Here's the example of the guy I looked into 21 year old signings. He'll hit his 2nd ST this season, so you should have a clue of where's he's going from his first ST line. Add in a few points here and there from the day of signing till his 1st ST line and you can come to the conclussion that:
http://whatifsports.com/HBD/Pages/Popups/PlayerProfile.aspx?pid=4233458
signed for $26.5 mil (way too much, but it was late and there was no where else to put it after missing out on 2 younger, better looking prospects), should improve about 5-6 points overall, 2-3 points in vL, control, and all his pitches (if that) and 6+ points in vR, stamina, and health. From my $18 mil IFA scouting bugets notes on the guy, they had his Control and velocity much higher than where they'll end up at, his vR a little higher, and everything else appears to be pretty much in line. He looked then, and does today as a solid back of the rotation type guy or ideally a Long A reliever.
Use past history as a guideline for your guy, but don't expect too much.