMarketing Metrics

Traditional Marketing Metrics

Market share

Sales Growth

Primary Customer Based metrics

Acquisition rate

Acquisition cost

Retention rate

Survival rate

P (Active)

Lifetime Duration

Win-back rate

Popular Customer Based metrics

Share of Category Requirement

Size of Wallet

Share of Wallet

Expected Share of Wallet

Strategic Customer Based metrics

Past Customer Value

RFM value

Customer Lifetime Value

Customer Equity

Primary Customer Based Metrics

• Customer Acquisition Measurements

– Acquisition rate

– Acquisition cost

• Customer Activity Measurements

– Average interpurchase time (AIT)

– Retention rate

– Defection rate

– Survival rate

– P (Active)

– Lifetime Duration

– Win-back rate

Acquisition Rate

• Acquisition defined as first purchase or purchasing in the first predefined

period

• Acquisition rate (%) = 100*Number of prospects acquired / Number of

prospects targeted

• Denotes average probability of acquiring a customer from a population

• Always calculated for a group of customers

• Typically computed on a campaign-by-campaign basis

Information source

Numerator: From internal records

Denominator: Prospect database and/or market research data

Evaluation

Important metric, but cannot be considered in isolation

Acquisition Cost

• Measured in monetary terms

• Acquisition cost ($) = Acquisition spending ($) / Number of prospects

acquired

• Precise values for companies targeting prospects through direct mail

• Less precise for broadcasted communication

Information source:

• Numerator: from internal records• Denominator: from internal records

Evaluation:

• Difficult to monitor on a customer by customer basis

Average Inter-purchase Time (AIT)

• Average Inter-purchase Time of a customer

= 1 / Number of purchase incidences from the first purchase till the current time period

• Measured in time periods

• Information from sales records

• Important for industries where customers buy on a frequent basis

Information source

Sales records

Evaluation:

Easy to calculate, useful for industries where customers make frequent

purchases

Firm intervention might be warranted anytime customers fall considerably

below their AIT

Retention and Defection

• Retention rate (%) = 100* Number of customers in cohort buying in (t)| buying

in (t-1) / Number of customers in cohort buying in (t-1)

• Avg. retention rate (%) = [1 – (1/Avg. lifetime duration)]

• Avg. Defection rate (%) = 1 – Avg. Retention rate

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Customer tenure (periods)

# o

f cu

sto

mer

s d

efec

tin

g

Plotting entire series of customers that defect each period, shows variation (or heterogeneity) around the average lifetime duration of 4 years.

Customer Lifetime Duration when the Information is Incomplete

Buyer 1

Buyer 2

Buyer 3

Buyer 4

Observation windowBuyer 1: complete information

Buyer 2 : left-censored

Buyer 3: right-censored

Buyer 4: left-and-right-censored

Life Table with only right censoring

Buyer 1

Buyer 2

Buyer 3

Buyer 4

Buyer 1: Withdrew late (still active when last observed)

Buyer 2 : Withdrew early (still active when last observed)

Buyer 3: Terminated late (did not survive past observed date)

Buyer 4: Terminated early (did not survive past observed date)

t

20 40 60

Months with service

2%

4%

6%

8%

10%

Per

cen

t

No Yes

20 40 60

Months with service

Case Processing Summary

726 100.0% 0 .0% 726 100.0%

274 100.0% 0 .0% 274 100.0%

churnNo

Yes

tenureN Percent N Percent N Percent

Valid Missing Total

Cases

Descriptives

40.47 .763

38.97

41.97

40.74

41.50

422.925

20.565

1

72

71

36

-.124 .091

-1.170 .181

22.43 1.062

20.34

24.52

21.39

17.00

309.316

17.587

1

69

68

25

.792 .147

-.392 .293

Mean

Lower Bound

Upper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

Mean

Lower Bound

Upper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

churnNo

Yes

tenureStatistic Std. Error

Life Tablea

1000 25 987.500 53 .05 .95 .95 .01 .009 .001 .01 .00

922 45 899.500 47 .05 .95 .90 .01 .008 .001 .01 .00

830 55 802.500 38 .05 .95 .85 .01 .007 .001 .01 .00

737 62 706.000 26 .04 .96 .82 .01 .005 .001 .01 .00

649 56 621.000 30 .05 .95 .78 .01 .007 .001 .01 .00

563 64 531.000 17 .03 .97 .76 .01 .004 .001 .01 .00

482 56 454.000 13 .03 .97 .74 .02 .004 .001 .00 .00

413 55 385.500 17 .04 .96 .70 .02 .005 .001 .01 .00

341 73 304.500 12 .04 .96 .68 .02 .005 .001 .01 .00

256 60 226.000 11 .05 .95 .64 .02 .005 .002 .01 .00

Interval Start Time0

6

12

18

24

30

36

42

48

54

NumberEnteringInterval

NumberWithdrawing

during Interval

NumberExposedto Risk

Number ofTerminalEvents

ProportionTerminating

ProportionSurviving

CumulativeProportion

Surviving atEnd of Interval

Std. Error ofCumulativeProportion

Surviving atEnd of Interval

ProbabilityDensity

Std. Error ofProbability

Density Hazard RateStd. Error ofHazard Rate

The median survival time is 60.00a.

