Prova questo. Non testato.
Codice PHP:
SELECT c.user_id,c.value, p.points AS max_pts
FROM values AS c
INNER JOIN points AS p ON p.user_id = c.user_id
INNER JOIN
(
SELECT A.value AS A_value, MAX( B.points ) AS A_max_pts
FROM values AS A
INNER JOIN points AS B ON B.user_id = A.user_id
WHERE A.field_id =16
GROUP BY A.value
) ON A_value = c.value AND A_max_pts = p.points
WHERE c.field_id =16
ORDER BY p.points DESC