Three Point Shootout Selection

Introduction

The participants for the all-star three point contest have been announced, and as always some of the selections were questionable -- James Jones, Joe Johnson, Mario Chalmers, Ryan Anderson, Kevin Love, and Anthony Morrow. Before I get into the merits of each player, first I need to discuss the common problems in evaluating three point shooting.

Judging three point shooting

1) Quantity is not quality -- the Antoine Walker problem. Named for the career 32.5% shooter with 1386 makes, some people often confuse volume shooting with skill. The leader in three point field goals, for instance, is not necessarily the best three point shooter, although every year a large section of the mainstream media pretends it's true. Imagine making the same argument for free throw shooting. Lebron is tied this year for the lead in free throws and last year Dwight Howard was third. Does that make them the best free throw shooters? Of course not. That's ridiculous, and it's apparent why -- they have the most opportunities, not the most shooting talent. Extending that to the contest, to say that hoisting a ton of shots in a game is key is silly because players aren't being guarded out there. There's certainly a point in that a higher number of shots per possession correlates with taking more difficult three pointers instead of just standing in the corner and waiting for a perfectly open look, but that doesn't mean volume by itself makes a great shooter. Also, this argument isn't about sample size, but who takes the most shots.

2) Yearly variations -- the streaky player problem. Long jump shots have a high variation in percentage converted. Rebounding, for example, has a lower variance meaning over time the statistics for rebounding are stable with fewer great dips or peaks in performance, while a player's three point shooting percentage can have significant changes year to year without a culprit like injuries or new mechanics. This is a well known pattern in NBA statistics, yet it's also ignored by most NBA analysts who cite someone's shooting percentage even 10 or 15 games into the season when discussing a player's shooting skill. With a higher variance, a greater sample size is needed, and as such it's usually better to look at a player's career percentage or, even better, his stats from the last three years.

So how does the league choose its participants? Is it done by feel and reputation, a human-based method? Or something more complicated statistically? Well it's actually only this. Yes, the league makes the two fundamental mistakes in evaluating three point shooting -- they sort players based on percentages for only half a season, and then select the players with the most attempts. In the Truehoop article linked above, Morrow wasn't chosen because he missed the first ten games and thus lagged behind in total makes. No, the league didn't look at three point shots per game or per minute, and they essentially eliminated players with low minutes due to reasons other than shooting from the contest. Luckily, the Nets have been so terrible this year they've been forced to give him huge minutes, and he was chosen based on his 100 plus three's. I know it doesn't seem worthwhile to criticize a pointless exhibition, but the prize money is equivalent to some family's yearly income and millions of people will watch what is supposed to be a showcase of the NBA's best talent.

2011-12 three point contest selections

Seeing how the league selects the participants, this year's six-man group is not surprising. I included a table below that summarizes the basic three point shooting stats of each guy. The outlier is James Jones because he's barely played this year, but since he's the defending champion he was invited back to defend the title (like it actually matters.) As you can see in the table, he is a good shooter, so it's not a travesty. His teammate Mario Chalmers, however, was invited because of his three point percentage, which if you look at his career is most likely a fluke. The Heat's best players aren't point guards, so he's been granted with a large chunk of minutes and open shots.

Player	2011-12 3FGA	2011-12 3FG%	2010-11 3FG%	Career 3FG%
Ryan Anderson	200	43.5	39.3	39.1
Mario Chalmers	123	46.3	35.9	36.5
Joe Johnson	154	35.1	29.7	36.5
James Jones	47	40.4	42.9	40.2
Kevin Love	127	36.2	41.7	36.9
Anthony Morrow	156	41.7	42.3	44.2

Ryan Anderson is a great choice given that the all-star game is in Orlando and he definitely has the "quality" down as well, with a high career and present year average in percentage. He's starting, but even on a per minute basis he's shooting a large number of shots and converting at a high rate. It it were an 82 game season, he'd be on pace to post one of the highest number of three point field goals in a season ever. (Ray Allen holds the record at 269.)

