Rumford was born and grew up in Perth, Western Australia. He started playing golf at age ten, quickly showing a natural hand–eye coordination which translated to a well-respected short game. He represented Australia in amateur golf (teamed with future PGA Tour players Aaron Baddeley and Brendan Jones along with Kim Felton) and was a member of the elite AIS golf program. He has always been known for his quiet personality and tremendous work ethic, which has helped him bounce back from 'flat' parts of his career. In 1999, Rumford won the PGA Tour of Australasia's ANZ Players Championship as an amateur, and he turned professional the following year. He has been a member of the European Tour since 2001, and has won three European Tour events, the 2003 Aa St Omer Open, the 2004 Irish Open and the 2007 Omega European Masters. His best year-end ranking on the Order of Merit has been 37th in 2004. Rumford played on the PGA Tour in 2008, after earning his card through qualifying school, finishing the season ranked 149th in the FedEx Cup standings. He returned to play on the European Tour in 2009.