Sum of one column grouped by 2nd column with groups made based on 3rd column - group-by

Question

Data
So my data looks like:
product user_id value id
pizza 1 50 1
burger 1 30 2
pizza 2 50 3
fries 1 10 4
pizza 3 50 5
burger 1 30 6
burger 2 30 7
Problem Statement
And I wanted to compute Lifetime values of customers of each product as a metric to know which product is doing great in terms of user retention.
Desired Output
My desired output is:
product
value_by_customers_of_these_products
total_customers
ltv
pizza
250
3
250/3 = 83.33
burger
200
2
200/2 = 100
fries
120
1
120/1 = 120
Columns Description:
value_by_customers_of_these_products : Total value generated by
customers of each product including orders which do not contain the
product
total_customers : Simple COUNT(DISTINCT user_id) GROUP BY product
Current Workaround
Currently I am doing this:
SELECT "pizza" AS product, SUM(value) value_by_customers_of_these_products, COUNT(DISTINCT user_id) users FROM orders WHERE user_id in (SELECT user_id FROM orders WHERE product = "pizza")
UNION ALL
SELECT "burger" AS product, SUM(value) value_by_customers_of_these_products, COUNT(DISTINCT user_id) users FROM orders WHERE user_id in (SELECT user_id FROM orders WHERE product = "burger")
UNION ALL
SELECT "fries" AS product, SUM(value) value_by_customers_of_these_products, COUNT(DISTINCT user_id) users FROM orders WHERE user_id in (SELECT user_id FROM orders WHERE product = "fries")
I have a python script obtaining DISTINCT product names from my table and then repeating the query string for each product and updating query from time to time. This is really a pain as I have to do every time a new product is launched and sky-rocketing length of query is another issue. How can I achieve this via built-in BigQuery functions or minimal headache?
Code to generate Sample Data
WITH orders as (SELECT "pizza" AS product,
1 AS user_id,
50 AS value, 1 AS id,
UNION ALL SELECT "burger", 1, 30,2
UNION ALL SELECT "pizza", 2, 50,3
UNION ALL SELECT "fries", 1, 10,4
UNION ALL SELECT "pizza", 3, 50,5
UNION ALL SELECT "burger", 1, 30, 6
UNION ALL SELECT "burger", 3, 30, 7)

Answer 1

Use below
with user_value as (
select user_id, sum(value) values
from `project.dataset.table`
group by user_id
), product_user as (
select distinct product, user_id
from `project.dataset.table`
)
select product,
sum(values) as value_by_customers_of_these_products,
count(user_id) as total_customers,
round(sum(values) / count(user_id), 2) as ltv
from product_user
join user_value
using(user_id)
group by product
if applied to sample data in your question - output is