Consider a typical cohorts scenario where we need to model the number of monthly active users within our cohorts. Typically this involves using a monthly retention rate and applying that to the number of users in each cohort as time progresses. The formula looks something like this:

**New Customers (cohort)**

The items ‘cohort’ and ‘t-cohort’ in the above formula are time modifiers for the referenced variables. Usually, we would use ‘current’ and this would retrieve the New Customers value from the month we are currently in (e.g. in Jan 22 it will return New Customers from Jan 22 and in Apr 22 it will return New Customers from Apr 22 etc.)

In this formula we have changed the time modifier to say ‘cohort’. By doing this we are asking Causal to return the New Customers for Jan 22 in the Jan 22 cohort, New Customers for Feb 22 in the Feb 22 cohort, New Customers for Mar 22 in the Mar 22 cohort etc.

Assuming 100 new customer a month, this is the result of the first half of the formula:

**Retention rate (t-cohort)**

In this formula we have changed the time modifier to say ‘t-cohort’. In simple terms we are asking Causal to use the 1st Retention rate for the first month of each cohort, the 2nd Retention rate for the second month of each cohort etc. In this case we have formatted the Retention rate variable to be ‘relative time’, so the 1st Retention rate is always the value in Jan 22 and the 2nd is always the value in Feb 22.

e.g. the Jan 22 cohort will use the Jan 22 Retention rate in its first month and the Apr 22 cohort will also use the Jan 22 Rentention rate for its first month. By assigning relative time we are essentially ignoring the period the value has been assigned to and the Jan 22 Retention rate should be viewed as the 1st Retention rate and not the Retention rate for the month of Jan 22.

This is the result of the second half of the formula:

**Final Result**

By multiplying the results from the first half of the formula by the results of the second half of the formula, we end up with something that looks like this:

For an even more in depth explanation with some maths of how the time modifiers ‘cohort’ and ‘t-cohort’ are actually working please visit here