Social network predicts churn in mobile telecommunications
When you change a mobile service plan or phone number, the first thing you’ll probably do is let your friends know, just in case they encounter problems reaching you at your new number or new service plan. So it’s natural to think that this “churn” behavior would propagate through the social network.
This study studies whether this “churn” spreads through a call graph network, and how you could use such a call graph to predict people who will churn in subsequent months. Some basics first. Study data is a small subset from a large mobile carrier during Mar 2007; the final size after some pruning and cleaning was 2.1 million users and 9.3 million calls. Many of these users are prepaid card users for whom the carrier has no demographic information. The authors then studied how probability of churning in April, May, June and July is related to each user’s local neighborhood of friends.
Result 1 – probability of churning is closely related to how many of your neighbors have churned. The diagram below shows that your likelihood to churn rises steadily with the number of churner neighbors until a plateau.
Result 2 – probability of churn is related to the number of neighbors who have churned AND are also connected.
The authors then proceed to study how certain variables, including social network metrics, might accurately predict people who churn. They used a standard decision tree classifier. This is a standard supervised machine learning or data mining problem. There were 3 types of input data
 Usage information (called DT1) – call frequency, number of calls, number of friends, call volume, duration of calls etc
 Connectivity (called DT2) – These are usage statistics but broken down by churner or nonchurner neighbors. So 2 examples are “number of churner neighbors” and “number of nonchurner neighbors who have churners as neighbors” The second example is closely related to the concept of eigenvector centrality of the churner network.
 Interconnectivity (called DT3) – These are network or graph type metrics which can only be calculated using graph methods. ”Number of adjacent pairs in the set of churner neighbors”, “Number of pairs in the churner friends connected by path length of 2″, number of pairs of churner friends whose shortest paths only include churner neighbors, “Total call volume on edges connecting adjacent churner friends”.
Results – Much more accurate churn prediction using social network metrics D3 and D2, compared to D1 alone. See graph below.
Recall that a lift curve shows how many of the actual churners were predicted by the decision tree classifer as you walk through all the subscribers in the dataset. When you walk through all 100% of the subscribers, you will catch 100% of the churners. But that is not very good, you need many marketing promotions or calls to use that. On the other hand, if you can identify 50% of the churners after walking through 10% of the subscribers, that’s pretty good.
The graph shows that using usage data (DT1), after walking through 10% of the base, they could predict about 10% of the churners. Not good.
Using DT2, after walking through 10% of the base, they could predict about 18% of the churners. A good improvement, but still not good.
Using DT3, after after walking through 10% of the base, they could predict about 40% of the churners. This is very good.
Backoftheenvelop business case calculation on why this matters
DT1 
DT3 

Total subscriber count 
2,000,000 
2,000,000 
Churn rate 
0.06 
0.06 
# churners 
120,000 
120,000 
% of churners identified in 10% of subscribers 
0.1 
0.4 
# churners identified 
12,000 
48,000 
Conversion rate of discount offer 
0.1 
0.1 
# churners converted/saved 
1,200 
4,800 
# churners lost 
118,800 
115,200 
Discount offer Rate 
0.05 
0.05 
Revenue from saved churners calculated as (1discount offer)*number of saved churners 
1,140 
4,560 
Number of non churners in 10% of subscribers 
188,000 
152,000 
Number of non churner who took the discount 
18,800 
15,200 
Lost revenue from discount to nonchurners 
940 
760 
Return on investment on churn marketing campaign  200  3,800 