Useful queries to evaluate database level stats

pg_stat_database.sql

-- Cache hit ratio.
-- Sweet spot here are values close to 100 which also means all necessary data were read from shared buffers. 
-- values near 90 or lower show that postgres read from disk time to time.
SELECT
    round(100 * sum(blks_hit) / sum(blks_hit + blks_read), 3) as cache_hit_ratio
FROM pg_stat_database;

-- estimate commit ratio and detect errors
-- values that are closer to 100 mean that you database has very few errors. 
SELECT
    datname, 100 * xact_commit / (xact_commit + xact_rollback) as commit_ratio
FROM pg_stat_database WHERE (xact_commit + xact_rollback) > 0;