Bucket and brick factories

Anyone who has been watching the playoffs does not need a graph to tell them that Carmelo can't find the bottom of the net, while Lebron can't seem to miss. But I made one anyway.

This graph shows the 32 most productive scorers in the NBA playoffs to date, defined by average time taken to score 2 points. The green dots show this statistic, with Tony Parker leading the way at a clip of 2 points every 2 minutes and 52 seconds, and Lebron only 8 seconds behind.

The red dots show time taken between missed FG attempts. Carmelo is blowing everyone away on this stat, missing it every 2 minutes and 32 seconds, producing significantly more bricks than buckets. As Dan Shaughnessy quipped about the Knicks today: "They have overrated ballhog Anthony pounding the ball, waiting to shoot, while four teammates stand and watch. It’s easy to defend."

Dwight Howard and Mike Dunleavy were particularly efficient (high points relative to misses) and productive (though that didn't prevent their teams from being swept), while Brandon Jennings and Corey Brewer join Melo in manufacturing far more bricks than buckets. 

The Celtics, with balanced scoring across the team throughout their series (if not enough in the second half for most of the games), do not have anyone in the top 32, though Pierce and Green come in at 37 and 38.

Note: anyone scoring fewer than 10 PPG was excluded.

Bomb it or take it to the hole? Player edition

In my previous post I looked at team's relative efficiency for 3-point vs. 2-point attempts. Now I'll turn to individual players.

I graphed average points scored per 3-pt attempt against average points per 2-pt attempt for all players this season who shoot more than 2.5 3's per game (top 25% in the  league) and who play more than 20 minutes per game (graph was too crowded otherwise, apologies to Steve Novak, who would be just on top of Ray Allen). Again, dot size corresponds to 3-pt attempts per game. The darker reference lines correspond to the league averages.

This shows again what a miserable 3-pt shooting season Kobe is having, and his 2-pt efficiency, while above league average, is only average for top shooters.

Melo and Raymond Felton stand out more: they are the only two players in the league who shoot a lot of threes, play a lot of minutes, but are significantly worse than the league average at 3-pt and 2-pt shooting efficiency. They are bad at everything they do.

Guys in the top right corner like Ray and James Harden are above average at both 3-pt and 2-pt efficiency, though it would be great if Ray could get more 3's (I know he tries) and James bombed a tad less.

Bomb it or take it to the hole?

If offenses had a high degree of control over shot selection, you would expect to see roughly equal average points per 3-point attempt compared to average points per 2-point attempt. This is not in fact the case.

For example, in the graph below, San Antonio scores 1.20 points per 3 that they shoot, but only 1.07 per 2-point attempt (note that I attributed all free throw attempts to 2-point attempts, which slightly biases downward the points per 3-point attempt). In contrast, Denver only scores 0.96 points per 3 point attempt, but 1.13 points per 2-point attempt.

The size of each team's dot corresponds to 3-point attempts per game, which is barely correlated with 3-point shooting percentage.

What does this information do for a team? Should teams such as San Antonio, Orlando and Golden State shoot more 3s? It's not clear from this analysis. For San Antonio, any 3 with an expected value above 1.066 (their 2-point average) is worth shooting (which means it must have a 35.5% chance of making it), so the recommendation is clearly not just to bomb away until the two averages converge.

Denver and Los Angeles are further way from the line of equality. Denver shoots 20.8 3's per game, 8th highest in the league, while shooting only 32.1% for 0.96 points per 3. Given that their game inside the arc is so efficient, second only to Oklahoma City, one has to think they are bombing too much. Making the simplifying (AKA wrong) assumption that shooting percentages would not change if they shot fewer 3s and more 2s, if Denver stopped shooting 3s, they would score 3.6 more points per game, enough to add a few more wins. Something less drastic would likely benefit them greatly, without letting the defense collapse in the paint.

Al Harrington is the worst offender on the Nuggets, bombing 4.5 3's per game, connecting on only 30% of them (0.91 PP3), even though he shoots 54% inside the arc (1.08 PP2 ignoring FTA, which would increase his PP2).

And yes, Kobe is a big reason why the Lakers are at the bottom frontier, heaving up 5.1 3's per game, only converting 29.6% of them (0.89 PP3). Metta World Peace only shoots half as many, but makes only 25.2% (0.76 PP3). Take it to the hole, boys!

