Newport, Monmouthshire born centre half Albert Groves began his football career as a forward with Welsh League Aberdare Athletic in 1908 and played in their Welsh League triumph of 1908-09, scoring 22 goals for them. This bought him to the attention of Second Division Wolverhampton Wanderers, who signed him in August 1909, with Groves making his Football League debut against Manchester City in April 1910. He played for Wolves both sides of the First World War, during which he served in the Armed Forces and guested for Port Vale and Bury, and for the Sunbeam Works team.
At the end of the War Groves returned to Molineux and was a regular performer during their first peacetime season of 1919-20, scoring a hat-trick playing as an emergency centre forward in a 4-0 win over Nottingham Forest in November 1919, but he lost his place in January 1920 after scoring 20 goals in 217 appearances for Wolves. He was then appointed player-manager at Birmingham League outfit Walsall in May 1920, before he was replaced by Joe Burchell in August 1921, but he stayed on as a player at Walsall and played 36 times in their inaugural Football League season of 1921-22, including being part of the line up that went to Lincoln City for their inaugural League match in August 1921.
In total he scored 16 times in 89 appearances while Walsall were a senior club (i.e. not including Birmingham League), before a serious knee injury suffered at Southport in February 1924 forced him to retire from professional football that summer. Already aged 38, Groves played for Birmingham & District League club Willenhall thereafter.
He was the older brother of George Groves, who played for Newport County both sides of the War, and (despite the different surname) was the father of Welsh international Billy Lucas, who played for Swindon Town, Swansea Town and Newport County both sides of the Second World War.