Introducing 3-PIGS, a New Way of Understanding Three-Point Variability in NBA Games

The rise of the three-point jump shot in the NBA has been well documented. Over the past five regular seasons the average team three-point attempt rate has spiked from 24.3% to 33.7%, per basketball-reference. The analytically driven Houston Rockets actually attempted more three-pointers than two-pointers this past season!

In this three-point happy league, analyzing an individual game after removing the effects of “hot” or “cold” three-point shooting can be very informative. It allows us to see how well the teams played in all aspects of the game except three-point accuracy. We can strip aside a particularly unusual shooting performance and observe the “fundamentals” of a game, in a certain sense.  This is what Three-Pointer Independent Game Score (abbreviated as 3-PIGS) does.

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Are Past Games in a Playoff Series Predictive of the Next Game?

I recently was building a simple model to forecast an NBA playoffs series. As I was building the model, I realized that I was not taking into account the possibility that each team’s strength could change over the course of the series. If a team dominates games 1 and 2, we might reasonably expect them to have a higher likelihood of winning game 3 than we did at the beginning of the series.

But perhaps we should not alter out initial belief too much. After all, the 2 games in the example above is not a very large sample. Sheer randomness and recency bias may be causing us to shift our thinking too much. My initial hunch was just that; the general public overreacts too much to a few performances.

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An Analysis of the 2-for-1 Strategy in the NBA

The appropriately named “2-for-1” is a strategy utilized at the end of a quarter in which a team tries to time their shot attempts so that, as the name suggests, they get two attempts while their opponents only have one. To execute the strategy, a team usually pushes the ball up the floor to take a shot with about 30 seconds left in the quarter, thus ensuring that their opponents cannot hold for the last shot.

Intuitively, this strategy seems perfectly reasonable. Just like holding for the last shot, a team which executes the 2-for-1 is gaining one extra possession. Who would not want an extra possession? Well, we could imagine a scenario where the two possessions are so rushed that their expected value is less than the value of the one “normal” possession the opponent is allowed. For example, suppose we value a conventional NBA possession at 1.09 expected points but the two rushed possessions usually generate bad shots and are only worth 0.5 expected points each. Then it might make more sense to execute a “1-for-1” strategy and simply grant the opponent the last shot.

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Which Team Statistics are Most Stable From the 1st Half of the Season to the 2nd?

In my work on the Threes and Layups NBA Net Rating Calculator, I have focused on 14 statistics (the same 7 on offense and defense) which capture a team’s performance across all areas of the game:

  1. 2-Point %
  2. 3-Point %
  3. 3-Point Attempt Rate
  4. Free Throw Attempts Per Field Goal Attempts
  5. Free Throw %
  6. Turnover Rate
  7. Rebound Rate (Offensive and Defensive)

The NBA Net Rating Calculator allows you to see how much a team’s regular season performance would be expected to change if you changed one of these statistics. But this leads to a natural question: which of these statistics is most likely to change?

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Are the Raptors Really a Bad Playoff Team?

The Toronto Raptors are in the middle of an impressive regular season. They have outscored opponents by 8 points per 100 possessions this season, the second best mark in the league behind only the Warriors, per basketball-reference. Regular season success is nothing new for the Raptors, as Toronto has posted a net rating of at least +3.5 in each regular season since 2013-14. This Raptors team has not only built upon the successful campaigns of the previous seasons, but also added new dimensions to their game. Their upgraded shot selection on offense has them currently ranked 7th in the NBA in 3-point attempt rate.

While the Raptor’s statistical profile is once again impressive, I can’t help but get the feeling that a lot of NBA fans are probably having right now: We’ve seen this story before. A strong regular season Raptors squad goes into the postseason and helplessly fizzles out. This feeling is backed up by the performances Toronto has put up in the playoffs since the 2014 season.

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Is the Celtic’s 3-Point Percentage Defense for Real? A Statistical Perspective

In a recent Dunc’d On podcast (which I highly recommend as a great listen for NBA fans), the hosts Danny and Nate briefly commented upon how the Celtics defense this season has been bolstered by the league’s second best 3-point defense, in terms of percentage of opponent makes. They also mentioned, however, that many NBA thinkers speculate 3-point percentage defense may be mostly due to luck and beyond the defense’s control. In fact, many argue that the best indicator of a good 3-point defense is the ability to limit opponent 3-point attempts, particularly the dangerous corner threes. I have previously written a little about 3-point defense for

With the conventional wisdom in mind, it also should be noted that the Celtics under coach Brad Stevens have consistently performed well in 3-point percentage defense. Boston has been a top five ranked team in this regard during each of the five years (if we include the current season) of the Stevens tenure. Perhaps there is something more than luck going on here? I decided to investigate this more deeply.

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Explanation of Threes and Layups NBA Net Rating Calculator


Today I released the Threes and Layups NBA Net Rating Calculator, an interactive web application that is an updated version of what I called the Threes and Layups Season Simulator before. To go to the app,  click the link above or click on the the link on the right side of the page under “Interactive Web Applications”.  Throughout the season, the application will be updated with up-to-date statistics.

First, a bit of background.

An NBA team’s Net Rating is simply the number of points per 100 possessions that they score (called Offensive Rating) minus the number of points per possessions that their opponents score (called Defensive Rating). A team’s Net Rating is essentially a one number summary of how well they have played.

The Threes and Layups NBA Net Rating Calculator allows you to see just how much better or worse a team would play if they improved or regressed in one of what I call the “fundamental” statistics. These statistics capture how well a team is doing in Dean Oliver’s “Four Factors”: shooting from the field, foul shooting, rebounding, and turnovers.

How to Use the App:

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