Topics discussed:

Strategic customer-based value metrics
 Popular customer selection strategies
 Techniques to evaluate alternative customer selection strategies
V. Kumar and W. Reinartz – Customer Relationship Management 2

Customer based
Value
Metrics
Popular Strategic
Size
Of
Wallet
Share of
Category
Reqt.
Share of
Wallet
Transition
Matrix
RFM
Past
Customer
Value
LTV
Metrics
Customer
Equity
V. Kumar and W. Reinartz – Customer Relationship Management 3

 RFM Value
 Past Customer Value

Lifetime Value Metrics
 Customer Equity
V. Kumar and W. Reinartz – Customer Relationship Management 4

Recency
• Elapsed time since a customer last placed an order with the company
Frequency
• Number of times a customer orders from the company in a certain defined period
Monetary value
• Amount that a customer spends on an average transaction
RFM Value

Technique to evaluate customer behavior and customer value
 Often used in practice
 Tracks customer behavior over time in a state-space
V. Kumar and W. Reinartz – Customer Relationship Management 5

 Example
 Customer base: 400,000 customers
 Sample size: 40,000 customers
 Firm ’s marketing mailer campaign: $150 discount coupon

Response rate: 808 customers (2.02%)
V. Kumar and W. Reinartz – Customer Relationship Management 6

 Recency coding
 Test group of 40,000 customers is sorted in descending order based on the criterion of
‘most recent purchase date’
 The earliest purchasers are listed on the top and the oldest are listed at the bottom

The sorted data is divided into five equally sized groups (20% in each group)
 The top-most group is assigned a recency code of 1, the next group a code of 2 until the bottom-most group is assigned a code of 5
 Analysis of customer response data shows that the mailer campaign got the highest response from those customers grouped in recency code 1 followed by those in code 2 etc.
V. Kumar and W. Reinartz – Customer Relationship Management 7

5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
4.50%
2.80%
1.50%
1.05%
0.25%
1 2 3
Recency Code (1 - 5)
4 5
 Graph depicts the distribution of relative frequencies of customer groups assigned to recency codes 1 to 5

Highest response rate (4.5%) for the campaign was from customers in the test group who belonged to the highest recency quintile (recency code =1)
V. Kumar and W. Reinartz – Customer Relationship Management 8

3.00%
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
2.45%
2.22%
2.08%
1.67% 1.68%
1 2 3
Frequency Code 1-5
4 5
 Graph depicts the response rate of each of the frequency-based sorted quintiles

The highest response rate (2.45%) for the campaign was from customers in the test group belonging to the highest frequency quintile (frequency code =1)
V. Kumar and W. Reinartz – Customer Relationship Management 9

2.50%
2.00%
1.50%
1.00%
0.50%
2.35%
2.05%
1.95%
1.90%
1.85%
0.00%
1 2 3 4 5
Monetary Value Code (1-5)

Customer data is sorted, grouped and coded with a value from 1-5
 The highest response rate (2.35%) for the campaign was from those customers in the test group who belonged to the highest monetary value quintile (monetary value code =1)
V. Kumar and W. Reinartz – Customer Relationship Management 10

Last purchase:
1 day ago
Step 1 Step 2
Group 1
Group 2
Step 3
Group 3
 R=1
 R=1
 R=1
 R=2
 R=2
 R=2 average response rate average response rate
 R=5
 R=5
 R=5 average response rate
Last purchase:
320 days ago
V. Kumar and W. Reinartz – Customer Relationship Management 11

 RFM method 1 independently links customer response data with R, F and M values and then groups customers belonging to specific RFM codes
 May not produce equal number of customers under each RFM cell since individual metrics
R, F, and M are likely to be somewhat correlated
 For example, a person spending above average (high M) is also likely to spend more frequently (high F)

For practical purposes, it is desirable to have exactly the same number of individuals in each RFM cell
V. Kumar and W. Reinartz – Customer Relationship Management 12

