Thursday, July 28, 2005

Defense for the big men: what do the adjusted plus/minus ratings say?

By Dan T. Rosenbaum

If I had a dime for every time I heard that you can't measure defense with stats, I would be a rich man. (Well maybe not rich, but I might have enough money for a nice dinner.)

Steals, blocks, and defensive rebounds - they give us only a snapshot of what a player does on defense. We would like to have more and better data to measure defense. One direction is to collect better defensive statistics, an effort that is being spearheaded by Roland Beech at

Another approach is to use plus/minus statistics to measure how a team defends when a player is in the game versus when he is not. It would seem odd to say that a player was a good defender when his team defended better when he was on the bench than when he was in the game.

Now, of course, it is important to account for who a player is playing with and against. Playing beside Ben Wallace might even make me appear to be a good defender. For that reason I compute adjusted plus/minus ratings that account for who a player is playing with and against. These adjusted plus/minus ratings can then be broken down into their offensive and defensive components.

In "Measuring How NBA Players Help their Teams Win" I describe the gory details of how I compute these adjusted plus/minus ratings. (I have made a few changes since then, along with adding another year of data.) It takes a lot of data for adjusted plus/minus ratings to tell us anything useful and for that reason it is useful to ask another question. What is the average adjusted plus/minus rating of players similar to a given player? Answering this question can give me a second estimate of a players' defensive productivity and help combat errors from adjusted plus/minus ratings due to lack of data.

So combining ratings of defense from a players' own adjusted plus/minus rating and that of players similar to him, which players are the best defenders? I list the best and worst by position among players playing 1,000 or more minutes in 2004-05. These ratings are predictions for the 2005-06 season assuming that younger players will improve their defense and older players may see a decline in their defense.

Top Five Centers:

  1. Ben Wallace
  2. Dikembe Mutumbo
  3. Theo Ratliff
  4. Jason Collins
  5. Joel Pryzbilla

Bottom Five Centers:

  1. Primoz Brezec
  2. Marc Jackson
  3. Predrag Drobnjak
  4. Mark Blount
  5. Eddy Curry

Ben Wallace by all accounts is a game changer as a defender, so it is comforting to see him at the top of this list. Wallace is joined by three of the top shot blockers in the league in Dikembe Mutumbo, Theo Ratliff, and Joel Pryzbilla. Jason Collins has consistently over the past three seasons had an above average adjusted plus/minus rating and the reason is because he is a very solid defender.

Primoz Brezec was a solid offensive player for Charlotte last season, but his poor defense resulted in the Bobcats playing worse when he was out on the court. Eddy Curry also has consistently had a below average adjusted plus/minus rating over the past three seasons, and the biggest reason is his poor defensive play.

Interestingly, Kurt Thomas who was recently acquired by the Phoenix Suns rates in the bottom third among centers in defense. It is rather surprising to hear analysts argue that a players who made the 5th worst defense (the Knicks) worse is going to help the 17th best defense (the Suns) get better.

Top Seven Power Forwards:

  1. Tim Duncan
  2. Kevin Garnett
  3. Nick Collison
  4. Tyson Chandler
  5. Nenê
  6. Andrei Kirilenko
  7. Rasheed Wallace

Bottom Seven Power Forwards:

  1. Matt Bonner
  2. Cliff Robinson
  3. Antawn Jamison
  4. Juwan Howard
  5. Austin Croshere
  6. Antoine Walker
  7. Shareef Abdur-Rahim

I am sure no one will be surprised to see Tim Duncan and Kevin Garnett at the top of the list on defense for power forwards. Nick Collison is a bit of a surprise to anyone who did not watch the Sonics play a lot. (Please note that with just one year of data, ratings for rookies like Collison are more prone to error.)

I am sure many will be surprised to see Cliff Robinson in the list of worst defensive power forwards, but last season he had a dreadful adjusted plus/minus rating. Both Golden State and New Jersey played better defense when he was on the bench.

It is time for bed now, so I will leave the other positions for the next installment. But as a sneak preview, there will be a player who is about to receive a maximum salary offer who will rate as the worst defensive player at his position. Can you guess who that might be?

For more comments about this methodology and these results from some of the top basketball statistics experts, as well as lots of other interesting discussions about basketball statistics, see the APBRmetrics message board.

Last updated: 5:45 PM, July 28, 2005


Anonymous Anonymous said...

I'm going to go w/Michael Redd as the worst defensive player about to get the max. Which does bring up how crazy it was for the Bucks to sign him to that deal instead of, say, trying to steal Chandler from Bulls to be an ideal sidekick for bogut...

7/28/2005 9:27 AM  
Anonymous Anonymous said...

It sounds like you are combining pure adjusted plus/minus rankings with statistical plus/minus rankings (linear weights estimates of pure adjusted plus/minus).

I wonder about the value of doing that for defensive rankings, where there are so few defensive stats. Adding in statistical defensive plus/minus would seem to unfairly hurt the rankings of great defenders who don't rack up steals and blocks (like Bruce Bowen).

I may be misunderstanding what you're doing though.

7/28/2005 12:19 PM  
Blogger Dan Rosenbaum said...

Yes, I am combining adjusted plus/minus ratings with statistical plus/minus ratings. The stats-based ratings are not quite linear weights estimates, but your point is well taken.

Bruce Bowen actually rates a bit higher with the stats-based rating than he does with the adjusted plus/minus based rating, so I think it is a bit misleading to think about the stats-based measure as being like other linear weights measures you have seen.

7/28/2005 12:32 PM  
Anonymous Anonymous said...

Will we get to see any more details on what you're doing?

When using traditional stats, how does the R^2 for defense compare to that for offense?

7/28/2005 1:38 PM  
Anonymous Anonymous said...

