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so they usually contain somewhat out-of-date values.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 68.

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 CREATE
STATISTICS, which see for more details. 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 types of extended statistics that are currently supported.

The simplest type of extended statistics tracks *functional dependencies*, a concept used in
definitions of database normal forms. We say that column
`b`

is functionally dependent
on column `a`

if knowledge of
the value of `a`

is sufficient
to determine the value of `b`

,
that is there are no two rows having the same value of
`a`

but different values of
`b`

. In a fully normalized
database, functional dependencies should exist only on
primary keys and superkeys. However, in practice many data
sets are not fully normalized for various reasons;
intentional denormalization for performance reasons is a
common example. Even in a fully normalized database, there
may be partial correlation between some columns, which can be
expressed as partial functional dependency.

The existence of functional dependencies directly affects the accuracy of estimates in certain queries. If a query contains conditions on both the independent and the dependent column(s), the conditions on the dependent columns do not further reduce the result size; but without knowledge of the functional dependency, the query planner will assume that the conditions are independent, resulting in underestimating the result size.

To inform the planner about functional dependencies,
`ANALYZE`

can collect measurements
of cross-column dependency. Assessing the degree of
dependency between all sets of columns would be prohibitively
expensive, so data collection is limited to those groups of
columns appearing together in a statistics object defined
with the `dependencies`

option. It
is advisable to create `dependencies`

statistics only for column
groups that are strongly correlated, to avoid unnecessary
overhead in both `ANALYZE`

and
later query planning.

Here is an example of collecting functional-dependency statistics:

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)

Here it can be seen that column 1 (zip code) fully determines column 5 (city) so the coefficient is 1.0, while city only determines zip code about 42% of the time, meaning that there are many cities (58%) that are represented by more than a single ZIP code.

When computing the selectivity for a query involving functionally dependent columns, the planner adjusts the per-condition selectivity estimates using the dependency coefficients so as not to produce an underestimate.

Functional dependencies are currently only applied when
considering simple equality conditions that compare columns
to constant values. They are not used to improve estimates
for equality conditions comparing two columns or comparing
a column to an expression, nor for range clauses,
`LIKE`

or any other type of
condition.

When estimating with functional dependencies, the planner assumes that conditions on the involved columns are compatible and hence redundant. If they are incompatible, the correct estimate would be zero rows, but that possibility is not considered. For example, given a query like

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

the planner will disregard the `city`

clause as not changing the
selectivity, which is correct. However, it will make the
same assumption about

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

even though there will really be zero rows satisfying this query. Functional dependency statistics do not provide enough information to conclude that, however.

In many practical situations, this assumption is usually satisfied; for example, there might be a GUI in the application that only allows selecting compatible city and zipcode values to use in a query. But if that's not the case, functional dependencies may not be a viable option.

Single-column statistics store the number of distinct
values in each column. Estimates of the number of distinct
values when combining more than one column (for example, for
`GROUP BY a, b`

) are frequently
wrong when the planner only has single-column statistical
data, causing it to select bad plans.

To improve such estimates, `ANALYZE`

can collect n-distinct statistics
for groups of columns. As before, it's impractical to do this
for every possible column grouping, so data is collected only
for those groups of columns appearing together in a
statistics object defined with the `ndistinct`

option. Data will be collected for
each possible combination of two or more columns from the set
of listed columns.

Continuing the previous example, the n-distinct counts in a table of ZIP codes might look like the following:

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)

This indicates that there are three combinations of columns that have 33178 distinct values: ZIP code and state; ZIP code and city; and ZIP code, city and state (the fact that they are all equal is expected given that ZIP code alone is unique in this table). On the other hand, the combination of city and state has only 27435 distinct values.

It's advisable to create `ndistinct`

statistics objects only on
combinations of columns that are actually used for grouping,
and for which misestimation of the number of groups is
resulting in bad plans. Otherwise, the `ANALYZE`

cycles are just wasted.

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