Welcome back to Hack a Stat! This is a new chapter for “Learn a Stat“. Today we explore shooting percentages and usage percentage.


When we talk about shots, the first stats that are mentioned are obviously the shooting percentages: there are those dedicated to the 2-point shot (2P%), to the 3-point shot (3P%), to the field goals ( FG%), and to free throws (FT%). However, there are advanced statistics that allow us to understand in a single value how a player/team is shooting: the first is the Effective Field Goals Percentage (eFG%), which takes into account all the field shots but giving greater importance to the 3-point shot. The second is the True Shooting Percentage (TS%) which takes into consideration all the shots, even the free throws.

If instead, we talk about possessions, in the chapter of Learn a Stat dedicated to the individual Offensive Rating we learned how to estimate the number of possessions used by a player: however, that is an absolute value. If you do not have all the values of the possessions of each player on a team, you cannot understand who is the one who has the ball most of the time. To overcome this there is the Usage Percentage, an advanced statistic that allows us to understand how many possessions a player concludes with respect to the number of total team possessions. In this way, you have a clear indication of which players are most involved in the offensive system.

Definition and starting data

The Effective Field Goals Percentage is the stat that gives greater importance to the 3-point shot than to the 2-point one; in numerical terms, a 3 point shot is worth 50% more than a shot inside the arc. This difference in value is used to give greater credit to long-range shooting in the formula of the eFG%.

The True Shooting Percentage is the stat that, taking into account all the shots, tries to return the scoring frequency. In other words, it is a way to understand how a team/player uses its/his shooting possessions.

To find these percentages we need the data related to the shot:

  • 2-point made [2PM];
  • 3-point made [3PM];
  • Points made [Pts];
  • Field goals attempted [FGA];
  • Free throws attempted [FTA];

Lastly, the Usage Percentage is the stat that estimates the number of possessions concluded by the player compared to the team ones.

To calculate it, we do not take into consideration the possessions estimated in the individual Offensive Rating calculation, but a simplified one.
The data are:

  • Field goals attempted [FGA];
  • Free throws attempted [FTA];
  • Turnovers [TO];
  • Team field goals attempted [TeFGA];
  • Team free throws attempted [TeFTA];
  • Team turnovers [TeTO];
  • Minutes played [MP];
  • Team minutes played [TeMP];

Formulas and calculation

All statistics relating to shooting percentages are identical, whether it is a team stat or a player stat. Let’s start with the Effective Field Goals Percentage:

\boldsymbol{eFG\%=\frac{2PM+1,5\cdot 3PM}{FGA}\cdot 100}

As was said during the definition, the number of 3-point shots is increased by 50%: in this way, for each shot made from beyond the arc, the percentage will assume greater values than the normal field goals percentage. Why increase 3-point shot by 50%? Simply because it is the same difference of points made with a 3-point shot compared to one inside the arc.

This statistic allows comparing the field percentages of all the players, without having to filter them by role. For example, if you use the FG%, the shooters would be penalized compared to the area players, since the big men will almost certainly have higher FG% than the shooters. By using eFG% this problem is solved.

True Shooting Percentage is calculated with this formula:

\boldsymbol{TS\%=\frac{Pts}{2\cdot \left ( FGA+0,44\cdot FTA \right )}\cdot 100}

By dividing the points made with the hypothetical points achievable through the possessions concluded, the True Shooting Percentage is obtained.

At the denominator, we find a partially familiar term: it is the formula for calculating possessions, except for the terms of turnovers and offensive rebounds.
The 2 is used to calculate the hypothetical points achievable with those shooting possessions: apparently it seems that the 3-point shot has the same importance as a shot from inside the area, but it is not. A player/team who has made many triples will have more points scored than those who, with the same number of shots, scored only from inside the arc. Therefore, by using that product at the denominator, the two shooting types have different weights.
So basically, the TS% allows us to understand how many times a player scores compared to the number of shots attempted: a very useful statistic in comparing the scoring skills.

Lastly, the Usage Percentage:

\boldsymbol{Usg\%=\frac{FGA+0,44\cdot FTA+TO}{\left (TeFGA+0,44\cdot TeFTA+TeTO \right )\cdot \frac{5\cdot MP}{TeMP}}}

For this stat, at the numerator we find the possessions of the player, while at the denominator we find the team possessions. This value is then multiplied by the percentage of minutes played to estimate the team possession played while the player was on the court. This last step is necessary only with the use of data taken from the box score.

How to read and analyze

To understand the usefulness of these statistics, let’s compare the shooting percentages of some NBA players in the current season (2019/2020). We take Young, Harden, Antetokounmpo, and Gobert.
If we compare their FG%, the best would be the French center. This is because his shots are all near the rim, while players like Young and Harden take many shots from beyond the arc.

For a more uniform comparison, therefore, we use eFG%.

In this case, we note that Gobert’s eFG% remains the same as his FG% (since he does not take shots from beyond the arc), while the eFG% of the two guards increase due to the use of the 3-point shot. The percentages no longer show us the true conversion of baskets scored, but rather a percentage that also considers the different weights of the shots made and attempted.

The eFG% is, however, outdated data: the TS% also includes free throws and, as we know, James Harden is a master in earning free throws.

Through TS% we understand how Harden makes better use of his possessions than Trae Young and Antetokounmpo; this information could not be obtained from the eFG% since Harden’s and Young’s eFG%s were practically identical. Similar speech for Giannis, also a player who often goes to the free throw line.

For Usage Percentage there is nothing difficult: the greater the value, the greater the possessions used by the player, in relation to the total team possessions.

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

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