 A list of 40,000 test group of customers is first sorted for recency and then grouped into 5 groups of 8,000 customers each
 The 8,000 customers in each group are sorted based on frequency and divided into five equal groups of 1,600 customers each - at the end of this stage, there will be RF codes starting from 11 to 55 with each group including 1,600 customers

In the last stage, each of the RF groups is further sorted based on monetary value and divided into five equal groups of 320 customers each
 RFM codes starting from 111 to 555 each including 320 customers
 Considering each RFM code as a cell, there will be 125 cells (5 recency divisions * 5 frequency divisions * 5 monetary value divisions = 125 RFM Codes)
V. Kumar and W. Reinartz – Customer Relationship Management 13

F
R
M
Customer
Database
Sorted Once Sorted Five
Times per R
Quintile
441
442
443
444
445
Sorted Twenty-Five
Times per R Quintile
V. Kumar and W. Reinartz – Customer Relationship Management 14

 Breakeven = net profit from a marketing promotion equals the cost associated with conducting the promotion
 Breakeven Value (BE) = unit cost price / unit net profit
 BE computes the minimum response rates required in order to offset the promotional costs involved and thereby not incur any losses

Example
 Mailing $150 discount coupons
 The cost per mailing piece is $1.00
 The net profit (after all costs) per used coupon is $45,

Breakeven Value (BE) = $1.00/$45 = 0.0222 or 2.22%
V. Kumar and W. Reinartz – Customer Relationship Management 15

 Breakeven Index (BEI) = ((Actual response rate – BE) / BE)*100
 Example
 If the actual response rate of a particular RFM cell was 3.5%
 BE is 2.22%,

The BEI = ((3.5% - 2.22%)/2.22%) * 100 = 57.66

Positive BEI value
 some profit was made from the group of customers
 0 BEI value
 Negative BEI value
 the transactions just broke even
 the transactions resulted in a loss
V. Kumar and W. Reinartz – Customer Relationship Management 16

Cell # RFM codes
213
214
215
221
222
223
224
225
144
145
151
152
153
154
155
211
212
134
135
141
142
143
124
125
131
132
133
111
112
113
114
115
121
122
123
28
29
30
31
32
33
34
35
23
24
25
26
27
19
20
21
22
14
15
16
17
18
9
10
11
12
13
7
8
5
6
3
4
1
2
V. Kumar and W. Reinartz – Customer Relationship Management
Cost per mail $ Net profit per sale Breakeven (%) Actual response
($) (%)
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
2.22
15.45
15.35
15.25
15.15
15.05
14.95
14.85
14.75
15.75
15.65
15.55
15.45
15.35
15.25
15.15
15.65
15.55
16.75
16.65
16.55
16.45
16.35
16.25
16.15
16.05
15.95
15.85
17.55
17.45
17.35
17.25
17.15
17.05
16.95
16.85
Breakeven index
595
591
586
582
577
573
568
564
609
604
600
595
591
586
582
604
600
631
627
622
618
613
654
649
645
640
636
690
685
681
676
672
667
663
658
17

1400
1200
1000
800
600
400
200
0
RFM Cell Codes
V. Kumar and W. Reinartz – Customer Relationship Management
Break-Even Index
18

 Customers with higher RFM values tend to have higher BEI values

Customers with a lower recency value but relatively highF and M values tend to have positive BEI values
 Customer response rate drops more rapidly for the recency metric
 Customer response rate for the frequency metric drops more rapidly than the one for the monetary value metric
V. Kumar and W. Reinartz – Customer Relationship Management 19

Average response rate
# of responses
Average Net profit/Sale
Net Revenue
# of Mailers sent
Cost per mailer
Mailing cost
Profits
Test
2.02%
808
$45
$36,360
40,000
$1.00
$40,000.00
(-$3,640.00)
Full customer base RFM Selection
2.02% 15.25%
8,080 2,732.8
$45
$363,600
400,000
$45
$122,976
17,920
$1.00
$400,000.00
($36,400.00)
$1.00
$17,920.00
$105,056.00
V. Kumar and W. Reinartz – Customer Relationship Management 20

