lakers4sho

09-24-2010, 11:05 PM

by lakers4sho

I. Introduction

Understanding the concept of "possessions" plays a central role in analyzing basketball statistics. Many respectable statisticians and analysts, including John Hollinger (ESPN), Dean Oliver (official statistician of the Denver Nuggets, as well as the author of the famous book Basketball on Paper), and many others, use possessions as the starting point of basketball statistics. In this thread, we take a look at the formal definition of a possession, and a few different ways on how team possessions are usually formulated.

II. What is a Possession?

A possession, using the most accepted definition of the term, starts when a team gains control of the basketball, and ends when the team loses control of the basketball. There are three different ways in which a team can theoretically lose "possession" of the ball:

(a) When that team makes a field goal or free throw that leads to the other team taking the ball out of bounds

(b) When the opposing team acquires an defensive rebound off of a missed shot

(c) When the team commits a turnover

In this definition, therefore, an offensive rebound does not lead to a new possession, but merely continuing the previous possession.

III. How possessions are estimated

Since there is no official definition of possession, it is usually approximated for both teams during a game. However, it can also be counted manually using play-by-play game logs.

A general formula to estimate possessions from box score data is:

Poss(x) = (FGM(x) + dFTM(x)) + a[(FGA(x) - FGM(x)) + d(FTA(x) - FTM(x)) - OREB(x)] + (1-a)DREB(y) + TO(x)

where:

Poss(x) signifies total possessions of Team X

FGM(x) signifies total field goal made by Team X

FGA(x) signifies total field goals attempted by Team X

FTM(x) signifies total free-throws made by Team X

FTA(x) signifies total free-throw attempts by Team X

OREB(x) signifies total offensive rebounds by Team X

DREB(y) signifies total defensive rebounds by Team Y

d is a constant signifying the fraction of free throws that end possessions

a is a value between zero and one (explained further below)

Using this formula, we see that our definition of a possession holds true: a made field goal, a made "possession-ending" free throw, and a turnover constitutes a possession. What happens with missed field goals (and possession ending FTs)? Each get an "a" (the variable) share of the possession, while the defensive rebounds gets "1-a" share of the possession. Offensive rebounds undo such misses, and thus get an "a" share of the possession (note that 1-a+a = 1).

One of the most common simplifications of this formula is to assume that a = 1 and d = 0.44 (based from data collected), which gives us the following simplified version:

POSS(x) = FGA(x) + 0.44(FTA(x)) - OREB(y) + TO(x)

This formula should should make much more intuitive sense to us.

It is sometimes known as possessions lost, but it is also important to note that it implies that defensive rebounds have no possession value. On the other side of the scale, possessions gained, assumes that a=0, implying that offensive rebounds, missed FGAs, and missed possession ending FTAs have no possession values.

On average, formulations with d=0.44 tend to be 1.5 possessions per game too high, while d=0.5 tend to be 3.1 possessions per game too high. Therefore, a third formula for estimating possessions can be used, which is averaged over both teams:

POSS(x) = 0.976 x [ FGA(x) + 0.44(FTA(x)) - OREB(x) + TO(x) ]

Note that this formula is our previous formula, multiplied by 0.976, in order to take into account the overestimating due to the value of d.

IV. Conclusion

Although there might be different estimations for possessions, these formulations are not particularly different from each other. Therefore, working with results from different estimates is possible by making a shift based on league averages. For example, if estimate A shows an average of 100 possessions, while estimate B shows an average of 99 possessions, then shifting values for A down by one or shifting values for B up by one allows us to make reasonable estimates by incorporating the results from both data sets.

I. Introduction

Understanding the concept of "possessions" plays a central role in analyzing basketball statistics. Many respectable statisticians and analysts, including John Hollinger (ESPN), Dean Oliver (official statistician of the Denver Nuggets, as well as the author of the famous book Basketball on Paper), and many others, use possessions as the starting point of basketball statistics. In this thread, we take a look at the formal definition of a possession, and a few different ways on how team possessions are usually formulated.

II. What is a Possession?

A possession, using the most accepted definition of the term, starts when a team gains control of the basketball, and ends when the team loses control of the basketball. There are three different ways in which a team can theoretically lose "possession" of the ball:

(a) When that team makes a field goal or free throw that leads to the other team taking the ball out of bounds

(b) When the opposing team acquires an defensive rebound off of a missed shot

(c) When the team commits a turnover

In this definition, therefore, an offensive rebound does not lead to a new possession, but merely continuing the previous possession.

III. How possessions are estimated

Since there is no official definition of possession, it is usually approximated for both teams during a game. However, it can also be counted manually using play-by-play game logs.

A general formula to estimate possessions from box score data is:

Poss(x) = (FGM(x) + dFTM(x)) + a[(FGA(x) - FGM(x)) + d(FTA(x) - FTM(x)) - OREB(x)] + (1-a)DREB(y) + TO(x)

where:

Poss(x) signifies total possessions of Team X

FGM(x) signifies total field goal made by Team X

FGA(x) signifies total field goals attempted by Team X

FTM(x) signifies total free-throws made by Team X

FTA(x) signifies total free-throw attempts by Team X

OREB(x) signifies total offensive rebounds by Team X

DREB(y) signifies total defensive rebounds by Team Y

d is a constant signifying the fraction of free throws that end possessions

a is a value between zero and one (explained further below)

Using this formula, we see that our definition of a possession holds true: a made field goal, a made "possession-ending" free throw, and a turnover constitutes a possession. What happens with missed field goals (and possession ending FTs)? Each get an "a" (the variable) share of the possession, while the defensive rebounds gets "1-a" share of the possession. Offensive rebounds undo such misses, and thus get an "a" share of the possession (note that 1-a+a = 1).

One of the most common simplifications of this formula is to assume that a = 1 and d = 0.44 (based from data collected), which gives us the following simplified version:

POSS(x) = FGA(x) + 0.44(FTA(x)) - OREB(y) + TO(x)

This formula should should make much more intuitive sense to us.

It is sometimes known as possessions lost, but it is also important to note that it implies that defensive rebounds have no possession value. On the other side of the scale, possessions gained, assumes that a=0, implying that offensive rebounds, missed FGAs, and missed possession ending FTAs have no possession values.

On average, formulations with d=0.44 tend to be 1.5 possessions per game too high, while d=0.5 tend to be 3.1 possessions per game too high. Therefore, a third formula for estimating possessions can be used, which is averaged over both teams:

POSS(x) = 0.976 x [ FGA(x) + 0.44(FTA(x)) - OREB(x) + TO(x) ]

Note that this formula is our previous formula, multiplied by 0.976, in order to take into account the overestimating due to the value of d.

IV. Conclusion

Although there might be different estimations for possessions, these formulations are not particularly different from each other. Therefore, working with results from different estimates is possible by making a shift based on league averages. For example, if estimate A shows an average of 100 possessions, while estimate B shows an average of 99 possessions, then shifting values for A down by one or shifting values for B up by one allows us to make reasonable estimates by incorporating the results from both data sets.