Free Throw Deep Dives: Launch Angle

This is the first post in a planned series of deep dives into free throw shooting (and shooting in general). Using SportVU data, which tracks the position of the basketball 25 times per second in all three dimensions, and combining that with a simple physics model, I have built a database of some 250,000+ field goal attempts and 100,000+ free throws from the past three seasons of NBA play. From this database, I can create a variety of new statistics with which to assess shooting. These include:

• Release angle (vertical) - at what vertical angle the ball leaves the players hand (higher angle = more arc)
• Release angle (horizontal) - can tell you whether a shot was on target (e.g. wide left, wide right, or on target).
• Release velocity - how fast the ball is going upon release
• Release position  - where precisely on the court the player releases the ball. 
• Release height - how high the ball is when released by the player
• Approach velocity - how fast the ball is moving when it reaches the hoop
• Approach angle - At what angle, relative to horizontal, the ball approaches the hoop.
• Effective hoop area - A function of approach angle, it shows how big the hoop appears to the ball on approach
• Approach position - where the ball crosses the plane of the hoop (i.e. a PitchF/x view of shooting).

This initial post will focus largely on the first metric: vertical release angle.

The tradeoff all shooters make

From a purely geometric perspective, it would seem a shot with a higher release angle (and higher arc) would have a better chance of going in. Shots with high arc approach the hoop at a more direct angle, making the hoop appear larger. But shooting is as much about physics as it is about geometry, and a high release angle comes with a penalty: speed.

As release angle increases, more speed is needed in order for the ball to reach the hoop. And presumably, a greater release velocity will be harder for the shooter to control, and lead to less accurate shooting. In addition, a higher release velocity also leads to a higher approach velocity, which decreases the likelihood of a friendly bounce for a slightly off-target shot. The chart below illustrates how these tradeoffs play out for a typical 6'3 shooter.

"Effective hoop area" is a measure of how big the hoop appears, expressed as a percentage of the hoop's full surface area. Effective hoop area steadily increases with launch angle (illustrated to scale on the chart at five degree intervals). In contrast though, required launch velocity is minimized at about an angle of 50 degrees. Releasing the ball with a lesser angle has no advantages, as speed increases (bad) while effective hoop area decreases (also bad).

So far, this is all theoretical. Isaac Newton can tell us what the tradeoffs are between release angle and speed, but we need the SportVU data to tell us how NBA players balance those tradeoffs in practice.

The blue line in the chart below shows how release speed and hoop area relate to each other as you adjust launch angle. What emerges is an "efficient frontier" of sorts for free throw shooting. And we can now see where NBA shooters place themselves along that frontier, crafting their own risk/return balance in the process.

For 6'3 shooters (with a minimum of 75 attempts), median launch angle by player falls within a seven degree band, ranging from Goran Dragic's 51 degree line drives, to Beno Udrih's 58 degree rainbow-like arcs. The typical 6'3 shooter launches their shot at a 53 degree angle. Note that no player appears to aim for the velocity minimizing angle of 50 degrees. The geometry of the shooting "frontier" provides a potential clue why this is so:

On the chart, increasing launch angle is equivalent to traveling along the blue line. Imagine you are a shooter that has chosen a launch angle that minimizes release velocity. You would find yourself on the leftmost point of the shooting frontier, with a launch angle of 50 degrees and a launch velocity of 23.5 feet per second. But this point on the frontier is where the tradeoff between velocity and hoop area is at its most forgiving. Tilting your launch angle up from 50 degrees to 55 degrees gets you 9% more hoop area with just an 0.2 feet per second increase in required velocity. But those returns diminish as you move further along the frontier. That first incremental 9% of hoop area came cheap. The next 9% increase in area will cost you an additional 0.9 feet/second (a 450% inflation rate).

The geometry of the shooting frontier can help explain why players choose the launch angle they do, and why they don't choose to just minimize velocity. The typical shooter is willing to tilt their shot up a few degrees because the gains in hoop area appear to be worth the minimal loss in accuracy stemming from higher shot velocity.

Launch angle and accuracy

From the previous chart, note that Steph Curry, a 90% free throw shooter, is at the high end of the launch angle range (second only to Beno Udrih). Udrih is also an above average free throw shooter at 84%. Perhaps a high arc is the secret to good free throw shooting?

