I’ve been ranting a lot about the so-called “value” of the three-point shot in “modern-day” basketball. I know! But, here is yet one more entry.

The common consensus is that teams are shooting more three point shots as discussed in the articles below:

- http://www.businessinsider.com/nba-three-point-shooting-2016-3
- http://www.nba.com/2014/news/features/john_schuhmann/11/07/history-of-the-three-point-shot/
- http://nyloncalculus.com/2016/03/08/three-pointers-and-skill-displacement/

There are several more where these have come from. My issue is that on one hand these analyses seem grossly oversimplified. Second, none of the analyses have looked at a **per-team*** *trend. From my observations of these articles, they are just looking at total number of three point shots taken/made every year over the past number of seasons.

Indeed, the standard approach is to look at the league averages from the past number of years, and note that the **average** number of three point shots and attempts has increased (well almost) year-to-year, but this is not entirely useful.

What one should do is look at the **probability** that *any* team attempts / makes more than a given number of three point shots per game in a given season. Below, we use a kernel density method to calculate these probabilities. One approach is to calculate the mean number and standard deviation of the number of three-point shots attempted and made per season for each of the previous sixteen seasons. These will generate time-dependent functions and .

One can in principle then solve a Fokker-Planck equation to obtain a time-dependent probability distribution for the number of three point shots attempted and another for the number of three-point shots made:

(where subscripts indicate partial derivatives). However, as one will quickly discover, this PDE is not separable!

My alternative approach then was to perform a non-parametric analysis using a kernel density method to fit a cumulative distribution function to each season for the past sixteen seasons. The following set of plots was generated from this method:

One sees from this analysis, specifically, from the density analysis above, in a given season, the probability that a certain team makes more than 10 3-Point shots per game never seems to exceed 10%, so while the probability of a given team attempting more three point shots may have increased, the probability of the same team making more than say 10 3-Point shots per game has essentially stayed the same over the past number of years.

The question then remains do only “good” / “efficient” teams attempt more three point shots, in particular, does this aid in their attempt to make the playoffs or eventually be a championship-calibre team. This question has been analyzed in detail and has resulted in the following paper, which is now on the arXiv.