7 Day Return/Retention Rate - postgresql

Question

I've been trying to calculate 7 Day Return Rate (also known as Classic Retention Rate, as described here: https://www.braze.com/blog/calculate-retention-rate/) and then taking a 30 day average to reduce noise in Postgresql.
However, I'm sure I'm doing something wrong. First of all, the numbers look waaay higher than intuitively I feel they should be (generally around 5% for the rest of the sector). Also, I believe the first 7 days should show 0, as theoretically users should take at least 7 days to count as a "return". However, I get around 40-70%, as shown below.
Would someone mind taking a look at the code below and seeing if there are any errors? 7 Day Return Rate is a really common metric for apps, and I haven't found any questions using postgresql that calculate it to this level of sophistication on Stack Exchange (or even the rest of the web), so I feel like a solid response could be very useful to a lot of people.
Sample data
Wednesday, August 1, 2018 12:00 AM 71.14
Thursday, August 2, 2018 12:00 AM 55.44
Friday, August 3, 2018 12:00 AM 50.09
Saturday, August 4, 2018 12:00 AM 45.81
Sunday, August 5, 2018 12:00 AM 43.27
Monday, August 6, 2018 12:00 AM 40.61
Tuesday, August 7, 2018 12:00 AM 39.38
Wednesday, August 8, 2018 12:00 AM 38.46
Thursday, August 9, 2018 12:00 AM 36.81
Friday, August 10, 2018 12:00 AM 35.94
with
user_first_event as (
select distinct id, min(timestamp)::date as first_event_date
from log
where
timestamp <= current_date
and timestamp >= {{start_date}} and timestamp <= {{end_date}}
group by id),
event as (
select distinct id, timestamp::date as user_event_date
from log
where timestamp <= current_date and timestamp >= {{start_date}}),
gap as (
select
user_first_event.id,
user_first_event.first_event_date,
event.user_event_date,
event.user_event_date - user_first_event.first_event_date as days_since_signup
from user_first_event
join event on user_first_event.id = event.id
where user_first_event.first_event_date <= event.user_event_date),
conversion_rate as (
select
first_event_date,
(sum(case when days_since_signup = 7 then 1 else 0 end) * 100.0 /
count(distinct id)
) as seven_day_retention_rate
from gap
group by first_event_date
)
SELECT first_event_date,
AVG(seven_day_retention_rate)
OVER(ORDER BY first_event_date ROWS BETWEEN 29 PRECEDING AND CURRENT ROW) AS rolling_avg_retention_rate
FROM conversion_rate

Answer 1

The problem is a bit easier than your query makes it seem, you can actually do it with just one subquery and one out query as follows:
select first_event_date
, avg(seven_day_return) as seven_day_return_day_only
, avg( avg(seven_day_return) ) OVER(ORDER BY first_event_date asc ROWS BETWEEN 29 preceding AND CURRENT ROW ) AS thirty_day_rolling_retention
from (
--inner query to get value for user, 1 if they retain and 0 if they do not
select min(timestamp)::date as first_event_date
, case when array_agg(timestamp::date) #> ARRAY[ (min(timestamp)::date + 7) ] then 1 else 0 end as seven_day_return
from log
group by id ) t
group by t.first_event_date;
Note that this weights each day equally rather than each user equally across days. If you want to weight the average by user across days then you can update the outer calculation using more aggregates and windows to compute the value with weightings.
Reference: http://sqlfiddle.com/#!17/ee17e/1/0
If you don't have access to array_agg (but have access to window functions) you can use:
select first_event_date
, avg(seven_day_return) as day_seven_day_return
, avg( avg(seven_day_return) ) OVER(ORDER BY first_event_date asc ROWS BETWEEN 29 preceding AND CURRENT ROW ) AS thirty_day_rolling_retention
from (
--inner query to get value for user
select min(timestamp)::date as first_event_date
, case when exists(select 1 from log l2 where l2.id = log.id and l2.timestamp::date = min(log.timestamp)::date + 7) then 1 else 0 end as seven_day_return
from log
group by id ) t
group by t.first_event_date;