MARK 7397
Spring 2007
Customer Relationship Management:
A Database Approach
Class 2
James D. Hess
C.T. Bauer Professor of Marketing Science
375H Melcher Hall
jhess@uh.edu
713 743-4175
Marketing Metrics
Marketing Metrics
Traditional
Market Share
Sales Growth
Primary
Customer-based
Customer
Acquisition
Popular
Customer-based
Customer
Activity
Strategic
Customer-based
Traditional and Customer Based
Marketing 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 Strategic Customer Based
metrics
Share of Category
Requirement
Size of Wallet
Share of Wallet
Expected Share of Wallet
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
# of customers defecting
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19
Customer tenure (periods)
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 window
Buyer 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
t
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)
Descriptives
tenure
churn
No
Case Processing Summary
Cas es
Mis sing
N
Percent
0
.0%
0
.0%
Total
N
726
274
Percent
100.0%
100.0%
Yes
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
Mean
95% Confidence
Interval for Mean
Lower Bound
Upper Bound
Lower Bound
Upper Bound
5% Trimmed Mean
Median
Variance
Std. Deviation
Minimum
Maximum
Range
Interquartile Range
Skewness
Kurtos is
No
Yes
8%
6%
4%
2%
20
40
Months w ith service
60
20
40
Months w ith service
Statis tic
40.47
38.97
60
Std. Error
.763
41.97
40.74
41.50
422.925
20.565
1
72
71
36
-.124
-1.170
22.43
20.34
.091
.181
1.062
24.52
21.39
17.00
309.316
17.587
1
69
68
25
.792
-.392
10%
Percent
tenure
churn
No
Yes
Valid
N
Percent
726
100.0%
274
100.0%
Mean
95% Confidence
Interval for Mean
.147
.293
Life Tablea
Interval Start Time
0
6
12
18
24
30
36
42
48
54
Number
Entering
Interval
1000
922
830
737
649
563
482
413
341
256
Number
Withdrawing
during Interval
25
45
55
62
56
64
56
55
73
60
a. The median survival time is 60.00
Number
Expos ed
to Ris k
987.500
899.500
802.500
706.000
621.000
531.000
454.000
385.500
304.500
226.000
Number of
Terminal
Events
53
47
38
26
30
17
13
17
12
11
Proportion
Terminating
.05
.05
.05
.04
.05
.03
.03
.04
.04
.05
Proportion
Surviving
.95
.95
.95
.96
.95
.97
.97
.96
.96
.95
Cumulative
Proportion
Surviving at
End of Interval
.95
.90
.85
.82
.78
.76
.74
.70
.68
.64
Std. Error of
Cumulative
Proportion
Surviving at
End of Interval
.01
.01
.01
.01
.01
.01
.02
.02
.02
.02
Probability
Dens ity
.009
.008
.007
.005
.007
.004
.004
.005
.005
.005
Std. Error of
Probability
Dens ity
.001
.001
.001
.001
.001
.001
.001
.001
.001
.002
Hazard Rate
.01
.01
.01
.01
.01
.01
.00
.01
.01
.01
Std. Error of
Hazard Rate
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
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)
1.0
S(t)
f(t)
t
0
S(t0+t)
---------= Conditional Survival = probability that customer lasts until
S(t0)
at least t +t given that they lasted until t
0
0
Hazard Rate and Related Stuff
f(t)
h(t)= -------- = Hazard Rate= prob that survival ends at t given
S(t)
that customer makes it to 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
1
h0
h(t)
S(t)=exp(-h0t)
t
Life Tablea
Interval Start Time
0
6
12
18
24
30
36
42
48
54
Number
Entering
Interval
1000
922
830
737
649
563
482
413
341
256
Number
Withdrawing
during Interval
25
45
55
62
56
64
56
55
73
60
a. The median survival time is 60.00
Number
Expos ed
to Ris k
987.500
899.500
802.500
706.000
621.000
531.000
454.000
385.500
304.500
226.000
Number of
Terminal
Events
53
47
38
26
30
17
13
17
12
11
Proportion
Terminating
.05
.05
.05
.04
.05
.03
.03
.04
.04
.05
Proportion
Surviving
.95
.95
.95
.96
.95
.97
.97
.96
.96
.95
Cumulative
Proportion
Surviving at
End of Interval
.95
.90
.85
.82
.78
.76
.74
.70
.68
.64
Std. Error of
Cumulative
Proportion
Surviving at
End of Interval
.01
.01
.01
.01
.01
.01
.02
.02
.02
.02
Probability
Dens ity
.009
.008
.007
.005
.007
.004
.004
.005
.005
.005
Std. Error of
Probability
Dens ity
.001
.001
.001
.001
.001
.001
.001
.001
.001
.002
Hazard Rate
.01
.01
.01
.01
.01
.01
.00
.01
.01
.01
Std. Error of
Hazard Rate
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
Proportional Hazard Rate Model
What if the event varies with customer/situational factors X?
h(t) = hB(t)  exp(bX),
where hB(t) is the baseline hazard rate.*
The baseline hazard rate hB(t) is metaphorically like an “intercept”
because when X=0, then exp(bX)=1.0  h(t) = hB(t).
If bX > 0, then exp(bX)>1.0, so hazard rates increase above baseline.
If bX < 0, then exp(bX)<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.
*Why not have hB(t)  bX? Hazard rates must be positive!
Cox Regression Survival Analysis
Case Processing Summary
N
Cas es available
in analysis
Cas es dropped
Eventa
Cens ored
Total
Cas es with miss ing
values
Cas es with negative time
Cens ored cas es before
the earlies t event in a
s tratum
Total
Total
274
726
1000
Percent
27.4%
72.6%
100.0%
0
.0%
0
.0%
0
.0%
0
.0%
1000
100.0%
a. Dependent Variable: tenure
Variables in the Equation
age
B
-.065
SE
.006
Wald
124.361
df
1
Sig.
.000
Exp(B)
.937
Survival Table
Time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Bas eline
Cum Hazard
.112
.146
.321
.454
.627
.703
.807
.887
1.010
1.137
1.269
1.343
1.435
1.499
1.612
At mean of covariates
Survival
SE
Cum Hazard
.992
.002
.008
.990
.003
.010
.979
.004
.022
.970
.005
.031
.959
.006
.042
.954
.006
.047
.947
.007
.054
.942
.007
.060
.934
.008
.068
.926
.008
.077
.918
.009
.085
.913
.009
.091
.908
.009
.097
.904
.009
.101
.897
.010
.109
Covariate Means and Pattern Values
age
Mean
41.684
Pattern
1
.000
Proportional Hazards Assuming
Constant Baseline Hazard
h(t|Age) = hB(t)  exp(bX) = 0.108  exp(-0.065 Age)
E[t0+t | customer of Age made it to t0] = t0 + exp(-bX)/h0
= t0 + exp(0.065 Age)/0.108
E[ t | Age made it to t0] =exp(-bX)/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