Over his career, Azcue threw out 45.17% of the base runners who tried steal a base on him, ranking him 10th on the all-time list. During the 1966 season, he threw out 62% of the base runners who tried steal a base, the fifth highest season percentage in major league history. He caught two no hitters in his career, Sonny Siebert in 1966 and Clyde Wright in 1970.
Azcue's career statistics reveal that he excelled at eliminating base runners attempting to steal on him, ranking him among the top 10 all-time. In the 1966 season, his success rate increased significantly, with a 62% catch rate, placing him fifth in major league history for that year. He also recorded two notable achievements: catching no-hitters by Sonny Siebert and Clyde Wright.