Joe Johnson is the worst selection of the contest. The only reason he was chosen is that he's taken a high number of three pointers. It's like the people behind the contest are conflating taking a high number of shots in a game with a high number of shots in a contest where the ball is placed on a rack in front of you with no defenders. Joe Johnson shot under 30 percent last year, and he's an inch above the league average of 34.7 this season. If an avid NBA fan listed the top ten three point shooters in the league, what are the chances he would be listed? I don't even think causal fans would make this mistake because it's Joe Johnson.

Fellow all-star Kevin Love makes me wonder if the committee had to include two guys who would play in the Sunday game so the contest would have "big names." Even then, these two aren't the best candidates because Steve Nash, who for his career is a 42.9% shooter, is also on the all-star squad. That's only eighth all-time. No big deal. Maybe he didn't want to be part of the contest, but there's also Chris Paul, shooting 44.8% this season and around 40% the two previous ones. Compared to non-all-stars, however, Kevin fares even worse, but he's playing a league high in minutes per game, and by the league's emphasis on volume he made the group. The problem with imposing a quota on certain types of players is that unqualified selections can occur, and there's really no point in trying to corral the all-star players into the contest when the guys aren't megastars and they are instead Joe Johnson and Kevin Love. Nevertheless, it will be interesting to see one of the best rebounders in the league try for a three point crown, as the current best rebounders who have won the contest Larry Bird and Nowitzki aren't near Love's elite level.

Finally there's Anthony Morrow with his first appearance. He should have been selected sooner, but it's great to see him this year as he's, you know, second all-time in three point percentage. He's always shot a high number of three pointers when he plays, but his defense limits his minutes and he normally misses a few games each year. That shouldn't matter in this contest, and Morrow has a decent chance to break the record for contest points (25) held by Craig Hodges and Jason Kapono.

Method

I can complain all I want, but if I'm not offering a solution it's armchair quarter-backing. Based on an earlier study I did to find the best shooter, I created a simple method for the selections. If you don't want to know the nitty-gritty of the math behind this, skip ahead to the next section. I looked at the past three seasons, and weighted this current season by 3, last season by 2, and two years ago with 1. The weighting essentially just means that you can multiply the three point field goals by that amount (3, 2 or 1) and it's done to give more value to recent performance. After that, I simply divide the three point field goals by the attempts.

Then I calculate the three point attempts per minute for each player from the past three seasons with the same weights. This is done to reward guys who take more shots, and thus more difficult ones, and punish those who only shoot when open, which raises their percentage compared to the players who take contested shots. It's not perfect, but it's a modest improvement. I implement this by creating a usage multiplier on a scale of 1 to 1.2; it's multiplied with the three point percentage from the past three years for a three point contest score. The scale is based on how a player's shots per minute ranks with everyone else -- the player with the highest rate gets 1.2, a player with zero shots per minute 1.0, and one with half the shot attempts per minute as the leader would receive 1.1.

After that, the adjusted percentages are standardized on a 100 scale. It's really simple to do so; you just divide each adjusted percentage by the maximum percentage found and multiply by one hundred. The maximum percentage leader has to have a minimum of 300 weighted shots. A weighted shot means that you only need 100 three point attempts total in the current season to qualify because the weighting for that season is 3. I use a 100 scale so it looks an academic grading system, and is thus easier to read and compare. Below are the results, and my thoughts on who should have been selected.

My selections

I can say with confidence that the top players on my list are better than the group selected by the league. The top player is surprising to most, but to NBA-junkies it's not. Yep, Steve Novak destroyed everyone else with his shooting percentages; it wasn't close. Not only was his 46.8% shooting the best out of anyone with enough attempts to qualify, but he also shot more three pointers per minute than anyone else. He barely cleared the minimum amount of shot attempts to qualify, but his track record in college was also impeccable and his lead is so large I think he deserves to be in the contest.

