# Predicting Player Churn of a Free-to-Play Mobile Video Game Using Supervised Machine Learning
## 3 Problem Description
### Definition of Churn Parameters  
The time constraints are defined as different time periods used in the process of tracking player behavior. Under the term player behavior, we consider the following features of player behavior, similarly to [25; 29]: (1) frequency features (i.e., how often events occur), (2) monetary features (i.e., lifetime value of the player), (3) lifetime and intensity features (i.e., what percentage of overall time is spent in the game at which point in a player's lifetime), and (4) game-specific features (e.g., chapters completed). As shown in Figure 1, player behavior tracking starts as soon as the player installs the game (the _firstInstallTime_ attribute). The feature extraction period lasts one, two, three, or seven days and is followed by the churn period, in which player churn is monitored and lasts between one and seven days. If the system notes any player activity in the churn period, the player is considered a non-churner. On the other hand, if no player activity is noted in the churn period, then the player is assumed to be a churner. The ground truth period serves as a cut-off time for monitoring player churn and lasts fourteen days after the feature extraction period has ended. This period serves as a validation period to check whether players which would be labeled as churners depending on the defined churn period will or will not return to the game.  
The aforementioned churn period is the period in which the users' activity is monitored and a prediction is made as to whether the player will quit the game or continue playing. Another way of looking at this is by tying a churn label to every player (the players' user profiles, to be exact), which serves the same purpose. If the user first installed the game on a certain date, and on the very next day, the system has not logged any activity from the same user, then the user is estimated to have churned and the churn label would be positive. Alternatively, if any activity is detected on the next day following installment, the churn label would be set to negative--the player has not churned. The churn label is, by definition, an estimate, and it is useful to calculate how accurate that estimate is with respect to the ground truth definition of a certain player's churn.  
To showcase how these periods are related and how accurate churn prediction is based on only one day, we plot values extracted from our dataset during a random time frame (Figure 2). The graph presents the period from 27 April 2020 to 24 May 2020. The graph portrays how many new users first installed the game on a certain date (numOfUsers), how many of those users were estimated to churn by not showing the next day (_churnEstimates_), and how many of the estimated churners were \"real\" churners (_churnReals_, according to the ground truth period definition of 14 days). Calculating the average accuracy of the churn estimates over the given period yields an estimate accuracy of 83.65% using just the one-day estimation.  
If we were to observe the user for one more day (i.e., two days after having installed the game), the accuracy of the estimation will rise to 90.09%. The graph shown in Figure 3 shows how the estimation accuracy rises with an increase in observation duration. If the user has not shown up in the game (i.e., no activity detected) for seven days, there is a 98% chance that they will not show up in the 14-day ground truth validation period.  
Figure 1: Time constraint definitions.