NOTABLE ONLY IN THEIR ABSENCE
How Mapping Shots In The NBA Changed It Forever
By Kirk Goldsberry  ESPN analyst and FiveThirtyEight contributor
Every year, NBA players take about 200,000 shots. Each season, 30 teams combine to play 1,230 games, and at the end of the regular season, you can bet the sum total of shots taken will be very close to 200,000. In the hands of a cartographer, a season’s worth of this shooting data is a veritable treasure trove of information. But here’s the thing: In the first decade of this century, there weren’t many cartographers working in the NBA league office or for analytics departments in any of the team front offices.
Back then, basketball analytics was still in its infancy; it was all about spreadsheets and linear regression, not spatial and visual reasoning. Still, whether the league knew it or not, by adding these little spatial references to their game data, basketball analytics was about to become a lot more than spreadsheets. Things like data visualization and spatial analyses were going to be very important.
Unfortunately, there weren’t many folks with those skills working in pro basketball, and even though countless analysts had access to all the data the league was collecting — including all of the shot data — nobody was applying a spatial treatment. Nobody was mapping the NBA.
When I first got my hands on these massive haystacks of shooting data, I was teaching cartography at Harvard. I’d found a way to retrieve five seasons’ worth of shooting data from the web, and I built a database that included over 1 million NBA ﬁeldgoal attempts, who shot them and where they shot them from. As an analyst, I knew there was amazing intelligence waiting to be revealed within the database. As a mapmaker, I was conﬁdent I could visualize some of it in cool new ways. And as a huge NBA fan, I couldn’t wait to see the results.
The graphic is more than just a shitload of dots. This basic plot shows us where on the floor the most important concentrations of ﬁeldgoal attempts occurred in 201415. We can see that there was a major hub of shooting activity near the basket and another band of activity out beyond the 3point arc. We can also see that the league’s shooters were generally less active in the 2point jumpshooting areas between the arc and the paint, but this plot says nothing about the relative values or successes of shots in different areas.
Each one of these dots has a backstory. Each one has a shooter attached, a team attached and an outcome attached. We know who took each shot and whether it went in or not. And we can smooth out these dots statistically and map out the overall ﬁeldgoal percentage of the NBA as a collective.
Aha. Now we’re getting somewhere. Now we can see that the probability of a shot going through the net greatly depends on where that shot came from. This insight is not surprising on its own, but it does reveal specifics about the basic relationships between distance, direction and ﬁeldgoal percentage. What did surprise me when I first studied this chart was learning that outside of 6 feet, there is no place on the court where shooters make more than 45 percent of their shots. I’d always thought that 50 percent was the magic ﬁeldgoal percentage threshold, but this graphic shows that the only place on the floor where players exceed that magic number is the tiny swath of space just in front of the basket.
The next thing I noticed was even more surprising. When you look at leaguewide shooting numbers between 6 and 25 feet, the league is strangely consistent. I expected to see a marked decrease in ﬁeldgoal percentage with greater distance: I thought shorter jump shots would go in at higher rates than longer jump shots. While this is true, the effect is much more subtle than I would have expected.
As it turns out, NBA players make only 40 percent of their shots between 8 and 9 feet from the rim, and that number drops to only 35 percent between 25 and 26 feet from the rim. When it comes to ﬁeldgoal percentage on jump shots, the effect of shot distance is pretty minor. It was a revelation, and it drove me to quickly build the following map, which would forever change the way I viewed scoring in the NBA.
Fieldgoal percentage is only part of the story, and in a league with a 3point line, it is a very misleading part of the story. After all, points are the ultimate currency in the NBA.
When we visualize the average points per shot according to shot location, only then does the true economic landscape of the contemporary NBA reveal itself. Only then does Daryl Morey’s economic vision become clear. Only then do we see the massive economic subsidy represented by the 3point line. And when we compare the pointspershot map with the ﬁeldgoal percentage map, we are left with a troubling thought about the contemporary geography of NBA basketball.
If it’s true that 3point shots go in 36 percent of the time and 10foot shots go in just 40 percent of the time, then why are we assigning 50 percent more value to shots from beyond that magical little arc?
The natural landscape depicted in the ﬁeldgoal percentage map demonstrates that jump shooting in the NBA is essentially a 35 to 45 percent proposition; however, some of those shots are worth 3 and some are worth 2. Naturally, as basic economics would predict, the behavior of players and teams has reacted in the form of shot selection. When we overlay the most common 200 shot locations in today’s NBA, we see that shot selection and economic efficiency are aligned.
No wonder 2point jump shooting is dying.
Excerpted from “SprawlBall: A Visual Tour of the New Era of the NBA” by Kirk Goldsberry. Copyright © 2019.
STEM 02: Problem Set  1

Find the perimeter of a basketball court.

What is the distance between the free throw line and the hoop?

What is the radius of the center circle on a basketball court?

If a basketball court is divided into two equal halves, what is the length of each half?
Solution: Each half of a standard basketball court would be 47 feet long. 
What is the area of a basketball court?

If a basketball court is divided into four equal sections, what is the area of each section?

If a basketball court has a 3point line, what is the distance between the hoop and the 3point line?

If a basketball court is divided into eight equal sections, what is the perimeter of each section?
The Four Factors
How do basketball teams win games? Dean Oliver identified what he called the "Four Factors of Basketball Success":

Shooting (40%)

Turnovers (25%)

Rebounding (20%)

Free Throws (15%)
The number in parentheses is the approximate weight Oliver assigned each factor. Shooting is the most important factor, followed by turnovers, rebounding, and free throws. These factors can be applied to both a team's offense and defense.
Shooting
The shooting factor is measured using Effective Field Goal Percentage (eFG%). The formula for both offense and defense is (2ptFG + (1.5 x 3ptFG))/ FGA. Where FGA = Field Goals Attempted. Note: that in most box scores, the initial field goal figure gives the total number of field goals so that the 3 points must be subtracted from the total to get the number of two pointers.
Turnovers
The turnover factor is measured using Turnover Percentage (TOV%). The formula for both offense and defense is TOV / (FGA + 0.44 * FTA + TOV). Where FTA = Free Throws Attempted. The factor 0.44 reflects the proportion of Free Throws where possession can be changed. For example, on a two or three shot foul, possession can only change on the final free throw.
Rebounding
The rebounding factor is measured using Offensive and Defensive Rebound Percentage (ORB% and DRB%, respectively). The formula for offense is ORB / (ORB + Opponent DRB), while the formula for defense is DRB / (Opponent ORB + DRB).
Free Throws
The free throw factor is a measure of both how often a team gets to the line and how often they make them. The formula for both offense and defense is FT/FGA.
STEM 02: Problem Set  2
Using the analysis components of the Four Factors, which team;

Had the highest eFG? What was is (round to the nearest tenth of a per cent). Do the same for the team with the lower percentage.

Which shooters (4 or more FGAs), had better than average games? Which shooters had worse than average games?

Which team had the most turnovers? Which players had the most turnovers?

Based on a quick look at the box score above, at the player level, is there a correlation between AST (assists) and TO (turnovers)?

Which team grabbed more boards? Using the above analysis, what would you conclude about the offensive rebounding of each team?

Does the +/ statistic measuring the team’s success rate correlate to the eFG of the players?

How does the TO (turnover) rate compare to the +/ statistic?

Given that the team +/ is 12 for Boston and 12 for Golden State, based on the above information, which players were most responsible for winning the game for Golden State, and which players were most responsible for losing he game for Boston?

Which four players committed the most frequent personal fouls per minute of playing time?

When you look at this box score, are there any particular numbers that look unusually good or bad?