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How to calculate possessions in basketball

Nylon Calculus 101: Possessions

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Nylon Calculus

by Justin 6 years agoFollow @AcrossTheCourt

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.

Learn a Stat: Possessions and Pace

The first chapter of Learn a Stat is dedicated to two statistics: possessions and Pace. Most of all advanced stats are based on possessions. Therefore, their understanding is essential to learn many other statistics.

ITALIAN VERSION

TABLE OF CONTENTS

1 POSSESSIONS
- 1.1 Introduction
- 1.2 Definition
- 1.3 Formula
- 1.4 How to read and analyze
2 PACE
- 2.1 Introduction
- 2.2 Definition
- 2.3 Formula
- 2.4 How to read and analyze

POSSESSIONS

Introduction

Possession is the unit of measurement of many advanced statistics: uniforming the number of points, assists, steals or turnovers referring to the number of possessions played allows a correct comparison, purifying them from the game speed. That’s because each team has its own pace: this factor affects the number of possessions in a game.

Therefore, compare assists per 100 possessions is better than use assists per game: a team that has run’n’gun in its DNA will probably produce more assists per game than a team with a low pace; not considering this fact is counterproductive for a correct analysis. In other words, we are not interested in the term “per game” but in terms of the possessions played.

Definition

First, we need to understand what “possession” means: we are in the mathematical field and, therefore, we have the necessity to define a value so that it has a unique meaning.
According to Dean Oliver, possession is a game action that starts when a player gets the ball and ends only in one of the following ways:

A field goal made or free throw made;
An opponent’s defensive rebound;
A turnover;

Pay attention to this: an offensive rebound does not generate a new possession in the statistical field. Does a team grab three offensive rebounds after three missed shots? It is ONE possession.
Knowing these important notions, we can observe the formula that allows calculating the possessions.

Formula

If we started from the definition of possession we would obtain the following formula:

There are these following elements:

FGA: attempted field goals;
FTA: free throws. This term is multiplied by a coefficient of 0.44 since obviously not all free throws conclude a possession. Following a foul on a shot, there are 2 (or 3) free throws; there is also the “and one” situation. That coefficient takes into account all these situations and allows obtaining an estimate of the free throws that actually concluded a possession. Drawn fouls after reached the bonus or as a result of techs / unsportsmanlike fouls cause the conclusion of possession as a normal shooting foul;
OR: offensive rebounds. Offensive rebounds must be subtracted, since, as we said, an offensive rebound does not generate new possession. So by subtracting this value the shots attempted later are excluded;
TO: turnovers;

Being in the statistical field, it is necessary to consider some variables that lead to a formula that is a bit more complicated, but with the same purpose (the previous formula remains valid: when you want to make a quick analysis it is certainly more convenient than the following):

In this second formula, offensive rebounds are not simply subtracted; this formula gives more weight to the offensive rebounds after a missed field goal (offensive rebounds after a free throw are quite rare and, therefore, Oliver preferred to not take this situation into consideration). For the rest, the terms are the same.

The two formulas shown calculate the possessions played by a single team; it’s easy to guess that the opponent also plays the same number of possessions. However, these are only estimations, so it is very rare to obtain the same number for the two teams: the coefficients related to free throws and rebounds generate some differences between the two team’s values. To get closer to the exact value of possessions played, the average of the two team’s values are calculated. Finally, this is the formula for calculating possessions for both teams:

How to read and analyze

The number of possessions serves to know the team pace: the greater the value, the greater the possessions played and consequently the game speed. Take for example the Italian Super Cup games and observe the possessions played in the two semifinals:

Using the second formula of the previous paragraph we can determine the estimated possessions for the four teams: here we can immediately notice how the values are similar but not equal, both for Milan – Trento and for Sassari – Venice. So by averaging the two values, we obtain a more correct number of possessions and this value will then be used for comparison and for the calculation of other statistics.

Now, let’s say that Milan – Trento ended after two overtimes, but with the same numbers of shots, turnovers, etc. We would get the same number of possessions, as can be seen in the table below:

It is a correct value for the use of the formula, but conceptually wrong: comparing the two games it would seem that there is a difference of 5/6 possessions, but actually the game ended after two extra periods will have had a very slower pace than the other game.
Pace, an evolution of possessions, comes to help us.