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.

To assess the value of the 2-for-1 empirically, I invented a statistic called **End of Quarter Difference (EQD)**. EQD, which is defined whenever possession of the ball switches teams, is simply the number of points that the team gaining possession of the ball outscores their opponent by over the remainder of the current quarter. As a simple example, suppose team A gains possession of the ball with 45 seconds left in the quarter and outscores their opponents 3 to 2 over the remainder of the quarter. Then the 45 second EQD for this quarter was +1.

Using data from basketball-reference, I calculated the EQD at all change of possessions in every regular season game over the past three NBA seasons. To analyze end of quarter strategy, I divided the last minute of the quarter into 4 second time buckets and measured the mean EQD of all possessions which began in each bucket. I only considered possessions in quarters 1-3 to avoid complicated end-of-game strategy, such as strategic fouling when a team is losing.

As an example of how to read the plot above, the point corresponding to “33-37” on the x-axis indicates that, on average, teams which gained possession of the ball with 33-37 seconds left in a quarter outscored their opponents by about 0.5 points over the remainder of that quarter.

What immediately stands out in this plot is the increase in mean EQD from 28-32 seconds to 23-27 seconds. This agrees with our intuition. If a team gains possession with 23-27 seconds left in the quarter, they can either take the last shot or take at least take the last “good” shot (i.e. one that is not a heave). If a team instead gains possession with 28-32 seconds left, their opponent will likely have the opportunity for at least one more somewhat decent field goal attempt in the quarter.

There are many ways to slice the data, but let’s give a concrete example where using EQD can help quantify the value of executing a 2-for-1. Suppose we gain possession with 37 seconds left in the quarter. For the sake of simplicity suppose we have only two options: take a quick shot with between 28-32 seconds left in the quarter (gaining a 2-for-1) or instead hold the ball a bit more and take a shot with 17-27 seconds left. The mean EQD for 28-32 seconds is +0.44 and the mean EQD for the 17-27 seconds is +0.68, so taking the quicker shots will cost our opponents 0.24 points on average. As long as we are not sacrificing more than 0.24 points of expected offense with a low percentage field goal attempt, going earlier and taking the 2-for-1 appears beneficial.

Interestingly, teams seem to recognize the value of the 2-for-1. The plot below shows the total number of possessions ending at each 1 second interval over the last three regular seasons. Once again, I restrict the data to only quarters 1-3. We can clearly see that many more shots are taken with 30 seconds left in the quarter than, for example, 24 seconds left.

I plan on doing more digging into the data. In particular, I would like to more precisely identify when the 2-for-1 is good strategy and when it is not. It would also be interesting to see which teams utilize the 2-for-1 the most, and quantify how effective they are at the end of quarters.