Born in Ilkeston, Derbyshire, Baker was originally a miner and played for various clubs in Derbyshire as an amateur, including Eastwood Rangers. During World War I he guested for Chesterfield, Crystal Palace and Huddersfield Town, although these appearances are not considered official. In 1919 he turned professional and signed for Arsenal; according to club legend, Arsenal manager Leslie Knighton signed Baker after meeting him at the pit where he worked, thus beating rivals for the player's signature who were waiting at his home. He made his debut for Arsenal against Newcastle United on 13 August 1919. Baker played seventeen matches that season, but in 1920-21 he became a first-team regular; he also had trials for England, though it would be another seven years before he won a cap. A Utility player, "Doughy" played in every position for Arsenal, including as an emergency goalkeeper on several occasions, though usually played as right half. He was made club captain in 1924. In the 1924-25 season, Buchan won two Football League representative caps and also played in the Charity Shield, which was a Professionals v.Amateurs match; the Professionals won 3–1. However, when new manager Herbert Chapman arrived at the end of that season, he made Charlie Buchancaptain instead of Baker; Baker continued to play for Arsenal for another five years, though. In 1927, Baker played in Arsenal's first ever FA Cup final; however Arsenal suffered an infamous 1–0 loss to Cardiff City after a mistake by Arsenal goalkeeper Dan Lewis. The following season, he was finally capped for England, appearing against Wales on 28 November 1927; England lost 2–1. It was his only international appearance. Baker finally won a major medal when he played in Arsenal's 1930 FA Cup final win over Huddersfield Town; by now he had nearly reached the end of his career. He played only one more game for the club before retiring from the game aged 33 in the summer of 1931. In all, he played 351 matches for Arsenal, scoring 26 goals.
Personal life
His brother Jim Baker was also a footballer who played for Leeds United. Baker later worked for Arsenal as a scout. He died in 1955, at the age of 56.