Rank	Player	Score
1	Steve Novak	100.0
2	Matt Bonner	87.6
3	Kyle Korver	87.3
4	Brandon Rush	87.2
5	Stephen Curry	86.8
6	Mike Miller	86.7
7	James Jones*	86.6
8	Anthony Morrow*	86.5
9	Ray Allen	85.9
10	Ryan Anderson*	85.0
29	Mario Chalmers*	77.4
61	Kevin Love*	73.2
129	Joe Johnson*	66.2

Out of 179 ranked players. Three years of three point shooting data.
*Selected participants

Even though none of the top six are in the contest, three of the picks are perfectly fine. James Jones is the defending champ and he's ranked 7th. Anthony Morrow is 8th, and his career percentages are even better. Also, note that the difference between the 5th and 8th guys is 0.3, which is virtually negligible. Ryan Anderson isn't far behind at 10th, and the contest is in his home arena. Mario Chalmers, however, is a stretch, especially if you consider his percentage this year to be a fluke. Kevin Love is far behind, and Joe Johnson is ranked in the bottom third of qualified players. In fact, he's in between other all-star teammates not known for their outside shooting -- Luol Deng, Carmelo Anthony, Andre Iguodala, and LeBron James. The worst player was Tyreke Evans with a score of 49.5. Another interesting tidbit? Klay Thompson, who did not qualify with enough attempts since he's a rookie, had a score of 101.9 (a score over 100 is possible because he did not qualify and thus beat the guy who set the curve.) With a limited number of attempts I'd expect his numbers to regress to the mean, but with his age it bears close attention.

I'm not saying my system is perfect, but it's fairly simple and the top six guys are undeniably better three point shooters than what the league picked. The one player without the same reputation is Brandon Rush, but he's leading the league this year in three point percentage and the last couple years he's been over 41%. Here are my picks using my created three point contest score listed as a guide: Steve Novak, Matt Bonner, Kyle Korver, Stephen Curry, Anthony Morrow, and Ryan Anderson. Alternates: Brandon Rush, then James Jones, then Klay Thompson.

Edit: Joe Johnson because of an injury is being replaced by Kevin Durant, who had a score of only 68.6 because he's been struggling with his outside shot the past couple years, but it's still better than Joe Johnson's and his career numbers are better.

Best Shooter of the Past Five Years

Introduction

Who is the best shooter in the NBA?

This question is a popular one, but there are no clear answers. You can bring up someone’s textbook form, how high the player releases the ball, or how quickly the shot is released, but it always goes back to whether or not the player makes the shot. Unfortunately, for most of the NBA’s history there is simply not enough information to reach a definitive conclusion. There’s field goal percentage, but all the jumpers are comingled with inside shots. Shaq’s near 60 percent for his career from the field, and no one confuses him with an excellent shooter. Three pointers are the ultimate weapon of great shooters; however, it’s only been used in the NBA since 1979. And how do you compare a guy who creates his own shot like Larry Bird with a spot-up shooter like Steve Kerr?

Methodology

I’ve given this question my best attempt with a public database that goes back to the 2006-07 season (Hoopdata.com.) Essentially we’re looking at the best shooters of the past five seasons. Shots are divided into zones, and I used three of these zones – shots from 10 to 15 feet, 16 to 23 feet, and beyond the three-point line, as well as free throws (one of the most objective basketball stats.) In a manner similar to what John Hollinger used (found here) I created a composite score based on the percentages from those distances with a few tweaks.

One adjustment was to award guys for unassisted attempts by a multiplier of a maximum 10 percent. This was to help guys who had to create their own shots versus role players who get to wait on the three point line to take one. For example, if a player was never assisted on any of his 16-23 foot field goals, then his percentage from that distance would be multiplied by 1.1. If, however, he was assisted on half, then the multiplier would be 1.05. I did something similar to shot attempts per minute because that roughly correlates with taking more contested and tougher shots. An extra 20 percent was awarded instead of 10, and the maximum allotment was based on the highest per minute attempts from someone with at least 150 attempts. Kobe Bryant had 0.788 attempts from 10 to 15 feet when the maximum was 1.113, so Kobe had a multiplier of 1.139 (0.788/1.113*1.2=1.139.) With his assist multiplier being 1.074, his percentage from that distance was adjusted from 47.8 to 58.5.