Basic Survival Math

S(t) = probability that customer will “survive” until at least time t = 1-F(t) where F(t) is the traditional “cumulative distribution”

f(t) = probability that survival ends at t = -S’(t)=F’(t)

t

f(t)

S(t)

1.0

0

---------- = Conditional Survival = probability that customer lasts until at least t0+t given that they lasted until t0

S(t0+t)

S(t0)

Hazard Rate and Related Stuff

h(t)= -------- = Hazard Rate= prob that survival ends at t given that customer makes it to t

f(t)

S(t)

H(t)=cumulative hazard rate = -ln[S(t)]S(t)=exp[-H(t)]

Constant Hazard Rate Model

h(t)=h0, a constant in time H(t)=h0 t S(t)=exp(-h0 t) f(t)=h0exp(-h0 t)

E[t]= 1/h0

E[t0+t | customer made it to t0] = t0 +1/h0

tS(t)=exp(-h0t)

h(t)

1

h0

Life Tablea

1000 25 987.500 53 .05 .95 .95 .01 .009 .001 .01 .00

922 45 899.500 47 .05 .95 .90 .01 .008 .001 .01 .00

830 55 802.500 38 .05 .95 .85 .01 .007 .001 .01 .00

737 62 706.000 26 .04 .96 .82 .01 .005 .001 .01 .00

649 56 621.000 30 .05 .95 .78 .01 .007 .001 .01 .00

563 64 531.000 17 .03 .97 .76 .01 .004 .001 .01 .00

482 56 454.000 13 .03 .97 .74 .02 .004 .001 .00 .00

413 55 385.500 17 .04 .96 .70 .02 .005 .001 .01 .00

341 73 304.500 12 .04 .96 .68 .02 .005 .001 .01 .00

256 60 226.000 11 .05 .95 .64 .02 .005 .002 .01 .00

Interval Start Time0

6

12

18

24

30

36

42

48

54

NumberEnteringInterval

NumberWithdrawing

during Interval

NumberExposedto Risk

Number ofTerminalEvents

ProportionTerminating

ProportionSurviving

CumulativeProportion

Surviving atEnd of Interval

Std. Error ofCumulativeProportion

Surviving atEnd of Interval

ProbabilityDensity

Std. Error ofProbability

Density Hazard RateStd. Error ofHazard Rate

The median survival time is 60.00a.

Proportional Hazard Rate Model

What if the event varies with customer/situational factors X?

h(t) = hB(t) exp(X),

where hB(t) is the baseline hazard rate.*

*Why not have hB(t) bX? Hazard rates must be positive!

The baseline hazard rate hB(t) is metaphorically like an “intercept”because when X=0, then exp(X)=1.0 h(t) = hB(t).

If X > 0, then exp(X)>1.0, so hazard rates increase above baseline.If X < 0, then exp(X)<1.0, so hazard rates decrease below baseline.

The coefficients b are chosen in a regression-like fashion, accounting for customer factors and censored data. In SPSS this is done in Survival/Cox Regression.

Cox Regression Survival Analysis

Case Processing Summary

274 27.4%

726 72.6%

1000 100.0%

0 .0%

0 .0%

0 .0%

0 .0%

1000 100.0%

Eventa

Censored

Total

Cases availablein analysis

Cases with missingvalues

Cases with negative time

Censored cases beforethe earliest event in astratum

Total

Cases dropped

Total

N Percent

Dependent Variable: tenurea.

Variables in the Equation

-.065 .006 124.361 1 .000 .937ageB SE Wald df Sig. Exp(B)

Survival Table

.112 .992 .002 .008

.146 .990 .003 .010

.321 .979 .004 .022

.454 .970 .005 .031

.627 .959 .006 .042

.703 .954 .006 .047

.807 .947 .007 .054

.887 .942 .007 .060

1.010 .934 .008 .068

1.137 .926 .008 .077

1.269 .918 .009 .085

1.343 .913 .009 .091

1.435 .908 .009 .097

Time1

2

3

4

5

6

7

8

9

10

11

12

13

BaselineCum Hazard Survival SE Cum Hazard

At mean of covariates

Covariate Means and Pattern Values

41.684 .000ageMean 1

Pattern

h(t|Age) = hB(t) exp(X) = 0.108 exp(-0.065 Age)

Proportional Hazards Assuming Constant Baseline Hazard

E[t0+t | customer of Age made it to t0] = t0 + exp(-X)/h0

= t0 + exp(0.065 Age)/0.108

E[ t | Age made it to t0] =exp(-X)/h0

=exp(0.065 Age)/0.108

Summary

• In the absence of individual customer data, companies used to rely on

traditional marketing metrics like market share and sales growth

• Acquisition measurement metrics measure the customer level success of marketing efforts to acquire new customers

• Customer activity metrics track customer activities after the acquisition stage

• Lifetime duration is a very important metric in the calculation of the customer

lifetime value and is different in contractual and non-contractual situations