Measuring Player Retention and Monetization using the Mean Cumulative Function

TL;DR

This paper introduces the use of the Mean Cumulative Function (MCF) to accurately measure player retention and monetization in free-to-play games, even with censored data, enabling timely and unbiased analytics.

Contribution

It presents a novel application of the MCF to generalize and improve metrics for censored game data, facilitating better decision-making in game development.

Findings

MCF provides unbiased estimates of player metrics with censored data

Application to real game data demonstrates practical utility

Enables early assessment of game changes and release readiness

Abstract

Game analytics supports game development by providing direct quantitative feedback about player experience. Player retention and monetization in particular have become central business statistics in free-to-play game development. Many metrics have been used for this purpose. However, game developers often want to perform analytics in a timely manner before all users have churned from the game. This causes data censoring which makes many metrics biased. In this work, we introduce how the Mean Cumulative Function (MCF) can be used to generalize many academic metrics to censored data. The MCF allows us to estimate the expected value of a metric over time, which for example may be the number of game sessions, number of purchases, total playtime and lifetime value. Furthermore, the popular retention rate metric is the derivative of this estimate applied to the expected number of distinct days played. Statistical tools based on the MCF allow game developers to determine whether a given change improves a game, or whether a game is yet good enough for public release. The advantages of this approach are demonstrated on a real in-development free-to-play mobile game, the Hipster Sheep.