 Regression techniques to compute the relative weights of the R, F, and M metrics

Relative weights are used to compute the cumulative points of each customer

The pre-computed weights for R, F and M, based on a test sample are used to assign RFM scores to each customer
 The higher the computed score, the more likely the customer will be profitable in future
 This method is flexible and can be tailored to each business situation
V. Kumar and W. Reinartz – Customer Relationship Management 21

 20 if within past 2 months, 10 if within past 4 months, 05 if within past 6 months, 03 if within past 9 months, 01 if within past 12 months, relative weight = 5
Customer
John
Smith
Mags
Purchase
Number
1
2
3
1
1
2
3
4
V. Kumar and W. Reinartz – Customer Relationship Management
Recency
(Month)
2
4
9
6
2
4
6
9
Assigned
Points
20
10
3
5
20
10
5
3
Weighted
Points
100
50
15
25
100
50
25
15
22

 Points for Frequency: 3 points for each purchase within 12 months; Maximum = 15 points;
Relative weight = 2
Customer
John
Smith
Mags
Purchase
Number
1
2
3
1
1
2
3
4
Frequency
V. Kumar and W. Reinartz – Customer Relationship Management
1
1
1
2
1
1
2
1
Assigned
Points
3
3
3
6
3
3
6
3
Weighted
Points
6
6
6
12
6
6
12
6
23

 Monetary Value: 10 percent of the $-value of purchase with 12 months; Maximum = 25 points; Relative weight = 3
Customer
John
Smith
Mags
Purchase
Number
1
2
3
1
3
4
1
2
Value of purchase ($)
$40
$120
$60
$400
$90
$70
$80
$40
Assigned
Points
4
12
6
25
8
4
9
7
V. Kumar and W. Reinartz – Customer Relationship Management
Weighted
Points
12
36
18
75
27
21
24
12
24

 Cumulative scores: 249 for John, 112 for Smith and 308 for Mags, indicates a potential preference for Mags
 John seems to be a good prospect, but mailing to Smith might be a misdirected marketing effort
Customer
John
Purchase
Number
1
2
3
Total Weighted
Points
118
92
39
Cumulative
Points
118
210
249
Smith
Mags
1
1
2
3
4
112
133
77
61
37
112
133
210
271
308
V. Kumar and W. Reinartz – Customer Relationship Management 25

 Computation of Customer Profitability (PCV)


PCV of customer i
Where:

T
GC i
 t
0
 t
 n
* ( 1
 
) t t

0 i = number representing the customer, t = time index, d
= applicable discount rate (for example 1.25% per month), t
0
= current time period,
T = number of time periods prior to current period that should be considered,
GC in
= gross contribution of transaction of customer in period t
 Since products / services are bought at different points in time during the customer ’s lifetime, all transactions have to be adjusted for the time value of money

Limitations
 Equation does not consider whether a customer is going to be active in the future and it does not incorporate the expected cost of maintaining the customer in the future
V. Kumar and W. Reinartz – Customer Relationship Management 26

Jan Feb March April
Purchase Amount ($) 800 50 50 30
GC 240 15 15
Gross contribution (GC) = purchase amount X contribution margin
9
May
20
6
 PCVi = 6*(1+0.0125) o +9*(1+0.0125) 1 +15*(1+0.0125) 2 +15*(1+0.0125) 3 + 240*(1+0.0125) 4
= 302.01486

The customer is worth $302.01 expressed in net present value in May dollars

Comparing the PCV of a set of customers leads to a prioritization of directing future marketing efforts
V. Kumar and W. Reinartz – Customer Relationship Management 27

 Multi-period evaluation of a customer ’s value to the firm

Lifetime Value (LTV)
Recurring
Revenues
Contribution margin
Recurring costs
Lifetime Profit
Acquisition cost
V. Kumar and W. Reinartz – Customer Relationship Management
LTV
28