In order to compare percentages, everything was standardized from 0 to 1 based on the maximum percentage with 150 attempts. Kobe’s adjusted percentage of 58.5 was changed to 0.955. Then the standardized scores were added with a 33.3 weight to three-pointers and free throws, and 16.7 to the midrange distances. Less weight was given to the latter so everything would be balanced between two-point jump shots, free throws, and three pointers. The weights were also chosen so the composite would be out of 100; think of an academic scale where 90 and above are A’s, 80 and above B’s, etc. A 100 is essentially a percent score for players with enough field goal attempts, although since the 10-15 range is less used for most shooters I let guys qualify for the final rankings with only 100 attempts instead of 150 like the other distances; that meant a score over 100 is possible. I also included an unadjusted composite score built the same way except multipliers for assisted shots and shots/minutes weren’t used.

Results

The results are fascinating. Out of 166 qualifying players from 2006-07 to 2010-11, the top adjusted composite score (ACS) was 99.3 from Steve Nash. Again, a score of 100 is virtually perfect, and the next closest guy was Anthony Morrow at 94.2. The top twenty players are shown in a table below. His dominance is astounding – not only is he the best free throw shooter, but he nearly had the best three-point percentage (although his adjusted three pointer percentage is best) and he had the top marks for unadjusted and adjusted from 10 to 15 feet. He’s also no slouch from 16 to 23 feet. That 51.6 percent from that awkward range? He was only assisted on 6 percent of those.

The rest of the list is intriguing but logical. One surprise is that Morrow is number two, but looking at his numbers you can see why – he’s Nash-like in his percentages from anywhere on the floor. Given that he’s only 26, it’ll be interesting to see where his numbers will end up when he retires. His weakness is that he’s a spot-up shooter, and thus makes easier shots so his adjusted score is lower than his unadjusted composite. Stephen Curry is even younger at 23 years, and if he could improve from 10 to 15 feet and stay upright despite glass ankles he has the only realistic shot at catching up to Nash. Dirk Nowitzki and Ray Allen aren’t surprising because anyone should list them near the top of a best shooters list, but Mo Williams probably is. He’s excellent from every spot, and he’s a point guard instead of a spot-up specialist who scores at a decent rate.

Some players are lower on the list than others would think, but for good reasons. Stojakovic is over 90 at the line, but he shot a lower percentage from both distances inside the three point line than outside. The same problem occurred for Szczerbiak, as my method punished three point specialists who couldn’t hit midrange shots. Kobe Bryant makes the list, helped by his attempts per minute and his mastery of the 10 to 15 foot range, but if Lakers fans complain that he should be even higher due to the high degree of difficulty, then why is his free-throw percentage so low? No one’s guarding him there. (Random note: without the minimum field goal requirement for ACS, Eddy Curry would be sitting on top with a score of 102.8 solely because he was 1 for 1 from behind the three point line. All his other percentages were terrible.)  

Rank	Player	10-15 ft. %	16-23 ft. %	Three pointer %	Free throw %	Composite score	Adj. comp. score
1	Steve Nash	51.6	47.7	44.2	91.7	99.1	99.3
2	Anthony Morrow	49.0	44.7	44.7	88.5	96.5	94.2
3	Stephen Curry	36.9	46.0	43.9	91.1	93.4	92.6
4	Dirk Nowitzki	47.5	48.6	38.6	89.6	93.2	92.2
5	Ray Allen	47.6	45.2	39.7	91.2	93.4	91.6
6	Mo Williams	49.2	45.1	39.4	87.6	92.4	91.5
7	Ben Gordon	43.9	44.6	39.7	87.0	90.5	90.2
8	Jason Kapono	40.0	47.5	44.4	83.5	92.5	89.5
9	Jason Terry	46.9	47.4	38.1	85.3	90.6	89.3
10	Kyle Korver	39.9	45.6	41.3	89.4	91.6	89.1
11	Chauncey Billups	40.8	41.0	38.9	90.8	89.1	88.9
12	Jose Calderon	43.2	46.4	39.5	87.8	91.0	88.4
13	Chris Paul	47.4	43.9	37.4	85.5	89.1	88.2
14	Luke Ridnour	45.6	46.7	37.6	86.3	89.9	88.1
15	Earl Boykins	44.4	39.3	37.4	87.4	87.3	86.3
16	Wally Szczerbiak	39.6	40.4	41.3	86.5	88.7	86.3
17	Kobe Bryant	47.8	40.5	34.3	84.3	85.4	86.2
18	Paul Pierce	44.4	40.8	39.2	83.7	87.8	85.9
19	Rashard Lewis	43.5	41.0	39.4	83.0	87.5	85.8
20	Peja Stojakovic	34.9	38.1	40.5	90.1	87.1	85.8

