He was a competitor in the Olympic Games as a middle-distance runner, both before and after the First World War, representing Great Britain in the 800 metres and 1500 metres at the 1912 Olympic Games in Stockholm. He reached the final of the 1500 metres, won by his fellow countryman Arnold Jackson. At the 1920 Summer Olympics in Antwerp Baker was captain of the British track team and carried the team's flag. He won his first race in the 800 metres, but then concentrated on the 1500 metres, taking the silver medal behind his teammate Albert Hill. He was captain again at the 1924 Summer Olympics in Paris, but did not compete.