Finally, New York Knicks, I know a guy named Steve Novak. Not sure about his defense, but boy can he shoot 3's. He fires away at a rate of 28 3's attempted per 48 minutes, connected on 48.8% (1.46 PP3, compared to the team's 0.96 average). Somehow let him shoot more of your 3s? He seems to have no trouble taking or making them.

Scoring, but living up to expectations?

Here's another look at whether Kobe and Carmelo are ball hogs. Punchline for impatient types: yes!

I took the data from the leagues top scorers (over 20 PPG), and predicted how many points each player would score if their shooting was as efficient as the other top scorers (linear regression: PPG = β₀ + β₁(shots per game) + ε, where free throws count as 0.44 shots, according to convention).

You can think of the expected PPG for Kobe as: how many PPG would the typical top scorer produce if they took a many shots as Kobe?

Kobe, Melo and Monta Ellis emerge as the least efficient among the top scorers. In the graph below green circles are expected PPG given SPG, red/blue dots are actual PPG for those below/above expectations:

This again illustrates the remarkably efficient shooting of Durant and LBJ this season.

Hit the open man: assists and offensive efficiency

RETRACTED: The previous version of this post used some incorrect data. The problem has now been fixed, which radically changes the findings. In reality, the % of field goals assisted has very little to do with shooting efficiency (points per shot) and with winning. Though PPS remains highly correlated with winning. Apologies for the error.

Here's the updated, far less interesting graph, which plots PPS vs. % of FG assisted, with dot size corresponding to winning %.

Do you want me to pass it? No! Ball hogs and offensive efficiency

There is a lot of research on individual and team offensive efficiency - this post combines the two concepts to produce a new metric: extra points per shot (EPPS), which is a rough measure of whether a player should shoot more or less, given who his teammates are.

First I calculated each player's points per shot using this formula:

points / (field goal attempts + (free throw attempts * 0.44))

which is similar to Hollinger's true shooting %.

Then I created a similar statistic for each player's team, apart from the points and shots that player was responsible for. The formula is:

(team points - player's points) / (team FGA - player's FGA + (team FTA - player's FTA)*0.44)

Finally I subtracted team points per shot from player points per shot to yield the extra points per shot (EPPS) each player averages, relative to their teammates. I like this measure better than a "pure" measure of offensive efficiency, because it allows for otherwise efficient scorers to shoot more when they have a weak supporting cast, and penalizes ball hogs with efficient teammates.

I graphed the EPPS against the percentage of a team's shots taken by a player for the top 120 players in the league by points scored per game:

The most striking finding is how much of an outlier Tyson Chandler is, which is not surprising given his 69% FG%. Why can't the Knicks create more shots for him? Is his game limited to wide-open dunks?

Steve Nash and Ray Allen also stand out as efficient scorers who should shoot more - is Nash trying to pad his assist stats to the detriment of his team? Would that make him the league's first selfish assister?

Among the league's top 5 scorers, Lebron James, Kevin Love and Kevin Durant stand out for their efficiency. Kobe Bryant is scoring just under his teammate's PPS, evidence of a not-quite-MVP season, but not of substantial ball-hogging.

Russel Westbrook emerges as the surprising ball-hog from this analysis. He scores an above average 1.10 PPS, close to Blake Griffin and slightly better than MVP Derrick Rose. But the rest of his team scores at 1.14 PPS, the highest in the league, thanks to high efficiency and PPG from James Harden (1.31 and 17.2 PPG) and Kevin Durant (1.22 and 27.9). Pass the ball Russel!

Carmelo Anthony was excluded from the ESPN database, but when included, his numbers are almost identical to Russel Westbrook's, and he does not have the excuse of playing for an efficient team. His absolute efficiency, 1.00 PPS is the 24th worst of the top 150 scorers in the league, placing him next to Antawn Jamison (0.99 PPS) and Tyler Hansbrough (1.00), whose coaches are not getting fired.

The overall least efficient shooter: Raymond Felton, who is apparently leading a mutiny against coach McMillan. That's bold when you're shooting 38% from the field, averaging 0.15 points fewer per shot than the rest of your teammates. They can't all be desperation shots with the shot clock about to expire.