Chapter 6:
Customer Analytics Part II
Overview
Topics discussed:

Strategic customer-based value metrics

Popular customer selection strategies

Techniques to evaluate alternative customer selection strategies
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2
Customer-based Value Metrics
Customer
based
Value
Metrics
Popular
Size
Of
Wallet
Share of
Category
Reqt.
Share of
Wallet
Strategic
Transition
Matrix
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RFM
Past
Customer
Value
LTV
Metrics
Customer
Equity
3
Strategic Customer-based Value Metrics

RFM Value

Past Customer Value

Lifetime Value Metrics

Customer Equity
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4
RFM Method
Recency
Frequency
Monetary
value
• Elapsed time since a
customer last placed an
order with the company
• Number of times a
customer orders from
the company in a
certain defined period
RFM Value
• Amount that a customer
spends on an average
transaction

Technique to evaluate customer behavior and customer value

Often used in practice

Tracks customer behavior over time in a state-space
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5
RFM Method

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%)
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6
RFM Method

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.
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7
RFM Method: Response and Recency
5.00%
Customer Response %
4.50%
4.00%
2.80%
3.00%
2.00%
1.50%
1.05%
1.00%
0.25%
0.00%
1
2
3
4
5
Recency Code (1 - 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)
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RFM Method: Response and Frequency
3.00%
2.45%
2.22%
2.50%
2.08%
Response Rate %
2.00%
1.67%
1.68%
4
5
1.50%
1.00%
0.50%
0.00%
1
2
3
Frequency Code 1-5

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)
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9
RFM Method: Response and Monetary Value
2.50%
2.35%
2.05%
1.95%
1.90%
1.85%
3
4
5
2.00%
Response Rate %
1.50%
1.00%
0.50%
0.00%
1
2
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)
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RFM Method: RFM procedure
Last purchase:
1 day ago
 R=1
Group 1
 R=1
average
response rate
 R=1
 R=2
Group 2
Step 1
Step 2
 R=2
Step 3
average
response rate
 R=2
...
...
...
Group 3
 R=5
 R=5
Last purchase:
320 days ago
V. Kumar and W. Reinartz – Customer Relationship Management
average
response rate
 R=5
11
RFM Method: Limitations

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
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12
RFM Method: Cell Sorting Technique

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)
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RFM Method: RFM Cell Sorting
F
R
11
12
M
131
132
133
1
13
14
2
15
135
3
41
42
441
4
43
44
5
45
134
442
443
444
445
Customer
Database
Sorted Once
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Sorted Five
Times per R
Quintile
Sorted Twenty-Five
Times per R Quintile
14
RFM Method: Breakeven Value (BE)

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%
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RFM Method: Breakeven Index

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
 the transactions just broke even

Negative BEI value
 the transactions resulted in a loss
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RFM Method: Combining RFM codes, breakeven
codes, breakeven index
Cell #
RFM codes
Cost per mail $
Net profit per saleBreakeven (%)
($)
Actual response Breakeven index
(%)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
111
112
113
114
115
121
122
123
124
125
131
132
133
134
135
141
142
143
144
145
151
152
153
154
155
211
212
213
214
215
221
222
223
224
225
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
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
17.55
17.45
17.35
17.25
17.15
17.05
16.95
16.85
16.75
16.65
16.55
16.45
16.35
16.25
16.15
16.05
15.95
15.85
15.75
15.65
15.55
15.45
15.35
15.25
15.15
15.65
15.55
15.45
15.35
15.25
15.15
15.05
14.95
14.85
14.75
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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
690
685
681
676
672
667
663
658
654
649
645
640
636
631
627
622
618
613
609
604
600
595
591
586
582
604
600
595
591
586
582
577
573
568
564
17
RFM codes versus BEI
1400
1200
1000
BEI
800
Break-Even Index
600
400
200
552
531
455
434
413
342
321
245
224
153
132
111
0
RFM Cell Codes
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RFM and BEI

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
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Comparison of profits for targeting campaign test
Test
Full customer base
RFM Selection
Average response rate
2.02%
2.02%
15.25%
# of responses
808
8,080
2,732.8
Average Net profit/Sale
$45
$45
$45
Net Revenue
$36,360
$363,600
$122,976
# of Mailers sent
40,000
400,000
17,920
Cost per mailer
$1.00
$1.00
$1.00
Mailing cost
$40,000.00
$400,000.00
$17,920.00
Profits
(-$3,640.00)
($36,400.00)
$105,056.00
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Relative Importance of R, F, and M

