Who are the biggest ball hogs in the NBA? And how do we figure out who they are?

In the past we've had to use things like shot attempts per game and assist rate to measure the degree to which a player hogs the ball.

If you don't have a lot of assists you must not be passing, the logic goes. And if you're taking a lot of shots, it inherently means you're not helping your teammates get shots.

But these stats are only tangentially related to the one thing that, by definition, makes a player a ball hog — he doesn't pass the ball.

To figure out the NBA's biggest ball hogs, we'd need raw data on which players pass the ball the least.

Now, thanks to the new camera tracking technology that the NBA installed in every arena, we have that data.

The NBA's awesome new stats site has data on touches per game and passes per game. To determine the league's biggest ball hogs, we came up with a simple formula called pass rate. It goes like this:

Pass rate = (Passes per game) / (Touches per game)

This is the percentage of time a player passes when he gets the ball. The higher the percentage, the more unselfish a player is. The lower the percentage, the more of a ball hog a player is.

Based on that formula, here are the 10 biggest ball hogs in the NBA (min. 20 minutes per game):

Brook Lopez (Brooklyn Nets): 47.7% pass rate Klay Thompson (Golden State Warriors): 49.4% pass rate Eric Gordon (New Orleans Pelicans): 50.8% pass rate Tony Wroten (Philadelphia 76ers): 52.6% pass rate C.J. Miles (Cleveland Cavaliers ): 54.6% pass rate Andrew Nicholson (Orlando Magic): 55.0% pass rate Maurice Harkless (Orlando Magic): 55.2% pass rate Kevin Durant (Oklahoma City Thunder): 55.4% pass rate Rudy Gay (Toronto Raptors): 55.8% pass rate Jamal Crawford (L.A. Clippers): 56.0% pass rate

The rest of the top 20 is as follows: Xavier Henry, Jodie Meeks, Dion Waiters, David Lee, Anthony Davis, Nick Young, Rodney Stuckey, James Harden, Corey Brewer.

Brook Lopez at No. 1! He's certainly not the type of player you think of when the words "ball hog" come to mind. But he gets a relatively low number of touches, and he almost never passes once he does get the ball in his hands. The average pass rate across the NBA is 70.1%, and Lopez is at 47.4%.

Eric Gordon strictly shoots. Chris Graythen/Getty Images When the ball goes into him in the post, more often than not it's not coming back out.

There are some obvious players on here as well (Jamal Crawford! Rudy Gay!). But the majority of these guys are scoring guards who play off the ball. They aren't primary ball handlers (so their touches are fairly low) but they take a ton of shots.

Eric Gordon is the ultimate example of this. He plays alongside Jrue Holiday — one of the most ball-dominant point guards in the league. So he essentially only gets the ball when he's in a position to shoot. By design, he's the terminal node in the offense.

Ditto for Kevin Durant, who is the rare elite scorer who actually doesn't get a ton of touches.

On the other end of the spectrum, here are the 10 most unselfish players in the league. They pass like crazy:

Pablo Prigioni (New York Knicks): 87.8% pass rate Shaun Livingston (Brooklyn Nets): 86.2% pass rate Josh McRoberts (Charlotte Bobcats): 85.1% pass rate Jose Calderon (Dallas Mavericks): 84.8% pass rate Shane Battier (Miami Heat): 84.3% pass rate Greivis Vasquez (Sacramento Kings): 82.7% pass rate Joakim Noah (Chicago Bulls): 82.6% pass rate Deron Williams (Brooklyn Nets): 82.4% pass rate John Henson (Milwaukee Bucks): 82.4% pass rate John Lucas III (Utah Jazz): 81.5% pass rate

These guys are broken into two groups: 1) point guards who play with volume shooters, and 2) ball-moving swing men. Noah is the only outlier, but a lot of Chicago's offense moves through him at the high post and gets a ton of touches for a center as a result.

The big lessons from all of this is that the degree to a player is a "ball hog" is often determined by his role within the offense. Klay Thompson might be a wonderful and willing passer, but within the Warriors offense his job is to stretch the floor knock down open shots created by Steph Curry.

Still, when you think "ball hog" you think Jamal Crawford. So it's pretty perfect that the stats back up what we all see with our eyes.