Defending the jump shot, particularly the 3-point shot, is one of those seemingly small topics that for some reason I keep coming back to. I think what first peeked my interest was a podcast in which a guest speculated that one of the biggest unanswered questions in basketball analytics was the degree of control the defense has on the offense’s 3-point field goal percentage. He said that some analysts guessed that much of the year-to-year variability in 3-point percentage defense was due to chance. The main source of control a defense has with to respect to 3-pointers could be limiting the number of attempts (particularly open and corner threes), rather than forcing a low percentage.

I dived right into some small projects inspired by this discussion. My first post examined whether the shooting ability of the players actually taking the 3-pointers against a particular defense had some ability to explain variability in 3-point percentage defense. I looked into whether the Celtics’ sustained run of top-5 3-point percentage defenses under Coach Brad Stevens could be a fluke of randomness (it’s highly likely it’s not). I also analyzed which team statistics were most likely to carry over from the first half of the regular season to the second, and found defensive 3-point percentage was low on that list.

Now, I have tried quantify exactly how many points of defensive rating (points per 100 possessions allowed) are subject to opponent shooting variability. Besides simply considering 3-pointers, I also looked at free throws and ‘deep’ 2-point attempts, where I defined deep as greater than 16 feet.

## Defining Net Shooting Points

Question: How many points would Team X’s defensive rating change if their opponents shot an ‘average’ percentage on 3-pointers? Well, the answer seems simple enough. Basketball-reference tells us how many 3-point attempts a particular defense allowed, per 100 possessions, and what percentage opponents shot on those attempts. We can simply move this percentage to league average and calculate how many points would be gained (or lost), right?

As it turns out, there is one other small adjustment we should make. Every missed shot has an opportunity to be rebounded by the offense. So a made 3-pointer that magically turns into a miss does not simply subtract 3 points from a team’s score; we have to add back the expected points that could be gained by an offensive rebound leading to a new possession. The percentage of missed shots which were offensive rebounded in 2017-18 was 22.3%, and the mean points scored per possession was about 1.086 (per basketball-reference). Multiplying 0.223 by 1.086 we get about 0.24, meaning that each missed 3-pointer yielded 0.24 points in value from potential offensive rebounds. (As an aside, one could use the precise offensive rebounding percentage on missed 3-point attempts and the expected points per possession after an offensive rebound, but the original numbers will do for my purposes.)

With this idea in mind, I will explain how I compute **Net Shooting Points**, the points a team’s defensive rating would increase if they allowed a league average percentage on 3-pointers, free throws, and long 2-pointers. To do this, I start by defining **Net 3-Point Shooting Points.**

**Net 3-Point Shooting Points = New 3-Point Shooting Points – Original 3-Point Shooting Points**

**= [(3 * 3-PT % Avg. * 3-PT FGA_per_100) + ( 3-PT FGA_per_100 * (1-3-PT % Avg.) * OReb % Avg. * ORtg Avg./100)] –**

[**(3 * 3-PT % * 3-PT FGA_per_100) + (3-PT FGA_per_100 * (1-3-PT %) * OReb % Avg. * ORtg Avg./100)]**

where 3-PT % Avg. is the league average 3-point percentage for the particular year, 3-PT FGA_per_100 is opponent 3-point field goal attempts per 100 possessions, OReb % Avg. is the average offensive rebounding percentage of that year, and ORtg/100 is the average offensive rating divided by 100 (i.e. points scored per possession).

Net 3-Point Shooting Points attempts to answer the question of how many more points per 100 possessions would a team have given up if they allowed the exact same number of 3-point attempts, but opponents shot a league average percentage. A positive value means a team would have given up *more* points had opponents shot the league average percentage, and thus had a worse defense, while a negative value means that their defense would have improved.