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
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Recency Score

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
Recency
Assigned
Weighted
Number
(Month)
Points
Points
1
2
20
100
2
4
10
50
3
9
3
15
1
6
5
25
1
2
20
100
2
4
10
50
3
6
5
25
4
9
3
15
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Frequency Score

Points for Frequency: 3 points for each purchase within 12 months; Maximum = 15 points;
Relative weight = 2
Customer
John
Smith
Mags
Purchase
Number
Frequency
Assigned
Points
Weighted
Points
1
1
3
6
2
1
3
6
3
1
3
6
1
2
6
12
1
1
3
6
2
1
3
6
3
2
6
12
4
1
3
6
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Monetary Value Score

Monetary Value: 10 percent of the $-value of purchase with 12 months; Maximum = 25
points; Relative weight = 3
Customer
John
Smith
Mags
Purchase
Number
Value of
purchase ($)
Assigned
Points
Weighted
Points
1
$40
4
12
2
$120
12
36
3
$60
6
18
1
$400
25
75
1
$90
9
27
2
$70
7
21
3
$80
8
24
4
$40
4
12
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
Cumulative scores: 249 for John, 112 for Smith and 308 for Mags, indicates a potential
preference for Mags

John seems to be a good prospect, but mailing to Smith might be a misdirected marketing
effort
Customer
Purchase
Number
Total Weighted
Points
Cumulative
Points
John
1
2
3
118
92
39
118
210
249
Smith
1
112
112
1
2
3
4
133
77
61
37
133
210
271
308
Mags
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Past Customer Value

Computation of Customer Profitability (PCV)
T

PCV of customer i   GCi t0 t n * (1   ) t

Where:
t 0
i = number representing the customer,
t = time index,
d
= applicable discount rate (for example 1.25% per month),
t0 = current time period,
T = number of time periods prior to current period that should be considered,
GCin = gross contribution of transaction of customer in period t

Since products / services are bought at different points in time during the customer’s lifetime,
all transactions have to be adjusted for the time value of money

Limitations

Equation does not consider whether a customer is going to be active in the future and it
does not incorporate the expected cost of maintaining the customer in the future
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Spending Pattern of a Customer
Jan
Purchase Amount ($)
GC
Feb
March
April
May
800
50
50
30
20
240
15
15
9
6
Gross contribution (GC) = purchase amount X contribution margin

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
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Lifetime Value Metrics

Multi-period evaluation of a customer’s value to the firm

Lifetime Value (LTV)
Recurring
Revenues
Recurring
costs
Contribution
margin
Lifetime of a
customer
customer
Lifetime Profit
LTV
Discount
rate
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Acquisition
cost
28
Basic LTV Model
t

æ 1 ö
LTVi = åGCit ç
÷
è
ø
1+
d
t=1

Where:
T
i = customer,
t = time period,
 = interest (or discount) rate,
GCit = gross contribution of customer i at time t,
T = observation time horizon,
LTVi = lifetime value of an individual customer i at net present value time t=0
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Basic LTV Model

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
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Caution:
If the time unit is different from a yearly
basis, the interest rate  needs to be
adjusted accordingly.
30
LTV with Splitted Revenues and Costs
t
 LTV = å( S - DC ) - MC ) × æç 1 ö÷
i
it
it
it
è 1+ d ø
t=1
T

Where:
i = customer,
t = time period,
 = interest (or discount) rate,
T = observation time horizon,
Sit = sales value to customer i at time t,
DCit = direct costs of products by customer i at time t,
MCit = marketing costs directed at customer i at time t,
LTVi = lifetime value of an individual customer i at net present value time
t=0
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LTV with Splitted Revenues and Costs

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
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LTV Including Customer Retention Probabilities
æ K
ö
æ 1 ö

LTVi = ((åç Õ Rrk ÷ GCit ç
÷ )) - ACi
è
ø
1+
d
ø
t=1 è k=1
t
T

Where:
i = customer,
t = time period,
 = interest (or discount) rate,
T = observation time horizon,
Rrt = average retention rate at time t (it is possible to use an individual
level retention probability
Rrit but usually this is difficult to obtain),
GCit = gross contribution of customer i at time t,
ACi = costs of acquiring customer i (acquisition costs)
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33
LTV Including Customer Retention Probabilities
t

