Baker was a keen cricketer, and as a right-handed batsman, he played for Haileybury College nine times between 1912 and 1914, and twice for Hertfordshire in the Minor Counties Championship in August 1914. Between 1925 and 1932 he made thirteen appearances for the Royal Air Force cricket team, eight at first-class level, and served as Team Captain between 1928 and 1930. He was also a member of the RAF hockey team in 1927.