LTV i
=
T å t
=
1
GC it
ç
æ
è
1
1
+ d
÷
ö
ø t
 Where: i = customer, t = time period,

= interest (or discount) rate,
GC it
= gross contribution of customer i at time t,
T = observation time horizon,
LTV i
= lifetime value of an individual customer i at net present value time t=0
V. Kumar and W. Reinartz – Customer Relationship Management 29


LTV is a measure of a single customer’s worth to the firm
 Used for pedagogical and conceptual purposes
 Information source

CM and T from managerial judgment or from actual purchase data.
 The interest rate, a function of a firm’s cost of capital, can be obtained from financial accounting
 Evaluation
 Typically based on past customer behavior and may have limited diagnostic value for future decision-making Caution :
If the time unit is different from a yearly basis, the interest rate
 needs to be adjusted accordingly.
V. Kumar and W. Reinartz – Customer Relationship Management 30


LTV i
=
T
t
=
1
(
S it
-
DC it
)
-
MC it
) × ç
æ
è
1
1
+ d
÷
ö
ø t
 Where: i = customer, t = time period,

= interest (or discount) rate,
T = observation time horizon,
S it
= sales value to customer i at time t,
DC it
= direct costs of products by customer i at time t,
MC it
= marketing costs directed at customer i at time t,
LTV i
= lifetime value of an individual customer i at net present value time t=0
V. Kumar and W. Reinartz – Customer Relationship Management 31


The cost element of this example is broken down into direct product-related costs and marketing costs
 Depending on data availability, it can be enhanced by including service-related cost, delivery cost, or other relevant cost elements
V. Kumar and W. Reinartz – Customer Relationship Management 32


LTV i
=
((
T
t
=
1
æ
è
K
k
=
1
Rr k
ö
ø
GC it
1
è
1
+ d
ö t
ø
))
-
AC i

Where: i = customer, t = time period,

= interest (or discount) rate,
T = observation time horizon,
Rr t
= average retention rate at time t (it is possible to use an individual
Rr it
GC it
= gross contribution of customer i at time t,
AC i
= costs of acquiring customer i (acquisition costs)
V. Kumar and W. Reinartz – Customer Relationship Management 33

 k t Õ
=
1
Rr k
SR t
 The retention rate is constant over time and thus the expression can be simplified using the identity: t
k
=
1
Rr k
=
( Rr ) t
V. Kumar and W. Reinartz – Customer Relationship Management 34

 Assuming that T   and that the retention rate and the contribution margin (CM) do not vary over time:
LTV i
=
GC i
Rr
è
1
-
Rr
+ d
ö
ø
AC i

The margin multiplier:
Rr
1
-
Rr
+ d
 How long is the Lifetime Duration?
 For all practical purposes, the lifetime duration is a longer-term duration used managerially

It is important to make an educated judgment regarding a sensible duration horizon in the context of making decisions
V. Kumar and W. Reinartz – Customer Relationship Management 35


Incorporating externalities in the LTV
 The value a customer provides to a firm does not only consist of the revenue stream that results from purchases of goods and services
 Product rating websites, weblogs and the passing on of personal opinions about a product or brand co-contribute substantially to the lifetime value of a customer

These activities are subsumed under the term word-of mouth (WOM)
V. Kumar and W. Reinartz – Customer Relationship Management 36


LTV i
=
((
T
t
=
1
è
K
k
=
1
Rr k
ö
( GC
ø it
+ n it
ACS t
1
)
è
1
+ d
ö t
ø
))
-
AC i

Where: i = customer, t = time period,

= interest (or discount) rate,
T = observation time horizon,
Rr t
= average retention rate at time t,
GC it
= gross contribution of customer i at time t, n it
= number of new acquisition at time t due to referrals customer i,
ACS t
= average acquisition cost savings per customer gained through referral of customer i at time t,
AC i
= costs of acquiring customer i (acquisition costs)
V. Kumar and W. Reinartz – Customer Relationship Management 37

