Среднее значение поля CASE WHEN

Вы можете использовать AVG():

SELECT AVG(CASE WHEN Basketball = '' THEN 0.0 ELSE 1 END + 
           CASE WHEN Baseball = '' THEN 0 ELSE 1 END + 
           CASE WHEN Football = '' THEN 0 ELSE 1 END
           ) AS avg_TotalTeamMembership
FROM PlayerMembership;

Вы можете использовать AVGагрегатную функцию:

SELECT AVG(TotalTeamMembership)
FROM (SELECT Player,
       CASE WHEN Basketball = '' THEN 0 ELSE 1 END + 
       CASE WHEN Baseball = '' THEN 0 ELSE 1 END + 
       CASE WHEN Football = '' THEN 0 ELSE 1 END AS TotalTeamMembership
      FROM PlayerMembership) s;