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Query planner / Analyse statistics bad estimate rows=1 with maximum statistics 10000 on PostgreSQL 10.2

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Hi All, 

I'm seeing some very slow queries and it looks like the query planner is deciding to do a 'Nested Loop Left Join' 
which is slow.  When I SET enable_nestloop=OFF for testing it does a 'Hash Left Join' which is much faster.

I think  I can see the cause of the problem in the examples below. I can't make sense of the statistics being written
by ANALYSE or the planners row estimates. 

Can anyone help me understand....

- Why the row estimate I get in the query below for school_id = 36 is 1 ?     ( I expect it to be higher)
- Why does '1' appear in the most_common_vals when it is actually the least common value.
- Why doesn't 36 appear in the most_common_vals (it is more common than 1)
- Does the analyse output below mean that it only scanned 51538 of 65463 rows in the table? Is school_id 36 just being missed in the sample? (This happens when the analyse is repeated )

Any help with understanding what's happening here would be much appreciated. 

I hope I've provided enough information below.

Thanks,

Mark

db=> explain analyse select * from common_student  where school_id = 36 ;
                                                                 QUERY PLAN                                                                 
--------------------------------------------------------------------------------------------------------------------------------------------
 Index Scan using idx_common_student_sid on common_student  (cost=0.41..8.39 rows=1 width=385) (actual time=0.264..1.691 rows=1388 loops=1)
   Index Cond: (school_id = 36)
 Planning time: 0.087 ms
 Execution time: 2.706 ms
(4 rows)

db=> select tablename,attname,most_common_vals,histogram_bounds,n_distinct from pg_stats where attname='school_id'  and tablename='common_stude
nt';
   tablename    |  attname  |                                                            most_common_vals                                                            | histogram_bounds | n_distinct 
----------------+-----------+----------------------------------------------------------------------------------------------------------------------------------------+------------------+------------
 common_student | school_id | {79,60,25,61,59,69,86,77,64,33,56,78,58,81,41,97,22,67,38,23,3,72,92,93,48,24,96,26,75,90,70,52,51,21,14,91,83,54,85,11,68,94,53,88,1} |                  |         45
(1 row)

db=> select count(distinct(school_id)) from common_student ;
 count 
-------
    55
(1 row)

db=> alter table common_student alter column school_id set statistics 100000;
WARNING:  lowering statistics target to 10000
ALTER TABLE
db=> analyse verbose common_student(school_id);
INFO:  analyzing "public.common_student"
INFO:  "common_student": scanned 7322 of 7322 pages, containing 65463 live rows and 49026 dead rows; 51538 rows in sample, 65463 estimated total rows
ANALYZE
db=> select tablename,attname,most_common_vals,histogram_bounds,n_distinct from pg_stats where attname='school_id'  and tablename='common_stude
nt';
   tablename    |  attname  |                                                            most_common_vals                                                            | histogram_bounds | n_distinct 
----------------+-----------+----------------------------------------------------------------------------------------------------------------------------------------+------------------+------------
 common_student | school_id | {79,60,25,61,59,69,86,77,64,33,56,78,58,81,41,97,22,67,38,23,3,72,92,93,48,24,96,26,75,90,70,52,51,21,14,91,83,54,85,11,68,94,53,88,1} |                  |         45
(1 row)

db=> explain analyse select * from common_student  where school_id = 36 ;
                                                                 QUERY PLAN                                                                 
--------------------------------------------------------------------------------------------------------------------------------------------
 Index Scan using idx_common_student_sid on common_student  (cost=0.41..8.39 rows=1 width=385) (actual time=0.542..4.022 rows=1388 loops=1)
   Index Cond: (school_id = 36)
 Planning time: 0.334 ms
 Execution time: 6.542 ms
(4 rows)

db=> select school_id, count(*) from common_student  group by school_id order by count(*)  limit 6 ;
 school_id | count 
-----------+-------
         1 |    50
        88 |   161
        53 |   252
        94 |   422
        31 |   434
        68 |   454
(6 rows)

dvpjxbzc=> select school_id, count(*) from common_student where school_id = 36  group by school_id ;                    
 school_id | count 
-----------+-------
        36 |  1388
(1 row)

db=> explain analyse select * from common_student  where school_id = 1 ;
                                                            QUERY PLAN                                                            
----------------------------------------------------------------------------------------------------------------------------------
 Bitmap Heap Scan on common_student  (cost=4.91..243.76 rows=64 width=385) (actual time=0.128..0.267 rows=50 loops=1)
   Recheck Cond: (school_id = 1)
   Heap Blocks: exact=16
   ->  Bitmap Index Scan on "unique common_student"  (cost=0.00..4.90 rows=64 width=0) (actual time=0.110..0.110 rows=50 loops=1)
         Index Cond: (school_id = 1)
 Planning time: 0.177 ms
 Execution time: 0.414 ms
(7 rows)

db=> select VERSION();
                                   version                                   
-----------------------------------------------------------------------------
 PostgreSQL 10.2 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 4.8.2, 64-bit
(1 row)


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