The Facts
Let's start off with the positive: the Celtics defense is second in the league at at 99.9 defensive rating (that's points allowed per 100 possessions).
Now for the bad news: our offense is ranked 17th in the league with a 106.8 offensive rating (points scored per 100 possessions).
So what?
Well over the last 10 years there has only been a single team to win a championship with an offensive rating this bad: the Detroit Pistons. Needless to say, our offense could use improvement if we want to have a serious chance at winning it all.
Where's the problem?
Well, offensive rating is determined by offensive efficiency, so let's look at some True Shooting %'s.
.614 -Paul Pierce
.620 -Ray Allen
.568 -Kevin Garnett
.499 -Rajon Rondo
.504 -Glen Davis
As we can see, Rajon Rondo and Glen Davis are less efficient than the Big 3. Much, much less efficient. This in and of itself isn't such a bad thing... championship teams have occasionally employed offensively inept players throughout history. Take Ben Wallace for example on that Pistons team I mentioned earlier. It's not a big deal as long as they don't shoot that much and drag the team's efficiency down, right?
Well unfortunately, that's exactly where this team's problem is. On a per minute basis, Glen Davis takes about as many shots as each of the Big 3 (around 13 shots per 36 min.). Rondo takes only a couple of shots less. Yikes. For comparison, Ben Wallace shot only about 5 shots per 36 min. the year that Pistons team won a championship.
So what do we do?
Fortunately, the solution is simple. Doc needs to tell Rondo and Davis to shoot less, and tell the Big 3 to shoot more.
There's an objection to this that's sure to follow: the same old, tired, incorrect "usage" argument. The argument is as follows "The more shots a player takes, the more their efficiency will decrease." There's an appeal to the logic of it... that the more a single player takes shots, the more the opposing defense will collapse on them. Makes sense.
Unfortunately, the facts show us that this happens to be a myth. David Berri over at Wages of Wins did a statistical regression and found no measurable link between field goal attempts and efficiency, and reasoned that if there was a connection, the correlation was minimal at best. For example, some of Kobe's most efficient years were the 3 years he led the league in field goal attempts.
So Pierce, Allen, and KG should take more shots, as it is unlikely to affect their efficiency.
But let's take it a step further and assume that the usage argument is correct. After all, didn't Ray, Paul, and KG all have lower TS%'s before coming to Boston? Indeed they did, but this could more likely be attributed to their terrible teammates. It's pretty easy to double Kevin Garnett when there isn't another threat on his team (that sort of thing).
Sorry, I'll get back on track. Let's say that the lower TS%'s were 100%, purely, and solely because the usage argument is correct. Guess what? Ray, Paul, and KG would all still be significantly more efficient than Rondo and Davis TAKING DOUBLE THE AMOUNT OF SHOTS THEY CURRENTLY TAKE, EVEN IF THE USAGE THEORY IS ASSUMED TO BE TRUE. Look at their stats and you'll see that history proves this.
So in conclusion, even if you think efficiency is correlated with field goal attempts, Ray, Paul, and KG should all be taking more shots if we want our offense to improve.