Nylon Calculus 101: Possessions

Nylon Calculus 101 is TNC’s ongoing effort to provide a syllabus for learning the analytic approach to the game of basketball as well as a reference for terms, concepts and topics within the field of basketball analytics. It will likely never been “complete” because analysis never stops. In this edition, Justin Willard examines the basic unit of basketball analysis, the possession.

The basketball possession is the equivalent of an atom in science. It’s a basic building block from which an entire field of analysis was born.

A possession is named as such because it marks the entire time a team possesses the ball. This should not be confused with plays, which are separated by shot (or free throw) attempts and turnovers. Offensive rebounds extend possessions, not plays. Note: not everyone calls that a “play” but it’s an important distinction to make with offensive rebounds.

While the definition of a possession is pedestrian[1. Though the exact delineation can be tricky in practice.], the stats possible from its use are not. Offensive and defensive efficiency, for example, are extremely popular measures born out of per possession analysis. In fact, the most influential facet of the possession is the philosophy of thinking about how players perform per possession rather than the standard per game. It’s a preferred method over per minute too, by the way, because faster teams give players more opportunities to accrue stats compared to other teams. There’s still a lot of debate in this area about evaluating players per possession, but research has shown that players perform better when they get to play longer stretches and bench players who get promoted see their stats stay the same or even improve. In any case, this type of analysis is so common at the team and individual level that it’s important to understand exactly how these stats are created.

How do possessions end?

This is basic, but it’s essential to basketball analysis: possessions generally end with a made shot, a made free throw, a rebound, or a turnover. Possessions end with a defensive rebound, of course, but offensive rebounds have to be correctly accounted for because they extend possessions. There’s also one tricky type of rebound that makes this analysis more difficult: the team rebound.

What’s a team rebound?

For accounting purposes, whenever there’s a missed shot or free throw there’s always a rebound, even when it’s the first free throw in a pair. Team rebounds are credited to a team but not to any individual player. Since most calculations for possessions are based on shots taken, defensive team rebounds aren’t an issue. However, when a missed shot is touched by the defense but goes out of bounds, it’s a team offensive rebound, and those generally aren’t provided, which actually changed in the late 60’s. Most calculations ignore those or assume a constant rate. There are team turnovers too, by the way, but those are usually credited with team stats on most sites[1. If you ever compare a team’s total turnovers from a team stat section with the sum of individual turnovers for that specific team, you’ll notice a discrepancy.].

What’s pace?

Pace is a measure of possessions per 48 minutes — it’s 48 minutes instead of per game because of overtime. Qualitatively, it’s used to judge how “fast” teams play, as teams with more fast break plays will usually have a higher pace. But pace also depends on how fast the other team plays and it can be confounded by offensive rebounds and the other teams style and defensive ability or lack thereof, so it’s not a perfect measure of speed. Rather it simply describes how many possessions teams have in a typical game with a standard length, and it can be used to create other advanced team stats. Note: most equations average the team’s stats with the opponents for a more accurate estimate. With more information, like through play-by-play logs, this is not needed.

How are possessions calculated for individuals?

This is a crucial point few people know about: most sites assume a team’s pace is the same for every player on the team. This is not true in practice, as many teams play faster with certain perimeter players, especially stars. Consequently, the majority of advanced stats are built from estimates (of estimates) and are incorrect by a slight degree. The magnitude of the error isn’t large in most cases, but it’s something to be aware about.

How does basketball-reference calculate possessions?

The influential site basketball-reference.com uses a long but straightforward formula to calculate possessions[2. 0.5 * ((Tm FGA + 0.4 * Tm FTA – 1.07 * (Tm ORB / (Tm ORB + Opp DRB)) * (Tm FGA – Tm FG) + Tm TOV) + (Opp FGA + 0.4 * Opp FTA – 1.07 * (Opp ORB / (Opp ORB + Tm DRB)) * (Opp FGA – Opp FG) + Opp TOV)).] Like most estimations, the inputs are field goals attempted, free throws attempts, offensive rebounds, and turnovers. However, b-ref is also trying to factor in team rebounds through an estimate. It’s not an exact method, but it’s more accurate than leaving it out entirely.

How does stats.NBA.com calculate possessions?

The NBA’s stats site is vague on how they define possessions, but after some guess-work it’s actually a simple equation: (FGA + .44*FTA – ORB + TOV)/2 with totals from both teams included. This does not correctly factor in team rebounds. At the team level, their possessions are less accurate.

The major distinction between stats.NBA.com and other sites, however, is how they have pace/possession stats individualized for every player. For instance, most sites assume every player on the same team has the same pace, but this site calculates possessions based on accrued stats while a specific player is on the court. This is significantly more accurate.

How does ESPN calculate possessions?

ESPN uses the same equation that stats.NBA.com does: (FGA + .44*FTA – ORB + TOV)/2 with totals from both teams included. Like stats.NBA.com, this is an overestimate of possessions because team rebounds aren’t properly factored in. Thus, their team offensive and defensive efficiency stats are underestimates.

How does Nylon Calculus calculate possessions?

Viewed here, our stats use the same basic equation used elsewhere but all rebounds are accounted for properly and so are free throws: (FGA + FT trip – ORB + TOV) where free throws pairs or triplets (i.e. taking three at a time) are counted and all others are ignored. The extra stats are pulled directly from play-by-play logs.

There’s actually another method used sometimes for calculating possessions and it’s the same as the stats.NBA.com/ESPN method but everything is multiplied by 0.96 to account for team offensive rebounds. For example, Kevin Pelton’s WARP uses this equation[3. Comparing it to Nylon’s pace and the stats.NBA.com/ESPN method, it actually wasn’t significantly accurate: it became an underestimate instead of an overestimate.].

The chart below compares the various methods to Nylon Calculus’s numbers from seasons 2014 and 2015. Basketball-reference is the closest match, but its variation is the same as the other standard method. This means that using possession stats with that method is fine as long as it’s being compared to other stats calculated using the same possession calculation. But it’s more accurate to use actual possession counts, like our own here (Nylon Calculus is no longer tracking possessions).

Possessions are essential to basketball analysis, but they’re not as understood as they should be in the NBA community. The vast majority of the numbers people use are estimates, and there’s still no accepted way to count possessions. How should we deal with end of a period possessions, for instance? What if a team gets the ball with 20 seconds left and they’re unable to shoot? Should a possession starting in tbe backcourt with .5 seconds count?  How about 1 second? 3 seconds? Isn’t that a defensive possession even if there was no shot, free throw, or turnover? There is no simple answer and at a certain point, consistency and ease of calculation trumps precision. Any and all of these estimates are accurate enough to do some excellent analysis, and with knowledge of the methods and limitations further errors can be avoided.