I'm playing around with the Lahman Baseball Database in a MySQL instance. I want to find the players who topped home runs (HR) for each year. The Batting table has the following (relevant parts) of its schema:

+-----------+----------------------+------+-----+---------+-------+
| Field     | Type                 | Null | Key | Default | Extra |
+-----------+----------------------+------+-----+---------+-------+
| playerID  | varchar(9)           | NO   | PRI |         |       |
| yearID    | smallint(4) unsigned | NO   | PRI | 0       |       |
| HR        | smallint(3) unsigned | YES  |     | NULL    |       |
+-----------+----------------------+------+-----+---------+-------+

For each year, every player has an entry (between hundreds and 12k per year, going back to 1871). Getting the top N hitters for a single year is easy:

SELECT playerID,yearID,HR
FROM Batting
WHERE yearID=2009
ORDER BY HR DESC LIMIT 3;
+-----------+--------+------+
| playerID  | yearID | HR   |
+-----------+--------+------+
| pujolal01 |   2009 |   47 |
| fieldpr01 |   2009 |   46 |
| howarry01 |   2009 |   45 |
+-----------+--------+------+

But I'm interested in finding the top 3 from every year. I've found solutions like this, describing how to select the top from a category and I've tried to apply it to my problem, only to end up with a query that never returns:

SELECT
    b.yearID, b.playerID, b.HR
FROM
    Batting AS b
LEFT JOIN
    Batting b2
    ON
    (b.yearID=b2.yearID AND b.HR <= b2.HR)
GROUP BY b.yearID HAVING COUNT(*) <= 3;

Where have I gone wrong?