The chart below summarizes launch angle for all players with a minimum 75 attempts over the past three seasons. In addition, the top 20 shooters are shown as green dots and the bottom 20 shooters are shown as purple dots.

From this data, it does not appear that a high launch angle is the key to making your free throws. Two of the best shooters in the league, Kyle Korver and James Harden, have lower than average launch angles for players of their height. And Andre Drummond, the league's worst free throw shooter, has a very high release angle.

The Plumlee brothers, Miles and Mason, make for an interesting contrast. Same height, same parents, similar free throw percentage (bad), yet markedly different shooting mechanics. At 55.8 degrees, Miles has the highest release angle of 6'11 NBA players. His brother's median shot angle is nearly a full 10 degrees lower. Yet both brothers are poor free throw shooters, making just slightly more than half their attempts.

If you run a proper linear regression on free throw percentage, using player height and release angle as independent variables, it turns out that the coefficient for release angle is slightly negative. In other words, for a given height, players with a lower release angle tend to have slightly better results. This result is significant at the 1% level, but the overall effect is still relatively small. A reduction of one degree in release angle is associated with an 0.6% improvement in free throw percentage.

I think the main takeaway from the data is that shot angle, within a reasonable range, is a matter of shooter preference. You find good shooters and bad shooters at both ends of that range.

Does height matter?

Returning to the chart above, note that the poor free throw shooters (the purple dots) tend to be the taller players. What can our simple physics model tell us about the challenges taller players face when shooting free throws?

As it turns out, taller players have an advantage over shorter players when it comes to release velocity:

The chart above illustrates two shooting "frontiers", one for a 6'3 player and another for a 6'11 player. Generally speaking, the further left the frontier, the better off you are. It means you can achieve the same effective hoop area with a lower launch velocity. For example, a 6'11 player can achieve a 70% effective hoop area with a launch velocity of 22.9 ft/s. A 6'3 player would need a launch velocity of 23.6 ft/s to achieve that same 70%.

However, while taller players have a release velocity advantage, the shorter player holds the upper hand on a different shot metric: approach velocity. The faster the ball approaches the rim, the more likely it is to rattle out, so minimizing approach velocity should improve accuracy. The chart below illustrates the approach velocity shooting frontiers for 6'3 and 6'11 players.

Our shooting frontiers have swapped places. For a given effective hoop area, the shorter player's shot approaches the rim at a lower velocity, increasing the likelihood of a friendly bounce.

So there are pluses and minuses to being a tall free throw shooter, and it isn't clear to me which is more important: release velocity or approach velocity. I suspect the real reason taller players are poorer shooters has less to do with the physics and geometry, and more to do with the relative size of the talent pool at each height. There are only so many 7+ foot males between the ages of 20 and 40, and 17% of them play in the NBA. That percentage drops to 0.07% for males between 6'6 and 6'8. So, at typical NBA heights, you are getting literally the top 0.1% or better in terms of basketball skills. But for seven footers, you get the top ~15%, so it shouldn't be surprising to see a drop off in basketball "fundamentals".

Consistency matters

So if a high, arching shot isn't the hidden secret to good shooting, what is? I imagine it comes down to consistency. A consistent shot angle is likely developed over multiple years of practice, coaching, and deliberate adjustments. Minor tweaks to shooting form likely occur at a subconscious level, as the brain subtly re-calibrates after each make and miss, like a World War I artillery gunner. And eventually, muscle memory takes hold, and the act of shooting becomes as rote as climbing stairs or tying your shoelaces. Good shooters don't aim, they breathe through their eyelids, like the lava lizards of the Galapagos.

One way to quantify shot angle consistency is to look at the standard deviation of each player's attempts. If the standard deviation is low, that means the player does a better job of releasing the ball at a consistent launch angle. A high standard deviation is a likely indication of poor and inconsistent shooting form.

The scatter plot below shows how consistency, as measured by standard deviation, correlates with free throw success.

Here we see a clear correlation between accuracy and consistency. Memphis point guard Mario Chalmers leads the league in shot angle consistency, with a standard deviation of just 1.31 degrees. Utah's Trevor Booker and Oklahoma City's Steven Adams have the least consistent launch angle, which may explain their below average free throw percentages.