In this equation the term Õ Rrk is actually the survival rate SRt
k=1

The retention rate is constant over time and thus the expression can be simplified using the
identity:
t
Õ Rr
k
= (Rr )t
k=1
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34
LTV with Constant Retention Rate and Gross Contribution

Assuming that T   and that the retention rate and the contribution margin (CM) do not
vary over time:
æ Rr ö
LTVi = GCi ç
÷ - ACi
è 1- Rr + d ø
Rr
1- Rr + d

The margin multiplier:

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
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LTV with Constant Retention Rate and Gross Contribution

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)
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36
Measuring and Incorporating Word-of-Mouth (WOM)

æ K
ö
æ 1 ö
LTVi = ((åç Õ Rrk ÷ (GCit + nit ACSt ) ç
÷ )) - ACi
è
1+ d ø
ø
t=1 è k=1

Where:
t
T
i = customer,
t = time period,
 = interest (or discount) rate,
T = observation time horizon,
Rrt = average retention rate at time t,
GCit = gross contribution of customer i at time t,
nit = number of new acquisition at time t due to referrals customer i,
ACSt = average acquisition cost savings per customer gained through
referral of customer i at time t,
ACi = costs of acquiring customer i (acquisition costs)
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Customer Value Matrix
Average CRV after 1 year
Average LTV
after 1 year
Low
High
High
Affluents
Champions
Low
Misers
Advocates
This table is adapted from Kumar, Petersen , and
Leone (2007)
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38
LTV

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
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39
Customer Equity

Customer equity (CE) = Sum of the LTV of all the customers of a firm
I
CE = å LTVi
i=1

Where:
i = customer,
I = all customers of a firm (or specified customer cohort or segment),
LTVi = 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
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40
Customer Equity

Customer Equity Share (CES): CES = CE /
j
j
K
åCE
k
K=1

Where:
CEj = 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
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41
Customer Equity Calculation Example
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
0
120
0.3
36
20
0.4
0.4
400
16
16
6,400
1
120
0.3
36
20
0.63
0.25
250
16
14
3,500
2
120
0.3
36
20
0.75
0.187
187
16
12
2,244
3
120
0.3
36
20
0.82
0.153
153
16
11
1,683
4
120
0.3
36
20
0.85
0.131
131
16
9
1,179
Total
customer
equity
V. Kumar and W. Reinartz – Customer Relationship Management
15,006
42
Popular Customer Selection Strategies

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
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43
Profiling

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
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Profiling: Using Profiling for New Customer Acquisition
Response
Variable
Internal
Variables
External
Variables
Transactions, demographics, lifestyle
Demographics, lifestyle
Individual A
Current
Customers
Individual B
Individual C
A
B
C
Individual 1
Individual 2
Potential
Customers
Individual 3
F
E
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Binary Classification Trees

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
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Binary Classification Trees

The algorithm procedure
1. To find out which of the explanatory variables Xi best explains the outcome Y,
calculate the number of misclassifications
2. Use the variable Xi 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
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Binary Classification Trees: Classification of Potential Hockey
Equipment Buyers
Male
Female
Total
Bought
hockey
Did not
buy
hockey
Bought
hockey
Did not
buy
hockey
Bought
hockey
Did not
buy
hockey
Bought
scuba
60
1,140
50
1,550
110
2,690
Did not
buy
scuba
1,540
2,860
80
1,320
1,620
4,180
Total
1,600
4,000
130
2,870
1,730
6,870
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Binary Classification Trees: Classification of Potential Hockey
Equipment Buyers

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
110 bought hockey equipment
2,690 did not buy hockey equipment
1,620 bought hockey equipment
Did not buy: 5,800
4,180 did not buy hockey equipment
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Binary Classification Trees: Classification of Potential Hockey
Equipment Buyers

Classification of hockey buyers by gender
Step 2
Buyer
Yes
No
1730
6870
Total
8600
Gender
Female
Buyer
Male
Buyer
Yes
1,600
Yes
130
No
4,000
No
2,870
Total
5,600
Total
3,000
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Binary Classification Trees: Classification of Potential Hockey
Equipment Buyers

