Estimate the lifetime value of players in a free-to-play mobile game

Gemlight Games makes “Zombie Unicorn Slayer”, a free-to-play game for Apple devices that earns its revenue from in-app purchases. The marketing team wants an estimate of the lifetime value (LTV) of an average user: the revenue a user will generate over their whole life playing the game.

You have the users who installed the game during the observation period, the days they played, and what they spent.

The data

• users — one row per user, keyed by udid (the player identifier): install_date, country, and hw_ver, the Apple device model.
• sessions — one row per user per day played: level_reached and sessions_played, the number of sessions the user logged that day.
• purchases — in-app purchases: daily_iap_rev is the revenue in dollars and purchases_made the number of purchases. Each row sums a user’s purchases for one day.

Your task

1. Build a model of the LTV of an average user, using as much of the data as you find relevant and meaningful. Describe your approach and how the model is laid out: its components, what each is estimated from, and how they combine.
2. What LTV do these users reach within the observation period, and what do you project it to be if they keep playing beyond it? State the horizon you project to and how you extrapolate, and give a range rather than a single number.
3. What are the key assumptions behind your estimate, and what are their weaknesses? Show which assumptions the answer is most sensitive to, including how much a few heavy spenders drive it.
4. Would you estimate the model for different groups of users rather than for all users together? Say which groups you would model separately (for example by country, device, install cohort or early play behaviour) and why, and how you balance more detail against noisier estimates.
5. The marketing team wants to use LTV to set how much it bids to acquire users in each country and on each device. How would you turn your model into that guidance, how accurate does it need to be for that use, and what could go wrong if the estimate is off?
6. How might the LTV of new users change as the game spends more time in the market? Say whether this data shows any sign of it, and what additional data you would want to improve your estimates and how you would use it.

What to deliver

A short report for the Head of Marketing that gives your LTV estimate, explains the model in plain terms and states its limits. Include an appendix with the model’s details and the queries or code behind each number.

All company names in this question are fictional.