It’s almost universally accepted among NBA stat geeks that players become less efficient as they use up a larger share of their team’s possessions hunting for shots. The very best players can remain efficient while sucking up 25 or 30 percent of possessions, but even they begin to fall off beyond that. Ask role players to take on that kind of burden, and their shooting percentages and other efficiency stats will come crashing down.

The debate mostly centers around the search for the proper balance on each team, and whether there is value in simply having guys who can create shot attempts — even if a few of those attempts each night are blatantly bad. Math in a vacuum suggests teams would be better off shifting possessions from heavy-usage players to low-usage players who have been monstrously efficient in their rare chances; this is the “get the ball to Tyson Chandler more often!” argument. Studies of actual basketball suggest that asking Chandler to do more would result in more bad stuff from him — turnovers, offensive fouls, misses, and air-balled mid-rangers like the one he launched last week in San Antonio. Having a ball hog like Carmelo Anthony — playing less like a ball hog this season — might actually have value, as he allows teammates to find their happy medium on offense.

The dream is to find the right balance, and there is no easy statistical formula for that. Roster context matters, and we haven’t even talked defense. For every example of a team’s offense sinking without a ball-dominant star (Hi, Pacers!), we could probably find another offense thriving without one (Sorry, Amar’e.)

The evidence is all over the place. With Thanksgiving upon us, let’s take a moment, though, to give thanks to some occasionally unpopular shot-chuckers who might have more value than their detractors think.

Danny Granger

Granger hasn’t exactly been unpopular with Indiana fans, but he makes a ton of money, and a segment of Pacer Nation has been tinkering with the trade machine for at least a year to find a way to dump Granger, bring back a big man, and shift Paul George to small forward.

Now Granger is gone, and the Pacers’ offense is a complete mess. Roy Hibbert can’t hit anything, Paul George has floundered under a heavier burden, and the Pacers have morphed from a low-turnover team into one throwing the ball all over the place.

Pinning all of this on Granger being gone is too much, obviously; his absence cannot explain Hibbert’s puzzling inability to hit a short hook shot (a nice performance against Washington on Monday notwithstanding). And Granger, despite still being a heavy-usage player last season, had begun shifting away from on-ball creation to more spot-up looks.

But he was still a high-usage guy whom opponents had to respect from long range. He soaked up a lot of shot attempts and tossed nice entry passes to Hibbert — something with which the Pacers have struggled at times this season. Hibbert and George are getting a significantly higher percentage of their baskets via the unassisted route this season, per Hoopdata, and suffering for it.

Again: It’s not all Granger; he isn’t an elite passer or shooter for his position. But opponents don’t give Gerald Green or Lance Stephenson the same respect, cramping the floor, and that probably has a trickle-down effect on Indy’s offense. The turnovers are especially interesting; the Pacers are a great offensive rebounding team, and you can’t rebound a turnover. There is probably a measurable value in simply attempting a shot for a team like Indiana.

Monta Ellis

Golden State’s offense is 23rd in points per possession, even after a hot streak over the team’s last few games. Stephen Curry, one of the best shooters alive, needed a breakout game against Dallas on Monday to crack 40 percent from the floor. Looking at Klay Thompson’s numbers will turn you to stone. David Lee is shooting 44 percent.

Is it possible Golden State misses Ellis, allegedly one of the league’s most irresponsible chuckers?

Maybe. Ellis has probably always been a bit underrated as an offensive player. His shooting percentages have rarely veered into Antoine Walker/Allen Iverson territory, he generates a decent number of foul shots, he doesn’t turn over the ball much, and he’s a very good passer. Ellis has always generated a higher-than-expected number of assists that lead to shots right at the rim, and data-tracking cameras installed in 13 NBA arenas (including Golden State and Milwaukee) have consistently found that Ellis’s teammates shoot a shockingly high percentage off passes from Ellis.

That said, Curry (in a limited sample size) generally shot a bit better and played about as efficiently with Ellis on the bench, per NBA.com. Milwaukee is hoping Brandon Jennings’s shooting will tick up now that he can split the creative burden with Ellis. That didn’t happen last season in a very limited sample, but it is happening so far this season in an even more limited sample; Jennings is 8-of-25 from the floor without Monta and an almost-decent 49-of-112 (44 percent) with Monta.

But this is where we get to defense. Ellis’s defensive fundamentals are awful, and his teams have hemorrhaged points whenever he has been on the floor. That has continued in Milwaukee. It may be that Ellis is a more valuable offensive player than we thought, but is such a poor defender as to nullify that value.

Carlos Boozer

Is there a more hated player among any team’s fan base right now than Boozer? Do they let fans bring “Amnesty Boozer!” signs into Chicago’s arena?

