A 6 ft 2 in (1.88 m), 172-pound right-hander, he appeared in 67 major league games, 37 as a starter, and ended his career with an 11–22 win–loss record and a 5.02 earned run average (ERA).

[1] Graham began his professional baseball career in 1923 with the Little Rock Travelers of the Southern Association, appearing in 51 games and compiling a 13–15 record and a 4.37 ERA.

[3] After his release by the Braves, Graham spent the next three years from 1927 to 1929 playing for the Seattle Indians in the Pacific Coast League.

[2] Late in the 1929 season, Graham returned briefly to the major leagues, appearing in 13 games for the Detroit Tigers.

[1] Graham concluded his playing career in 1930 with the Toronto Maple Leafs in the International League, compiling a 9–4 record with a 4.50 ERA.