Curiously, Andre Drummond maintains a fairly consistent shot angle, yet still struggles to hit two out of every five foul shots. Andre's problems seem to stem from a lack of horizontal, rather than vertical, control.

Next Steps (plus a data dump)

In future posts, I plan to extend the framework I built here to other facets of free throw shooting (e.g. release height, horizontal launch angle, etc.). All of the data used in this post can be found in the table below. The table is sortable, searchable, and scrollable. Feel free to point out any interesting relationships you notice, either here in the comments, or on Twitter @inpredict.

player	height	FT%	launch angle	bench-mark	diff	stdev
Andre Drummond	83''	38.8%	55.5	50.9	4.7	1.86
Clint Capela	82''	41.4%	56.9	51.1	5.8	1.78
DeAndre Jordan	83''	41.5%	51.0	50.9	0.2	2.32
Ed Davis	82''	50.3%	47.8	51.1	-3.3	2.24
Josh Smith	81''	50.9%	49.2	51.5	-2.3	2.35
Ian Mahinmi	83''	51.6%	50.7	50.9	-0.2	2.05
Hassan Whiteside	84''	52.1%	52.5	50.6	1.9	2.25
Rajon Rondo	73''	53.0%	55.0	53.9	1.1	2.37
Dwight Howard	83''	53.2%	53.7	50.9	2.9	2.32
John Henson	83''	53.2%	53.1	50.9	2.2	2.17
JJ Hickson	81''	53.3%	52.3	51.5	0.8	2.25
Miles Plumlee	83''	54.1%	55.9	50.9	5.1	2.18
Steven Adams	84''	54.4%	50.1	50.6	-0.5	3.07
Kendrick Perkins	82''	54.5%	49.7	51.1	-1.5	2.09
Mason Plumlee	83''	55.6%	46.1	50.9	-4.7	1.89
Thomas Robinson	82''	55.6%	51.7	51.1	0.5	2.12
Nene Hilario	83''	57.1%	46.5	50.9	-4.4	1.69
Maurice Harkless	81''	57.3%	51.9	51.5	0.4	1.94
Nick Calathes	78''	57.4%	55.6	52.3	3.4	1.47
Elfrid Payton	76''	57.5%	52.9	52.8	0.1	2.01
Bismack Biyombo	81''	58.7%	47.6	51.5	-3.9	2.17
Nerlens Noel	83''	59.1%	49.9	50.9	-1.0	2.40
Jason Thompson	83''	59.8%	50.4	50.9	-0.5	1.82
Dante Cunningham	80''	60.0%	52.0	51.9	0.1	1.84
Rudy Gobert	85''	60.1%	54.1	50.4	3.7	2.00
Omer Asik	84''	60.5%	52.6	50.6	2.0	2.31
Donatas Motiejunas	84''	60.8%	52.0	50.6	1.4	1.80
Amir Johnson	81''	60.9%	52.5	51.5	1.0	2.30
Luc Mbah a Moute	80''	61.3%	55.8	51.9	3.8	1.61
Andre Iguodala	78''	61.3%	55.8	52.3	3.6	1.48
Trevor Booker	80''	62.3%	52.4	51.9	0.5	3.20
Terrence Jones	81''	62.3%	52.6	51.5	1.1	2.05
Jusuf Nurkic	83''	62.4%	51.3	50.9	0.4	2.66
DeJuan Blair	79''	62.6%	52.3	52.3	0.0	2.31
Tony Allen	76''	62.8%	49.2	52.8	-3.6	1.83
Draymond Green	79''	63.2%	51.5	52.3	-0.8	1.85
Jerami Grant	80''	63.3%	53.3	51.9	1.4	2.19
Kosta Koufos	84''	63.5%	46.3	50.6	-4.3	2.04
