Friday, January 31, 2014

Defending the Three

Before Paul George broke out as an offensive force, he was widely known for his suffocating defense. But is he a good enough defender to make shooters miss wide-open threes?


That was a trick question. Of course not! This video is not an example of good defense but rather Paul George getting lucky that an open shooter missed a wide-open shot.

In a previous article, I developed a framework for calculating defensive XPPS based on Ian Levy's Expected Points per Shot. Let's apply this method but focus specifically on three-point shooting and determine which players are getting lucky. Have Paul George's opponents missed a ton of open shots?

In order to understand what constitutes an open shot, let's revisit some of Vantage's definitions for shot defense.

Altered shot: Defender is within 3 feet of shooter and hand is up. Offensive player must change shooting angle or release point while in the air.

Altered shot:

Contested shot: Defender is within 3 feet of shooter and hand is up. Offensive player does not alter shooting angle or release point.

Pressured shot: Defender is within 3 feet of shooter but does not have his hand up.

Guarded shot: Defender is within 5 feet of shooter but not within 3 feet.

Open shot: Defender is not within 5 feet of shooter.

So what are the league's percentages on threes when left open versus contesting a shot?

Shot Location     contest       altered    guarded     open  pressured
a 34.97% 0.00% 44.21% 42.50% 35.20%
b 34.51% 0.00% 39.58% 41.04% 32.36%
c 32.37% 12.50% 35.81% 39.95% 30.35%
d 32.69% 0.00% 39.65% 41.18% 33.51%
e 35.53% 0.00% 38.81% 48.27% 42.22%
*there were only 35 altered 3 point attempts in the sample of data
(Note: See location chart at the bottom of this post.)

For the most part, the biggest differences in three point shooting occur when pressuring/contesting the shooter as opposed to guarding him. The one exception to this is for threes attempted in the right corner, where we see some odd splits. We also see that straightaway threes are the worst type of three with lower percentages at every level of shot defense (besides altered shots, where the sample size is small).

We can use these percentages - in the form of points per shot - to calculate defensive XPPS and develop a Luck statistic. Based on the percentages above, we know it is important for defenders to at least pressure the opposing shooter. So to calculate our Luck statistic, we'll add up the points that a defender gave up on guarded and open shots and subtract the number of points they would be expected to give up based on the league wide rates for guarded and open shots. 

Let's look at an example using Paul George. First, we need to calculate the points per shot for each type of shot defense at each three-point location. We can do this by multiplying all the values in the table above by 3. Next, we multiply these values by the number of field-goal attempts against Paul George. For example, in the left corner, opponents attempted 3 open shots against George. We multiply this value times the league points per shot value on open shots (so from the table, .425*3=1.275*3 open shots=3.825). We do this for both open and guarded shots and get the following table for Paul George:

     points exp points
a 9 5.151
b 9 13.368
c 3 7.892
d 12 12.171
e 3 8.434
Total 36 47.016
Luck -11.016

As shown in the table, after calculating the points and expected points for each shot location, we add it up and then subtract the expected points from the actual points to get a "Luck" statistic. A negative value represents the fact that Paul George gave up less actual points than he was expected to give up on guarded and open shots given the league wide rates. A positive value would indicate the player has been unlucky due to giving up more points than expected. 

Of course, there are a few issues with the Luck statistic calculated above. First, we are using a counting statistic, which will reward those who give up more open/guarded shots. The more open/guarded shots the defender gives up, the more likely it is that his Luck statistic will be larger in either direction. This will also favor those players who have defended the most shots in the sample because they are also more likely to have defended more open/guarded shots. We can address this by dividing the Luck statistic by field goal attempts. However, those players who give up a ton of open/guarded shots should be penalized and we get a better idea of which players those are by looking at "Luck" as a counting statistic.

With the flaws of Luck in mind, let's look at Luck versus Points per Shot:

note: minimum 50 3pt FGAs defended

As we see here, Paul George has gotten lucky with his opponents missing about 11 points on open shots. Other notable players who have gotten lucky with their opponents missing more open shots than they should include Steve Nash, Rudy Gay, Avery Bradley, Kevin Durant, Paul Pierce and Jrue Holliday. Tayshaun Prince leads the way with opponents missing about 23 points on open shots.

How about if we divide Luck by field goal attempts? (note: this will adjust for how many shots a player defended) What does Luck/FGA versus Points per Shot look like?

Many of the same players appear in the same places but some high minute players like Kevin Durant and Paul George are closer to average (zero) after the conversion of Luck to a rate statistic.

Let's now look at Contest+ (defined as blocking, altering or contesting a shot). Which players contest the most three point shots? What is the range for Contest+?

To answer the questions above, Willie Green contests the highest percentage of his 3 point shots (80.3%) while Chris Paul contests the lowest percentage of his 3 point shots (34.1%). The range for contest frequency is 46.3% which we can see in the histogram below:

The range in contest+ for defending threes was larger than it was for rim protection rate (37.8%) but we also had a smaller sample for rim protection rate. We can look at the distribution of both rim protection rate and contest+ for defending threes in the histogram below:

Keep in mind, the sample size is smaller for rim protection rate so the distribution will be smaller. However, we can see there were more players with contest+ rates in the 30%-35% bin for shots close to the basket (light green). This is not surprising as the league average contest+ frequency is lower for shots near the basket than for three-point shots.

Finally, let's plot XPPS (expected points per shot) versus actual PPS and see which defenders are under-performing or over-performing their expected points per shot: 

In the graph above, the x- and y-axis scales are the same so we can visualize the magnitude of "luck" or "hidden skill" that many of these defenders have in regard to their actual points per shot versus what would be expected given league average shot defense rates. As we see in the graph above, there is a much wider distribution in actual points per shot versus XPPS.

Let's increase the scale for the x-axis so it is easier to determine the different players:

Tony Allen is the best player at defending threes according to XPPS and his actual points allowed per shot is pretty much the same. We can also tell from the size of the circle that Allen contests a large majority of his three-point attempts which isn't surprising since Allen is regarded as one of the best wing defenders in the league. We can also see that players such as Nicolas Batum and Jeremy Lin (upper left quadrant) have been unlucky (or lack a "hidden skill") with their PPS being much higher than their XPPS. Conversely, we see that JJ Redick and Kyle Lowry (bottom right quadrant) have been lucky (or possess a "hidden skill") with their PPS being much lower than their XPPS.

Note: Due to the odd splits for threes attempted from the right corner, we decided to include pressured shots from the right corner in the luck statistic. In general, pressured shots are considered to be open shots (see this article) but for three-point shots, there is almost no difference between contesting a shot and pressuring it. However that is not the case for shots from the right corner.

Disclaimer: These statistics include the previous two years but not this year (2013-14).