SELECT people1.ID, people1.name
FROM People people1,
GROUP BY people1.ID -- Can probably skip this?
HAVING 0 < COUNT(--For each person, counts how many times they did not have the worst score for each sport
    SELECT *
    FROM
        (SELECT results1.sportID, MAX(results1.RESULT)
        FROM Results results1,
        WHERE results.peopleID == people1.ID
        GROUP BY results1.sportID) AS personBest, -- For each person, creates a table with his best score for each sport
        (SELECT results1.sportID, MIN(results1.RESULT)
        FROM Results results1
        WHERE results1.sportID IN
            (SELECT UNIQUE results.sportID
            FROM Results results
            WHERE results.peopleID == people1.ID)
        GROUP BY results1.sportID) AS sportWorst -- For each person, creates a table with the worst score for each sport the person played in
    WHERE sportWorst.sportID = personBest.sportID AND sportWorst.RESULT != personBest.RESULT
    )