Hesketh graduated from Frontier High School before matriculating at the State University of New York at Buffalo where he finished his 25 starts with 10 complete games (UB record) and an overall ERA of 1.77 (0.91 his junior year). After being named the 1980 ECAC New York-New Jersey District Player of the Year, he was drafted by the Montreal Expos and pursued every kid’s dream of playing in the major leagues. 

He was picked up by the Montreal Expos (1984) after being named the American Association Pitcher of the Year with a 12-3 record and a 3.05 ERA while dressing for the Indianapolis team. Joe made the big club in 1985, and made an immediate impact. For most of the summer, it appeared Hesketh would battle Cincinnati’s Tom Browning for National League Rookie of the Year honors with his 10-5 record and a sparkling 2.49 ERA. But, in late August, a home-plate collision with Dodger catcher Mike Scioscia broke Hesketh’s leg and ended his season.

Hesketh never regained the level of excellence he achieved in 1985, and after several discouraging and injury plagued seasons, it seemed that he was headed towards retirement. But in 1991, the Boston Red Sox picked him up, and he rewarded them with a 12-4 record and a 3.29 ERA. Because of his resilience, the Sox fans honored Hesketh with the Tenth Player Award which marked only the second time in eighteen seasons that a pitcher was chosen.