One of five children (brothers Bill, Jim, and John, and sister Mary), the family moved to Stuart when Shaw was ten, where high school football had been abolished because of a fatality.
Shaw enrolled at Creighton University in Omaha in the fall of 1918 and went out for football; he played one game before the rest of the schedule wiped out by the flu epidemic.
"I had a heck of a time getting on my feet," explained Shaw, "Santa Clara could only afford to hire us on a seasonal basis in those years, and I was working for Standard Oil when I became head coach in 1936 after Clipper resigned to go to Villanova".
Shaw, while waiting for the professional All-America Football Conference to get off the ground, managed to build up the University of California squad, defeating a Frankie Albert-led St. Mary's Pre-Flight team, 6–0.
In 1944 and 1945, before World War II ended, the Morabito brothers, Victor and Tony, began organizing the San Francisco 49ers for entry into a new professional league, the All-America Football Conference (AAFC).
Shaw and his assistant, Al Ruffo, were hired by the 49ers, but then were permitted to accept a one-year contract at California when the AAFC league kickoff was delayed until 1946.
In 1946, Shaw took over the 49ers, and with the left-handed Frankie Albert leading and directing the attack, the team placed second to the Cleveland Browns four times (1946–1949) in the Western Division of the AAFC.
[3] As coach Shaw entered the 1954 campaign, his 9th season with the club, expectations of team owner Tony Morabito for a conference championship were acute.
"[7] After his termination in San Francisco, Shaw returned to the college ranks, becoming the second varsity head football coach at Air Force Academy.
He immediately dealt Buck Lansford, Jimmy Harris, and a first-round draft choice to the Los Angeles Rams for 32-year-old, nine-year veteran quarterback Norm Van Brocklin.
It was made by center/linebacker "sixty-minute-man" Chuck Bednarik, who because of early season injuries at linebacker revived, at Shaw's request, the long-discarded concept of two-way football.
Shaw was the oldest head coach to win an NFL championship for over 39 years, until Dick Vermeil's victory with the St. Louis Rams in Super Bowl XXXIV in early 2000.
After retiring from coaching, Shaw returned to California to work for a paper products company, and spent the later years of his life in Menlo Park.
SCU '32), former players, friends, and fans of Shaw banded together to form the Bronco Bench Foundation to raise money for and build a football stadium on the Santa Clara University campus in his honor.