Barrow was born in Springfield, Illinois, the oldest of four children, all male, born to Effie Ann Vinson-Heller and John Barrow. Barrow's father fought in the Ohio Volunteer Militia during the American Civil War. Following the war, Barrow's parents, with John's mother, brothers, and sisters, traveled in a covered wagon to Nebraska; Barrow was born on a hemp plantation belonging to relatives during the trip. The Barrows lived in Nebraska for six years before moving to Des Moines, Iowa.

Barrow returned to baseball in 1910, managing Montreal. The Eastern League hired Barrow as its president the next year, giving him an annual salary of $7,500 ($196,982 in current dollar terms). He served in this role from 1911 through 1917, and engineered the name change to "International League" before the 1912 season. As league president, he contended with the creation of the Federal League in 1914, which competed as a major league, and established franchises in International League cities, including Newark, New Jersey, Buffalo, New York, and Baltimore, Maryland. He attempted to gain major league status for the league in 1914, but was unsuccessful. When the Federal League collapsed, Barrow was the only league president to forbid the outlaw players from playing in his league.  After the 1917 season, Barrow attempted to organize the "Union League", to compete against the AL and NL as a third major league, by merging four International League clubs with four teams from the American Association. Several International League owners opposed Barrow's policies, including his attempt to form the Union League, and felt he was too close personally to Ban Johnson. When the league's owners voted to cut his pay to $2,500 after the 1917 season ($47,753 in current dollar terms), Barrow resigned.  Barrow became manager of the Boston Red Sox in 1918. As the team lost many of its better players during World War I, Barrow encouraged owner Harry Frazee to purchase Stuffy McInnis, Wally Schang, Bullet Joe Bush, and Amos Strunk from the Philadelphia Athletics for $75,000 ($1,220,243 in current dollar terms). During the season, Barrow feuded with his assistant, Johnny Evers, who undermined Barrow's leadership. The Red Sox won the 1918 World Series. Recognizing that star pitcher Babe Ruth was also a great power hitter, Barrow had Ruth pinch hit on days when he wasn't scheduled to pitch. When Ruth told Barrow that he could only pitch or hit, Barrow decided that Ruth's bat was more useful than his pitching, and transitioned him from a pitcher into an outfielder.  After the 1918 season, Frazee, now in debt, began selling the contracts of star players. He traded Dutch Leonard, Duffy Lewis, and Ernie Shore to the New York Yankees, obtaining Ray Caldwell, Slim Love, Frank Gilhooley, Roxy Walters, and cash. Frazee sold Carl Mays to the Yankees during the 1919 season. The Red Sox struggled in 1919, finishing sixth in the AL. Frazee sold Ruth to the Yankees after the season, against Barrow's warnings. The Red Sox finished in fifth in 1920.

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