Dorgan was born in Middletown, Connecticut in 1853. His parents were Cornelius Dorgan and Mary Dorgan, both of whom were immigrants from Ireland. His younger brother, Jerry Dorgan, also played Major League Baseball.
Dorgan made his major league debut in May 1877 with the St. Louis Brown Stockings of the National League. He appeared in 60 games for St. Louis, 50 of them as an outfielder, and compiled a.308 batting average with nine doubles, seven triples, and 23 RBIs.
Syracuse
Dorgan returned to the Syracuse Stars for the 1878 and 1879 seasons. In 1879, the Stars joined the National League and attained major league status. Dorgan appeared in 59 games for the Stars in 1879, playing in the outfield and at first base, third base, shortstop, catcher, pitcher, and second base. He compiled a.267 batting average with 11 doubles, five triples, a home run, and 17 RBIs. Dorgan also served as the team's manager in 1879, leading the team to a 17-26 record.
Providence
In 1880, Dorgan played for the Providence Grays of the National League. He appeared in 79 games, 77 as an outfielder, and compiled a.246 batting average with 10 doubles, a triple and 31 RBIs. Dorgan was also the manager of the 1880 Providence team, compiling a 26-12 record.
Worcester and Detroit
In 1881, Dorgan played for the Worcester Ruby Legs and Detroit Wolverines, both of the National League. In 59 games with the two teams, 27 at first base and 28 in the outfield, Dorgan compiled a.272 batting average with six doubles and 23 RBIs. He was the manager of the Worcester club for a portion of the 1881 season, leading the Ruby Legs to a 24-32 record.
In 1883, Dorgan joined the New York Giants and spent the next five years there. He appeared in 425 games with the Giants, over 400 of them as an outfielder. In his five seasons with the Giants, Dorgan compiled a.281 batting average with 255 runs scored, 68 doubles, 21 triples, three home runs, 234 RBIs and 31 stolen bases.
Return to Syracuse
Dorgan concluded his major league playing career in 1890 with the Syracuse Stars, then part of the American Association. Dorgan appeared in 33 games, all as an outfielder, and compiled a.216 batting average. He appeared in his last major league game on June 9, 1890, at age 36.
Later years
After retiring from baseball, Dorgan owned and ran a cafe and worked as a bartender for a number of years. Dorgan was married to Jennie Dorgan, and they had two sons, William and Harry, and a daughter, Mary. At the time of the 1900 United States Census, and also the 1905 New York Census, Dorgan was living in Syracuse, New York with his wife, Jennie, and three children and was employed as a "barkeeper." Dorgan later moved to Hartford, Connecticut, where he worked for the American Bridge Company. In February 1909, Dorgan underwent an operation on his knee to repair an old baseball injury. He developed blood poisoning and died at St. Francis Hospital in Hartford, Connecticut six weeks after the operation. Dorgan was age 55 when he died. He was buried at St. Agnes Cemetery in Syracuse, New York. Dorgan was posthumously inducted into the Syracuse Hall of Famein 1999.
