Moriarty was born in Chicago, where he grew up near the . He made his major league debut on September 7, 1903 at the age of 19 with the Cubs. He was an average hitter but an outstanding baserunner, with 20 or more stolen bases in eight consecutive seasons and 248 career stolen bases, including eleven steals of home. He played his last major league game on May 4, 1916 with the White Sox.

Afterward, he became an American League umpire from 1917 to 1940, interrupted only by a 2-year stint as manager of the Tigers in 1927-28. He was one of the AL's most highly regarded umpires in his era, working in the 1921, 1925, 1930, 1933 & 1935 World Series (as crew chief in 1930 & 1935), as well as the second All-Star Game in 1934.

On Memorial Day in 1932, Moriarty worked behind the plate for a Cleveland Indians home game against the White Sox. When several Chicago players took exception to his calls, he challenged them to settle the dispute under the stands of League Park after the game. Pitcher Milt Gaston took him on first but Moriarty knocked him flat, breaking his hand. Several White Sox, including manager Lew Fonseca and catcher and future AL umpire Charlie Berry, took him on in turn. The next day, AL president Will Harridge issued numerous fines and a 10-day suspension for Gaston.

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