Postgresql becomes unresponsible when new index va

In my app I have a concept of "seasons" which change discretely over time. All the entities are related to some season. All entities have season based indices as well as some indices on other fields. When season change occurs, postgresql decides to use filtered scan plan based on season index rather than more specific field indices. At the beginning of the season the planning cost of such decision is very little, so it's ok, but the problem is - season change brings MANY users to come at the very beginning of the season, so postgresql scan based query plan becomes bad very fast - it simply scans all the entities in the new season, and filters target items. After first auto analyze postgres decides to use a good plan, BUT auto analyze runs VERY SLOWLY due to contention and I suppose it's like a snowball - the more requests are done, the more contention is due to a bad plan and thus auto analyze works slowly and slowly. The biggest time for auto analyze to work was about an hour last week, and it becomes a real problem. I know postgresql architects decided to disable the possibility to choose the index used in query, but what is the best way to overcome my problem then?

Just to clarify, here is a DDL, one of the "slow" queries and explain results before and after auto analyze.

DDL

CREATE TABLE race_results (
  id INTEGER PRIMARY KEY NOT NULL DEFAULT nextval('race_results_id_seq'::regclass),
  user_id INTEGER NOT NULL,
  opponent_id INTEGER,
  season_id INTEGER NOT NULL,
  type RACE_TYPE NOT NULL DEFAULT 'battle'::race_type,
  elo_delta INTEGER NOT NULL,
  opponent_elo_delta INTEGER NOT NULL DEFAULT 0,
);
CREATE INDEX race_results_type_user_id_index ON race_results USING BTREE (season_id, type, user_id);
CREATE INDEX race_results_type_opponent_id_index ON race_results USING BTREE (season_id, type, opponent_id);
CREATE INDEX race_results_opponent_id_index ON race_results USING BTREE (opponent_id);
CREATE INDEX race_results_user_id_index ON race_results USING BTREE (user_id);

Query

SELECT 1000 + COALESCE(SUM(CASE WHEN user_id = 6446 THEN elo_delta ELSE opponent_elo_delta END), 0)
        FROM race_results
        WHERE type = 'battle' :: race_type AND (user_id = 6446 OR opponent_id = 6446) AND
              season_id = current_season_id()

Results of explain before auto analyze (as you see more than a thousand items is already removed by filter and soon it becomes hundreds of thousands for each request)

Results of explain analyze after auto analyze (now postgres decides to use the right index and no filtering needed anymore, but the problem is - auto analyze takes too long partly due to contention of ineffective index selection in previous picture)

ps: Now I'm solving the problem just turning off the application server after 10 seconds after season changes so that postgres gets new data and starts autoanalyze, and then turn it on, when autoanalyze finishes, but such solution involves downtime, which is not desirable and overall it looks weird

Finally I found the solution. It's not perfect and I will not mark it as the best one, however it works and could help someone.

Instead of indices on season, type and user/opponent id, I now have indices

CREATE INDEX race_results_type_user_id_index ON race_results USING BTREE (user_id,season_id, type);
CREATE INDEX race_results_type_opponent_id_index ON race_results USING BTREE (opponent_id,season_id, type);

One problem which appeared - I needed and index on season anyway in other queries, but when I add index

CREATE INDEX race_results_season_index ON race_results USING BTREE (season_id);

the planner tries to use it again instead of those right indices and the whole situation is repeated. What I've done is simply added one more field: 'season_id_clone', which contains the same data as 'season_id', and I made an index against it. Now when I need to filter something based on season (not including queries from the first post), I'm using season_id_clone in query. I know it's weird, but I haven't found anything better.