Problems with MYSQL query (efficiency) - php

Question

I'm having real problems with my Mysql statement, I need to join a few tables together, query them and order by the average of values from another table. This is what I have...
SELECT
ROUND(avg(re.rating), 1)AS avg_rating,
s.staff_id, s.full_name, s.mobile, s.telephone, s.email, s.drive
FROM staff s
INNER JOIN staff_homes sh
ON s.staff_id=sh.staff_id
INNER JOIN staff_positions sp
ON s.staff_id=sp.staff_id
INNER JOIN reliability re
ON s.staff_id=re.staff_id
INNER JOIN availability ua
ON s.staff_id=ua.staff_id
GROUP BY staff_id
ORDER BY avg_rating DESC
Now I believe this to work although I am getting this error "The SELECT would examine more than MAX_JOIN_SIZE rows; check your WHERE and use SET SQL_BIG_SELECTS=1 or SET SQL_MAX_JOIN_SIZE=# if the SELECT is okay".
I think this means that I have too many joins and because it is shared hosting it won't allow large queries to run I don't know.
What I would like to know is exactly what the error means (I have googled it but I don't understand the answers) and how I can work round it by maybe making my query more efficient?
Any help would be appreciated. Thanks
EDIT:
The reason I need the joins is so I can query the tables based on a search function like so...
SELECT
ROUND(avg(re.rating), 1)AS avg_rating
, s.staff_id, s.full_name, s.mobile, s.telephone, s.email, s.drive
FROM staff s
INNER JOIN staff_homes sh
ON s.staff_id=sh.staff_id
INNER JOIN staff_positions sp
ON s.staff_id=sp.staff_id
INNER JOIN reliability re
ON s.staff_id=re.staff_id
INNER JOIN availability ua
ON s.staff_id=ua.staff_id
WHERE s.full_name LIKE '%'
AND s.drive = '1'
AND sh.home_id = '3'
AND sh.can_work = '1'
AND sp.position_id = '3'
AND sp.can_work = '1'
GROUP BY staff_id
ORDER BY avg_rating DESC
EDIT 2
This was the result of my explain. Also I'm not great with MYSQL how would I set up foreign keys?
id select_type table type possible_keys key key_len ref rows Extra
1 SIMPLE ua ALL NULL NULL NULL NULL 14 Using temporary; Using filesort
1 SIMPLE re ALL NULL NULL NULL NULL 50 Using where; Using join buffer
1 SIMPLE sp ALL NULL NULL NULL NULL 84 Using where; Using join buffer
1 SIMPLE sh ALL NULL NULL NULL NULL 126 Using where; Using join buffer
1 SIMPLE s eq_ref PRIMARY PRIMARY 4 web106-prestwick.ua.staff_id 1
EDIT 3: Thanks lc, it was my foreign keys, they were not set up correctly. Problem sorted

Answer 1

Maybe you should use more and/or better indexes on the tables.

Answer 2

According to the db you're using, the optimization may be faster or not with subqueries.
There may be 2 bottlenecks on your query:
try to remove the average function of your query. If your query speeds up, try to replace it with a subquery and see what happens.
The multiple joins often reduce performances, and there's nothing you can do except modifying your db schema. The simplest solution would be to have a table that precomputes data and reduces the work for your db engine. This table can be fulfilled with stored procedures triggered when you modify the data on the implied tables, or you can also modify the table values from your php application.