Why did the index make this query slower?

Question

The table contains 1,500,000 entries, of which 1,250,000 have the field = 'z'.
I need to select a random non-z field.

$random = mt_rand(1, 250000);  
$query = "SELECT field FROM table WHERE field != 'z' LIMIT $random, 1";

It is working fine.

Then I decided to optimize it and indexed it fieldin a table.

The result was strange - it was slower ~ 3 times . I tested it. Why is it slower? Shouldn't such indexing be accelerated?

my isam

explain with index:  
id  select_type  table  type  possible_keys  key   key_len  ref  rows     Extra  
1   SIMPLE       table  range field          field 758      NULL 1139287  Using  

explain without index:  
id  select_type  table  type  possible_keys  key  key_len  ref  rows     Extra  
1   SIMPLE       table  ALL   NULL           NULL NULL     NULL 1484672  Using where

Answer 1

Summary

The problem is that fieldit is not a good candidate for indexing due to the nature of b-tree .

Explanation

, 500 000 , - 1 () 0 ():

CREATE TABLE toss (
    id int NOT NULL AUTO_INCREMENT,
    result int NOT NULL DEFAULT '0',
    PRIMARY KEY ( id )
)

select result, count(*) from toss group by result order by result;
+--------+----------+
| result | count(*) |
+--------+----------+
|      0 |   250290 |
|      1 |   249710 |
+--------+----------+
2 rows in set (0.40 sec)

(), , , .

select * from toss where result != 1 limit 123456, 1;
+--------+--------+
| id     | result |
+--------+--------+
| 246700 |      0 |
+--------+--------+
1 row in set (0.06 sec)

explain select * from toss where result != 1 limit 123456, 1;
+----+-------------+-------+------+---------------+------+---------+------+--------+-------------+
| id | select_type | table | type | possible_keys | key  | key_len | ref  | rows   | Extra       |
+----+-------------+-------+------+---------------+------+---------+------+--------+-------------+
|  1 | SIMPLE      | toss  | ALL  | NULL          | NULL | NULL    | NULL | 500000 | Using where |
+----+-------------+-------+------+---------------+------+---------+------+--------+-------------+

, , .

toss, , 250 000 .

create index foo on toss ( result );
Query OK, 500000 rows affected (2.48 sec)
Records: 500000  Duplicates: 0  Warnings: 0

select * from toss where result != 1 limit 123456, 1;
+--------+--------+
| id     | result |
+--------+--------+
| 246700 |      0 |
+--------+--------+
1 row in set (0.25 sec)

explain select * from toss where result != 1 limit 123456, 1;
+----+-------------+-------+-------+---------------+------+---------+------+--------+-------------+
| id | select_type | table | type  | possible_keys | key  | key_len | ref  | rows   | Extra       |
+----+-------------+-------+-------+---------------+------+---------+------+--------+-------------+
|  1 | SIMPLE      | toss  | range | foo           | foo  | 4       | NULL | 154565 | Using where |
+----+-------------+-------+-------+---------------+------+---------+------+--------+-------------+

, 0,06 0,25 . ? , , .

:

show index from toss;
+-------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| Table | Non_unique | Key_name | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment |
+-------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| toss  |          0 | PRIMARY  |            1 | id          | A         |      500000 |     NULL | NULL   |      | BTREE      |         |
| toss  |          1 | foo      |            1 | result      | A         |           2 |     NULL | NULL   |      | BTREE      |         |
+-------+------------+----------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+

PRIMARY : 500 000 500 000 . BTREE .

foo - : 500 000 , 2 . , , BTREE - .

Answer 2

order by, LIMIT $random, 1 undefined.

, .