Learn a Stat: rebound percentages

Welcome back to Hack a Stat! With this chapter of Learn a Stat, we go to examine the advanced stats for the rebounds, both team and single player: the Rebound Percentages; there are three types: Offensive Rebound Percentage, Defensive Rebound Percentage, and Total Rebound Percentage.

ITALIAN VERSION

Introduction

I will be never tired to say that the number of rebounds grabbed by a team or player does not give important indications: in fact, almost unconsciously we compare that number with the opponent’s one or with the seasonal averages.
This is because the absolute number is not useful: what we really want is the comparison between the grabbed rebounds and the lost ones.
We are not concerned with absolute value, but with relative value. Specifically for this purpose, there are statistics such as OR% (Offensive Rebound Percentage), DR% (Defensive Rebound Percentage) and TR% (Total Rebound Percentage), values that allow us to know the percentage of rebounds grabbed and immediately understand if a team (or a player) was good under the basket.

Definition and starting data

Team Rebound Percentages indicate the number of rebounds grabbed by one team relative to the other.

For the player’s Rebound Percentages is quite the same. In this case, however, the comparison will be between the player being analyzed and all the others on the court.
Individual Rebound Percentage gives us the percentage of rebounds taken by the player compared to the total number of rebounding opportunities.

To know these values, the following data are enough:

Team’s Rebound Percentage

  • Team offensive rebounds [TeOR];
  • Team defensive rebounds [TeDR];
  • Team total rebounds [TeTR];

Individual Rebound Percentage

  • Player’s offensive rebounds [OR];
  • Player’s defensive rebounds [DR];
  • Player’s total rebounds [TR];
  • Minutes played [MP];
  • Team offensive rebounds [TeOR];
  • Team defensive rebounds [TeDR];
  • Team total rebounds [TeTR];
  • Opponent offensive rebounds [OppOR];
  • Opponent defensive rebounds [OppDR];
  • Opponent total rebounds [OppTR];
  • Team minutes played [TeMP];

Formulas and calculation

Team Rebound Percentages

The formulas for calculating team Rebound Percentages always have the same form, whether we are talking about defensive, offensive or total rebounds: the concept is to make the ratio between the grabbed rebounds and the grabbable ones.

For the Offensive Rebound Percentage, the ratio is between the team’s offensive rebounds and the amount of the same plus the opponent’s defensive rebounds. The opponent’s defensive rebounds are in fact offensive rebounding chances lost by the team.

\boldsymbol{TeOR\%=\frac{TeOR}{TeOR+OppDR}\cdot 100}

For the Defensive Rebound Percentage, the ratio is between the team’s defensive rebounds and the amount of the same plus the opponent’s offensive rebounds. The opponent’s offensive rebounds are in fact defensive rebounding chances lost by the team.

\boldsymbol{TeDR\%=\frac{TeDR}{TeDR+OppOR}\cdot 100}

For the Total Rebound Percentage, the ratio is between the team’s total rebounds and the amount of the same plus the opponent’s total rebounds. The opponent’s total rebounds are in fact rebounding chances lost by the team.
Pay attention: Total Rebound Percentage is not the sum of OR% and DR%.

\boldsymbol{TeTR\%=\frac{TeTR}{TeTR+OppTR}\cdot 100}

It is common to multiply the result by 100 to express it in hundreds. This ratio can also be expressed as a percentage: in this case, the % symbol will be postponed.

For a simple mathematical fact, the sum of the team OR% and the opponent DR% will always give 100 (or 1). Same thing with inverted terms and for totals.

The accuracy of these statistics is high. Except for those dirty rebounds and those following a block (which slightly change the precision of the numbers), the percentages obtained give us an indication very close to reality: they are very reliable tools to understand if a team is good at rebound.

Individual Rebound Percentages

The concept behind these formulas is the same as team statistics; it is the ratio between rebounds grabbed by the player and total rebounds the player can grab. In this case, however, it is necessary to establish how many rebounds are actually grabbable by a player.

One way to get this number is with the play by play.
If, on the other hand, the calculation is being performed from the box scores, the most logical choice is to correlate the number of total catches with the player’s presence on the court. As for the individual Defensive Rating, this proportion is not accurate, but in the absence of more precise data, it remains the most reliable.

A further consideration is that a player may find himself unable to catch a rebound because he is far from the basket: this situation can be found only through video tagging; neither the play by play nor the box scores can provide such indications.

The formulas are as follows: for the individual Offensive Rebound Percentage, the ratio between the player’s offensive rebounds and the sum of the team’s offensive rebounds plus the opponent’s defensive rebounds will be performed, all multiplied by the player’s percentage of minutes on the court.

\boldsymbol{OR\%=\frac{OR}{\left (TeOR+OppDR \right )\cdot \frac{5\cdot MP}{TeMP}}\cdot 100}

For the individual Defensive Rebound Percentage, the ratio between the player’s defensive rebounds and the sum of the team’s defensive rebounds plus the opponent’s offensive rebounds will be performed, all multiplied by the player’s percentage of minutes on the court.

\boldsymbol{DR\%=\frac{DR}{\left (TeDR+OppOR \right )\cdot \frac{5\cdot MP}{TeMP}}\cdot 100}

For the individual Total Rebound Percentage, the ratio between the player’s total rebounds and the sum of the team’s total rebounds plus the opponent’s total rebounds will be performed, all multiplied by the player’s percentage of minutes on the court.

\boldsymbol{TR\%=\frac{TR}{\left (TeTR+OppTR \right )\cdot \frac{5\cdot MP}{TeMP}}\cdot 100}

As you can see, the formulas are the same as the team Rebound Percentages, except for the ratio of minutes played. The 5 in the numerator must be entered only if the team minutes in the denominator are expressed as the total sum of all players (200 minutes for FIBA games ended at regular times, 240 minutes for the NBA). If 40 or 48 is used, the 5 must be omitted, since 200/5 gives 40 (240/5 = 48).

In this case, the accuracy of these statistics is lower than the team’s ones. Specifically for the considerations expressed at the beginning of the paragraph, we will never have the real percentage of rebounds caught by the player but only the trend values.

How to read and analyze

For these statistics, actually, since there are not tricky theories, the examples are very linear. Basically, the higher the stat value, the better the work done at rebounds by a team or a player.

A very useful feature of the rebound percentages is that they are independent of the shooting percentages: I report a quick version of my previous article about this aspect.

If we intersect the opponent’s field goals percentages with the number of team’s defensive rebounds, we notice a strong correlation:

rebound percentages

This is simply because the number of rebounds increases as the missed shots increase. The shifts from the trend line are due to the teams’ rebound ability, but the strong correlation is real.

If, on the other hand, we insert the corresponding advanced statistic on the abscissas:

rebound percentages

A heterogeneous distribution, just to confirm that the rebound percentages are independent of the shooting percentages. They are a better tool for analyzing rebounding skills than simple numbers. This is in fact influenced by another game aspect, which makes it inadequate for making comparisons and analyses.

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

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