Born in Louth, Lincolnshire, England, Savage played for Stewton F.C. and Lincoln before he was bought by Reds manager George Patterson in May 1931, he made his debut on 26 September 1931 in a First Division match at Anfield, Grimsby were the visitors and were comfortablely beaten by 4 goals to 0, the game couldn"t have gone any better for Savage as he scored twice in the 66th and 82nd minutes, as did the great Gordon Hodgson, 26th and 85th. Robert was able to get the chance to score the goals as he was played in the forward line instead of his usual position of wing-half. Ironically the two strikes against Grimsby were the only goals he would score during his time at Liverpool, in fact Savage struggled to hold down a starting role for the Anfield club, his best seasons in a red shirt were the 35/1934 and the following campaign of 35/36 when he played in 54 of the 84 matches, 27 in each season, Robert was mainly used as a "bit part" player during other campaigns, although this was very much the case he put together 105 appearances, 100 of which were in the league.
Savage"s final Liverpool outing came in a league game at Molineux on 16 October 1936 with Wolves running out 2-0 winners.
He went on to become a journeyman playing for Wrexham in North Wales, Carlisle in Cumbria, West Ham, Chelsea and Fulham in London, all this travelling added to spells in Lincolnshire, Merseyside and Lancashire
He also played for Millwall and York (add Yorkshire to the list) as a wartime guest. Liverpool (1931–1938) - 105 appearances, 2 goals.