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
Marital status
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
Not married
Buyer
Yes
30
No 870
Total 2,100
Total 900
51
Logistic Regression

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
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Logistic Regression: Examples

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
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Logistic Regression: Examples

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
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Linear and Logistic Regression

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
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Logistic Regression: Formula

y = a + b x+ e

Where:
y= dependent variable,
x= predictor variable,
a = constant (which is estimated by linear regression and often called
intercerpt),
b = the effect of x on y (also estimated by linear regression),
e = error term
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Logistic Regression: Transformation Steps

p
Step 1: If p represents the probability of an event occurring, take the ratio 1  p
Since p is a positive quantity less than 1, the range of this expression is 0 to infinity

 p 
Step 2: Take the logarithm of this ratio: log  1  p 


This transformation allows the range of values for this expression to lie between
negative infinity and positive infinity
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Logistic Regression: Transformation Steps

æ p ö
z=
log
ç
÷ can be considered as the dependent variable and a linear
Step 3: The value
è 1- p ø
relationship of this value with predictor variables in the form z = a + b x+ e can be written.
 and b coefficients can be estimated

Step 4: In order to obtain the predicted probability p, a back transformation is to be done:
æ
ö
Since log  p  = z = a + b x+ e  ez = ç p ÷
1 p 
è 1- p ø



Then calculate the probability p of an event occurring, the variable of interest, as
æ ez ö æ 1 ö
p=ç
=
z÷ ç
-z ÷
è 1- e ø è 1+ e ø
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Logistic Regression: Interpretation of Coefficients

Interpret the coefficients carefully

If the logit regression coefficient β = 2.303
eb = e2.303 =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
1
4
0
6
0
2
1
4
1
8
0
3
0
0
0
2
0
5
0
0
1
2
1
8
1
4
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Logistic Regression: Interpretation of Coefficients
Odds of Logistic Regression Example

It expects that sales calls impact the probability of contract extension. Thus, it estimates the
model:
 Prob (contract extension)
1



   ( sales calls) 
1 e

 The resulting estimates are: α= -1.37; β= 0.39

Odds of logistic regression example
Sales calls = 0
Sales calls = 1
Odds (exp(α+β *sales
calls))
0.253
0.375
Probability of contract
extension
0.202
0.273
Difference in probabilities
0.071
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Logistic Regression: Evaluation

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
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Techniques to Evaluate Alternative Customer Selection
Strategies

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
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62
Misclassification Rate

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
Predicted
1
0
Observed
Totals
Totals
1
726
56
782
0
173
504
677
899
560
1,459
 The number of mispredictions is the sum of the off-diagonal entries (56+173=229)
 Misclassification Rate: 229/ 1,459 = 15,7%
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LIFT Analysis

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
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Lift Performance Illustration

Lift and Cumulative Lift
Number of
decile
Number of
customers
Number of
buyers
Response
rate %
Lift
Cumulative
lift
1
5,000
1,759
35.18
3.09
3.09
2
5,000
1,126
22.52
1.98
5.07
3
5,000
998
19.96
1.75
6.82
4
5,000
554
11.08
0.97
7.80
5
5,000
449
8.98
0.79
8.59
6
5,000
337
6.74
0.59
9.18
7
5,000
221
4.42
0.39
9.57
8
5,000
113
2.26
0.20
9.76
9
5,000
89
1.78
0.16
9.92
10
5,000
45
0.90
0.08
10.00
Total
50,000
5,691
11.38
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65
Lift Performance Illustration

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
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Lift Performance Illustration
Lift Analysis
3.50
3.09
3.00
2.50
Lift
1.98
2.00
1.75
1.50
0.97
1.00
0.79
0.59
0.39
0.50
0.20
0.16
0.08
8
9
10
0.00
1
2
3
4
5
6
7
Deciles

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
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Lift Performance Illustration
Cumulative Lift Analysis
10
9
Cumulative Lift
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Decile

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
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Lift Performance Illustration
Comparison of Models
10
9
Cumulative Lift
8
7
Logistic
6
Past Customer Value
5
RFM
4
No Model
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Deciles

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
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Minicase: Akzo Nobel, NV- Differentiating Customer Service
According to Customer Value

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
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Summary

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
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