Probably a good time to look at the actual results since 2005 when the rules became the current rules
FR = freshmen
SO = sophomore
JR = junior
SE = senoir
FO = foreign/D League
2006
Picks 1-10 1 FR, 3 SO, 1 JR, 3 SE, 2 FO
Picks 11-20 1 FR, 1 SO, 3 JR, 3 SE, 2 FO
Picks 21-30 0 FR, 3 SO, 3 JR, 2 SE, 2 FO
2nd round 0 FR, 1 SO, 7 JR, 12 SE, 10 FO
2007
Picks 1-10 5 FR, 0 SO, 4 JR, 0 SE, 1 FO
Picks 11-20 2 FR, 2 SO, 3 JR, 2 SE, 1 FO
Picks 21-30 1 FR, 1 SO, 1 JR, 4 SE, 3 FO
2nd round 0 FR, 2 SO, 6 JR, 14 SE, 8 FO
2008
Picks 1-10 5 FR, 3 SO, 1 JR, 0 SE, 1 FO
Picks 11-20 3 FR, 3 SO, 1 JR, 2 SE, 1 FO
Picks 21-30 2 FR, 2 SO, 1 JR, 3 SE, 2 FO
2nd round 1 FR, 1 SO, 6 JR, 14 SE, 8 FO
2009
Picks 1-10 2 FR, 3 SO, 3 JR, 0 SE, 2 FO
Picks 11-20 1 FR, 3 SO, 3 JR, 3 SE, 0 FO
Picks 21-30 1 FR, 0 SO, 2 JR, 3 SE, 4 FO
2nd round 0 FR, 3 SO, 5 JR, 15 SE, 7 FO
2010
Picks 1-10 3 FR, 4 SO, 3 JR, 0 SE, 0 FO
Picks 11-20 3 FR, 2 SO, 4 JR, 0 SE, 1 FO
Picks 21-30 1 FR, 2 SO, 2 JR, 5 SE, 0 FO
2nd round 3 FR, 4 SO, 5 JR, 12 SE, 6 FO
2011
Picks 1-10 4 FR, 1 SO, 1 JR, 1 SE, 3 FO
Picks 11-20 1 FR, 2 SO, 6 JR, 0 SE, 1 FO
Picks 21-30 1 FR, 1 SO, 1 JR, 6 SE, 1 FO
2nd round 1 FR, 3 SO, 6 JR, 12 SE, 8 FO
2012
Picks 1-10 5 FR, 3 SO, 1 JR, 1 SE, 0 FO
Picks 11-20 1 FR, 5 SO, 1 JR, 2 SE, 1 FO
Picks 21-30 2 FR, 3 SO, 3 JR, 2 SE, 0 FO
2nd round 1 FR, 2 SO, 2 JR, 17 SE, 8 FO
2013
Picks 1-10 3 FR, 5 SO, 1 JR, 1 SE, 0 FO
Picks 11-20 2 FR, 2 SO, 2 JR, 0 SE, 4 FO
Picks 21-30 1 FR, 0 SO, 4 JR, 2 SE, 3 FO
2nd round 2 FR, 1 SO, 5 JR, 15 SE, 7 FO
TOTALS
Picks 1-10 28 FR, 22 SO, 15 JR, 6 SE, 9 FO
Picks 11-20 14 FR, 20 SO, 23 JR, 12 SE, 11 FO
Picks 21-30 9 FR, 12 SO, 17 JR, 27 SE, 15 FO
2nd round 8 FR, 17 SO, 42 JR, 111 SE, 62 FO
PERCENTAGE OF PLAYER CHOSEN IN EACH ROUND
Picks 1-10 35% FR, 27.5% SO, 18.75% JR, 7.5% SE, 11.25% FO
Picks 11-20 17.5% FR, 25% SO, 28.75% JR, 15% SE, 13.75% FO
Picks 21-30 11.25% FR, 15% SO, 21.25% JR, 33.75% SE, 18.75% FO
2nd round 3.33% FR, 7.08% SO, 17.5% JR, 46.25% SE, 25.83% FO
PERCENTAGE OF CLASS CHOSEN PER POSITION
Picks 1-10 47.45%% FR, 30.99% SO, 15.46% JR, 3.84 SE, 9.27% FO
Picks 11-20 23.72% FR, 28.17% SO, 23.71% JR, 7.69% SE, 11.34% FO
Picks 21-30 15.25% FR, 16.9% SO, 17.52% JR, 17.31% SE, 15.46% FO
2nd round 13.56% FR, 23.94% SO, 43.3% JR, 71.15% SE, 63.97% FO
So interpret the results as you wish but I think a few things are very clear.
- Freshmen are most likely, 71+% of the time, to be chosen in the first 20 picks.
- Sophomores tend to be distributed most evenly throughout the draft in relation to where they are chosen
- Senoirs and Foreign/D-League players are most likely to be chosen in the 2nd round by far.
- The numbers reflect what the OP suggested might be the truth regarding as you get older the chances are you are probably being picked later.