Similarly, we can define **Net Free Throw Shooting Points **and **Net** **Deep 2-Point Shooting Points**:

**Net Free Throw Shooting Points = [(FT % Avg. * FTA_per_100) + ( FTA_per_100 * (1 – FT % Avg.) * 0.114 * ORtg Avg./100 * 0.553)] **–

[**(FT % * FTA_per_100) + ( FTA_per_100 * (1 – FT %) * 0.114 * ORtg Avg./100 * 0.553)] **

**Net Deep 2-Point Shooting Points = [(Deep 2-PT % Avg. * Deep 2-PT_per_100) + (Deep 2-PT FGA_per_100 * (1-Deep 2-PT % Avg.) * OReb % Avg. * ORtg Avg./100)] **–

[**(Deep 2-PT % * Deep 2-PT_per_100) + (Deep 2-PT FGA_per_100 * (1-Deep 2-PT %) * OReb % Avg. * ORtg Avg./100)]**

If you stare at these formulas, you might ask what the 0.114 and 0.553 represent in the Net Free Throw Shooting Points equation. The 0.114 represents the fact that 11.4% of missed free throws which had the opportunity to be offensive rebounded were, in fact, offensive rebounded in 2017-18 (11.4% is close to the 11.5% figure Seth Partnow found in 2015). The 0.553 is there because only the second free throw in a 2-shot foul (or the third in a 3-shot) can be offensive rebounded. By sifting through play-by-play data, I found that 55.3% of free throw attempts had the opportunity to be offensive rebounded in 2017-18.

With all of the above definitions, we can define

**Net Shooting Points = Net 3-Point Shooting Points + Net Free Throw Shooting Points + Net Deep 2-Point Shooting Points**

In other words, Net Shooting Points are simply the estimated additional points per 100 possessions that a defense would have given up if their opponents shot a league average percentage on 3-pointers, free throws, and deep 2-pointers (greater than 16 feet).

## Net Shooting Points for 2017-18

Let’s dive right in and see where each team stood in terms of Net Shooting Points in the 2017-18 regular season. The link below goes to a spreadsheet showing where each team stacks up in each component of Net Shooting Points. An important reminder: Net shooting points represents the additional points per 100 possessions that a defense would have given up had opponents shot league average on 3-pointers, long twos, and free throws. *So a positive Net Shooting Points value means that the defense would have gotten worse had opponents shot league average (opponents shot poorly in actuality) and a negative value means that the defense would have gotten better (opponents shot well).*

### Table of 2017-18 Team Net Shooting Points

The following graph displays Net Shooting Points visually:

To interpret the graph, think of the red dot as where we might *expect* each defense to be, after accounting for Net Shooting Points, and the blue circle as where they actually were. The Net Shooting Points value is the red dot value minus the blue circle value. If the red dot position is greater than the blue circle position, than the team had positive Net Shooting Points (and vice-versa).

We can see from the table and graph that the three teams with the most positive Net Shooting Points, the 76ers, Celtics and Rockets, each allowed about 2 points per 100 possessions *less* than would have been the case had opponents shot league average. If we simply recorded the number of 3-pointers, free throws, and deep 2-pointers that opponents attempted against these teams, but did not know the percentage that went in, we might expect these teams to allow about 2 points per possession more than they actually gave up. The three bottom teams, the Hawks, Hornets and Kings, each allowed about 1.5 points per 100 possessions *more *than expected thanks to above average opponent shooting.

So how big a deal is 2 points per 100 possessions? Well, according to a regression I ran previously, every point of net rating is equal to, on average, about 2.5 wins over the course of the 82 game season. So a +2 net rating team is usually around 46 wins while a +0 net rating team is often about average (41 wins). 2 points of net rating is a big deal!

One fairly intuitive observation you will make by scanning the table in the link above is that Net Shooting Points tend to be dominated by Net 3-Point Shooting Points. This makes sense given the high volume of 3-point attempts and the fact that 3-pointers are worth more than deep twos and free throws. To further illustrate this, the average absolute value of Net 3-Point Shooting Points in 2017-18 was 0.72 points, while this number was 0.21 and 0.17 for Net Free Throw Shooting Points and Net Deep 2-Pointer Shooting Points, respectively.

