[1] A left hander listed as 6 feet (1.8 m) tall and 180 pounds (82 kg), Shaw was born in Pittsburgh but graduated from Grover Cleveland High School in Reseda, California, in Los Angeles' San Fernando Valley.

After two seasons in New York's farm system, Shaw made the 1967 Mets' roster out of spring training and spent his entire rookie campaign with them, working in 40 games, all in relief, and posting a 4–5 record and three saves, with a 2.98 earned run average.

Shaw struggled in the ninth inning, allowing a walk and three hits, including a three-run, pinch-hit home run by Duffy Dyer, but he departed with Montreal still ahead 11–10.

[2] With Shaw making 35 appearances, the 1969 Expos would go on to lose 110 games in 1969 and finish last in their division; the "Miracle Mets" would stun baseball by winning the National League pennant and 1969 World Series.

Shaw started the 1970 season in Triple-A, and his contract was sold to the Cardinals in mid-May; he got into only 14 games all year due to a broken hand[1] and didn't return to MLB until April 1971, when he was recalled from Tulsa and added to the St. Louis bullpen corps.