Du måste ha en annan underfråga för detta,
SELECT c.Givenname, c.Familyname, COUNT(r.places) AS TotalPlaces
FROM Competitors c
INNER JOIN Results r ON r.Competitornum = c.Competitornum
WHERE r.place IN (1,2,3)
GROUP BY c.Givenname, c.Familyname
HAVING COUNT(r.places) =
(
SELECT MAX(TotalPlaces)
FROM
(
SELECT COUNT(g.places) AS TotalPlaces
FROM Competitors f
INNER JOIN Results g ON f.Competitornum = g.Competitornum
WHERE g.place IN (1,2,3)
GROUP BY f.Givenname, f.Familyname
)
)