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Heading into this season, many thought that the Lakers would cruise through the western conference, but this has simply not been the case. After beginning the season 8-0, the Lakers have struggled against several of the lowliest teams in the NBA, including most recently the then 9-46 Cleveland Cavaliers, and have just two total wins against the top seven teams in the league.
A trade involving Anthony going to the Lakers would almost certainly involve Los Angeles trading away their young center Andrew Bynum. While Bynum has played very well at times when healthy, he is one of the most injury prone players in the league. In fact, Bynum, who skipped college, missed significant time due to injury during his junior and senior years of highschool.
The problem is that, while Bynum may be prone to getting hurt, and does not put up the offensive numbers that Anthony consistently produces, the Lakers' losing Bynum would significantly hurt their defense.
Without Anthony, the Lakers have a respectable defense that is old, but that consists of two seven footers, as well as great defenders Kobe Bryant and Ron Artest.
A Laker team with Anthony instead of Bynum would have probably the best offense in the NBA, but one of the weaker defenses, as Anthony is not one of the most active or conscientious defenders in the league. The Lakers and Phil Jackson want to win a championship this season, and they know that defense wins championships, so losing Bynum and acquiring Anthony would likely hurt their chances of three-peating.