His participation in the island's local basketball league was very limited in 1958 and 1959 because he continued to pursue his academic education in Madrid, Spain. During his stay in Spain, he played from 1957 to 1961 for the Real Madrid basketball team that won the "Generalísimo" Cup, now known as the King's Cup. While playing in Spain, he caught the eye of a young royal whose grandfather was the owner of the Real Madrid team and who became one of his best-known fans. That young royal is now known as King Juan Carlos, who corresponded with Báez in 2006 to wish him a speedy recovery from his illness. Báez represented Puerto Rico in the 1959 Pan American Games, celebrated in Chicago, Illinois. In the tournament which included American basketball stars, Oscar Robertson and Jerry West, Báez was the champion scorer. Báez and fellow Puerto Rican Juan "Pachín" Vicéns were named to the All-Star team.