Wednesday, March 9, 2016

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

3 comments:

  1. The real tradeoff for a shooter is not between launch angle and velocity, but between launch angle and the travelling distance of the ball.

    ReplyDelete
  2. Wondering about the effect of rotation on "negating" velocity.

    ReplyDelete
  3. That first chart is a ballistics chart and so it doesn't show a parabola because of friction losses. Those losses won't be noticeable at 23.5 feet per second since friction is f(v^2).

    ReplyDelete