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These are players who are with the team for training camp and preseason but have very little chance of making the final roster. For these guys, a chance to catch on in the D-League would be a good opportunity, because the chances of them catching on with the Lakers seems remote.
At 7'1" and 250 pounds, Aguilar obviously has the requisite size to play center in the NBA. The trouble is that at 25 years old, he's likely too old and too raw for the team to bank on his upside. With Sacre, the Lakers have a player who's younger and more talented, so if the Lakers were to keep a developmental center it would be Sacre. That leaves no room for Aguilar.
Douglas-Roberts has played in the NBA before. In fact, he'll likely play in the NBA again at some point. But with the depth on the Lakers and with younger, more promising players populating Douglas-Roberts' primary positions (shooting guard and small forward), it's hard to envision a scenario where he makes the team.
Nelson has plenty of talent. He showed that when he was named to the All-Pac-10 team following his sophomore season at UCLA. He's a powerful rebounder and a solid defender. But he doesn't have a guaranteed contract, he's never played in the NBA before and he's behind multiple players on the depth chart.
Given that he was dismissed from UCLA's team for off-the-court issues, he would be lucky to get a chance to prove himself in the D-League.
If you thought Aguilar had the size needed to play center in the NBA, then take a look at Greg Somogyi. At 7'3" and 242 pounds, he's an absolute beast. He's also two years younger than Aguilar, which should give him a greater chance of making the team.
The problem is that despite his incredible size, Somogyi simply doesn't produce at a level that's acceptable. As a senior at UC Santa Barbara last season, Somogyi averaged 11.8 minutes, 3.1 points, 3.3 rebounds, 1.6 blocks and shot 47.7 percent from the field. Those numbers simply don't equate to an NBA-ready player.
With his size and youth, Somogyi may be able to someday play in the NBA. But given his struggles to impact the game as a college senior, there's no way he could step into the NBA, especially on a team as talented as the Lakers.