Baker represented the Liberal Party of Australia in the electoral district of Waite, formerly Mitcham in the House of Assembly. Baker became Treasurer of South Australia in the Dean Brown Liberal government after the 1993 state election, but was deposed as deputy leader in favour of Graham Ingerson when John Olsen was successful in a November 1996 leadership coup. Baker announced his retirement two months before the 1997 state election, which some interpreted as an act of revenge.
Hailing from the moderate faction in his party, he won the seat of Mitcham at the 1982 state election from Democrat Member of Parliament Heather Southcott, the only single-member lower house seat anywhere in Australia to be held by a Democrat. The hastily conducted preselection resulted in a win for the conservative faction, whose candidate Martin Hamilton-Smith defeated moderate Robert Lawson, which prompted Brown to complain of interference by federal conservative MPs Nick Minchin, Grant Chapman and Andrew Southcott.
