Individual Defensive Efficiency Ratings Extracted from Play-by-Play Data
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In my last post I presented individual offensive efficiency ratings that were extracted from play-by-play data. In this post I will present individual defensive efficiency ratings that I have extracted from play-by-play data.
As with the individual offensive efficiency ratings, I’ve constructed these individual defensive efficiency ratings in a similar fashion as Dean Oliver does in Basketball on Paper.
Calculating Individual Defensive Efficiency Rating
The purpose of the individual defensive efficiency rating is to estimate an individual’s impact on the number of points their team allows per hundred possessions the individual is on the court. As Dean explains in Basketball on Paper, there is a lot of defensive data left to collect that would allow us to better understand defense numerically.
Thanks to the play-by-play, a small fraction of this data is available to us so that we do not have to approximate it from the box score (such as the number of free throws players allow by way of fouls). We still, however, do not have data for key elements of defense, such as:
- Number of field goals defenders force to be missed or allow to be made
- Number of turnovers defenders force the opponent to commit
Even with this data, there is a case to be made for how coaching impacts individual defensive efficiency ratings. We can’t overlook this, even if we don’t yet have a way to quantitatively estimate this coaching effect with the data we have available to us.
That said, here is a list of the things defenders do that impact defensive efficiency:
- Allowing shots to be made
- Preventing shots from being made (like blocking shots)
- Forcing turnovers (like stealing passes and taking charges)
- Grabbing defensive rebounds
- Fouling opponents (that lead to free throws)
These events lead to the opponent scoring zero or more points, and credit is assigned as follows:
Assigning Credit: Made Shots
Because we don’t have information pertaining to which defender(s) contested the shot, all defenders receive 20% credit for allowing a field goal to be made.
Assigning Credit: Free Throws
Defenders that commit fouls that lead to made free throws are assigned full credit for allowing the opponent to score these points.
Assigning Credit: Turnovers
When the opponent commits a turnover, we currently have three ways of assigning credit. First, when there is a steal, the defender credited with the steal receives full credit for forcing the turnover. Second, when there is an offensive foul turnover, the defender credited with drawing the offensive foul receives full credit for forcing the turnover. Lastly, all defenders receive 20% credit when we do not have explicit defender information associated with a turnover.
Assigning Credit: Defensive Rebounds
On defensive rebounds, the player forcing the shot to be missed receives credit proportional to:
where DFG% is the defensive team’s probability of forcing the opponent to miss, and DOR% is the defensive team’s probability of allowing an offensive rebound. As Dean discusses in Appendix 3 of Basketball on Paper, this formula estimates the relative difficulty between forcing the opponent to miss a shot and obtaining a defensive rebound.
When there is a block, we give the player that blocks the shot credit equal to . The player that rebounds the shot is then assigned credit equal to .
If there is no block, then the credit for forcing the missed shot is distributed evenly between the five defenders. This means each defender gets credit equal to .
Similar rules are applied when there is a team defensive rebound with and without a block.
The Defensive Ratings
Below is a list of the players that have the top 15 defensive ratings from the 2008-2009 regular season (minimum 500 defensive possessions used):
|Rank||Team||Player||Rating||Std Error||95% Confidence Interval|
|1||BOS||Kevin Garnett||90||2.4||(84.9, 94.2)|
|2||ORL||Dwight Howard||90||1.7||(86.2, 92.9)|
|3||CLE||LeBron James||92||1.9||(88.3, 95.6)|
|4||LAC||Marcus Camby||92||2.2||(88.2, 96.7)|
|5||CHA||Gerald Wallace||93||2.0||(89.1, 96.8)|
|6||NOH||Chris Paul||95||1.8||(91.5, 98.7)|
|7||POR||Joel Przybilla||95||2.2||(90.5, 99.3)|
|8||BOS||Rajon Rondo||96||2.0||(92.0, 99.8)|
|9||CLE||Anderson Varejao||96||2.1||(92.1, 100.3)|
|10||UTA||Andrei Kirilenko||96||2.4||(91.7, 101.3)|
|11||HOU||Luis Scola||97||2.0||(93.0, 100.7)|
|12||LAL||Lamar Odom||97||2.0||(93.5, 101.4)|
|13||SAS||Tim Duncan||97||2.0||(93.7, 101.3)|
|14||DEN||Chris Andersen||98||2.6||(92.6, 102.7)|
|15||LAL||Trevor Ariza||98||2.2||(93.9, 102.6)|
The following spreadsheet lists the defensive ratings for each player from the 2008-2009 regular season (including other applicable statistics):
The data is grouped and sorted by teams and players, and it contains the following data:
- Drtg: the player’s defensive efficiency rating
- Std Err: the standard error of the rating
- 95% CI: a 95% confidence interval for the rating
- Usg%: the percentage of possessions used by this player while on the court
- Total Used: the total number of possessions this player used
- %Shots: percentage of possessions used that were shots
- %Fouls: percentage of possessions used that were fouls
- %Drebs: percentage of possessions used that were defensive rebounds
- %Turnovers: percentage of possessions used that were turnovers
Not a Perfect Measure of Defense
I believe these ratings give us a little better look at defense than what we glean from the box score, but these ratings aren’t exactly perfect either. There is still much data we’re not building in, specifically which defenders are contesting which shots (other than those shots that are blocked). Even with this data, there are still issues with splitting credit between teammates since, for example, a player not contesting a given shot could be responsible for allowing the shot to take place and should split some credit with the contesting player.
With these difficulties in mind, my hope is to construct similar defensive ratings using counterpart information to attempt at figuring out which players are perhaps responsible for the opponents shots. With this data we could then rate both offensive and defensive ratings by taking into account the level of competition on both sides of the ball.
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