In 1977, after being named the Most Valuable College Player (he went 14–0 for the University of South Carolina), he was drafted 12th overall by the Cubs.

This 6 ft 4 in (1.93 m), 210 pound pitcher saw moderate success in the minors before making his Major League debut on September 6, 1980 at the age of 24 and wearing #34.

In his first game, he pitched six innings, giving up five walks and five hits for the loss.

On January 25, 1983, Martz was traded with Scott Fletcher, Pat Tabler and Dick Tidrow to the White Sox for Steve Trout and Warren Brusstar.

In 1991, he became the head coach at Lewis and Clark Community College until his retirement at the end of the 2021 season.