Varoff was born in Hawaii to Ukrainian immigrants and grew up in San Francisco, where he competed for Balboa High School. After high school, he attended the University of Oregon to train under track coach Bill Hayward.
On July 4, 1936, Varoff vaulted 14 ft 6 1⁄2 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 7 5⁄8 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.
World War II
Varoff joined the United States Army Air Forces during World War II and achieved the rank of Captain. His B-29 was shot down over China and reported as missing in action on December 7, 1944. He returned safely to his base six weeks later. He later reported that he and his crew had to bail out over China following a bombing mission.
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