I think his stats will probably go up or at least stay the same.
There has been quite a few freshman in the Big 12 recently that have had great numbers and I think the college game is evolving to fit the style of play that a lot of freshman have. I mean, Beasley is breaking records that people like Wayman Tisdale set decades ago. Augustin, Durant, Rush, Ford, Stinson, a whole bunch of guys who were freshman that were really good. You can definitely make the case that the game is more open than ever to players coming in and smashing records.
For example Beasley as a junior averaged 20.1 ppg, 10.4 rpg and 4.0 bpg. So far this year he is averaging 25.7 ppg, and 12.6 rpg. His block numbers are down from high school.
Eikmeier as a junior averaged 25.9 ppg, and 5.5 apg. Since I don't know his rpg we can't extrapolate that number, but if his scoring increases just like Beasley's then he will average about 33.1 ppg for us next year if he doesn't redshirt.
I struggled a bit with why Beasley's numbers would go up like that in the Big 12 but Beverly from Arkansas had his numbers go down but there was a couple of reasons that I could think of.
First off the Big 12 is not the SEC and if you look at Beverly's stats that becomes pretty clear. Beverly is playing powerhouses like LSU all the time. In four career games against LSU Beverly has only had 14, 9, 9, and 17 points. That average of 12.25 points is almost 25 points off of his high school numbers. If Beasley had to play LSU you would expect him to score only about 6 or 7 points based on Beverly's performance, so it is safe to assume that Wes would also struggle against SEC teams.
The other reason is probably that there are a lot of new coaches in the Big 12 who are anxious to get their own players playing. Pretty much only Scott Drew, Bill self, and Rick Barnes have been there for any amount of time. McDermott is one of the longer tenured coaches after only 1.75 years. I didn't bother to check but since the SEC has been around a lot longer I bet their coaches have been too, so they probably have a bunch of established players and they play favorites/don't play the freshman as much. Because McDermott has had a lot of players leave, especially guards, I would bet Eikmeier will put up great numbers.
Hope this look at the Big 12 and SEC helped you out with what to realistically expect from Eikmeier his first year.