Optimizing End Of Quarter Shot-Timing In The NBA

Everyone Knows About The 2 For 1, But What About The 3 For 2?

Jesse Fischer • February 15, 2015

LeBron James pulls down the rebound and brings the ball up the court…under 40 seconds left in the quarter…the announcer jumps in: "this is a really great opportunity for the offense to go '2-for-1' right here"…almost on cue LeBron pulls up for a quick shot with 30 seconds remaining…proudly the announcer chimes in on the quick shot: "that was some great coaching to get the '2-for-1' there".

Sound familiar? It doesn't take an analytical genius to understand why the '2-for-1' is a good idea, if you can get an extra possession compared to your opponent then why wouldn't you? While witnessing such a situation sometime last year I got an idea: Why does it have to stop at the '2-for-1'? What about a '3-for-2' or even a '4-for-3'!? Are there such kinds of opportunities? Would they provide any real value? Does a '3-for-2' even make sense as the '2-for-1' is really what matters? The '2-for-1' is a simple concept which most people probably think of as common sense more than as basketball analytics. Could a '3-for-2' ever turn into something as commonplace?

These are some of the questions I set out to answer in a research paper I recently submitted to the 2015 Sloan Sports conference research paper contest.

Optimizing End Of Quarter Shot-Timing In The NBA: "Everyone Knows About The 2 For 1, But What About The 3 For 2?"

(Link to Full Paper)


Since the advent of the shot clock, the "2-for-1" has become a common end of quarter strategy in the NBA. With this approach, a team will strategically time their shot in hopes of ensuring a second possession while limiting their opponent to a single possession. Prior research has shown the effectiveness of the "2-for-1" strategy but no well-known public study has explored extending this strategy to "3-for-2" or beyond. This paper summarizes a study which: (1) analyzes the effects that possession timing has on behavior as well as outcome; (2) quantifies the cost-benefit tradeoff of strategically "timing a possession;" and (3) proposes the optimal possession timing strategy to maximize expected points (as opposed to simply possessions). The research reveals how to improve end of quarter behavior in the NBA by better understanding the math behind why, and when, a "2-for-1" is beneficial and suggests how to extend this further to a "3-for-2".

I will be following this post up with a multi-part series on the topic of possession timing. This will include new visuals and further analysis, so be on the lookout for that!