You can't use a field alias in that WHERE
clause. What you can do is use your assignment again in the WHERE
clause like this:
SELECT
First_Name,
Last_Name,
Team,
Pos, GP, G, A,
(G+A) AS Points
FROM stats
WHERE
(G+A) BETWEEN '$b1' AND '$b2'
ORDER BY Points DESC
Standard SQL doesn't allow you to refer to a column alias in a WHERE clause. This restriction is imposed because when the WHERE code is executed, the column value may not yet be determined.
MySQL docs: http://dev.mysql.com/doc/refman/5.0/en/problems-with-alias.html