Walsall, Staffordshire born right back Edwin “Teddy” Groves began his football career with Talbot Stead Tube Works in 1920 and joined newly admitted Third Division (North) club Walsall in March 1922, making his Football League debut at Crewe Alexandra in April at right back, his only appearance of his debut season. After a further appearance at right half that September, he came into the team at centre forward on a regular basis in December 1922, scoring 13 goals in 22 appearances before the season end, finishing the season as Walsall’s leading goalscorer.
He continued in the centre forward role during 1923-24, bagging another 13 goals in the campaign and again finishing at the top of Walsall’s goalscoring charts, but after a variety of roles in 1924-25 he settled in at right back during 1925-26, missing only two matches as Walsall struggled to a 21st place finish. He missed only 8 more matches in the following three seasons but eventually lost his first team place in February 1930, playing only twice more before leaving Walsall at the end of the season to join Birmingham & District League club Shrewsbury Town in July 1930 after 27 goals in 257 appearances for The Saddlers. He had three seasons at Gay Meadow before joining Wellington Town in 1933 before his eventual retirement later the same year.