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Before PostgreSQL executes a query, the planner must decide how to run it: sequential scan vs. index scan, nested loop vs. hash join, which table to drive a join from. Every one of these decisions hinges on a single guess: how many rows will each step produce?

• If the planner thinks a filter returns 5 rows, an index scan + nested loop looks cheap.
• If it thinks the same filter returns 5 million rows, a sequential scan + hash join wins.

These row-count guesses are called cardinality estimates. When they are wrong, the planner picks a bad plan even though its cost model is perfectly sound. This lesson traces exactly where those numbers come from.

Every node in an EXPLAIN plan reports the planner's estimate. The rows= value is the estimated cardinality for that node. Run EXPLAIN ANALYZE to compare it against the real count.

• (cost=… rows=120 …) is the estimate.
• (actual … rows=118 …) is the truth.

A large gap between estimated and actual rows is the single most common root cause of slow plans. Train your eye to scan for it first.

The planner does not look at your data at plan time. It reads pre-computed summaries from the system catalog pg_statistic, populated by ANALYZE (run automatically by autovacuum). The human-readable view over it is pg_stats.

For each column, pg_stats exposes the building blocks of estimation:

• null_frac — fraction of NULLs.
• n_distinct — number of distinct values.
• most_common_vals / most_common_freqs — the MCV list.
• histogram_bounds — buckets for the non-MCV remainder.

Selectivity is the fraction of rows a predicate is estimated to keep, between 0 and 1. The estimated row count is simply:

• estimated_rows = selectivity × total_rows

where total_rows comes from pg_class.reltuples (also refreshed by ANALYZE). So estimation reduces to two questions: what is the table's row count, and what fraction survives each predicate? Everything else is detail about how that fraction is computed.

For column = 'value', the planner first checks the most_common_vals (MCV) list. If the value is there, it uses the exact frequency from most_common_freqs — no math, just a lookup.

Example: if most_common_vals = {shipped, pending, cancelled} and most_common_freqs = {0.62, 0.25, 0.08}, then status = 'shipped' has selectivity 0.62. On a 1,000,000-row table that estimates 620,000 rows.

MCVs make skewed distributions estimate accurately — the planner knows exactly how popular the hot values are.

If the value is not in the MCV list, the planner assumes all non-MCV values are equally likely. It computes the leftover probability mass and spreads it evenly:

• residual = 1 − sum(most_common_freqs) − null_frac
• n_distinct_residual = n_distinct − count(MCVs)
• selectivity = residual / n_distinct_residual

This is why estimates for rare values can be poor when the long tail is itself skewed: the uniform assumption inside the residual breaks down. MCVs cover the head; the residual is a flat approximation of the tail.

For inequalities like amount > 500 or created_at BETWEEN …, the planner uses histogram_bounds. These bounds divide the non-MCV values into buckets each holding roughly the same number of rows (equi-depth, not equi-width).

To estimate amount < X, it finds where X falls among the bounds and interpolates linearly within the containing bucket. With N buckets, each represents about 1/N of the non-MCV rows, so the planner counts whole buckets below X plus a fractional slice of the boundary bucket.

With multiple AND conditions on different columns, PostgreSQL multiplies their selectivities, assuming the columns are statistically independent:

• sel(A AND B) = sel(A) × sel(B)

If status = 'shipped' is 0.62 and country = 'DE' is 0.10, the planner estimates 0.062 of the table. But if shipped orders are mostly German, the real fraction could be 0.30 — a 5× underestimate. Correlated columns are where single-column stats fail and plans collapse.

When columns are correlated, create extended statistics with CREATE STATISTICS. The dependencies kind teaches the planner functional dependencies; mcv stores multi-column most-common-value combinations so AND predicates are estimated jointly instead of multiplied.

After creating the object you must run ANALYZE on the table to populate it. Then the planner reads the joint distribution and stops assuming independence for those columns.

Join row counts build on the per-table estimates. For an equi-join, PostgreSQL estimates output rows roughly as:

• rows ≈ (outer_rows × inner_rows) / max(n_distinct_outer, n_distinct_inner)

using the join key's n_distinct from each side. This is why a bad single-table estimate cascades: if the planner thinks a filtered side has 5 rows when it really has 50,000, every join above it inherits the error and may choose a nested loop that runs 50,000 times instead of a hash join.

Estimates are only as good as the statistics behind them. Practical levers:

• Run ANALYZE after bulk loads; let autovacuum keep stats fresh.
• Raise resolution on skewed columns with ALTER TABLE … ALTER COLUMN … SET STATISTICS n (larger MCV list and histogram).
• Add CREATE STATISTICS for correlated column groups.
• Compare EXPLAIN ANALYZE estimated vs. actual rows to find the node where the guess first goes wrong.

You debug from the bottom of the plan up: the first node with a large estimate/actual gap is usually the real culprit.

Apply the estimation rules to a concrete case.

You can now trace a row estimate end to end:

• ANALYZE fills pg_statistic / pg_stats and sets reltuples.
• Equality uses the MCV list when the value is common, otherwise the uniform residual over n_distinct.
• Ranges interpolate within equi-depth histogram_bounds.
• Multiple ANDs multiply selectivities, assuming independence — the main source of estimation error.
• Extended statistics (dependencies, mcv) fix correlated columns.
• Joins combine per-side estimates via join-key n_distinct, so single-table errors cascade upward.

Selectivity × row count produces the cardinalities that drive scan, join, and order choices. Master this and EXPLAIN output stops being mysterious — it becomes a story you can read.