Just looking at the Fangraphs Royals' starters page.
Francis has 2 WAR, with a 4.65 ERA and a 3.84 FIP. It might be a good idea to see if he'll sign for next year. If not, trade him now.
Chen has 0.6 WAR, with a 3.30 ERA and a 4.48 FIP. Of course, he missed some time. Sign him up for next year, too. If he's unwilling, trade him now.
Luke has 0.5 WAR with a 5.29 ERA and a 4.91 FIP. He's had enough chances. Send him to the pen, and if that doesn't work either, DFA him.
DFA Davies tomorrow.
That leaves us with a rotation next year, assuming we don't keep any of these guys, of Paulino and Duffy. We're going to have to find three starting pitchers somewhere. Aaron Crow might be one of them. Mike Montgomery doesn't look like he's ready yet. Jake Odorizzi and Noel Arguelles need more experience.
MLB Trade Rumors says that Doug Fister and Kevin Slowey are available. What do you think it would cost to get them? Would it be worth it? How much would Edwin Jackson cost as a free agent?