Shooting stars

Finding out the NBA's most -- and least -- efficient shooters

While Tracy McGrady and Kobe Bryant are busy making it a two-horse race for the title of the league's most prolific scorer, another question remains unanswered: Who is the league's most efficient scorer? In other words, who gets the most out of his shot attempts?

At first, one might look to field-goal percentage to answer this question. Shaquille O'Neal is running away with the league lead at 55.9 percent. So does that settle it? Not exactly.

For one thing, the top 10 in field-goal percentage consist entirely of forwards and centers. There are no guards because they're the ones taking all the 3-point shots, which are lower percentage but worth an extra point. Shooting 38 percent on those, for instance, is better than as Shaq shooting 55.9 percent on lay-ups and dunks.

For another, there are free throws. Shaq spends huge chunks of the game at the line, where he hits just 61 percent of his tries. Perhaps a player with a lower field-goal percentage but a more respectable mark from the line is actually more effeicient.

To settle this, I created a stat called points per shot attempt, or PSA. To compute it, take free-throw attempts and multiply by 0.44, then add field-goal attempts. Take the player's points and divide by that number, and you're done:

PSA = Points / (FGA + (FTA *0.44))

(Why multiply by 0.44? Because one free throw attempt is equivalent to 0.44 field goal attempts. It would be 0.5 exactly if every foul resulted in two shots, but one-shot fouls after made baskets, technical fouls and lane violations bring the number down.)

So enough with the numbers already. Who are the best?

Here's this year's top 10 in PSA:

The top 10
Points per shot attempt, minimum 500 minutes
Player  Team  PPG  FG%  FT%  PSA 
Eduardo Najera  Dal  7.3  61.7  .720  1.323  
Andrei Kirilenko  Uta  12.2  51.1  .811  1.281  
Reggie Miller  Ind  13.7  45.0  .883  1.266  
Eric Piatkowski  LAC  9.5  48.4  .828  1.230  
P.J. Brown  NO  10.5  53.8  .866  1.230  
Doug Christie  Sac  10.4  48.4  .814  1.222  
Jake Voskuhl  Pho  3.5  55.2  .692  1.216  
Brad Miller  Ind  14.2  51.1  .824  1.212  
Tony Battie  Bos  7.6  55.7  .763  1.203  
Yao Ming  Hou  13.5  51.8  .798  1.196  
Dallas' Eduardo Najera, a decent shooter who nonetheless mostly accepts dunks and layups from Steve Nash and Nick Van Exel, has been the most efficient scorer in the league. Of course, he only averages seven points a game because he's such an afterthought in the Mavericks' offense.

In fact, most of the players on the list above are third options or worse for their teams. While all of them have been fantastic when they get opportunities, none is among the game's elite scorers. As a result, let's modify the top 10 list a bit by restricting it to players who are averaging 15 or more points per game:

Top 10 major scorers
Points per shot attempt, players averaging 15 points or more
Player  Team  PPG  FG%  FT%  PSA 
Shaquille O'Neal  LAL  25.9  55.9  61.0  1.195 
Matt Harpring  Uta  18.4  50.6  79.7  1.184 
Bobby Jackson  Sac  18.0  49.2  85.4  1.180 
Peja Stojakovic  Sac  18.9  46.9  84.8  1.179 
Pau Gasol  Mem  18.1  50.6  73.5  1.168 
Dirk Nowitzki  Dal  23.6  46.8  85.9  1.165 
Steve Nash  Dal  17.9  45.9  91.3  1.157 
Wally Szczerbiak  Min  16.5  47.2  85.3  1.145 
Shareef Abdur-Rahim  Atl  19.9  46.7  82.9  1.140 
Corey Maggette  LAC  16.4  44.7  77.7  1.137 
O'Neal, despite his awful free-throw shooting, is still the most efficient scorer among the league's prominent offensive weapons. In fact, he has a fairly sizable lead over the next closest player, Utah's Matt Harpring, despite a sore toe that's bothered Shaq all season. The only other 20-point scorer to crack the top 10 is Dallas' Dirk Nowitzki, whose 46.8 field-goal percentage isn't that remarkable until you consider all the 3-pointers he's taken.

