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.

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:

  1. A field goal made or free throw made;
  2. An opponent’s defensive rebound;
  3. 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:

\boldsymbol{Poss=FGA+0,44\cdot FTA-OR+TO}

There are these following elements:

  1. FGA: attempted field goals;
  2. 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;
  3. 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;
  4. 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):

\boldsymbol{Poss=FGA+0,44\cdot FTA-1,07\cdot \frac{OR}{OR+oppDR}\cdot (FGA-FGM)+TO}

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:

\boldsymbol{Poss=\frac{Poss_{team1}+Poss_{team2}}{2}}

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.

PACE

Introduction

The Pace is used for remedying situations like the one shown before. Where the minutes are different from the canonical 40 (or 48), the classic considerations cannot be made by comparing the values of the possessions.

Definition

The Pace is the number of possessions spread over 40 (or 48) minutes. It is clear that by using Pace, we lost the real number of possessions played, but it does not matter: statistics almost always show trends and not real values.

Formula

To calculate it, the number of possessions has to be divided with the actual minutes of the game and then multiply by 40: with this simple formula, even the games ended after overtime(s) can be compared with those finished at regular times.

\boldsymbol{Pace=\frac{Poss}{Min}\cdot 40}

In statistical basketball, it is common to measure the minutes of the game as the sum of the players’ minutes played: this means that it is easy to come across 200 minutes (end of regular time, 40 minutes for each player, so 40 * 5) or 225 minutes (ending after an extra time, 45 minutes for each player, then 45 * 5). So if you divide the number of possessions by this sum of minutes, the multiplication factor will no longer be 40 but obviously 200 (40 * 5).

How to read and analyze

The analysis and the use of Pace are the same as those explained for the possessions: for convenience, this stat is always and only used for game pace comparisons.
Taking again the previous example, we can calculate the Pace and make a direct comparison between the two semi-finals:

So the semi-final Milan – Trento ended after two extra periods was a very slow match compared to the other semi-final and we can notice it only thanks to Pace.

A very common question about Pace is: are there limit values that understand whether a team plays at a high or low speed? The answer is no; Pace (and possessions) are relative values that have to be compared with other values. It is convenient to calculate the League average Pace: knowing this value, you can make your considerations. Take for example a past regular season of LBA:

The average League Pace is around 74 possessions per game. Knowing this data and observing the teams’ Pace, you can understand which are the fastest and the slowest: in this case, Brindisi is the fastest, Sassari the slowest.

This Learn a Stat ends here. See you soon, your friendly neighborhood Cappe!

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