GetFit is a company that runs outdoor health fitness classes with a monthly cycle that begins on the first day of each month. Each customer has choice to renew or cancel their subscription at the beginning of the month. We are predicting retention rate using 2,132 customers’ data. Those selected customers began their subscription in either January, February, March or April this year.
Main Finding
We assumed that all customers have different purchasing behavior. Each customer has different possibility of renewal or cancelling the service at the beginning. Customer purchasing behavior is not affected by each other. Using beta-geometric model and past user data, we find some crucial parameters that can help us to determine retention rate for other customers in the future, or other customers that are not included in this group of customers, if statring time and cancelling time is provided.
\[a=0.829 \\ b=1.565 \\ LL=-3602\] The first two parameters, a and b, are for helping us finding the best retention rate. Those two parameter shapes retention distribution and give us the distribtuion that most likely fit GetFit customer retention pattern. Maxiumum likelihood estimate, using beta-geometric model, is 3602.33; two parameters - a and b, are 0.829 and 1.566 repectively. With a smaller than one, b bigger than one, distribution of “churn” is “L” shaped, meaning most customers churn in the beginning, if they choose to churn. Churn rate will decrease over time.
\[E= \frac {0.829} {0.829 + 1.565}= 0.35\] The mean of the beta distribution is 0.35.
\[var= \frac {0.829* 1.565} {(0.829 + 1.565)^2(0.829 + 1.565 + 1)}=0.07\] The variance of the beta distribution is 0.07.
The retention distribution shown below:
Scenario
Random Selected Current Customer
We used the expected survival equation listed below:
\[\frac{B(a,b+t)}{B(a,b)}\]
a and b are calcualted as 0.829 and 1.565 respectively. To calculate the probability of customer cancel service after one month, the t value would be 1. And to calculate the probability of customer who cancel service after two month, t value of would be 2. And to calcaulte the probility of a customer that still active, t value would be 8. Therefore, a random selected customer has a 34.6% chance to cancel sevice after only one month. \[1-\frac{B(0.829,1.565+1)}{B(0.829,1.565)}=0.346\] A randomly selected customer has a 50.6% chance to cancel his/her service after two months. \[1-\frac{B(0.829,1.565+2)}{B(0.829,1.565)}=0.506\] A randomly selected customer has a 21.5% chance to still remain in service. \[\frac{B(0.829,1.565+9)}{B(0.829,1.565)}=0.215\]
New Customers Acquired in September
Now, given 800 new customers, we are interested in how many people choose to renew our subscription when opportunity presents. Assume those 800 customers adapt similar pattern. The following time presents number of customer at the beginning of each month, starting at September:
|
Month
|
Retention
|
|
Sep
|
800
|
|
Oct
|
523
|
|
Nov
|
395
|
|
Dec
|
321
|
|
Jan
|
271
|
|
Feb
|
236
|
|
Mar
|
210
|
|
Apr
|
189
|
|
May
|
172
|
|
Jun
|
159
|
Rentention Curve
In the beginning, the curve is extremely stiff, which represents that the customers have lower retention rate. However, as time goes by, the curve becomes flatter as the customers who have higher probability to churn have already canceled the membership. As a result, the customers remained have higher probability to retain with GetFit.
|
month
|
retention_rate
|
|
1
|
0.6537304
|
|
2
|
0.7557540
|
|
3
|
0.8113401
|
|
4
|
0.8463159
|
|
5
|
0.8703515
|
|
6
|
0.8878858
|
|
7
|
0.9012422
|
|
8
|
0.9117551
|
|
9
|
0.9202451
|
|
10
|
0.9272448
|
|
11
|
0.9331150
|
|
12
|
0.9381086
|