Churn Prediction in
Mobile Social Games:
Towards a Complete
Assessment Using Survival
Ensembles
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África Periáñez, Alain Saas, Anna Guitart, Colin Magne
IEEE/ACM DSAA 2016
Montreal, October 19th, 2016

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Churn prediction in Free-To-Play games
We focus on the top spenders: the whales
➔ 0.2% of the players, 50 % of the revenues
➔ Their high engagement make them more likely to answer positively to
action taken to retain them
➔ For this group, we can define churn as 10 days of inactivity
◆ The definition of churn in F2P games is not straightforward

Features selection
◎ Game independent features:
○ player attention: time spent per day, lifetime
○ player loyalty : number of days connecting, loyalty index (number of days
played over lifetime), days from registration to first purchase, days since
last purchase
○ player intensity: number of actions, sessions, amount in-app purchases,
action activity distance (total average actions compared to last days
behaviour)
○ player level: concept common to most games)
◎ Game dependent features researched but ultimately not part of our model:
○ participation in a guild (social feature)
○ actions measured by categories
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The model
Survival Ensembles
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Challenge: modeling churn
◎ Survival analysis focuses on predicting the
time-to-event, e.g. churn
○ when a player will stop playing?
◎ Classical methods, like regressions, are appropriate
when all players have left the game
◎ Censoring Problem: dataset with incomplete churning
information
◎ Censoring is the nature of churn
➔ Survival analysis is used in biology and medicine to
deal with this problem
➔ Ensemble learning techniques provide high-class
prediction results
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◎ We focus on whales
◎ Cumulative survival probability (Kaplan-Meier estimates)
◎ Step function that changes every time that a player churns
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Output of the model

◎ Two approaches:
○ Churn as a binary classification
○ Churn as a censored data problem
◎ One model: Conditional Inference Survival Ensembles1
○ deals with censoring
○ high accuracy due to ensemble learning
Survival Analysis
➔ Survival analysis methods (e.g. Cox regression) does not follow any
particular statistical distribution: fitted from data
➔ Fixed link between output and features: efforts to model selection and
evaluation
1) Hothorn et al., 2006. Unbiased recursive partitioning: A conditional inference framework 7
Challenge: modeling churn

Survival Tree
➔ Split the feature space
recursively
➔ Based on survival statistical
criterion the root node is
divided in two daughter nodes
➔ Maximize the survival
difference between nodes
➔ A single tree produces
instability predictions
Conditional Survival Ensembles
➔ Outstanding predictions
➔ Make use of hundreds of trees
➔ Conditional inference survival
ensemble use a Kaplan-Meier
function as splitting criterion
➔ Overfit is not present
➔ Robust information about
variable importance
➔ Not biased approach
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Conditional inference survival ensembles

Conditional inference survival tree partition with
Kaplan-Meier estimates of the survival time which
characterizes the players placed in every terminal node group
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Linear rank
statistics as
splitting criterion
Survival tree

◎ Two steps algorithm:
○ 1) the optimal split variable is selected: association between
covariates and response
○ 2) the optimal split point is determined by comparing two sample
linear statistics for all possible partitions of the split variable
Random Survival Forest
➔ RSF is based on original random forest algorithm1
➔ RSF favors variables with many possible split points over variables
with fewer
101) Breiman L. 2001. Random Forests.
Conditional inference survival ensembles

The Results
With “Age of Ishtaria” Game Data
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Binary classification results and comparison with other
models

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Predicted Kaplan-Meier survival curves as a function
of time (days) for new or existing players
Censored data problem results

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Validation - Churn prediction

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Validation - Churn prediction

◎ Censoring problem is the right approach
○ the median survival time, i.e. time when the percentage of
surviving in the game is 50%, can be used as a time threshold
to categorize a player in the risk of churning
◎ Binary problem -- static model
○ also bring relevant information
○ useful insight for a short-term prediction
◎ SVM, ANN, Decision Trees, etc. are useful tools for regression or
classification problems.
○ in their original form cannot handle with censored data
○ 1) modification of algorithm or 2) transformation of the data
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Survival ensembles approach

◎ Application of state-of-the-art algorithm “conditional inference
survival ensembles”
○ to predict churn
○ and survival probability of players in social games
◎ Model able to make predictions every day in operational
environment
◎ adapts to other game data: Democratize Game Data Science
◎ relevant information about whales behaviour
○ discovering new playing patterns as a function of time
○ classifying gamers by risk factors of survival experience
◎ Step towards the challenging goal of the comprehensive
understanding of players
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Summary and conclusion

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Other work of the authors related to Game Data Science
Discovering Playing Patterns:
Time Series Clustering of Free-To-Play Game Data
Alain Saas, Anna Guitart and África Periáñez
IEEE CIG 2016
Special Session on Game Data Science
Chaired by Alain Saas and África Periáñez
IEEE/ACM DSAA 2016
www.gamedatascience.org