'The Little Big Game' was played annually between the 2 rival Catholic institutions located in the San Francisco Bay Area.

The name was reference to 'The Big Game' rivalry between larger Bay Area universities, Stanford and Berkeley.

Highlighting Shaw's tenure at the Bronco helm were a pair of Sugar Bowl victories over heavily-favored Louisiana State, 21–14, in 1937, and 6–0, in 1938.

During that 1942 season Fears won All-Pacific Coast honors before joining the Air Force in World War II.

His 1949 Santa Clara Broncos football team beat Bear Bryant's Kentucky in the 1950 Orange Bowl.

Brent Jones helped the Broncos to two Western Football Conference championships and was named to the all-conference team three times.