Tony Wroten	78''	64.3%	52.1	52.3	-0.1	1.78
Tristan Thompson	81''	65.0%	50.9	51.5	-0.6	2.38
JaKarr Sampson	81''	65.2%	50.1	51.5	-1.4	2.42
Lavoy Allen	81''	65.3%	49.3	51.5	-2.2	1.94
Kenneth Faried	80''	65.4%	53.7	51.9	1.8	1.90
Julius Randle	81''	65.7%	48.5	51.5	-3.0	2.13
Austin Rivers	76''	65.7%	54.7	52.8	1.9	1.74
Michael Kidd-Gilchrist	79''	65.8%	49.9	52.3	-2.4	2.13
Marcus Smart	76''	65.9%	53.5	52.8	0.7	1.86
Robert Sacre	84''	66.0%	50.0	50.6	-0.6	2.27
Joakim Noah	83''	66.0%	51.9	50.9	1.0	1.98
Thaddeus Young	80''	66.1%	51.4	51.9	-0.6	2.03
Udonis Haslem	80''	66.1%	54.2	51.9	2.2	2.22
Anthony Bennett	80''	66.4%	51.7	51.9	-0.3	1.96
J.R. Smith	78''	66.8%	54.0	52.3	1.7	1.77
Ish Smith	72''	66.9%	54.3	54.3	0.1	1.85
Tyson Chandler	85''	67.0%	49.5	50.4	-0.9	1.98
Al Jefferson	82''	67.1%	53.4	51.1	2.3	1.96
Derrick Favors	82''	67.3%	50.5	51.1	-0.7	2.35
Glen Davis	81''	67.5%	47.8	51.5	-3.7	1.80
Kent Bazemore	77''	67.9%	53.3	52.5	0.8	1.89
Tyler Hansbrough	81''	68.0%	55.8	51.5	4.3	1.86
Archie Goodwin	77''	68.5%	52.9	52.5	0.4	1.62
Lance Stephenson	77''	68.8%	51.1	52.5	-1.4	1.77
Michael Carter-Williams	78''	68.8%	55.1	52.3	2.8	2.39
Omri Casspi	81''	69.3%	56.3	51.5	4.8	1.79
Dion Waiters	76''	69.4%	55.6	52.8	2.8	1.84
Brandan Wright	82''	69.6%	55.8	51.1	4.6	2.01
Chris Andersen	82''	69.7%	46.9	51.1	-4.3	1.88
Marcin Gortat	83''	69.9%	49.5	50.9	-1.3	2.00
Alex Len	85''	69.9%	51.5	50.4	1.2	2.03
Jared Dudley	79''	70.0%	55.9	52.3	3.7	1.70
Al-Farouq Aminu	81''	70.0%	54.9	51.5	3.4	1.79
Hollis Thompson	80''	70.1%	52.0	51.9	0.1	1.89
Richard Jefferson	79''	70.2%	50.5	52.3	-1.8	2.09
Anderson Varejao	83''	70.3%	49.3	50.9	-1.5	1.78
Jordan Hill	82''	70.3%	49.5	51.1	-1.6	2.29
Jeff Withey	84''	70.5%	52.4	50.6	1.8	2.02
James Johnson	81''	70.6%	54.9	51.5	3.4	1.99
Carlos Boozer	81''	70.9%	56.4	51.5	4.9	1.62
Tiago Splitter	83''	71.0%	48.1	50.9	-2.7	2.14
Nick Collison	82''	71.0%	51.4	51.1	0.2	1.59
Greg Monroe	83''	71.0%	53.0	50.9	2.2	2.28
Chandler Parsons	81''	71.3%	50.5	51.5	-1.0	2.24
Harrison Barnes	80''	71.4%	50.7	51.9	-1.2	1.94
Jon Leuer	82''	71.4%	53.0	51.1	1.9	2.08
Luis Scola	81''	71.5%	52.8	51.5	1.3	1.74
Josh McRoberts	82''	71.5%	50.9	51.1	-0.2	1.77
Mirza Teletovic	81''	71.6%	51.7	51.5	0.2	2.08
Derrick Williams	80''	71.6%	52.4	51.9	0.5	1.93
Otto Porter	80''	71.7%	53.6	51.9	1.7	2.11
Alonzo Gee	78''	71.7%	53.6	52.3	1.4	1.64
