As you can see, the Royals have been remarkably consistent over the 13 years. They have averaged a 26th place in ERA. That is clearly one of the worst, and probably the worst over that time period (the other usual suspects like the Orioles and Rockies have fluctuated enough that they're probably a bit better). The Royals, who are a pleasant surprise at 13-9 aren't hitting much (20th in runs, 12th in OPS) and while they have some good hitters, they're not going to hit their way to the playoffs.
How have they done it? They're 6th in starting ERA and 7th in bulllpen ERA, making for a balanced attack. Last year, they were 6th in bullpen ERA and 26th in starting ERA. The reason this might continue is that their starting rotation is almost completely different from last year.
In 2012, they got starts from Bruce Chen (34 starts), Luke Hochevar (32), Luis Mendoza (25), Jeremy Guthrie (14), Will Smith (16), Jonathan Sanchez (12) and a handful from a few others.
In 2013, they have a starting rotation of Ervin Santana, James Shields, Wade Davis, Jeremy Guthrie and Luis Mendoza. Chen and Hochevar were moved to the bullpen and are pitching very well (1 ER in 15 IP). They acquired Santana in a trade with Angels last October, with Shields and Davis coming from Tampa in a trade last December. No one is mistaking Santana for Justin Verlander, and while he underachieved the last few years, he won 17 games as recently as 2010.
The Royals are lucky to be in a division that will probably have only one other good team (Tigers). The Tigers came out of nowhere in 2006, the Orioles did in last year (although going 16-2 in extra inning games would be hard to replicate), and the Royals have a shot at the playoffs this year if the starters continue to pitch well.