That player would be Michael Redd Dan.

What's my prize?

7/28/2005 1:40 PM  
Anonymous Anonymous said...

Ha. I posted my guess before I read any of the comments, and I now see that a previous poster also picked Michael Redd.

Let's get some more picks posted. Don't be shy.

7/28/2005 1:43 PM  
Blogger BLAZER PROPHET said...

As to your list of centers, ever hear of a player called Shaq?

As to Mutumbo, isn't he about 96 yeals old?

7/28/2005 1:43 PM  
Anonymous Anonymous said...

Sorry, I'm not guessing anybody besides Redd. We know his offense is pretty good, but his plus-minus numbers are terrible. Plus, there are only a few guys getting the max...

7/28/2005 1:54 PM  
Blogger Dan Rosenbaum said...

I do apologize for the details here being little more than a tease and for this explanation being quite vague. But I have to let a situation play out.

The R^2 is lower predicting defense than for offense, but it is better for big guys than little guys.

I have had more hits from Blazers fans in the last couple hours than I have had in total on my record day, so thank you.

Randolph barely missed this list of poor defensive power forwards. Also, note that these are projections for next season, so that is why Abdur-Rahim is included as a power forward.

Shaq is my top rated center overall, but his defense is not quite what it used to be. He is good but not great on defense.

7/28/2005 2:09 PM  
Anonymous Anonymous said...

(yet another Blazer fan here)

It would be interesting if there was a way to account for who the player is guarding. Abdur-Rahim, for example, would look especially bad if he's guarding a small forward, compared to when he guards a bigger player. A player might also look better than they deserve (Shaq?) when they are only guarding the other team's worst offensive big man. Zone vs. man-to-man might make quite a difference, too, since some players might look better or worse depending on a coaching change (compared to players on other teams, they might go up or down in rank, though their skill hasn't changed). I suppose this all gets balanced out to some degree, but it would be nice if there was some way to control for it.

Thanks for the interesting post, as usual.

- DonD

7/28/2005 2:40 PM  
Anonymous Anonymous said...

Where does Yao rank on the list of centers?
From what i see in the games he seems to anchor the defense very well and alters a lot of shots though he doesn't block them. Also on rebounding though his numbers are relatively low he boxes out extremely well.

7/28/2005 3:48 PM  
Anonymous Anonymous said...

I haven't watched enough to say, but I've read commentary that Yao's terrible at defending the pick and roll.

7/28/2005 5:49 PM  
Blogger Mateo said...

Kurt Thomas' numbers are probably bad because he had to play a lot of center last year out of necessity. He's only 6'9" and has never played any center throughout his career. He's a PF, and while not nearly as good a defender as the recent hype has made him out to be, he's certainly not as bad as this data seems to suggest either. Above average.

7/28/2005 6:28 PM  
Anonymous Chris said...

Here's where the numbers don't tell the whole story. Dikembe isn't quite the defensive threat his numbers show, and that's where blocks can be misleading. A block is only good if you can regain the ball. If you are in a critical playoff game and your block goes into the hands of Big Shot Bob Horry (as Blazer fans know all too well from 2000), you've turned a 2-point play into a 3-point play.

Although it is more difficult to do, stats will better tell the story if a block leads to a defensive stop, and of course, these stats aren't kept.

7/29/2005 1:35 PM  
Blogger Dan Rosenbaum said...

Yao rates as an above average but not great defender. That suggestst that he does some things very well on defense and other things not so well.

Chris, Mutumbo's adjusted plus/minus rating is higher than his stats-based rating. The adjusted plus/minus rating is based only on team performance, so blocks matter only to the extent that they lead to a defensive stop. Thus, the numbers suggest that Mutumbo is creating defensive stops.

7/29/2005 2:52 PM  
Anonymous Kevin Pelton said...

Not only are these stats kept, but Mutombo rated as one of the best in the league at turning blocks into his team's basketball, so he seems a curious choice to question based on this theory:

Someone like Stromile Swift who specializes in sending the ball into the 20th row would seem a better choice without knowing how he rates by's data.

7/29/2005 5:41 PM  
Anonymous Anonymous said...

Joe Johnson.

7/30/2005 9:59 PM  
Anonymous kevo said...

I've had a question about your adjusted plus/minus rating for some time now, and I guess I'll ask it now. The Margin formula you use includes one variable for each player on the floor and one for home court advantage.

I was wondering if there shouldn't be a variable that represents the combination of players on the court at any given time. For example, if you have five Ben Wallaces out on the floor, your team is going to be terrible. So the adjusted plus/minus for each will be very low. But if instead you had Ben Wallace on the court with the Phoenix Suns his adjusted plus/minus would be very high.

It seems to me adding a variable for the particular combination would explain away some variation in your results.

7/31/2005 4:13 PM  
Anonymous indocat said...

Hi Dan!

Suns fans here.
I've cited your work on prediction of cap and tax threshold, thanks for posting those researchs (for free, he he).

Now on to KT issue, I'd like to let you know that I quoted your work on "the bad news about KT defense" :( on this discussion on goazcats board.

Suns just lost offensive gunners JJ & Q, and replaced by Bell & KT who're supposedly defensive oriented guys.

I went to knickerblogger to read their ongoing discussion about PER on Q to have a feeling how to quantify the losses, and voila :D, you have a refreshing idea about defensive measurement.

for now, as a newbie, i only have a vague idea on how your formula works, but i'll continue reading your blog on this matter.


8/02/2005 2:06 PM  
Blogger Antoine Safford said...

That is a very interesting statistical category you have when rating a player's defense.

8/03/2005 11:56 PM  
Anonymous Anonymous said...

Cliff Robinson is the best defender in the league and you put him in the worst defenders!!!

2/20/2006 7:00 AM  

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