Garrett Temple	78''	71.8%	53.1	52.3	0.8	1.98
Ray McCallum	75''	71.8%	53.0	53.2	-0.1	1.91
DeMarre Carroll	80''	71.9%	49.4	51.9	-2.5	1.87
Iman Shumpert	77''	71.9%	53.0	52.5	0.5	1.91
Taj Gibson	81''	72.5%	52.4	51.5	0.9	1.99
Blake Griffin	82''	72.5%	48.6	51.1	-2.6	1.90
Kelly Olynyk	84''	72.6%	51.6	50.6	1.0	2.12
Amar'e Stoudemire	82''	72.7%	53.8	51.1	2.7	1.98
Shabazz Muhammad	78''	73.0%	55.0	52.3	2.7	1.90
Corey Brewer	81''	73.0%	52.4	51.5	0.9	1.96
Pero Antic	83''	73.1%	49.8	50.9	-1.0	1.92
Giannis Antetokounmpo	83''	73.2%	52.2	50.9	1.3	2.21
Ersan Ilyasova	82''	73.3%	51.1	51.1	-0.1	1.89
Kyle O'Quinn	82''	73.3%	47.0	51.1	-4.1	1.77
Tim Duncan	83''	73.3%	45.2	50.9	-5.7	1.68
Marcus Morris	81''	73.3%	48.0	51.5	-3.5	1.88
Jeremy Evans	81''	73.3%	51.1	51.5	-0.4	2.13
Thabo Sefolosha	79''	73.4%	53.7	52.3	1.5	1.96
Jared Sullinger	81''	73.5%	52.7	51.5	1.2	2.13
Dwight Powell	83''	73.7%	54.9	50.9	4.0	1.59
LeBron James	80''	73.8%	51.8	51.9	-0.1	2.00
Chris Kaman	84''	73.8%	50.9	50.6	0.3	1.72
Al Horford	82''	74.3%	49.7	51.1	-1.5	1.94
Wilson Chandler	80''	74.5%	51.6	51.9	-0.4	1.87
Boris Diaw	80''	74.5%	52.0	51.9	0.0	2.25
Quincy Acy	79''	74.6%	52.1	52.3	-0.2	2.05
James Anderson	78''	74.6%	53.3	52.3	1.0	1.88
KJ McDaniels	78''	74.6%	52.4	52.3	0.1	1.63
Cody Zeller	84''	74.6%	51.1	50.6	0.5	1.77
Tyreke Evans	78''	74.7%	50.7	52.3	-1.5	1.80
Kirk Hinrich	76''	75.0%	55.3	52.8	2.5	1.65
PJ Tucker	78''	75.0%	53.0	52.3	0.8	2.18
Timofey Mozgov	85''	75.1%	51.6	50.4	1.3	2.12
Norris Cole	74''	75.1%	53.7	53.6	0.1	2.01
Jabari Parker	80''	75.2%	52.1	51.9	0.2	1.78
DeMarcus Cousins	83''	75.3%	53.4	50.9	2.6	2.34
Shane Larkin	71''	75.4%	55.2	54.6	0.6	1.77
Kentavious Caldwell-Pope	77''	75.4%	56.3	52.5	3.8	1.65
Paul Millsap	80''	75.4%	52.4	51.9	0.4	1.85
Quincy Pondexter	79''	75.4%	50.4	52.3	-1.8	1.76
Andrew Wiggins	80''	75.4%	53.1	51.9	1.2	1.72
Andrew Nicholson	81''	75.5%	52.0	51.5	0.5	2.13
Dwyane Wade	76''	75.5%	49.7	52.8	-3.1	1.81
David Lee	81''	75.5%	50.8	51.5	-0.7	1.85
Nikola Vucevic	84''	75.6%	51.2	50.6	0.6	2.06
CJ McCollum	76''	75.6%	52.7	52.8	-0.1	1.50
David West	81''	75.6%	49.8	51.5	-1.7	1.84
Andre Miller	74''	75.7%	51.5	53.6	-2.0	1.61
Andray Blatche	83''	75.7%	51.9	50.9	1.1	2.07
Alec Burks	78''	75.9%	52.8	52.3	0.5	1.62
Spencer Hawes	85''	75.9%	50.4	50.4	0.1	2.11
Anthony Tolliver	80''	76.0%	50.6	51.9	-1.3	1.65
Goran Dragic	75''	76.1%	51.1	53.2	-2.1	2.03
