$18M seems high to me also. For Bauer, I see one year out of five with an ERA under 4. Keuchel had 4 out of 6 under 4 with 3 under 3 and he didn't get his money in free agency. Granted, Bauer is younger and throws harder, but a replication of his one good year is no certainty. It would make an interesting arbitration case. I suspect the figures will be further apart than typical.
As an aside, I have no idea how the Reds feel about him. His stuff is good, but does DJ believe he can work with him? Bauer looked to me as if he would get ahead of hitters and then experiment with secondary pitches. It made for high pitch counts and walks. I've heard that he has a multitude of different pitches. I wish he would concentrate on his best three, but it is not clear he thinks that way.