After backing up starting quarterback Phil Bradley during his entire sophomore season in 1978, he grew discontented and looked to transfer.
[2] Jeffrey called Baylor head coach Grant Teaff and was told he would have to earn the starting job, but he transferred anyway.
He then beat out the other quarterbacks to earn the starting job for the 1980 season and guided the Bears to a Southwest Conference championship with a 10–1 record.
The Crimson Tide, led by Hall of Fame coach Bear Bryant, won the game 30 to 2, however, and Baylor ended their season with a 10–2 overall record.
[2] Jeffrey graduated from school in the spring of 1982 and followed former Baylor football assistant John O'Hara to Southwest Texas State University.
[2] Jay Jeffrey, his older brother Neal, and his father James are all inductees into the Baylor Athletic Hall of Fame.