The Anatomy of the Three-Point Shot: Spatial Bias, Fractals and the   Three-Point Line in the NBA
  Even though it might have taken some time, the three-point line ultimately changed the way the game is played as evidenced by the increase in the three-point shot attempts over the years. However, during the last few years we have experienced record-breaking seasons in terms of both three-point attempts and field goals made. This brings back to the surface questions such as "What is the rationale behind the three-point line?", "Is the three-point shot distance appropriate?" and many more similar questions. In this work, even though we do not take a stand against the three-point line, we provide evidence that challenge its distance. In particular, we analyze shot charts and we identify a statistically significant discontinuity in the shot attempts between 1-feet zones just inside and outside the three-point line. In addition we introduce a metric inspired by fractal theory to quantify this bias and our results clearly indicate that the space dimensionality in these areas of the court is not fully exploited. By further examining the field goal percentages in the zones considered, we do not identify a similar discontinuity, i.e., the field goal percentage just inside the three-point line and just outside the line are statistically identical. Therefore, even though the shooting behavior of the teams appears to be rational, it raises important questions about the rationality of the three-point line itself. 
Konstantinos Pelechrinis
stat.AP