Average CRV after 1 year
Average LTV after 1 year
High
Low
This table is adapted from Kumar, Petersen , and
Leone (2007)
Low
Affluents
Misers
High
Champions
Advocates
V. Kumar and W. Reinartz – Customer Relationship Management 38

 Alternative ways to account for externalities
 The value of a customer’s referrals can be separated from the LTV , for example by calculating a separate customer referral value (CRV) for each customer
 A joined evaluation of both metrics helps the management to select and determine how to develop its customers
 Information source

Information on sales, direct cost, and marketing cost come from internal company records

Many firms install activity-based-costing (ABC) schemes to arrive at appropriate allocations of customer and process-specific costs
 Evaluation
 LTV (or CLV) is a forward looking metric that is appropriate for long-term decision making

It is a flexible measure that has to be adapted to the specific business context of an industry
V. Kumar and W. Reinartz – Customer Relationship Management 39

 Customer equity (CE) = Sum of the LTV of all the customers of a firm
CE
=
I
LTV i
=
1 i
 Where: i = customer,
I = all customers of a firm (or specified customer cohort or segment),
LTV i
= lifetime value of customer i
 Indicator of how much the firm is worth at a particular point in time as a result of the firm ’s customer management efforts

Can be seen as a link to the shareholder value of a firm
V. Kumar and W. Reinartz – Customer Relationship Management 40


Customer Equity Share (CES): CES j
=
CE j
/
K
K
=
1
CE k

Where: CE j
= customer equity of brand j, j = focal brand,
K = all brands a firm offers
 Information source

Basically the same information as for the LTV is required
 Evaluation
 The CE represents the value of the customer base to a company
 The metric can be seen as an indicator for the shareholder value of a firm
V. Kumar and W. Reinartz – Customer Relationship Management 41

1
Year from
Acquis-ition
2
Sales per
Customer
3.
Manufacturer
Margin
4.
Manufacturer
Gross
Margin
5.
Mktg and
Servicing
Costs
6.
Actual
Retention
Rate
7.
Survival
Rate
8.
Expected
Number of
Active
Customer
9
Profit per
Customer per period per Manufacturer
10.
Discounted
Profit per
Customer per Period to
Manufacturer
11.
Total
Disctd.
Profits per
Period to the
Manufactu
-rer
3
4
0
1
2
Total customer equity
120
120
120
120
120
0.3
0.3
0.3
0.3
0.3
36
36
36
36
36
20
20
20
20
20
0.4
0.63
0.75
0.82
0.85
0.4
0.25
0.187
0.153
0.131
400
250
187
153
131
16
16
16
16
16
16
14
12
11
9
6,400
3,500
2,244
1,683
1,179
15,006
V. Kumar and W. Reinartz – Customer Relationship Management 42

 Techniques

Profiling

Binary Classification Trees
 Logistic regression
 Techniques to Evaluate Customer Selection Strategies

Missclassification Rate

Lift Analysis
 CRM at Work: Tesco
 Example where a company combines analytical skills, judicious judgment, knowledge about consumer behavior and careful targeting of customers
V. Kumar and W. Reinartz – Customer Relationship Management 43


The intuitive approach for customer selection is based on the assumption that the most profitable customers share common characteristics
 Based on this assumption the company should try to target customers with similar profiles to the currently most profitable ones

Disadvantage
 Only customers that are similar to existing ones are considered
 Profitable customer segments that do not match the current customer base might be missed
V. Kumar and W. Reinartz – Customer Relationship Management 44

Response
Variable
Internal
Variables
Transactions, demographics, lifestyle
Individual A
Individual B
Individual C
A
B
Current
Customers
C
External
Variables
Demographics, lifestyle
Individual 1
Individual 2
Individual 3
F
E
Potential
Customers
D
V. Kumar and W. Reinartz – Customer Relationship Management 45

