Friday, February 17, 2012

Three Point Shootout Selection


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.

2011-12 3FGA
2011-12 3FG%
2010-11 3FG%
Career 3FG%
Ryan Anderson
Mario Chalmers
Joe Johnson
James Jones
Kevin Love
Anthony Morrow

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.


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.

Steve Novak
Matt Bonner
Kyle Korver
Brandon Rush
Stephen Curry
Mike Miller
James Jones*
Anthony Morrow*
Ray Allen
Ryan Anderson*
Mario Chalmers*
Kevin Love*
Joe Johnson*
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.

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