The Effects of Shot Volume and Shot Percentage on Defensive Efficiency

Author: Jeremy Brooks (Weinberg ’20)

Two possible pathways to quality defense in basketball are to force opponents to miss
their shot attempts (regardless of what area of the court they shoot from), or force opponents to
have a high distribution of shot attempts in typically inefficient zones of the court (such as long
mid range shots). In the NBA, achieving both is important for a strong defense, however the
relative importance of each pathway may vary.

To understand the influence of field goal volume versus field goal percentage, the effect
of each was considered for different areas on the court. The court was divided into five distinct
locations: three that correspond with high quality shots (restricted area, corner threes, and
above-the-break threes), and two that correspond with low quality shots (non-restricted area
paint, mid range), based on average points per field goal attempt. For each location, both the
allowed field goal attempts and the allowed field goal percentage were plotted against team
defensive rating for the 2017-2018 NBA regular season. The R^2 value was calculated for each
plot in order to examine which variable best explains defensive rating for each area on the court.

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Determining whether the allowed field goal attempts or the allowed field goal percentage
is a better predictor of defensive efficiency is dependent on field goal location. For shots taken in
the non-restricted area of the paint and threes taken in the corner, field goal attempts have the stronger correlations with defensive rating. For the other three locations (restricted area, mid
range, and above-the-break three pointers), field goal percentage has much stronger correlations
with defensive rating.

One implication that arises from the data is that all observed data sets have relatively low R^2
values, indicating weak correlations. This is not surprising, as defensive efficiency has many
confounding factors independent of field goal attempts and percentage in particular locations.
Numerous other variables – including turnovers, free throws allowed, proximity of the nearest
defender, and fatigue – affect defensive efficiency, meaning that any one variable is expected to
have a limited correlation with defensive rating.

However, what may explain the observed disparities in correlations for field goal
attempts and field goal percentage for different shot locations? The first piece of the puzzle
relates to overall field goal attempts: notably, the two zones where field goal attempts had the
strongest correlation (non-restricted area paint and corner three) were also the areas in which
total field goal attempts were lowest. Similarly, these two areas also had the greatest spread of
data as a percentage of the median (calculated as the standard deviation over median).

The second piece of the puzzle is that these two areas of the court are each “efficiency
extremes”. Shots in the non-restricted area of the paint are very inefficient, meaning that any
attempt in that area is mathematically a “win” for the defense on average. The example of the
Atlanta Hawks illustrates this concept: they were the league’s worst (in 2017-2018) at defending
shots in the non-restricted area paint, allowing opponents to hit 43.7% from this range. However,
holding opponents to 43.7% on any subset of two-point shots is an extremely powerful defensive tactic (this would translate to an unprecedented 87.4 defensive rating, neglecting possible free
throws from and-ones).

Conversely, corner three-point attempts are extremely efficient, so any attempt from that
range is mathematically a “loss” for the defense on average. The Philadelphia 76ers were one of
the league’s best at defending corner threes, allowing opponents to hit only 37.3% of their shots.
But because of the efficiency of these shots, this relative excellence in corner three point defense
translates to a 111.9 defensive rating (again neglecting free throw attempts from and-ones),
which would be the worst in the NBA by a substantial margin. Therefore, because both shot
locations represent efficiency extremes over nearly the entire range of field goal percentage, the
dominant control on defensive rating for those shot locations is number of attempts, not field
goal percentage. Combining this understanding of efficiency extremes with the already high
variance in field goal attempts in those locations from team to team explains why field goal
attempts more strongly correlate with defensive rating than field goal percentage.

For the other three locations (restricted area, paint, and above-the-break-threes), field
goal percentage is expected to be a significant indication of defensive efficiency because
percentage is most directly related to points allowed, and because these three locations have
relatively high numbers of field goal attempts and relatively low spreads of data.

Analyzing the correlations of both field goal attempts and field goal percentage with
defensive rating in different zones of the court reveals information about the importance of
different shot types on defensive efficiency. This understanding of the highly variable influences
of field goal attempt volume and field goal percentage on defensive rating can be used to
construct defensive strategies with differing priorities based on the area of the court defended.


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