Bullpens don't usually work that way. They usually regress if you don't make major changes. And actually, the easiest way to improve a team is to improve the bullpen at the top. Add a better closer, everybody moves down a slot in their roles and you've improved upon each role. But this team's pen regressed last season, mainly due to the closer, and it normally means it will continue to regress without changes.
As for Williams and other posters who bring up his first 4 seasons here, I throw those away. This is the first year he was handed money to work with. So comparing to other seasons when anyone without red-colored glasses on knew they were not going to be good, is apples and oranges. That said, this year doesn't look good and it's not because of changes he made to the offense(it will come around if season continues) it's lack of change to the bullpen.