Looking closer at the last two charts, Dallas' three international N's: Najera (Mexico), Nowitzki (Germany), and Nash (Canada), go a long way toward explaining why the Mavs have such a deadly offense. The two featured players, Nash and Nowitzki, are in the top seven in the league in PSA among players averaging 15 or more; meanwhile, Najera easily has the highest PSA in the league. Shawn Bradley just missed being in the top 10 as well.

But enough about the good guys. I know what you're thinking already: What about the worst guys? I won't disappoint you. Here's the NBA's bottom ten in PSA among players who have played at least 500 minutes:

The bottom 10
Points per shot attempt, minimum 500 minutes
Player  Team  PPG  FG%  FT%  PSA 
DeSagana Diop  Cle  1.4  34.3  39.1  0.712 
Jeff Foster  Ind  1.9  33.3  52.4  0.747 
Junior Harrington  Den  5.0  34.9  56.7  0.767 
Bimbo Coles  Cle  4.9  28.6  79.4  0.769 
Nikoloz Tskitishvili  Den  3.5  29.2  72.9  0.773 
Pat Burke  Orl  4.0  35.9  75.0  0.798 
Damon Stoudamire  Por  5.2  32.7  69.0  0.813 
Juaquin Hawkins  Hou  2.7  37.3  66.7  0.833 
Trenton Hassell  Chi  4.6  37.8  69.0  0.849 
Jeryl Sasser  Orl  2.8  33.1  73.2  0.858 
If DeSagana Diop is about to shoot it, there's a good chance somebody on the bench is yelling "Nooooooooo!!!" Cleveland's lottery bust is managing the difficult feat of shooting below 40 percent from both the field and the foul line, leading to a ghastly 0.712 PSA. Diop isn't the only Cav on the list either; teammate Bimbo Coles is fourth from the bottom at .769.

The Nuggets are on pace to be the worst offense in NBA history, so it's no surprise that they also placed two players in the bottom five. Rookie point guard Junior Harrington has struggled from the field and the line en route to the third-worst mark. But the guy who might have the most to worry about is rookie forward Nikoloz Tskitishvili. An alleged shooter, his putrid 29.2 percentage has raised eyebrows among Nuggets fans wondering why he was picked ahead of Amare Stoudemire.

Yet the bottom list is a bit disappointing as well, because it's made up of players that we already knew couldn't play. What we really want to find out is who, among the NBA's prominent scorers, isn't cashing in enough of their shots? To answer that, I limited the following list to players averaging 10 or more points per game:

Please stop shooting
Lowest points per shot attempt, players averaging 10 or more points
Player  Team  PPG  FG%  FT%  PSA 
Michael Olowokandi  LAC  12.3  42.7  65.7  0.923 
Malik Allen  Mia  10.4  43.8  73.7  0.926 
Dajuan Wagner  Cle  14.0  37.0  80.0  0.952 
Antoine Walker  Bos  20.9  39.1  61.9  0.959 
Morris Peterson  Tor  14.8  38.8  78.8  0.968 
Caron Butler  Mia  14.1  39.4  82.2  0.974 
James Posey  Hou  10.6  38.0  82.2  0.974 
Antonio Davis  Tor  14.3  40.9  74.0  0.975 
Vince Carter  Tor  18.2  42.8  76.2  0.981 
Cliff Robinson  Det  12.6  40.7  65.2  0.981 
As we can see, the Clippers' strategy of feeding the ball to Michael Olowokandi is highly questionable when one considers his low-impact shooting (not to mention all the turnovers, but that's a story for another day).

Two more surprising names on the list are Antoine Walker and Vince Carter. Walker has been just as erratic as ever from the field this year (a career-low 39 percent), and has also hurt himself with a free-throw mark that has plummetted to 61.9. Carter, meanwhile, has compounded his low-percentage shooting by making himself a rare visitor to the free-throw line. He takes nearly six field-goal attempts for every free throw, clobbering his PSA in the process.

Overall, PSA is superior tool to field-goal percentage because it also takes in 3-point shooting and free-throw success. While accurate shooters shouldn't necessarily be featured scorers -- I don't imagine the Mavs are drawing up plays for Najera right now -- it does reflect which players make the most of their scoring chances.