Boozer probably falls into the Ellis category — underrated offensively, but so bad defensively, with the slow feet, fruitless reaching, and annoying screaming/pointing routine, as to outweigh whatever value he has offensively.

But I’d posit this: Eliminate Boozer, and this Chicago offense, without Derrick Rose and totally bereft of 3-point shooting, would rank among the half-dozen worst in the league. (The Bulls were 18th in points per possession entering Wednesday’s action.) The versatility of the Joakim Noah/Boozer combination is now the foundation of Chicago’s offense, and Boozer’s mid-range shooting and underrated passing help Chicago manufacture spacing on an otherwise tight floor.

Of course, Boozer is struggling early without Rose to absorb possessions as a no. 1 option; he’s shooting 44 percent and has scored in single digits in four of Chicago’s first 10 games. Given his defense, Boozer’s value nearly disappears when he plays like this. He struggled in the postseason without Rose, especially with turnovers, and it could be that he just isn’t up to working as a pseudo-lead option as he gets older.

Roster context is everything: With Rose back to run things, does Chicago need Boozer’s offense and spacing? That’s unclear. The Taj Gibson/Noah frontcourt thrived on both sides of the floor in about 330 minutes last season — about half of which came with Rose — but the Bulls have scored at a rate below their so-so overall average with those two together this season. Can they score enough to win a title with that starting front line? Nikola Mirotic might help, but he has to prove himself in the NBA.

Al Jefferson

A fascinating case of searching for balance. Utah last season sported a great offense and a porous defense, mirroring the game of its highest-paid player. Utah’s defense was off-the-charts better when Jefferson sat, but the bench-heavy units that held opponents down scored at laughably low rates; low-usage players such as Derrick Favors, Earl Watson, Enes Kanter, and others were stretched too far.

But Jefferson’s post game is literally the hub of Utah’s offense. He shoots a decent percentage and never turns over the ball, and many of Utah’s pet sets involve sending cutters around Jefferson post-ups on the left side.

What would happen to Utah’s offense if the Jazz let him walk in free agency this summer, re-signed Paul Millsap as their new hub, and built around a Favors-Millsap starting front line? Millsap has generally performed quite well without Jefferson, per NBA.com, but would that hold up? What if Gordon Hayward or Alec Burks, the latter on the fringes of Ty Corbin’s rotation, made a leap? What if Favors developed a more controlled post game?

For now, Corbin is working with what he has, and that means mixing and matching his big men — including starting all three of Millsap, Favors, and Jefferson in recent games — to find the ideal two-way synergy.

Andrea Bargnani

Bargnani may have surpassed Boozer in the unpopularity contest. He’s shooting 37 percent, his free throws have dropped off, and he has somehow regressed on the boards and as a help defender. The cries to dump Bargnani get louder with each late-game Toronto collapse, the latest of which featured Jrue Holiday blowing by Bargnani on a switch and hitting Jason Richardson for a clutch 3.

But the Raptors scored at a bottom-three rate without Bargnani last season, and a big man with legit 3-point range that can be deployed at high volumes is enormously valuable simply for floor spacing.

Which brings us back to context and defense. Bargnani’s a liability on the latter front, outside of some decent one-on-one post defense, and the context is changing in Toronto. Kyle Lowry is a borderline All-Star who can penetrate the defense, and DeMar DeRozan, flashing an improved post game, can at least tread water as a no. 1 option in Lowry’s injury-related absence. Jonas Valanciunas will get better down low. Bargnani’s contract is amnesty-eligible, and he has two years left after this one at a relatively affordable price.

Jordan Crawford

The owner of perhaps the league’s most egregious shot selection, Crawford ranked 18th in usage rate last season — above Granger, Jefferson, Blake Griffin, and Dwight Howard, among others — despite a career 39 percent mark from the floor. Washington’s league-worst offense has been no better this season with Crawford on the court, and its slightly less miserable offense last season improved by only a small margin when he played.

But watch this guy, and you come away thinking there has to be a use for him in the NBA. He can beat almost anyone off the dribble and can make incredibly difficult shots. Randy Wittman is trying to make it work, inserting Crawford into the starting lineup last week and turning over much of the point guard duties to him; Crawford has responded by blowing away his career assist numbers and showing a nifty passing game.

Can any team ever coax the proper balance out of him? And can he defend? The Wiz were much worse defensively with him on the floor last season, and they’ve been a bit worse — about three points per 100 possessions — so far this season.

