I've done a lot of work on transfer players and there is an equivalence adjustment. Depending on the conference moving from and the conference moving to, there is a clear and distinct trend line.
Hitters see a more distinct reduction (which you'd expect as pitching increases).
ACC & SEC see similar results, though the SEC is clearly the toughest league.
Big 12 is a clear tier lower.
Sun Belt, Mountain West, C-USA, MVC, Big-10, American are next tier.
The further down you go, the more adjustment needed. You've seen multiple players who are POY types in their conference, who come up to SEC etc. and are total busts (Treyson Hughes types) and then transfer back down.
The type of hitter they are also impacts what to expect from them. Power over hit types tend to see biggest reductions (think Derek Williams type) will see real reductions on average.
OBP types tend to translate that skill pretty well, but not if they're HBP driven rather than zone awareness driven (again a Derek Williams knock).
If you K a lot at lower levels, you tend to hit even less.
Hitters with physical size, who control the barrel, and have rotational athleticism are the cluster type that's seen the most success moving up in my dataset.
Ogden is coming up from a low level without a ton of physical traits. You should expect a large drop in his numbers from his last level. Derek Williams should really see a large drop from his last stop. Hudson has size and rotational athleticism, I'd expect him to translate pretty well (90% or so). Marsh should be 90% as well.
I'm speaking in averages, of course, the data doesn't correlate at 1 (straight line), you will see some above, some below.
Transfer hitters also tend to start slowly at their new teams. A hypothesis is transition and adjustment takes some time, but that hasn't been tested in any way by me.
For pitchers, it's varied. The biggest key actually tends to be simply getting on the field. The SEC takes a ton of physical projection types and then sorts it out after a year. Just because a pitcher was on an SEC team doesn't actually portend success at the next stop. In fact, if they didn't even get an appearance at their last stop they probably aren't good and the team just cut bait. 0 IP pitchers tend to also be pretty meh at their next stops.
What you're looking for with arms is their stuff and underlying metrics. Also, poise and competitiveness on swing counts. Guys who throw 100 but throw a bunch of non-competitive pitches on 3-2 counts will tend to play down.
In my view, Miami did an excellent job of identifying pitchers to take and bring in. On the hitting side, I felt like they undervalued athleticism and looseness in their swings in favor of strength-based swings.
Add to it they took a bunch of strength-based swings and asked them to move positions and you've got a recipe for a lot of slow starts.