 Used to identify the best predictors of a 0/1 or binary dependent variable

Useful when there is a large set of potential predictors for a model
 Classification tree algorithms can be used to iteratively search the data to find out which predictor best separates the two categories of a binary (or more generally categorical) target variable
V. Kumar and W. Reinartz – Customer Relationship Management 46


The algorithm procedure
1.
To find out which of the explanatory variables X i best explains the outcome Y, calculate the number of misclassifications
2.
Use the variable X i with the lowest misclassification rate to separate the customer base
3.
This process can be repeated for each sub segment until the misclassification rate drops below a tolerable threshold or all of the predictors have been applied to the model
 Evaluation
 Problem with the approach: prone to over-fitting
 The model developed may not perform nearly as well on a new or separate dataset
V. Kumar and W. Reinartz – Customer Relationship Management 47

Male
Bought hockey
Did not buy hockey
Female
Bought hockey
Did not buy hockey
Total
Bought hockey
Did not buy hockey
Bought scuba
Did not buy scuba
Total
60
1,540
1,600
1,140
2,860
4,000
50
80
130
1,550
1,320
2,870
110
1,620
1,730
2,690
4,180
6,870
V. Kumar and W. Reinartz – Customer Relationship Management 48

 Possible separations of potential hockey equipment buyers
Step 1
Separation by gender
1,600 bought hockey equipment
Male: 5,600
4,000 did not buy hockey equipment
130 bought hockey equipment
Female: 3,000
2,870 did not buy hockey equipment
Separation by purchase of scuba equipment
Bought: 2,800
Did not buy: 5,800
110 bought hockey equipment
2,690 did not buy hockey equipment
1,620 bought hockey equipment
4,180 did not buy hockey equipment
V. Kumar and W. Reinartz – Customer Relationship Management 49

 Classification of hockey buyers by gender
Step 2
Buyer
Yes 1730
No 6870
Total 8600
Buyer
Yes
No
Total
Male
1,600
4,000
5,600
Gender
Female
Buyer
Yes
No
Total
130
2,870
3,000
V. Kumar and W. Reinartz – Customer Relationship Management 50


Classification tree for hockey equipment buyers
Step 3
Buyer
Yes
No
1730
6870
Total 8600
Gender
Male
Buyer
Yes 1,600
No 4,000
Total 5,600
Female
Buyer
Yes 130
No 2,870
Total 3,000
Bought scuba equipment
Bought scuba
Buyer
Yes 60
No 1,140
Total 1,200
Not bought scuba
Buyer
Yes 1,540
No 2,860
Total 4,400
V. Kumar and W. Reinartz – Customer Relationship Management
Married
Buyer
Yes 100
No 2,000
Total 2,100
Marital status
Not married
Buyer
Yes 30
No 870
Total 900
51


Method of choice when the dependent variable is binary and assumes only two discrete values
 By inputting values for the predictor variables for each new customer – the logistic model will yield a predicted probability

Customers with high
‘predicted probabilities’ may be chosen to receive an offer since they seem more likely to respond positively
V. Kumar and W. Reinartz – Customer Relationship Management 52

 Example 1: Home ownership
 Home ownership as a function of income can be modeled whereby ownership is delineated by a 1 and non-ownership a 0

The predicted value based on the model is interpreted as the probability that the individual is a homeowner
 With a positive correlation between increasing income and increasing probability of ownership, one can expect results as

Predicted probability of ownership is .22 for a person with an income of $35,000
 Predicted probability of .95 for a person with a $250,000 income
V. Kumar and W. Reinartz – Customer Relationship Management 53


Example 2: Credit Card Offering
 Dependent Variable - whether the customer signed up for a gold card offer
 Predictor Variables - other bank services the customer used plus financial and demographic customer information

By inputting values for the predictor variables for each new customer, the logistic model will yield a predicted probability
 Customers with high
‘predicted probabilities’ may be chosen to receive the offer since they seem more likely to respond positively
V. Kumar and W. Reinartz – Customer Relationship Management 54

