Cumulative Gains and Lift Charts


Example Problem 1

A company wants to do a mail marketing campaign. It costs the company $1 for each item mailed. They have information on 100,000 customers. Create a cumulative gains and a lift chart from the following data.
Cost ($) Total Customers Contacted Positive Responses
100000
100000
20000
Cost ($) Total Customers Contacted Positive Responses
10000
10000
6000
20000
20000
10000
30000
30000
13000
40000
40000
15800
50000
50000
17000
60000
60000
18000
70000
70000
18800
80000
80000
19400
90000
90000
19800
100000
100000
20000

Cumulative Gains Chart:


Lift Chart:


Analyzing the Charts: Cumulative gains and lift charts are a graphical representation of the advantage of using a predictive model to choose which customers to contact. The lift chart shows how much more likely we are to receive respondents than if we contact a random sample of customers. For example, by contacting only 10% of customers based on the predictive model we will reach 3 times as many respondents as if we use no model.
 

Evaluating a Predictive Model

We can assess the value of a predictive model by using the model to score a set of customers and then contacting them in this order. The actual response rates are recorded for each cutoff point, such as the first 10% contacted, the first 20% contacted, etc. We create cumulative gains and lift charts using the actual response rates to see how much the predictive model would have helped in this situation. The information can be used to determine whether we should use this model or one similar to it in the future.
 

Example Problem 2

Using the response model P(x)=100-AGE(x) for customer x and the data table shown below, construct the cumulative gains and lift charts. Ties in ranking should be arbitrarily broken by assigning a higher rank to who appears first in the table.
 
Customer Name
Height
Age
Actual Response
Alan
70
39
N
Bob
72
21
Y
Jessica
65
25
Y
Elizabeth
62
30
Y
Hilary
67
19
Y
Fred
69
48
N
Alex
65
12
Y
Margot
63
51
N
Sean
71
65
Y
Chris
73
42
N
Philip
75
20
Y
Catherine
70
23
N
Amy
69
13
N
Erin
68
35
Y
Trent
72
55
N
Preston
68
25
N
John
64
76
N
Nancy
64
24
Y
Kim
72
31
N
Laura
62
29
Y

1.  Calculate P(x) for each person x

2.  Order the people according to rank P(x)

Customer Name P(x) Actual Response
Alex 88 Y
Amy 87 N
Hilary 81 Y
Philip 80 Y
Bob 79 Y
Catherine 77 N
Nancy 76 Y
Jessica 75 Y
Preston 75 N
Laura 71 Y
Elizabeth 70 Y
Kim 69 N
Erin 65 Y
Alan 61 N
Chris 58 N
Fred 52 N
Margot 49 N
Trent 45 N
Sean 35 Y
John 24 N
3.  Calculate the percentage of total responses for each cutoff point
Total Customers Contacted
Number of Responses
Response Rate
2
1
10%
4
3
30%
6
4
40%
8
6
60%
10
7
70%
12
8
80%
14
9
90%
16
9
90%
18
9
90%
20
10
100%
4.  Create the cumulative gains chart:
5.  Create the lift chart: