I also want to address a few points that have been made:
As I expected, a lot of people have come in this thread reiterating the same old usage argument. These posts all follow the same formula where the poster says that if the Big 3 take more shots they'll be less efficient for reasons x, y, and z without even attempting to address the stats I have brought up in the original post which show that the usage argument is bogus.
To use a slightly different example than the Big 3, look at BBD:
Glen Davis (last 3 years):
FGA TS%
5.9 .502
5.2 .500
10.2 .504
Glen Davis essentially doubled his number of shots over the course of one year and his TS% went UP. Further, when he decreased shots the previous 2 years his TS% went DOWN. This is more evidence that the number of shots one takes isn't strongly correlated efficiency. Partially or slightly correlated? Sure, maybe. Strongly? Not at all.
The bottom line is this: the Big 3 could definitely take a lot more shots without their efficiency dropping significantly, and they should do so.
The usage argument is a load of junk. It really, really is. If the correlation exists, it's very weak. And nobody has given me stats that prove otherwise, and until they do, I'm not inclined to agree with their position. Yet it's so very hard for people to let go of the usage argument because it's so-called "common sense". It sounds logical. GM's, coaches, players, the media, and most fans all believe it.
But there is just mounting evidence showing it's just. not. true. What it boils down to is this: good players can almost always get "their" shots. They can get to their spots on the floor and get what they want offensively due to the rules the NBA has on defense. Efficient shooters tend to be efficient shooters regardless of the number of shots they take. And if you really don't want to believe this, don't take my word for it. Go scour the TS% history of dozens of players like I have and see what you find. You might be surprised at what you see.
I honestly don't know much about these stats, but this just doesn't work for me.
First, pointing out one example of a player whose shots have increased, but whose role as a non-primary scorer has not changed tells us nothing.
I am not sure about the details of specific usage stats, but from a simple, logical breakdown of basketball strategy, for "usage" to have an effect on a players shooting percentage, it would have to change enough that it changes the type of shots they take.
Your example of Big Baby doesn't work, because even though he is taking 5 more shots a game, they are still just as wide open as they were a year ago, and they are still from generally the same spots on the floor. His "usage" has not reached the tipping point where the defenses treat him as a primary threat.
For stars who are seen as primary threats by defenses, such as the Big 3, their usage is relatively low, simply because they are a primary threat, which means defenses key on them, and make it harder for them to get "their" shots. They could increase their usage, but since they have crossed that tipping point where the defenses are keying on them, then the majority of the extra shots will be lower percentage.
Basically, this is just not a linear thing, which makes it so difficult to argue with stats on. Every change that is made is countered and confounded by the other team, as well as who else is on the floor.