Tiant was signed in 1959 for $150 a month, and for the next three years he divided his time between the Tigers and the Havana Sugar Kings in the International League.

But with the rise of Fidel Castro's regime in his native Cuba—specifically, after heightened tensions following the U.S.-sponsored Bay of Pigs invasion in April of that year—it was impossible for Tiant to return home.

"[1] After pitching to a 15–1 record at Triple-A Portland, which included a no-hitter and a one-hitter in consecutive starts, Tiant was called up by the Indians in mid-July 1964.

In 1968, Tiant had one of the greatest pitching seasons in major league history, leading the American League in ERA (1.60), shutouts (nine, including four consecutive), hits per nine innings (a still-standing franchise record 5.30, which broke Herb Score's 5.85 in 1956 and would be a Major-League record until surpassed by Nolan Ryan's 5.26 in 1972), and strikeouts per nine innings (9.22), while finishing with a 21–9 mark.

Tiant began the process of reinventing himself as a pitcher by altering his delivery so that he turned away from home plate during his motion, in effect creating a hesitation pitch.

[5] Twisting and turning his body into unthinkable positions, Tiant would spend more time looking at second base than he did the plate as he prepared to throw.

He would win 20 games in 1973, and 22 in an All-Star 1974 en route to becoming known as El Tiante at Fenway Park, one of the greatest and most beloved pitchers in Red Sox history and an enduring idol in Boston.

[6] Though hampered by back problems in 1975, he won 18 games for the American League Champion Red Sox, then excelled in the postseason.

His father and mother were in Fenway Park that game to watch their son defeat the Reds 6–0 in a five-hit shutout,[7] having been allowed to visit from Cuba under a special visa.

He also appeared in 21 games (all starts) for the Pirates' Triple-A Portland Beavers of the Pacific Coast League, posting a 13–7 record with 3.82 ERA.

Tiant competed in the Venezuelan Professional Baseball League in parts of seven seasons spanning 1963–1982, while compiling a record of 37–24 including 29 complete games, a 2.27 ERA,[11] and a no-hitter in 1971.

[13] Tiant competed in the Senior Professional Baseball Association in 1989, initially signing with the Winter Haven Super Sox.

[14] He was subsequently traded to the Gold Coast Suns, in exchange for outfielder Ralph Garr and 500 Teddy Ruxpin toy bears (for use as a fan giveaway item).

In 2002, Tiant was the pitching coach for Boston's Class A Short Season affiliate, the Lowell Spinners, and has continued to serve as a special assignment instructor for the Red Sox.

[15] Tiant, along with former batterymate Carlton Fisk, threw out the ceremonial first pitch before what proved to be the Red Sox' championship-winning Game 6 of the 2013 World Series at Fenway Park.

Sam Malone (Ted Danson) agrees to do a television beer commercial, co-starring with and "relieving" Tiant when the latter begins to fail in his promotion of the product.