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:

Cumulative Gains


Lift 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 xand 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:

cumulative gains

5. Create the lift chart:

lift chart 2