Henry Sims	82''	76.2%	53.9	51.1	2.8	1.85
Ty Lawson	71''	76.4%	54.4	54.6	-0.2	1.57
Enes Kanter	83''	76.5%	51.8	50.9	1.0	2.15
Patrick Patterson	81''	76.5%	52.6	51.5	1.1	2.03
Jonas Valanciunas	84''	76.7%	52.0	50.6	1.4	2.27
Patrick Beverley	73''	76.9%	52.2	53.9	-1.8	1.65
Gorgui Dieng	83''	76.9%	47.7	50.9	-3.1	1.85
Cory Joseph	75''	77.0%	55.8	53.2	2.6	2.01
Tyler Zeller	84''	77.0%	49.7	50.6	-0.9	2.09
Matt Barnes	79''	77.1%	54.6	52.3	2.4	1.70
Wesley Johnson	79''	77.1%	50.7	52.3	-1.5	2.24
Evan Fournier	79''	77.2%	52.4	52.3	0.1	1.61
Monta Ellis	75''	77.4%	51.4	53.2	-1.8	1.91
Markieff Morris	82''	77.6%	52.4	51.1	1.2	2.09
Raymond Felton	73''	77.7%	53.2	53.9	-0.7	1.55
George Hill	75''	77.7%	56.3	53.2	3.1	1.49
Pau Gasol	84''	77.7%	48.6	50.6	-1.9	2.03
Mario Chalmers	74''	77.7%	55.9	53.6	2.3	1.31
Tony Parker	74''	77.8%	52.0	53.6	-1.6	2.11
Alan Anderson	78''	78.0%	50.8	52.3	-1.5	1.90
Brandon Jennings	73''	78.0%	56.6	53.9	2.6	1.76
Nikola Pekovic	83''	78.0%	51.7	50.9	0.8	1.80
Cole Aldrich	83''	78.0%	51.1	50.9	0.2	1.89
Luol Deng	81''	78.2%	47.3	51.5	-4.2	2.06
Devin Harris	75''	78.2%	54.4	53.2	1.3	1.67
Jonas Jerebko	82''	78.4%	50.4	51.1	-0.8	1.94
Gerald Henderson	77''	78.5%	51.8	52.5	-0.7	2.08
Mike Scott	80''	78.5%	53.6	51.9	1.7	1.81
Ramon Sessions	75''	78.6%	55.6	53.2	2.4	1.82
CJ Watson	74''	78.6%	52.2	53.6	-1.4	1.66
Serge Ibaka	82''	78.7%	50.2	51.1	-0.9	1.93
Jae Crowder	78''	78.9%	52.6	52.3	0.3	2.21
John Wall	76''	79.3%	55.1	52.8	2.4	1.84
Eric Bledsoe	73''	79.3%	53.9	53.9	0.0	2.07
Kris Humphries	81''	79.4%	50.6	51.5	-0.9	1.97
Nikola Mirotic	82''	79.4%	50.2	51.1	-0.9	1.92
Marvin Williams	81''	79.5%	51.6	51.5	0.1	1.83
Anthony Davis	82''	79.5%	52.2	51.1	1.1	1.91
Chris Bosh	83''	79.5%	50.9	50.9	0.0	2.07
Tobias Harris	81''	79.5%	50.8	51.5	-0.7	2.40
Avery Bradley	74''	79.5%	55.4	53.6	1.8	2.19
Marreese Speights	82''	79.5%	51.0	51.1	-0.1	2.08
Jose Juan Barea	72''	79.5%	55.7	54.3	1.4	1.54
Alexey Shved	78''	79.6%	52.8	52.3	0.5	2.06
Isaiah Canaan	72''	79.6%	55.6	54.3	1.3	1.50
Bradley Beal	77''	79.6%	51.0	52.5	-1.5	2.01
Robin Lopez	84''	79.7%	49.5	50.6	-1.1	2.11
Kyle Singler	80''	79.7%	54.2	51.9	2.3	2.39
Carl Landry	81''	79.8%	47.9	51.5	-3.6	1.85
Lance Thomas	80''	79.9%	54.4	51.9	2.4	1.96
Manu Ginobili	78''	79.9%	51.1	52.3	-1.2	1.81
Ben McLemore	77''	80.0%	52.7	52.5	0.2	1.82
Dennis Schroder	73''	80.1%	54.4	53.9	0.5	2.03
Victor Oladipo	76''	80.1%	54.2	52.8	1.4	1.87
