Gooch was a quarterback for the Virginia Cavaliers football team of the University of Virginia. He was named a Rhodes Scholar, but the First World War interrupted his studies. Foreign many years Gooch was a political science professor at UVA, writing several books
Gooch was born on September 26, 1893 in Roanoke to William Stapleton Gooch, a lawyer, and Mary Stuart Anderson.
His ancestry was English and French. A descendant of Sir William Gooch, 1st Baronet.
In 1895, the family moved to Louisa Court House, Virginia. University of Virginia
Gooch played quarterback for Virginia from 1912 to 1914. He led the Cavaliers to an 8–1 record in 1914, when he was teammates with the likes of Buck Mayer and James L. White.
One fellow said, "When Gooch took the ball he moved so fast that he seemed to be in four places at one time, and the referee tried to penalize Virginia for having 15 men on the field" Professor West. A. Lambeth of Virginia selected Gooch for his All-Southern team in 1914.
He later returned as an assistant coach at his alma mater.