*Minimum attempts: 100 from 10-15 feet and 150 from the other three distances

There were a few players who just missed the field goal attempts cut-off who warrant mentioning. Steve Novak had an ACS of 96.8, but has rarely gotten to the line and has only taken 12 shots from 10 to 15 feet. After only a rookie year, Gary Neal had an ACS of 91.2; he should qualify with enough attempts after another year. He also deserves to be on a short list of the most underrated shooters in the league. JJ Redick, known more as a sharpshooter than Neal, also should make the top twenty after another year in the league with an ACS of 87.0. Brent Barry nearly made the cut (ACS of 90.3), but needed to shoot more from inside the three point line.

Since I have a score for every player in the league, I have also the ACS for the bad shooters as well. Below is a table showing the twenty worst shooters according to this metric, and to reiterate this is among players who qualified. Otherwise Ben Wallace, DeAndre Jordan, and Andris Biedrins would be competing for this dubious honor. With a terrible score of 60.7, the worst shooter is Josh Smith. He attempted to quit three pointers cold turkey, and based on his numbers I can see why he tried. However, I will note that since it’s three points instead of two it may be better to give up midrange shots instead, although tactically it’s more difficult to completely abstain. Rondo is third, but would be higher if it weren’t for his skill at those awkward shots that sometimes fly from 10 or more feet. It’s surprising to see Spencer Hawes with such a low score because when a seven-footer eschews the inside game for an outside one he better have a good reason. Luckily, this year he has given up and is rebounding and scoring near the basket more than ever.  

Rank	Player	10-15 ft. %	16-23 ft. %	Three pointer %	Free throw %	Composite score	Adj. comp. score
166	Josh Smith	23.9	33.5	28.1	66.7	64.2	60.7
165	Trevor Ariza	17.9	32.7	31.8	66.8	64.8	62.3
164	Rajon Rondo	41.0	38.1	24.2	62.2	66.8	63.8
163	Marquis Daniels	41.8	32.6	22.8	69.2	66.7	64.1
162	Spencer Hawes	36.3	40.4	30.4	63.9	71.3	67.0
161	Corey Brewer	33.6	33.3	31.2	70.0	70.9	67.5
160	Thabo Sefolosha	32.1	37.8	30.5	71.3	71.8	67.6
159	Andre Miller	41.7	39.3	18.0	81.2	69.7	68.2
158	Thaddeus Young	32.4	35.1	33.8	71.6	73.6	69.4
157	Lamar Odom	35.4	40.1	32.2	67.9	73.7	69.7
156	Al Thornton	37.8	35.7	29.3	74.8	73.4	70.3
155	Shawn Marion	39.7	36.3	29.5	77.2	75.2	70.7
154	Devin Brown	27.9	31.9	33.4	78.1	73.1	70.7
153	Jamaal Tinsley	38.2	34.7	29.0	72.7	72.1	70.8
152	Andre Iguodala	28.8	37.8	31.8	74.4	72.9	71.0
151	Antonio Daniels	32.8	36.5	29.5	80.6	74.3	71.2
150	Zach Randolph	34.5	40.6	28.4	77.8	74.4	71.4
149	Luke Walton	36.6	35.4	34.2	72.3	75.6	71.5
148	Jeff Green	31.6	34.4	33.7	77.3	75.1	71.8
147	Rodney Carney	37.6	34.3	33.8	70.4	74.6	71.8