Roy Hibbert	86''	80.1%	48.7	50.2	-1.4	2.19
Marc Gasol	85''	80.1%	52.1	50.4	1.8	1.86
Zaza Pachulia	83''	80.1%	49.4	50.9	-1.4	1.86
CJ Miles	78''	80.2%	52.5	52.3	0.3	1.63
Brook Lopez	84''	80.3%	49.9	50.6	-0.6	1.99
Jeremy Lin	75''	80.4%	55.5	53.2	2.3	1.91
Langston Galloway	74''	80.4%	55.5	53.6	1.9	2.15
Klay Thompson	79''	80.4%	52.8	52.3	0.5	1.56
Evan Turner	79''	80.4%	51.0	52.3	-1.2	2.14
Chase Budinger	79''	80.5%	55.3	52.3	3.1	1.54
Martell Webster	79''	80.5%	53.8	52.3	1.5	1.83
Tony Snell	79''	80.8%	54.9	52.3	2.7	1.38
Paul Pierce	79''	80.8%	48.8	52.3	-3.4	1.94
Joe Johnson	79''	80.9%	54.5	52.3	2.3	1.81
Jordan Clarkson	77''	81.0%	54.6	52.5	2.1	1.78
Jeff Green	81''	81.0%	51.8	51.5	0.3	1.82
Shaun Livingston	79''	81.0%	51.9	52.3	-0.4	2.12
Kobe Bryant	78''	81.0%	53.7	52.3	1.4	1.87
Trevor Ariza	80''	81.0%	53.4	51.9	1.5	2.00
Shelvin Mack	75''	81.1%	51.4	53.2	-1.8	2.05
Kevin Love	82''	81.1%	47.4	51.1	-3.8	1.74
Eric Gordon	76''	81.2%	53.3	52.8	0.5	1.37
Bojan Bogdanovic	80''	81.2%	49.4	51.9	-2.5	1.96
Trey Burke	73''	81.2%	52.6	53.9	-1.3	1.69
Marcus Thornton	76''	81.2%	53.1	52.8	0.3	1.81
Jrue Holiday	76''	81.2%	54.2	52.8	1.5	1.69
Robert Covington	81''	81.2%	53.8	51.5	2.3	2.02
Ryan Kelly	83''	81.4%	51.0	50.9	0.1	2.04
Jeremy Lamb	77''	81.5%	53.7	52.5	1.2	1.75
Jimmy Butler	79''	81.5%	51.9	52.3	-0.4	1.62
Vince Carter	78''	81.5%	51.6	52.3	-0.7	1.93
Gordon Hayward	80''	81.5%	54.3	51.9	2.3	1.85
Ricky Rubio	76''	81.5%	50.1	52.8	-2.7	1.66
Kawhi Leonard	79''	81.5%	51.5	52.3	-0.7	2.10
Darrell Arthur	81''	81.6%	52.7	51.5	1.2	1.71
Tim Hardaway Jr.	78''	81.6%	53.0	52.3	0.8	1.62
Jameer Nelson	72''	81.7%	55.2	54.3	0.9	1.59
Wesley Matthews	77''	81.9%	51.7	52.5	-0.8	1.91
Derrick Rose	75''	81.9%	52.8	53.2	-0.4	1.74
Andrea Bargnani	84''	82.1%	48.4	50.6	-2.2	2.05
Terrence Ross	79''	82.1%	54.1	52.3	1.8	1.93
Darren Collison	72''	82.5%	52.4	54.3	-1.8	1.65
Nicolas Batum	80''	82.7%	51.5	51.9	-0.4	1.68
Rodney Stuckey	77''	82.7%	52.5	52.5	0.0	1.95
Will Barton	78''	82.7%	52.1	52.3	-0.2	1.43
LaMarcus Aldridge	83''	82.7%	50.1	50.9	-0.8	1.85
Jerryd Bayless	75''	82.8%	53.4	53.2	0.2	1.50
Jason Smith	84''	82.8%	51.4	50.6	0.8	1.84
Kyle Lowry	72''	82.9%	53.4	54.3	-0.9	1.87
Aron Baynes	82''	82.9%	51.6	51.1	0.4	2.22
Arron Afflalo	77''	82.9%	49.7	52.5	-2.8	1.61
Gerald Green	80''	83.0%	49.7	51.9	-2.2	1.89
Deron Williams	75''	83.0%	51.2	53.2	-2.0	1.64
