# Introduction - Analysing Customer Churn

March 2019 · 4 minute read

At first glance, analysing customer churn seems pretty easy. All we have to know is how many customers we have at a certain point in time and how many customers chose to leave our business over a given period in order to calculate a churn rate.

We could simply define customer churn rate as:

$\text{Churn Rate } = \frac{\text{# Customers Churned in Period}}{\text{# Customers Beginning of Period}}$ But this definition assumes that we lose customers linearly over a given period and that our customer base does not change except for the customers we lose, i.e. we are not acquiring any new customers.

We could change the denominator from number of ‘# Customers Beginning of Period’ to ‘Average # of Customers over Period’ defined by (# BoP + # EoP)/2, but then we would implicitly assume that we acquire customers at a constant rate. Moreover, we need to be careful if we want to calculate churn for periods with different lengths, say for February and March where period lengths can differ by around 10%.

Ideally, we need a metric to calcualte churn that takes the number of opportunities into account that a customer has in order to churn. So we could use something like this:

$\text{Churn Rate } = \frac{\text{# Customers Churned in Period}}{\text{# Customer Active Days in Period}} \times \text{Period Length}$

‘# Customer Active Days in Period’ is defined as the number of days in a given period during which a customer is considered active. Imagine we have two customers and one of them churns at the end of a 7 day period. We get a churn rate of about:

n_churned = 1
n_active_days = 7 + 6
period_length = 7

churn_rate = n_churned/n_active_days * period_length
churn_rate
##  0.5384615

While we would get a churn rate of 1 if the customer churned immediately at the beginning of the period. This definition also allows us to calculate churn rates for different period lengths quite easily.

We could go one step further still and consider a churn rate where we not only calculate a weighted number of active customers over a given period but also a weighted churn number. Clearly, if a customer churns at the end of a period it is better than if he churns at the beginning? We could define a churn rate like so: $\text{Churn Rate } = \frac{\text{# Customer Inactive Days in Period}}{\text{# Customer Active Days in Period}}$ However, imagine the following scenario: You have two customers and one of them churns at the second day of our 7 day period. Your churn rate would be:

n_inactive_days = 6
n_active_days = 7 + 1
period_length = 7

churn_rate = n_inactive_days/n_active_days
churn_rate
##  0.75

How would you calculate churn rates for the next 7 day period? You still have two customers, one of them has 0 active days the other 7. You get 7 inactive days, so your churn rate would be 100%. Or should your churn rate be 0%, because the customer is actually lost and should not count towards inactive days? So we could introduce a new customers status called ‘lost’ and a ‘lost’ customer does not count towards inactive days anymore. Which raises the question, when should we consider a customer lost?

Wait a minute, we still have not considered how we define if a customer is considered ‘churned’!