On July 4, 1936, Varoff vaulted 14 ft  in (4.43 m) at the Amateur Athletic Union (AAU)'s national championship meet, setting a new world record. However, the Olympic Trials were held separately the following week; at the Trials, Varoff only placed fourth and failed to qualify for the United States team for the 1936 Olympics. Varoff won the AAU championship again in 1939; he set his personal best, 14 ft  in (4.46 m), at the 1937 AAU meet, but lost on countback as three other men also cleared the same height. With the cancellation of the 1940 and 1944 Olympics due to World War II, he never competed in the Olympics.