Learn a Stat: assists and turnovers

Welcome back to Hack a Stat! For this chapter of Learn a Stat, after analyzing the rebounds, we move on to the advanced statistics related to assists and turnovers.



Assists and turnovers are two very important statistics in the evaluation of a player (or a team). Normally the assist is used as a measure to understand when a team plays chorally, or how much a player is a playmaker.
The turnover is instead used to account for part of the mistakes made by the team/player. As we have already learned, the mere number shown on the box score provides us a partial view of the game: for this reason, there are advanced statistics that allow us to have a clearer view of these two contributions. For assists, we have Assist Percentage and Assist Ratio, while there is the Turnover Ratio for turnovers. All these statistics exist both for teams and for players.

Definition and starting data

Team Assist Percentage gives us the percentage of baskets made following an assist with respect to the total number of shots made. This percentage is very important because the single value of the assists does not show if a team has performed many or few winning passes. Two teams can make the same amount of assists, but if the first has made twice the number of baskets compared to the second, the number of assists alone does not allow us to understand that the second team has played more chorally than the first.

Individual Assist Percentage instead gives us the same percentage but compared to the number of player’s assists. The higher the value, the greater the team baskets that the player has assisted.

The Assist Ratio is the distribution of assists over 100 possessions.

Lastly, the Turnover Ratio (also known as Turnover Percentage) takes on the same meaning as the previous statistic but, in this case, obviously, we will talk about turnovers.

The distribution over 100 possessions, as we have now understood, allows us to make comparisons on a common basis, thus purifying the values from the game speed, which varies from game to game.

To calculate these statistics we need this data.

Team advanced stats

  • Team assists [TeAst];
  • Team turnovers [TeTO];
  • Team field goals made [TeFGM] and attempted [TeFGA];
  • Team free throws attempted [TeFTA];

Individual advanced stats

  • Player’s assists [Ast];
  • Player’s turnovers [TO];
  • Player’s field goals made [FGM] and attempted [FGA];
  • Player’s free throws attempted [FTA];
  • Team field goals made [TeFGM];
  • Player’s minutes played [MP];
  • Team minutes played [TeMP];

Formulas and calculation

Team advanced stats

As for the rebounds, the formulas are quite simple and allow us to understand the idea behind these advanced statistics.

Team Assist Percentage is calculated as follows:

\boldsymbol{Ast\%=\frac{TeAst}{TeFGM}\cdot 100}

The assists are divided by the baskets made, in order to obtain the percentage of assisted baskets. All this is multiplied by 100 to have numbers that are easier to read (or to obtain the percentage value). The greater the result, the greater the baskets made following an assist.

The team Assist Ratio is found with the following formula:

\boldsymbol{AstRatio=\frac{TeAst}{TeFGA+0,44\cdot TeFTA+TeTO}\cdot 100}

At the denominator we find the simplified formula for calculating possessions: in this case, however, the offensive rebounds are not subtracted because all the second shooting attempts would be lost, which can also be scored thanks to an assist.

The team Turnover Ratio uses the same calculation philosophy, but of course, the turnovers are used at the numerator:

\boldsymbol{ToRatio=\frac{TeTO}{TeFGA+0,44\cdot TeFTA+TeTO}\cdot 100}

Individual advanced stats

Now let’s move on to individual stats, starting again with the player’s Assist Percentage.

\boldsymbol{Ast\%=\frac{Ast}{\left (TeFGM\cdot \frac{5\cdot MP}{TeMP} \right )-FGM}\cdot 100}

The formula is similar to the team one: in this case, however, the number of field shots are multiplied by the percentage of minutes played. This is because you do not want to calculate the ratio on the total shots, but on the shots made while the player is on the court: this information can only be found from the Play by Play. If, on the other hand, information is taken from the box score, the same approximation of the rebound statistics is used to know this number: assuming that the shots are equally distributed throughout the entire game, the total number is multiplied by the portion of time played by the player, thus obtaining the assistable ones. It’s always the same: it is an approximation, it will never give us an exact value, but it is still reliable and acceptable in the absence of more accurate data. The result is then reduced by the number of shots scored by the player himself. With this statistic, we can understand which are the players who make more assists.

The player Assist Ratio, on the other hand, is calculated in the following way:

\boldsymbol{AstRatio=\frac{Ast}{FGA+0,44\cdot FTA+Ast+TO}\cdot 100}

At the denominator we find the formula for calculating the player’s possessions, who can conclude his action by attempting a shot, losing the ball or making an assist. By dividing the number of assists with the possessions used, the assists distributed over 100 individual possessions are obtained. This value helps us to understand how a player behaves on the court: depending on the value we can understand if he is a player who prefers the shot or the pass.

The last statistic is the player’s Turnover Ratio: the formula is the same as the previous statistic, but in this case, of course, we find the turnovers at the numerator.

\boldsymbol{TORatio=\frac{TO}{FGA+0,44\cdot FTA+Ast+TO}\cdot 100}

As for the Assist Ratio, therefore, this statistic helps us to understand how many balls a player loses on a basis of 100 possessions: this value is very useful for comparisons between multiple players.

How to read and analyze

Even for this group of statistics, as for the rebounds, their reading is very simple. Having percentage values or distributed over 100 possessions, we are able to make more precise comparisons. The depuration from the game speed allows us to avoid trivial errors, such as comparing the number of assists or turnovers between two teams that play at diametrically opposite pace.

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

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