Oct 30 2009

# Individual Defensive Efficiency Ratings Extracted from Play-by-Play Data

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:

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:

$FMweight=\displaystyle\frac{(DFG\%)(1-DOR\%)}{(DFG\%)(1-DOR\%) + (1-DFG\%)(DOR\%)}$,

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 $FMweight$. The player that rebounds the shot is then assigned credit equal to $1-FMweight$.

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 $\frac{1}{5}(FMweight)$.

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):

[table id=6 /]

The following spreadsheet lists the defensive ratings for each player from the 2008-2009 regular season (including other applicable statistics):

08-09 Basketball on Paper Defensive Ratings from Play-by-Play

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.

### 12 Comments on this post

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November 8th, 2009 at 1:27 pm
2. Adjusting Individual Defensive Efficiency Ratings wrote:

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January 7th, 2010 at 2:12 pm
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1. BWoods said:

Interesting analysis. Did you consider (or would it have even been feasible) allocating extra “credit” to the player theoretically matched up with the scorer, simply based on lineup?

On the subject of actual observation of individual field goal defense, that’s something I’ve been advocating for
and tracking for Wizards games:
http://www.bulletsforever.com/2009/10/30/1107605/four-factors-box-for-opening-night
http://www.bulletsforever.com/2009/11/1/1109710/ff-box-score-for-10-31

With all of the data already directly collected, why shouldn’t the league track/publish defensive data mirroring that for offense?

November 3rd, 2009 at 5:27 pm
2. Ryan said:

The stuff you refer to is exactly where I would like to head next. Using the lineups we can estimate (guess?) which player is guarding the other and use that to assign credit for some of the game events.

Thanks for linking your work. I really like the defensive data, and you’re right, it’s exactly the sort of thing that should be collected. The debate of course comes from what to do when more than a single defender is contesting the shot, but certainly some data is better than none!

November 3rd, 2009 at 7:13 pm
3. tywill said:

Ryan,

Yes! on yoru last comment. Can you do that? Roland Beech has just deep sixed his “counterpart opponent” statisitcs. It seems as though you’re a baby step away from providing something that’s actually better. It would be easy to match players up. If you go by height and a consideration of weight (a smaller but much heavier player will move right on the position spectrum — DeJuan Blair) you can effortlessly match defender to player.

Can you do it Geek??

BTW, love your work, promote it all the time.

TyWill, Courtside Analyst

April 8th, 2010 at 1:33 pm
4. Ryan said:

TyWill, defense is really hard to do right and I would like at some point to provide something that is a blend of counterpart statistics with overall “team” defense. Defense is more complicated than simple one guy against another, and hopefully I can figure out a better way to quantify defense. Thanks for the comment, and hopefully I can provide something useful in the future. 🙂

April 8th, 2010 at 2:21 pm
5. tywill said:

Ryan,

Can you give a dummied down explanation of exactly how you extract and assign the statistical information from the NBA’s “play-by-play” data? I’d like to produce, or contract with someone to produce, simple “reverse statistics” for each NBA player. 82games used to provide them, but I think their site will soon come to an end.

I realize reverse statistics are not a perfect measure of defense. But they would provide us with some more insight into the productive tendencies of the most likely counterpart opponents for each player. I think that would be valuable. And I need them to calculate the number of wins and losses each player produced.

Thanks.

Ty

April 14th, 2010 at 11:52 am