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We consider user retention analytics for online freemium role-playing games (RPGs). RPGs constitute a very popular genre of computer-based games that, along with a player’s gaming actions, focus on the development of the player’s in-game virtual character through a persistent exploration of the gaming environment. Most RPGs follow the freemium business model in which the gamers can play for free but they are charged for premium add-on amenities. As with other freemium products, RPGs suffer from the curse of high dropout rates. This makes retention analysis extremely important for successful operation and survival of their gaming portals. Here, we develop a disciplined statistical framework for retention analysis by modelling multiple in-game player characteristics along with the dropout probabilities. We capture players’ motivations through engagement times, collaboration and achievement score at each level of the game, and jointly model them using a generalized linear mixed model (glmm) framework that further includes a time-to-event variable corresponding to churn. We capture the interdependencies in a player’s level-wise engagement, collaboration, achievement with dropout through a shared parameter model. We illustrate interesting changes in player behaviours as the gaming level progresses. The parameters in our joint model were estimated by a Hamiltonian Monte Carlo algorithm which incorporated a divide-and-recombine approach for increased scalability in glmm estimation that was needed to accommodate our large longitudinal gaming data-set. By incorporating the level-wise changes in a player’s motivations and using them for dropout rate prediction, our method greatly improves on state-of-the-art retention models. Based on data from a popular action based RPG, we demonstrate the competitive optimality of our proposed joint modelling approach by exhibiting its improved predictive performance over competitors. In particular, we outperform aggregate statistics based methods that ignore level-wise progressions as well as progression tracking non-joint model such as the Cox proportional hazards model. We also display improved predictions of popular marketing retention statistics and discuss how they can be used in managerial decision making.

 

Abstract Blocked randomized designs are used to improve the precision of treatment effect estimates compared to a completely randomized design. A block is a set of units that are relatively homogeneous and consequently would tend to produce relatively similar outcomes if the treatment had no effect. The problem of finding the optimal blocking of the units into equal sized blocks of any given size larger than two is known to be a difficult problem—there is no polynomial time method guaranteed to find the optimal blocking. All available methods to solve the problem are heuristic methods. We propose methods that run in polynomial time and guarantee a blocking that is provably close to the optimal blocking. In all our simulation studies, the proposed methods perform better, create better homogeneous blocks, compared with the existing methods. Our blocking method aims to minimize the maximum of all pairwise differences of units in the same block. We show that bounding this maximum difference ensures that the error in the average treatment effect estimate is similarly bounded for all treatment assignments. In contrast, if the blocking bounds the average or sum of these differences, the error in the average treatment effect estimate can still be large in several treatment assignments.