## Analysis

So, what should we make of all this? The Sixers ‘gained’ 2.3 points of net rating last season from opponent poor shooting, as the title of the post implies. So were they just lucky? And what’s up with all these really good teams like the Celtics, Rockets, and Warriors benefitting from opponent bricks from outside?

The story is probably a bit more complicated than just pure luck. After all, we can imagine a good defense effectively contests outside shots and does not allow as many easy open looks as a poor defense. I need to do more research to study the *quality* of the outside shots given up by each team. Moreover, for the Sixers in particular, we might suspect that a strong interior defense could scare opponents away from the paint and entice more bad outside jumpers. And the Celtics, the league’s best 3-point percentage defense, have been near the top of the league in this stat for a while, stubbornly offering a point against the theory that 3-point percentage defense is mostly luck.

Examining the graph above, it stands out that each of the 10 worst defenses in the NBA would have been improved had their opponents shot merely league average on jumpers, while many of the top defenses would have fallen off. Perhaps this is a point in favor of the idea that defending the perimeter is something which the defense exerts a good deal of control over. Of course, it also makes some sense that the worst defenses in the NBA actually performed that way because opponents made a lot of outside shots. The causality probably runs in both directions. That is, bad defenses allow opponents to hit a higher percentage of jumpers but, also, good opponent outside shooting can lead to a poor defensive rating.

Because I was curious how predictive Net Shooting Points from one year were of the next year, I went back to the 2005 regular season and computed this value for each team. I then normalized each Net Shooting Points score by subtracting the mean and dividing by the standard deviation of each particular year (giving us a z-score for those statistically inclined). Next I used a linear regression to predict the next year’s Net Shooting Points from the previous year.

The result was that the next year’s Net Shooting Points was, on average, .244 times the previous year’s value (i.e. about 25% of previous year). The intercept term equaled 0. The coefficient from this regression was, in fact, significant (even at the 0.01 level), meaning that previous year Net Shooting Points has an association with the next year’s value which is probably not due to sheer chance.

It might be reasonable to start, at the beginning of the next season, with the baseline ‘expectation’ that each defense’s Net Shooting Points will be about 0.25 times the Net Shooting Points of the previous season, on average. The uncertainty around this estimate is really high though. The standard error from the regression was almost 1 point, indicating that the 95% confidence bound is 0.25 times previous season Net Shooting Points plus or minus 2 points.

The result of the regression makes some sense to me. Perhaps there is an element (maybe even a large-ish element) of opponent outside shooting which is fairly random. But there is some part of this which the defense is actively influencing. A good defense might hamper opponent outside shooting by not allowing open looks from good shooters, force teams to settle for bad shots after stalled possessions, and do other important things well which cause opponents to shoot a poor percentage.

We should perhaps begin with the belief that the Sixers will be closer to a +0.6 Net Shooting Points defense in 2018-19, rather than the +2.3 that they put up in 2017-18. Interestingly, the Sixer’s Net Shooting Points for 2014-15, 2015-16, and 2016-17 were -0.3, -1.3, and +0.1, respectively, though the previous year’s Sixers, especially the 2014-15 and 2015-16 editions, bore little resemblance to last year’s squad.

It should be pointed out that my analysis is limited by the fact that there is more to perimeter defense than just allowing a low percentage of makes. It also matters the volume of shots that opponents are taking from long range. And perimeter defense is obviously heavily intertwined with the other parts of defense, such as interior defense. It makes sense to look at all the parts of good NBA defense together.

Still, I think it is good to start quantifying the effect opponent outside shooting has on overall defense. I hope Net Shooting Points can be useful in this regard.

### References:

Data for this post was obtained from basketball-reference.com.