Bossy scored a then record 53 goals as a rookie, won the Calder Trophy for rookie of the year, and was named a Second Team All-Star. Bossy and Wayne Gretzky are the only players to have scored 50 or more goals for nine consecutive seasons. Additionally, both are the only players ever to have scored 60 or more goals in as many as six seasons. Unlike Gretzky, however, who played 20 seasons, Bossy was healthy enough only for 10, of which only the first nine were full. During Bossy's final season, his bad back limited him to 63 games but he still managed 38 goals.

As he never played long enough for his skills to diminish, his scoring averages remain quite high. Bossy averaged .762 goals per game in the regular season, more than any other player in NHL history, and .659 in the playoffs, second only to Mario Lemieux at .710. Lemieux is second to Bossy in the regular season, at .754. Comparatively to other goal leaders, Gretzky scored .601 in the regular season and .587 in the playoffs; Brett Hull, .586 and .510; Phil Esposito, .559 and .469; Maurice Richard, .556 and .617; Bobby Hull, .547 and .521; Marcel Dionne, .542 and .429; Guy Lafleur, .497 and .453; Mike Gartner, .494 and .352. Many thus regard Bossy along with Lemieux (as well as Bobby Hull and Richard) as the best pure goal scorers ever to play the game. (It should be noted, however, that if Gretzky had retired after his first 10 years in the league, his numbers on a per game basis would have eclipsed all other players. Most of Gretzky's major records were all achieved before 1990, including his record as the only player ever to exceed 200 points in a single season, which he had done more than once).

In 1980-81, he scored 50 goals in 50 games, the first to do so since than the great Maurice Richard thirty-six years earlier. Richard was on hand to congratulate Bossy for achieving that milestone. Bossy was also known for being able to score goals in remarkable fashion, the most incredible, perhaps, in the 1982 Stanley Cup finals when, up-ended by a check and several feet in the air, parallel to the ice, Bossy nonetheless managed to hook the puck with his stick and score.

Bossy earned the Conn Smythe Trophy as playoff MVP in 1982, and scored 17 goals in three straight playoffs -- 1981, 1982, and 1983 -- the only player ever to do so. In reaching the Stanley Cup Finals five times, between 1980 and 1984, Bossy scored 69 goals. By contrast, in Gretzky's five Stanley Cup Finals playoffs during his peak years with the Edmonton Oilers, he scored 59 goals.

Bossy played on a line with Bryan Trottier and Clark Gillies. Bossy was noted for his clean play, almost never resorted to fighting, and won the Lady Byng Trophy for gentlemanly play three times: 1983, 1984, and 1986. Also notable about Bossy's game was his strong defensive play which enabled him to be on regular penalty-killing duty; this distinguished him from Gretzky and Mario Lemieux.

Bossy has haboured some animosity towards Gretzky and the Oilers, stating that the Islanders got little recognition for their dynasty (1980-1983) compared to the Montreal Canadiens (1976-1979) or Edmonton Oilers (1984-1990). The dominant scoring star of the late 1970s was Guy Lafleur but his skills waned in the 1980s. In 1982, Bossy set a scoring record for right-wingers with 147 points in 80 games (Jaromir Jagr would break it with 149 points in 1995-1996 season which was an 82 game schedule). Though Bossy also won the Stanley Cup and the Smythe Trophy, far more attention was given to Gretzky who not only won the Hart Trophy and Art Ross Trophy, but also shattered scoring records with an unheard of 212 points and 92 goals. Although the Islanders swept the Oilers in the 1983 final to win a fourth consecutive championship, Gretzky and his Oilers still recieved the most attention.

The Islanders made a fifth consecutive Stanley Cup final in 1984 but they were outmatched by the Oilers who defeated them 4 games to 1. Bossy had a playoff slump, scoring only 9 goals after 17 in the past three postseasons, which could not counter the Oilers' powerful offense. Afterwards, the Islanders would slowly decline, while injuries would take their toll on Bossy's back.

Bossy earned 5 First Team All-Star selections, one of only four right wings ever to do so, again a notable achievement considering that the other three had much longer careers (Gordie Howe - 26 years; Maurice Richard - 18 years; Guy Lafleur - 17 years). He was inducted into the Hockey Hall of Fame in 1991. His #22 jersey was retired by the Islanders on March 3, 1992.