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.

Continue reading “An Analysis of the 2-for-1 Strategy in the NBA”

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?

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

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.

Continue reading “Are the Raptors Really a Bad Playoff Team?”

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.

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

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:

Continue reading “Explanation of Threes and Layups NBA Net Rating Calculator”

How many possessions does an NBA lineup need to play before we are confident it is good?

Plus-minus data is at the bedrock of a lot of thoughtful NBA analysis. If I tell you that the Celtics have outscored their opponents by 153 points in the 350 minutes that Jaylen Brown, Marcus Smart, and Al Horford have shared the court this season (per basketball reference), then you might reasonably conclude that these players are doing something right when they are playing together. At the end of the day, a valuable lineup needs to have a good raw plus-minus score (points scores minus opponents points scored). If a lineup of players is, over time, consistently outscored by the opposing lineups then this lineup cannot be considered effective.

The key question is what exactly does over time mean? One of the problems with looking at raw-plus minus scores for lineups are that they are heavily effected by small sample sizes. Especially early in the season, a good game or two can make an entirely average lineup look like world beaters.

Continue reading “How many possessions does an NBA lineup need to play before we are confident it is good?”

Usage and True Shooting Tracker

I made a web app that allows you to see how the players on each team rate according to usage and true shooting. You can quickly get a sense for how players compare to one another and can sort by team or position.  The points are also sized and colored according to a player’s offensive rating, so you can see how much better (or worse) the team’s offense has been while they are on the court. The app will be updated as the season progresses so you can always see current stats.

As a bit of explanation, usage percentage is a measure of the percentage of possessions that a player “uses up” when they are on the floor. True shooting percentage is a measure of how efficient a player is shooting the ball.  It takes into account free throw shooting and the fact that 3’s are worth more than 2’s. High usage, high true shooting players are obviously really valuable.

Try it out!


(All data is courtesy of