As we saw in the previous section, the query planner needs to estimate the number of rows retrieved by a query in order to make good choices of query plans. This section provides a quick look at the statistics that the system uses for these estimates.

One component of the statistics is the total number of entries in each table and index, as well as the number of disk blocks occupied by each table and index. This information is kept in the table pg_class, in the columns reltuples and relpages. We can look at it with queries similar to this one:

SELECT relname, relkind, reltuples, relpages
FROM pg_class
WHERE relname LIKE 'tenk1%';

       relname        | relkind | reltuples | relpages
----------------------+---------+-----------+----------
 tenk1                | r       |     10000 |      358
 tenk1_hundred        | i       |     10000 |       30
 tenk1_thous_tenthous | i       |     10000 |       30
 tenk1_unique1        | i       |     10000 |       30
 tenk1_unique2        | i       |     10000 |       30
(5 rows)

Here we can see that tenk1 contains 10000 rows, as do its indexes, but the indexes are (unsurprisingly) much smaller than the table.

For efficiency reasons, reltuples and relpages are not updated on-the-fly, and so they usually contain somewhat out-of-date values. They are updated by VACUUM, ANALYZE, and a few DDL commands such as CREATE INDEX. A VACUUM or ANALYZE operation that does not scan the entire table (which is commonly the case) will incrementally update the reltuples count on the basis of the part of the table it did scan, resulting in an approximate value. In any case, the planner will scale the values it finds in pg_class to match the current physical table size, thus obtaining a closer approximation.

Most queries retrieve only a fraction of the rows in a table, due to WHERE clauses that restrict the rows to be examined. The planner thus needs to make an estimate of the selectivity of WHERE clauses, that is, the fraction of rows that match each condition in the WHERE clause. The information used for this task is stored in the pg_statistic system catalog. Entries in pg_statistic are updated by the ANALYZE and VACUUM ANALYZE commands, and are always approximate even when freshly updated.

Rather than look at pg_statistic directly, it's better to look at its view pg_stats when examining the statistics manually. pg_stats is designed to be more easily readable. Furthermore, pg_stats is readable by all, whereas pg_statistic is only readable by a superuser. (This prevents unprivileged users from learning something about the contents of other people's tables from the statistics. The pg_stats view is restricted to show only rows about tables that the current user can read.) For example, we might do:

SELECT attname, inherited, n_distinct,
       array_to_string(most_common_vals, E'\n') as most_common_vals
FROM pg_stats
WHERE tablename = 'road';

 attname | inherited | n_distinct |          most_common_vals
---------+-----------+------------+------------------------------------
 name    | f         |  -0.363388 | I- 580                        Ramp+
         |           |            | I- 880                        Ramp+
         |           |            | Sp Railroad                       +
         |           |            | I- 580                            +
         |           |            | I- 680                        Ramp
 name    | t         |  -0.284859 | I- 880                        Ramp+
         |           |            | I- 580                        Ramp+
         |           |            | I- 680                        Ramp+
         |           |            | I- 580                            +
         |           |            | State Hwy 13                  Ramp
(2 rows)

Note that two rows are displayed for the same column, one corresponding to the complete inheritance hierarchy starting at the road table (inherited=t), and another one including only the road table itself (inherited=f).

The amount of information stored in pg_statistic by ANALYZE, in particular the maximum number of entries in the most_common_vals and histogram_bounds arrays for each column, can be set on a column-by-column basis using the ALTER TABLE SET STATISTICS command, or globally by setting the default_statistics_target configuration variable. The default limit is presently 100 entries. Raising the limit might allow more accurate planner estimates to be made, particularly for columns with irregular data distributions, at the price of consuming more space in pg_statistic and slightly more time to compute the estimates. Conversely, a lower limit might be sufficient for columns with simple data distributions.

Further details about the planner's use of statistics can be found in Chapter 71.

It is common to see slow queries running bad execution plans because multiple columns used in the query clauses are correlated. The planner normally assumes that multiple conditions are independent of each other, an assumption that does not hold when column values are correlated. Regular statistics, because of their per-individual-column nature, cannot capture any knowledge about cross-column correlation. However, PostgreSQL has the ability to compute multivariate statistics, which can capture such information.

Because the number of possible column combinations is very large, it's impractical to compute multivariate statistics automatically. Instead, extended statistics objects, more often called just statistics objects, can be created to instruct the server to obtain statistics across interesting sets of columns.

Statistics objects are created using the CREATE STATISTICS command. Creation of such an object merely creates a catalog entry expressing interest in the statistics. Actual data collection is performed by ANALYZE (either a manual command, or background auto-analyze). The collected values can be examined in the pg_statistic_ext catalog.

ANALYZE computes extended statistics based on the same sample of table rows that it takes for computing regular single-column statistics. Since the sample size is increased by increasing the statistics target for the table or any of its columns (as described in the previous section), a larger statistics target will normally result in more accurate extended statistics, as well as more time spent calculating them.

The following subsections describe the kinds of extended statistics that are currently supported.

CREATE STATISTICS stts (dependencies) ON zip, city FROM zipcodes;

ANALYZE zipcodes;

SELECT stxname, stxkeys, stxdependencies
  FROM pg_statistic_ext
  WHERE stxname = 'stts';
 stxname | stxkeys |             stxdependencies               
---------+---------+------------------------------------------
 stts    | 1 5     | {"1 => 5": 1.000000, "5 => 1": 0.423130}
(1 row)

SELECT * FROM zipcodes WHERE city = 'San Francisco' AND zip = '94105';

SELECT * FROM zipcodes WHERE city = 'San Francisco' AND zip = '90210';

CREATE STATISTICS stts2 (ndistinct) ON zip, state, city FROM zipcodes;

ANALYZE zipcodes;

SELECT stxkeys AS k, stxndistinct AS nd
  FROM pg_statistic_ext
  WHERE stxname = 'stts2';
-[ RECORD 1 ]--------------------------------------------------------
k  | 1 2 5
nd | {"1, 2": 33178, "1, 5": 33178, "2, 5": 27435, "1, 2, 5": 33178}
(1 row)