Carmelo Anthony	80''	83.1%	51.6	51.9	-0.4	1.77
Rudy Gay	80''	83.3%	51.6	51.9	-0.4	1.97
Rodney Hood	80''	83.3%	52.5	51.9	0.6	1.71
Solomon Hill	79''	83.3%	51.2	52.3	-1.1	1.91
DeMar DeRozan	79''	83.5%	54.6	52.3	2.4	1.81
Alexis Ajinca	86''	83.5%	49.2	50.2	-0.9	1.85
Zach LaVine	77''	83.6%	55.4	52.5	2.9	1.48
Brandon Knight	75''	83.7%	52.7	53.2	-0.5	1.85
Mike Conley	73''	83.7%	57.6	53.9	3.6	1.34
Mike Dunleavy	81''	83.7%	53.3	51.5	1.8	1.60
O.J. Mayo	77''	83.7%	52.7	52.5	0.1	1.84
Danny Green	78''	83.8%	54.0	52.3	1.7	1.73
Aaron Brooks	72''	83.8%	53.7	54.3	-0.6	1.34
Russell Westbrook	75''	83.9%	51.4	53.2	-1.8	1.78
Beno Udrih	75''	84.0%	57.5	53.2	4.3	1.33
Kemba Walker	73''	84.1%	55.8	53.9	1.9	1.59
Channing Frye	83''	84.1%	53.8	50.9	3.0	2.10
Randy Foye	76''	84.2%	52.8	52.8	0.0	1.47
Greivis Vasquez	78''	84.3%	55.2	52.3	3.0	1.78
Caron Butler	79''	84.8%	52.5	52.3	0.2	1.81
Lou Williams	73''	84.8%	51.6	53.9	-2.3	1.74
Paul George	81''	84.8%	53.0	51.5	1.5	1.62
Nick Young	79''	84.9%	50.7	52.3	-1.5	2.02
Anthony Morrow	77''	84.9%	51.8	52.5	-0.7	1.85
Kristaps Porzingis	85''	85.4%	52.1	50.4	1.7	2.05
Jose Calderon	75''	85.6%	52.1	53.2	-1.1	2.10
Jeff Teague	74''	85.7%	54.8	53.6	1.2	1.65
Marco Belinelli	77''	85.7%	51.5	52.5	-1.0	1.74
Reggie Jackson	75''	85.8%	56.2	53.2	3.0	1.89
Kyrie Irving	75''	86.2%	52.8	53.2	-0.4	1.91
Danny Granger	81''	86.6%	50.5	51.5	-1.0	1.69
Damian Lillard	75''	86.7%	52.9	53.2	-0.3	1.45
Khris Middleton	79''	86.7%	49.1	52.3	-3.2	1.80
Jordan Crawford	76''	86.8%	51.4	52.8	-1.4	1.77
Kevin Durant	81''	86.9%	52.7	51.5	1.2	1.75
Isaiah Thomas	69''	86.9%	54.6	55.2	-0.5	1.72
Patty Mills	72''	87.0%	55.0	54.3	0.7	1.81
Courtney Lee	77''	87.0%	53.9	52.5	1.4	1.68
Gary Neal	76''	87.1%	51.9	52.8	-0.9	1.81
D.J. Augustin	72''	87.1%	54.2	54.3	0.0	1.55
Jarrett Jack	75''	87.3%	54.4	53.2	1.3	2.08
James Harden	77''	87.3%	49.9	52.5	-2.6	2.14
Mo Williams	73''	87.5%	52.8	53.9	-1.1	1.76
Jodie Meeks	76''	87.7%	51.3	52.8	-1.5	2.17
Chris Paul	72''	87.8%	55.6	54.3	1.3	1.57
Ryan Anderson	82''	88.2%	52.0	51.1	0.8	2.04
Danilo Gallinari	82''	88.6%	48.7	51.1	-2.4	1.75
Kevin Martin	79''	88.9%	51.6	52.3	-0.7	1.73
Dirk Nowitzki	84''	89.0%	51.0	50.6	0.4	1.81
Jamal Crawford	77''	89.1%	54.0	52.5	1.5	1.53
Stephen Curry	75''	89.8%	56.4	53.2	3.2	1.64
Kyle Korver	79''	90.0%	50.7	52.3	-1.6	1.87
JJ Redick	76''	90.4%	51.9	52.8	-0.9	1.62
Brian Roberts	73''	92.1%	54.4	53.9	0.5	1.64