How Netflix measures the value of subscriber acquisition and retention using causal inference and Markov chain
Deep dive into how Netflix uses causal inference and Markov Chain models to evaluate the value of acquisition and retention
Quick summary
Hello 👋 In this article, I will explain how Netflix measure values of acquiring or retenting a subscriber on the following areas:
Business scenario
Customer lifetime value
Markov Chain model
Incrementality calculation
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Business scenario
To measure the long-term value of acquiring or retaining a subscriber in Netflix. This is important for subscription-based streaming platform like Netflix, because often one would like to know monetary benefits of certain marketing campaigns or product developments to increase acquisition of new subscribers or retention of existing subscribers.
Methodology
Need for causal model
As subscription is a self-selected behaviour, meaning that we could not control if a user subscribes or not (and hence it is not possible to conduct a AB test), one will need to rely on causal techniques to solve this problem.
Customer lifetime value (CLV)
The naive usage of CLV in this case is likely an over-estimation because a off-service subscriber could resubscribe in the future, hence the CLV from these customers are actually non-zero and have to be considered when calculating the value of acquisition or retention.
The method
Netflix data scientists come up with a nice method which combines Markov chain and causal inference to solve the problem (For an quick introduction to Markov chain, you can visit the wikipedia page here).
A Markov chain can be specified by the set of states and transition probabilities.
State definition — each subscriber (on or off-service) is represented by a state s. This state represents the number of consecutive billing cycles that the subscriber is in or not in. Each subscriber is in one of the state:
where a positive index i means that the subscriber has subscribed to the service with i consecutively billing cycle, while negative index -i means instead the subscribers has not subscribed to the service with i consecutively billing cycle. N and M are assumed to be very large.
Transition probabilities — transition probabilities between states
can also be determined by calculating empirical means or fitting a model using the historical data.
Value of a subscriber — the value function (often used in the Markov chain problem or reinforcement learning) describes the cumulative expected rewards from a state s. In this case, given a state s, the value function can be written as:
where r is the discounted factor (often used in MC or RL), I is a indicator function equal to 1 if the household is subscribed to the service at kth cycle given the current state s, and c is the price of the service. The value function can be obtained by running numerical simulations or solving the Bellman’s equation.
Calculating incremental values — After calculating the value functions or for all the states, we can then calculate the incremental value in various acquisition and retention scenarios. The value of acquiring a new subscriber is
Similarly, the value of acquiring a subscriber who has stopped the service for k months is
Summary
This post summarises the essential concepts used by Netflix data scientists on the business problem of estimating the value of customer acquisition and retention. For those who are interested more detail, you can access the paper here.
