Born in Warren, Ohio, Ames was a third or fourth starter for the New York Giants during their early period of dominance under John McGraw. He made his debut on September 14, 1903, pitching an abbreviated five-inning no-hitter against the Cardinals, but wasn't in the rotation full-time until 1905, when his 22 wins and 2.74 ERA helped the Giants to their first twentieth-century world championship. This was by far his best season, for although the Giants were perennial contenders during this time, injury and wildness kept him from becoming a star even though he was the Opening Day pitcher three years running. A career ERA of 2.63 ties him with Cy Young.
He pitched in three World Series with the Giants (1905, 1911, 1912), but because he was only a third or fourth starter in an era when top pitchers pitched more games than they do today he appeared almost entirely in relief in the fall classic, starting only once, the last game in 1911, which he lost decisively to the world champion Philadelphia Athletics. He was traded to the Reds in 1913, and never again approached his earlier success with the Giants.
Ames' greatest distinction was being one of the wildest pitchers in history with a curveball charitably described as "dramatic." Other of his notable accomplishments are leading the National League in saves with 6 in 1914 and 8 in 1916, and in strikeouts per 9 innings pitched in 1905 (6.78), 1906 (6.90) and 1907 (5.63).
On Opening Day, April 15, 1909, he achieved the unique feat of losing a no-hitter in a game in which he didn't give up a hit until the 10th inning or a run until the 13th, but still got credit for 9 no-hit innings.