 In linear regression, the effect of one unit change in the independent variable on the dependent variable is assumed to be a constant represented by the slope of a straight line
 For logistic regression the effect of a one-unit increase in the predictor variable varies along an s-shaped curve . At the extremes, a one-unit change has very little effect, but in the middle a one unit change has a fairly large effect
V. Kumar and W. Reinartz – Customer Relationship Management 55

 y
= a + b x
+ e

Where: y= dependent variable, x= predictor variable, a
= constant (which is estimated by linear regression and often called intercerpt), e b
= the effect of x on y (also estimated by linear regression),
= error term
V. Kumar and W. Reinartz – Customer Relationship Management 56

 Step 1: If p represents the probability of an event occurring, take the ratio p p
Since p is a positive quantity less than 1, the range of this expression is 0 to infinity

Step 2: Take the logarithm of this ratio: log

 p
1
 p


This transformation allows the range of values for this expression to lie between negative infinity and positive infinity
V. Kumar and W. Reinartz – Customer Relationship Management 57

 Step 3
æ
è
ç
1
p p
÷
ö
ø
 a + b x
+ e
 Step 4 : In order to obtain the predicted probability p, a back transformation is to be done:
Since
1 p
 p


= z = a + b x
+ e  e z
=
æ
è p
1
p
ö
ø
 Then calculate the probability p of an event occurring, the variable of interest, as p
=
æ
ç e z
è
1
e z
ö
ø
1
è
1
+ e
z
ø
V. Kumar and W. Reinartz – Customer Relationship Management 58

 Interpret the coefficients carefully

If the logit regression coefficient
β = 2.303
e b = e
2.303
=
10
 When the independent variable x increases one unit, the odds that the dependent variable equals 1 increase by a factor of 10, keeping all other variables constant.
 Sample of contract extension and sales
Contract extension Number of sales calls
1 2
0
1
1
0
1
4
6
2
4
8
1
1
1
0
0
0
0
0
3
0
2
5
0
2
8
4
V. Kumar and W. Reinartz – Customer Relationship Management 59


It expects that sales calls impact the probability of contract extension. Thus, it estimates the model:
 Prob (contract extension)

1
 e
 
1
 
( sales calls )
 The resulting estimates are : α= -1.37; β= 0.39

Odds of logistic regression example
Sales calls = 0
0.253
Sales calls = 1
0.375
Odds (exp (α+β *sales calls))
Probability of contract extension
Difference in probabilities
0.202
0.071
0.273
V. Kumar and W. Reinartz – Customer Relationship Management 60

 Evaluation

For logistic regression the effect of a one-unit increase in the predicor variable varies along an s-shaped curve
 This means that at the extremes, a one-unit change has a very little effect, but in the center a one-unit change has a fairly large effect
V. Kumar and W. Reinartz – Customer Relationship Management 61

 A critical step to decide which model to use for selecting and targeting potential customers is to evaluate alternative selection strategies
 When several alternative models are available for customer selection, we need to compare their relative predition quality
 Divide the data into a training (calibration) dataset (2/3 of the data) and a holdout (test) sample (1/3 of the data)

The models are estimated based on the training dataset
 Select the model that generalizes best from the training to the data
 Techniques
 Misclassification Rate

Lift Analysis
V. Kumar and W. Reinartz – Customer Relationship Management 62

 Estimate the different models on two thirds of the available data
 Calculate the misclassificaion rate on the remaining third to check for model performance
 Example
Observed
Totals
1
0
Predicted
1 0 Totals
726 56 782
173
899
504
560
677
1,459

The number of mispredictions is the sum of the off-diagonal entries (56+173=229)

Misclassification Rate: 229/ 1,459 = 15,7%
V. Kumar and W. Reinartz – Customer Relationship Management 63

 Lift Charts

Lifts charts show how much better the current model performs against the results expected if no model was used (base model)
 Can be used to track a model ’s performance over time , or to compare a model ’s performance on different samples

