In November, the Royals sent outfielder David DeJesus to the Oakland A's in a deal that brought back pitcher Vin Mazzaro. So it's Mazzaro with three other right-handers, Luke Hochevar, Kyle Davies and Sean O'Sullivan, who figure to be in the rotation.
The fifth spot is wide open, with a host of young pitchers, including Aaron Crow, John Lamb and Danny Duffy, likely to get a good look.
The Greinke deal brought no immediate replacement, although Jake Odorizzi, 20, is billed as a future top-of-the-rotation type.
With Carl Pavano apparently heading back to the Twins, the thin free-agent market still includes Kevin Millwood, linked earlier with the Royals, and their top winner from last year, lefty Bruce Chen. Millwood's name doesn't stir much response from Moore.
What about Chen?
"We're still open-minded with that. He performed very well with us last year and he showed us what he had, and we've got a comfort level there," Moore said.
There's a new Zach -- right-hander Zach Miner has a Spring Training invitation -- but he won't be in the picture right away.
"Zach is coming off Tommy John surgery and we don't even expect him to be ready until about June some time," Moore said. "He filled a lot of roles in Detroit -- he started, pitched in the middle, did some late. He was pretty effective for a few years and was really one of their more consistent bullpen arms during their runs in that time frame. [Tigers manager] Jim Leyland had a lot of confidence in him in a variety of roles."
Pulling off a trade for a starting pitcher remains a possibility.
"It's something that we'll continue to look at, and it might be Spring Training or early next year," Moore said.
"You're always looking to get better, so it's not out of the question we might make some kind of move, and pitching is one of those areas where you can never have enough depth. And we don't want to be in a position where we're force-feeding some of those kids, either."
Moore isn't changing his stance on the catching situation, where Jason Kendall's shoulder surgery is likely to keep him out for a while.
"Right now, we'll probably go with what we have at this point. We expect Kendall back in the first half, probably later in the first half, so we're going to look at Brayan Pena and [Lucas] May and give them a good opportunity," Moore said.
The Greinke deal, which included shortstop Yuniesky Betancourt, brought the Royals a starting shortstop in Alcides Escobar.
"He's a very talented young shortstop with all the ability to be very successful. We control him for the next five years and we really like him," Moore said.
Also in the deal was a potential center fielder in Lorenzo Cain, although he ranks behind veteran Melky Cabrera at the moment.
"We're going to be open-minded to it, but we expect [Cain] to be on the team at some point next season. I'm not here to say it'll be right out of camp. We've got to wait and see," Moore said.
The fourth player who arrived, right-hander Jeremy Jeffress, is in the crowded bullpen picture.
"We want to improve the depth of our pitching staff as it pertains to starters, but we probably won't do much with the bullpen," Moore said.