The NBA in 2021 is very different from what it was in 1979. The introduction of the three-point line changed the economics and strategy of the sport entirely. Despite teams in the NBA taking a long time to fully realize the value that the three-pointer has, and adapt their offense to maximize its use, it seems like we have finally reached the pinnacle of basketball efficiency.
As we can see from the graph above, the aggregate amount of three-point attempts that teams are taking each game has increased rapidly over the past 30 years. Even before the perimeter-oriented Golden State Warriors dynasty proved that you can win championships by living behind the arc, teams were slowly beginning to modernize their offense and take more threes. As it was all happening, NBA front offices began to realize the value in long-range shots that were worth an additional point, and their roster-building strategies transformed as well.
From the graph above, we can gather that as these perceptions within front offices have shifted, so has the quality of shooting on the court. The average three-point percentage in the NBA has been on an upward trend, with three-point attempts approximately 5% more likely to fall today than they would have been in 1990. While it might not seem like a massive difference, it’s certainly shaped the way that the game is played.
As Kirk Goldsberry, a scout for the San Antonio Spurs details in his New York Times bestselling novel, SprawlBall, modern basketball has essentially killed the mid-range jumper. All other variables ignored, what would be the purpose of shooting an 18-foot jumper on the baseline worth two points, when you could step back a few feet, get a more open look, and knock down an equally difficult shot worth 150% as many points? There’s a simple answer to this question, and it’s a philosophy that has led to the inception of the shot chart below:
With all of this in mind, I decided to dive into my own statistical experiment. The word consistency is often loosely thrown around in basketball. “I like Ja Morant, but his scoring ability seems inconsistent,” or “The L.A. Clippers have a lot of talent, but they just can’t bring it consistently enough to be pegged as title favourites.” With the prevalence of three-point shooting in today’s game, my quest was to determine whether or not a team’s consistency in how well they shot the ball from behind the arc would affect their winning percentage, and conversely, whether or not a team’s consistency in how well they defend the three-point line would affect their winning percentage.
In mathematical terms, I defined consistency as the variation of a team’s shooting, by calculating the variation of shooting percentage in each game. With that, I found the standard deviation, and assumed that all values throughout a 72 game season would become normally distributed around the mean. In order to compare apples-to-apples, I converted each team’s distribution to a standard normal distribution and calculated the Z-Score, before ultimately calculating the average of the absolute value of all Z-Scores throughout the season. If a team had a lower Z-score, it would imply that their three-point shooting was more consistent, and if a team had a higher Z-score, it would imply that their three-point shooting was less consistent.
For example: let’s say that the Raptors’ three-point shooting was fluctuating wildly from one game to the next. In English terms, this would be defined as inconsistent shooting. Through the derivations explained above, this would be demonstrated through a higher average Z-Score.
After running the calculations for 72 games on all thirty NBA teams for the 2020-2021 season, the rankings of offensive three-point consistency and defensive three-point shooting consistency turned out as follows:
With this data, I decided to determine whether or not a team’s shooting consistency from beyond the arc was correlated to their winning percentage. In short, it was not, as one could have probably assumed based off the rankings alone. While I was a little bit surprised by this outcome, one aspect of shooting that my formula fails to capture is how well each team is actually shooting the ball. A team can be extremely consistent shooting it – but that could also mean they’re consistently bad – therefore a higher level of offensive shooting consistency has no correlation to how well a team performs in the long run.
Secondly, I was intrigued to see whether a team’s consistency in guarding the three-point line could point towards whether the team performs well or not. To calculate this, my primary metric was opponent three-point percentage. Upon graphing defensive three-point consistency against a team’s winning percentage, I was able to find a moderate correlation between the two variables. Teams that are more consistent in defending the three-point line actually do win more games. With an R-Squared value of 0.2302, we can see that just over 23% of the independent variable’s fluctuations (winning percentage) can be explained by changes in the dependent variable (defensive three-point consistency).
To further dive into whether this relationship was a fluke or if it was legit, I decided to graph each team’s defensive three-point consistency against their defensive rating. My hypothesis was that if there was a correlation between defensive three-point consistency and defensive rating, then the defensive three-point consistency’s correlation with winning percentage could be explained by the fact that consistency guarding the three-point line produces a stronger overall defense. Regardless of whether that team was consistently bad at guarding the three-point line, or consistently good, it would still provide a measure of how well the team’s personnel was able to stick to its defensive game plan.
Ultimately, the graph illustrates that 22.72% of fluctuations in a team’s defensive rating can be attributed to changes in the team’s defensive three-point consistency. While this relationship would need to be proved as a causal one by yet another exogenous factor, it does help to solidify the theory that consistency guarding the three-point line is directly tied to a team’s winning percentage.
People love to hate on math geeks who try to wiggle their way into sports conversations – even Kevin Durant – and I understand that perspective as well. Does all of this really matter at the end of the day? If a team has three superstar players who are all healthy, then who cares about numbers? Their probability of winning a championship is going to be pretty damn high regardless of how their coach leverages their skills.
While that may hold true, it doesn’t mean that numbers should be ignored. Let’s look at some real-life applications of defensive three-point shooting consistency, and how it has led to more wins for our very own Toronto Raptors.
In the 2019-2020 season, the Toronto Raptors had the second highest ranked defensive rating – yet they allowed their opponent to shoot the corner three-pointer more than any team in NBA history, beating the second highest ranked team by 27%. Given that the corner three is highly regarded as one of the most efficient shots in basketball, how exactly was it possible for these two rankings to synchronize? The simple explanation could be that the roster was equipped with plenty of excellent individual defenders. Maybe a more mathematical explanation could be that last year, the Raptors had a defensive three-point consistency of 0.7728: a figure which would have placed them 2nd among all teams in that category this season.
Ultimately, defensive three-point consistency is far from a flawless stat, however it certainly provides a backbone for the argument that consistency guarding the most important shot in basketball is… well… important.