Lift% = (Response rate for each decile) / (Overall response rate) *100

Cumulative lift% = (Cumulative response rate) / (Overall response rate) *100
 Cumulative response rate = cumulative number of buyers / Number of customers per decile
V. Kumar and W. Reinartz – Customer Relationship Management 64

 Lift and Cumulative Lift
4
5
6
7
8
2
3
Number of decile
1
9
10
Total
5,000
5,000
5,000
5,000
5,000
Number of customers
5,000
5,000
5,000
5,000
5,000
50,000
554
449
337
221
113
Number of buyers
1,759
1,126
998
89
45
5,691
11.08
8.98
6.74
4.42
2.26
Response rate %
35.18
22.52
19.96
1.78
0.90
11.38
Lift
0.39
0.20
0.16
0.08
3.09
1.98
1.75
0.97
0.79
0.59
V. Kumar and W. Reinartz – Customer Relationship Management
Cumulative lift
3.09
5.07
6.82
7.80
8.59
9.18
9.57
9.76
9.92
10.00
65


The Decile analysis distributes customers into ten equal size groups
 For a model that performs well, customers in the first decile exhibit the highest response rate
V. Kumar and W. Reinartz – Customer Relationship Management 66

Lift Analysis
3.50
3.00
2.50
2.00
1.50
1.00
0.50
0.00
3.09
1
1.98
1.75
0.97
0.79
0.59
0.39
0.20
8
0.16
9
0.08
10 2 3 4 5
Deciles
6 7
 Lifts that exceed 1 indicate better than average performance

Less than 1 indicate a poorer than average performance
 For the top decile the lift is 3.09; indicates that by targeting only these customers are expected to yield 3.09 times the number of buyers found by randomly mailing the same number of customers
V. Kumar and W. Reinartz – Customer Relationship Management 67

Cumulativ e Lift Analysis
10
9
6
5
4
8
7
3
2
1
0
0 1 2 3 4 5
Decile
6 7 8 9 10

The cumulative lifts for the model reveal what proportion of responders we can expect to gain from targeting a specific percentage of customers using the model

Choosing the top 30 % of the customers from the top three deciles will obtain 68% of the total responders
V. Kumar and W. Reinartz – Customer Relationship Management 68

Comparison of Models
7
6
5
4
3
2
1
0
10
9
8
0 1 2 3 4 5
Deciles
6 7 8 9 10
Logistic
Past Customer Value
RFM
No Model
 Logistic models tend to provide the best lift performance
 The past customer value approach provides the next best performance

The traditional RFM approach exhibits the poorest performance
V. Kumar and W. Reinartz – Customer Relationship Management 69

 One of the world's largest chemical manufacturers and paint makers

The polymer division, which serves exclusively the B-to-B market, established a
“tiered customer service policy
” in the early 2000’s
 Company developed a thorough list of all possible service activities that is currently offered
 To formalize customer service activities, the company implemented a customer scorecard mechanism to measure and document contribution margins per individual customer

Service allocation, differentiated as:
 Services are free for all types of customers
 Services are subject to negotiation for lower level customer groups
 Services are subject to fees for lower level customers

Services are not available for the least valuable set of customers
V. Kumar and W. Reinartz – Customer Relationship Management 70

 The higher the computed RFM score , the more profitable the customer is expected to be in the future
 The PCV is another important metric, in which the value of a customer is determined based on the total contribution (toward profits) provided by the customer in the past after adjusting for the time value of money

The LTV reflects the long-term economic value of a customer

The sum of the LTV of all the customers of a firm represents the customer equity (CE)
 Firms employ different customer selection strategies to target the right customers
 Lift analysis, decile analysis and cumulative lift analysis are various techniques firms use to evaluate alternative selection strategies

Logistic Regression is superior to past customer value and RFM techniques
V. Kumar and W. Reinartz – Customer Relationship Management 71