Postgresql – Inconsistent statistics on jsonb column with btree index

I noticed that the performance of a query involving a jsonb column varied significantly between VACUUM ANALYZE runs while testing it. I get completely different execution plans seemingly randomly after analyzing the table.

I'm using Postgres 9.6 here. The setup for my tests is the following, I'm inserting a single key "x" into the jsonb column "params" with values between 1 and 6, with 1 being the rarest value and 6 the most common. I also have a regular int column "single_param" that contains the same distribution of values for comparison.:

CREATE TABLE test_data (
    id      serial,
    single_param    int,
    params      jsonb
);

INSERT INTO test_data
SELECT 
    generate_series(1, 1000000) AS id, 
    floor(log(random() * 9999999 + 1)) AS single_param,
    json_build_object(
        'x', floor(log(random() * 9999999 + 1))
    ) AS params;

CREATE INDEX idx_test_btree ON test_data (cast(test_data.params->>'x' AS int));
CREATE INDEX idx_test_gin ON test_data USING GIN (params);
CREATE INDEX ON test_data(id)
CREATE INDEX ON test_data(single_param)

The query I'm testing is a typical query for paginating results, I'm sorting by id and limiting the output to the first 50 rows.

SELECT * FROM test_data where (params->>'x')::int = 1 ORDER BY id DESC LIMIT 50;

I get one of the two explain analyze outputs randomnly after running VACUUM ANALYZE:

Limit  (cost=0.42..836.59 rows=50 width=33) (actual time=39.679..410.292 rows=10 loops=1)
  ->  Index Scan Backward using test_data_id_idx on test_data  (cost=0.42..44317.43 rows=2650 width=33) (actual time=39.678..410.283 rows=10 loops=1)
        Filter: (((params ->> 'x'::text))::integer = 1)
        Rows Removed by Filter: 999990"
Planning time: 0.106 ms
Execution time: 410.314 ms

or

Limit  (cost=8.45..8.46 rows=1 width=33) (actual time=0.032..0.034 rows=10 loops=1)
  ->  Sort  (cost=8.45..8.46 rows=1 width=33) (actual time=0.032..0.032 rows=10 loops=1)
        Sort Key: id DESC
        Sort Method: quicksort  Memory: 25kB
        ->  Index Scan using idx_test_btree on test_data  (cost=0.42..8.44 rows=1 width=33) (actual time=0.007..0.016 rows=10 loops=1)
              Index Cond: (((params ->> 'x'::text))::integer = 1)
Planning time: 0.320 ms
Execution time: 0.052 ms

The difference is that the estimate for the number of columns matching the where clause is different between the two plans. In the first one the estimate is 2650 rows, in the second one 1 row while the real number is 10 rows.

The following version of the query that can potentially use the GIN index does seem to use a default estimate for the json column of 1%, which also results in the bad query plan like above:

SELECT * FROM test_data where params @> '{"x": 1}' ORDER BY id DESC LIMIT 50;

My original assumption was that Postgres would not have any statistics on the jsonb column and always use an estimate like it does for the query using the @> operator. But for the query that is written to be able to use the btree index I created, it uses different estimates. Sometimes those are good enough, and sometimes they're bad.

Where do those estimates come from? I guess they're some kind of statistic Postgres creates with the index. For column statistics there is the option to collect more accurate statistics, is there anything like that for these statistics here? Or any other way to get Postgres to pick the better plan in my case?