By Andrew Mooney, Boston.com Correspondent

It’s hard to know where the problems with this year’s Celtics begin and end. Defense has been lacking, the new acquisitions are underperforming, and above it all hangs the specter of age, gradually taking its toll on the tired legs of Paul Pierce and Kevin Garnett. Over a third of the way through the season, the Celtics sit below .500, and if they hope to turn things around, they need to identify the sources of their problems now.

A good place to start the evaluation is with their personnel. There is a simple way to measure player value that looks beyond traditional box score statistics: taking the difference between how a team performs with a player on the court and off the court, or plus-minus.

Of itself, this is somewhat of a crude metric, as it doesn’t factor in game situation or who else is on the court. That’s where adjusted plus-minus—the best holistic measure of NBA player performance that advanced stats has to offer—comes in. APM accounts for teammate and opponent strength, as well as the pace at which a team and its opponents play. It’s not meant to be applied to individual games and is most accurate over the course of two or three years, but over the span of a season, APM can give a reasonable estimate of what people want to measure most of all: who helps a team win and lose games, encompassing offense, defense, and even intangibles. (For a more complete discussion of APM, its calculation, and its flaws, click here.)

Jeremias Engelmann compiles and regularizes these numbers for every team in the NBA, and I’ve listed the data for the 2012-13 Celtics below, limiting it to those players who have played 20 percent of the team’s total minutes. For the purposes of interpretation, each number signifies the amount of points per 100 possessions a player adds or takes away relative to a league-average player (APM = 0).

The names at the top are no surprise—one doesn’t need an advanced metric to tell you Kevin Garnett, Rajon Rondo, and Paul Pierce are the Celtics’ three best players. What’s interesting, though, is just how much better Garnett has been than the rest of his team; the gap between him and second-place Rondo is larger than the difference between fourth-place Courtney Lee and tenth-place Leandro Barbosa.

Garnett ranks seventh in the league in APM, above All-NBA types like Kobe Bryant, Russell Westbrook, and Carmelo Anthony. His contributions have come mostly on the defensive end, which becomes apparent every time he’s on the bench; the Celtics have allowed 12 more points per 100 possessions with KG off the court than on it.

The performance of his supporting cast has been…underwhelming. Jeff Green and Brandon Bass, both thought to be potentially key contributors before the season, have been among the least valuable players on the roster.

Things may improve with the return of Avery Bradley, but not sufficiently for the Celtics to make a serious playoff push unless the rest of the team shows quick and drastic improvement. Granted, it was through about this many games last year that people were proclaiming a premature end to the current era of Celtics basketball. We’ll see if this team is capable of a similar late-season turnaround.