*Minimum attempts: 100 from 10-15 feet and 150 from the other three distances

As a bonus, I’ll also list the top guys from each distance with adjusted (assist rate and attempts per minute) and unadjusted percentages. Nash’s shooting prowess is showcased here very well – he has four out of seven top spots, and in only one category is he not in the top five. There are also a few surprising names – Sean May as a marksmen with a midrange jumper, Shaun Livingston’s skill from 10 to 15, and the forgotten Mikki Moore who lived on two-point jumpers.

10 to 15 feet:

Player	Unadjusted %	Player	Adjusted %
Steve Nash	51.6	Steve Nash	61.2
Beno Udrih	51.2	Dirk Nowitzki	60.3
Mo Williams	49.2	Beno Udrih	59.7
Anthony Morrow	49.0	Shaun Livingston	59.0
Shaun Livingston	47.9	Kobe Bryant	58.5

*Minimum attempts: 150

16 to 23 feet:

Player	Unadjusted %	Player	Adjusted %
Steve Novak	49.2	Dirk Nowitzki	59.5
Sean May	48.7	Steve Nash	57.0
Dirk Nowitzki	48.6	Sean May	56.8
Matt Bonner	48.5	Jose Calderon	56.0
Mikki Moore	48.1	Luke Ridnour	55.8

*Minimum attempts: 150

Three point:

Player	Unadjusted %	Player	Adjusted %
Anthony Morrow	44.7	Steve Nash	51.4
Jason Kapono	44.4	Anthony Morrow	50.3
Steve Nash	44.2	Steve Novak	50.2
Stephen Curry	43.9	Stephen Curry	50.1
Brent Barry	42.5	Gary Neal	49.3

*Minimum attempts: 150

Free throws:

Player	%
Steve Nash	91.7
Ray Allen	91.2
Stephen Curry	91.1
Chauncey Billups	90.8
Peja Stojakovic	90.1

*Minimum attempts: 150

I’m also including the top rates for field goals attempted from the three court ranges. Marc Jackson is a surprising leader, and note this is a former Warriors player and not the current head coach with over 10,000 career assists (he spells his name “Mark.”) In retrospect, maybe 150 was too low a threshold for something like FGA/min, but it ultimately didn’t mess with the rankings. The leading three point shooters per minute is an eclectic list of players who have little in common besides their favorite shot.

10 to 15 feet:

Players	FGA/min
Elton Brand	0.113
Dirk Nowitzki	0.112
Yao Ming	0.101
Jermaine O'Neal	0.096
Sam Cassell	0.089

*Minimum attempts: 150

16 to 23 feet:

Players	FGA/min
Marc Jackson	0.206
Tracy McGrady	0.197
Dirk Nowitzki	0.196
Sam Cassell	0.190
Kobe Bryant	0.180

*Minimum attempts: 150

Three point:

Players	FGA/min
Steve Novak	0.234
J.R. Smith	0.219
Juan Carlos Navarro	0.204
Damon Jones	0.204
Ryan Anderson	0.203

*Minimum attempts: 150

Conclusion

There’s no perfect way to rate a shooter, and maybe there are problems adjusting based on how many shots are assisted and how many you take per minute. The adjustment, however, doesn’t change the rankings too much. Specialists who wait until they’re open are hurt a little like Kapono, and stars who typically take more contested shots like Kobe benefit by moving up a few spots. No matter how you slice the numbers it’s hard not to rate Nash as the best shooter because he’s one of the top from every location and has to lead an offense while doing so. We don’t have data for decades back so we can’t compare him to Larry Bird or Mark Price, but it’s hard to believe anyone who could shoot better. Steve Nash is the greatest shooter of the past five seasons, and he has a legitimate argument for greatest of all time.