Byron Mullens

Mullens isn’t a huge usage guy, but he’s become a lightning rod thanks to his 5.4 3-point chucks per 36 minutes, nonexistent free throw attempts, and wildly inconsistent defense and rebounding. But the numbers, at least on the surface, suggest Charlotte fans might miss Mullens when he’s gone. The Kitties have scored 102 points per 100 possessions when Mullens plays and just 92.7 when he sits; the first mark is about a point higher than league average, while the second would rank only above the Wizards.

Mullens had a similar impact last season, lifting Charlotte’s offense from the nether regions of NBA history to a level that would still have ranked dead last, but was at least within sight of no. 29. Again: Bigs who can shoot have value.

But does Mullens? Or are these numbers simply the product of his inept and/or inexperienced replacements?

Lou Williams

It’s baffling how many fans think Williams, no. 20 in usage rate last season, is a remorseless ballhog — a misconception that stems in part from Doug Collins designating Williams as Philly’s main crunch-time option. Williams averaged 4.7 assists per 36 minutes last season, about the same as Holiday (4.8), and he’s a underrated passer who gets to the line almost at will and hits a decent percentage from deep.

The Sixers’ offense scored nearly five more points per 100 possessions when Williams played last season, and the team ranks a putrid 26th in that category overall this season, with Williams in Atlanta and Andre Iguodala in Denver. Holiday is leading the league in turnovers as he assumes full creative responsibility, a small price to pay in an experiment that has generally been a success — at least on the individual level. The return of Andrew Bynum would obviously change everything, but Philly could use a secondary ball handler.

Two Gunners It’s OK to Hate Without Regret

Nick Young

Young is averaging 1.9 assists per 36 minutes, up from 1.2 last season, and he has dished four assists in two separate games over the last 10 days. That’s good, right? Young has now assisted on 9.5 percent of Philly’s buckets while on the floor this season, an assist rate that (wait for it) would have ranked 87th among the 98 guards who logged at least 1,000 minutes last season. He has never shot 45 percent in any season, doesn’t get to the line much, rebounds like a fearful point guard, and is a neutral presence defensively — on a good night.

Young has two usable NBA skills: the size to credibly play both wing positions, and an ability to sprint with glee to the corners in transition and knock down 3s off the catch. That skill swung Game 1 of the Clippers’ first-round series over Memphis last season, but those games are rare.

Michael Beasley

He’s trying. Beasley has 31 assists already this season after dishing just 45 all of last year, and he has recorded at least seven assists in two games — something he did just three times before landing in Phoenix. But he’s shooting just 36 percent while gunning nearly 18 shots per 36 minutes — on pace to be the second-highest mark of his career. Beasley’s foul shots are down a bit, and his attention to detail on defense — both on the ball and on the weak side — waxes and wanes; Alvin Gentry has benched Beasley in favor of the relatively unknown P.J. Tucker down the stretch a few times this season.

Be Careful What You Wish For

Pau Gasol

Gasol doesn’t fit this category at all, but it’d be remiss to overlook the puzzling determination among a segment of Laker fans to deal one of the league’s great all-around players. That’s not to say there are no grounds for trading Gasol. As I’ve written before, he’s a center the Lakers have had to shoehorn into a power forward role over the last two seasons, a makeshift setup that (along with shaky perimeter shooting at other positions) cramps the Lakers’ spacing; there’s a reason the Lakers almost always closed games with Lamar Odom and just one of the Gasol/Bynum duo, back when Odom was actually an NBA player. With three $1 players already onboard, it might make sense to deal Gasol for two 65-cent players who bring shooting and fit Mike D’Antoni’s offense. (Let’s ignore that one of those $1 players is recovering from back surgery, and another is almost 39 and dealing with a broken leg.)

But the “trade Gasol” fervor has masked — in some corners of Laker Land — what a brilliant player Gasol is. And though Kobe Bryant has backed Gasol publicly, his habit of chastising Gasol for alleged passivity, including after Bryant shot the Lakers out of Game 4 against the Thunder last season, has emboldened that fervor.

The Lakers’ offense has remained pretty efficient overall because Gasol is the rare 7-footer with the versatility to make the awkward setup work. He can hit 18-footers consistently, though he needs space and time to load up. He may be the world’s best passing big, though his brother is giving him a run in Memphis. He is unselfish and team-oriented despite a prodigious individual skill set. And though he’s an uneven defender, at times badly overextended as a power forward, he works hard at it and has the right instincts.

Want to deal this guy? Fine. Understand that it might not work out as well as you’d hope. Gasol is 32, due $19 million this year and $19.3 million next season; the other 29 teams appreciate Gasol, but not many are stoked about taking on that contract, even though it will become an expiring deal before you know it. The Lakers’ ceiling may be higher without him, given the right package, but take a minute to appreciate Gasol’s game while you can.