Tuesday, August 02, 2005

Defense on the perimeter: what do the adjusted plus/minus ratings say?

By Dan T. Rosenbaum

It has been interesting seeing the reaction to my list of best and worst big men defenders. This writer never claimed for a minute that these were THE definitive lists (in the exact right order) of defensive big men. That is not the nature of statistical evidence. (If we are honest with ourselves, we would realize that this is the nature of most non-statistical evidence as well.)

With statistical evidence we generally are painting with broad strokes because the results are rarely precise enough to distinguish a player rated #3 from one rated #7. That said, these results with a handful of exceptions, do tell us that the players in the "best" lists are better than average defenders and the players in the "worst" lists are not. Context does matter, but watching players who change teams it appears that context does not typically change a defender from an elite defender to an average one.

And remember that these lists are based upon plus/minus statistics that measure how a team defends when a player is in the game versus when he is not. Since how a team defends when a given player is in the game IS what we care most about, when we see odd results we have to ask ourselves why the team defends so well (or so poorly) when that player is in the game.

And remember I am accounting for who a player is playing with and against and for garbage/clutch time play. So for these adjusted plus/minus ratings it does not matter who a player's substitute is, like it does with unadjusted plus/minus ratings.

Now these results are a combination of adjusted plus/minus ratings (based upon three seasons with most of the weight on last season) and statistical plus/minus ratings (based upon just last season) that average in the adjusted plus/minus ratings of players similar to a given player. I get a lot of objections to including this statistical plus/minus rating because supposedly players without gaudy defensive stats will be hurt by this statistical plus/minus ratings.

But players like Bruce Bowen and Tayshaun Prince turn out to be more highly rated by the statistical plus/minus rating than the adjusted plus/minus rating. (On average, players selected to the All-Defensive teams were more highly rated by the statistical plus minus/rating.)

Now again 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.) 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.

And remember if you don't like the ratings (and the player is not a rookie who with only one year of data is more prone to error), ask yourself two questions.

Why does the player's team defend a lot better (or worse) when that player is in the game? Why do the teams of players similar to that player defend a lot better (or worse) when they are in the game?

And now that I have bored you to tears, here are the lists.

Top Six Small Forwards (best to worst):

  1. Shane Battier
  2. Darius Miles
  3. Trevor Ariza
  4. Shandon Anderson
  5. Paul Pierce
  6. Bruce Bowen

Bottom Six Small Forwards (worst to best):

  1. Peja Stojakovic
  2. Matt Harpring
  3. Lee Nailon
  4. Wally Szczerbiak
  5. Tim Thomas
  6. Carmelo Anthony

Remember that Ron Artest did not make this list because he did not play 1,000 minutes last season. The big surprises here probably are Ariza, Harpring, and the absence of Tayshaun Prince.

Ariza is a rookie who did not play a lot of minutes so take his rating with a grain of salt. Harpring has not been an effective defender in each of the last three seasons, but I think last season he was a bit worse because of nagging injuries.

Prince seems to benefit a great deal from playing with the two Wallaces. His raw plus/minus is very good, but once I account for the fact that he plays with the two Wallaces, it falls apart. When he plays without them, Detroit struggles on defense, whereas the Wallaces just do not seem to miss him much when he is out of the game. That said, Prince plays so many of his minutes with the two Wallaces that it is a bit difficult to separate out their relative contributions.

Top Eight Shooting Guards (best to worst):

  1. Tony Allen
  2. Andre Iguodala
  3. Josh Smith
  4. Ben Gordon
  5. Aaron McKie
  6. Gerald Wallace
  7. Manu Ginobili
  8. Eddie Jones

Bottom Eight Shooting Guards (worst to best):

  1. Michael Redd
  2. DeShawn Stevenson
  3. Jalen Rose
  4. Keith Bogans
  5. Latrell Sprewell
  6. Raja Bell
  7. Ricky Davis
  8. J.R. Smith

For this best list to be dominated by rookies is very different from last season when the rookies as a group were terrible on defense. This season they were quite good and look even better in this list because this is a projection for next year and I would expect their defense to get better with experience. But remember to take these rookie ratings with a grain of salt. We really need another season to get an accurate assessment of their defense using plus/minus ratings.

In particular, Gordon is a puzzle since he has a reputation of being a terrible defender. He played the bulk of his minutes with Tyson Chandler and it appears to me he is getting credit for a lot of Chandler's handiwork because the few times Gordon was in but Chandler was not, the Bulls played great defense. On the other hand, in the few times when Chandler was in but Gordon was not, the Bulls played pretty poor defense.

Statistically, this implies that it was Gordon and not Chandler that was the reason for the Bulls' good defense. And thus he gets more credit for the good defense during the times when they were both in the game. Gordon may be a better defender than he has gotten credit for, but I suspect that part of this is just good fortune. Once we have another season to try to separate Chandler and Gordon, it should be easier to assess Gordon's defensive effectiveness.

And yes, it is Redd who is the max player who is rated the worst defender at his position. The Bucks over the past three seasons have consistently been better when Redd has been out of the game. (In fact, it is striking how consistent the results have been.) And the reason is because he has been a horrible defender - just plain horrible. There has been no player who has played anywhere near the minutes he has over the past three seasons that has rated as consistently horrible on defense as Redd has. But I think what we learn from all of this is that defense may win championships, but it does not pay the bills.

Interestingly, Bell who is being signed by the Suns in order to shore up their defense rates as a bad defender. What is remarkable about Bell's results is that he has played for several teams over the past three seasons and yet his defensive ratings have been consistently bad. That strongly suggests that putting him in a new context with the Suns is not going to markedly improve his defense.

Top Five Point Guards (best to worst):

  1. Chris Duhon
  2. Marcus Banks
  3. Earl Watson
  4. Jason Kidd
  5. Eric Snow

Bottom Seven Point Guards (worst to best):

  1. Troy Hudson
  2. Tyronn Lue
  3. Tierre Brown
  4. Damon Stoudamire
  5. Carlos Arroyo
  6. Nick Van Exel
  7. Leandro Barbosa

Interestingly, two of the best defending point guards (Duhon and Watson) are still available in the free agent market. Now again we only have one season with Duhon (but a lot of minutes in that season and results that are consistent across the adjusted and statistical plus/minus ratings), so we should be a big skeptical of his results. But Watson has consistently over the last three seasons been an elite defender at the point guard position. He seems to be another example of the adage that defense may win championships, but it does not pay the bills.

Lue has a reputation of being a good defender, but like Bell he has played in a number of places and consistently been an ineffective defender. His reputation must rest pretty heavily on his play in the Finals when he was somewhat effective against Allen Iverson. That performance has stuck in people's minds in face of conflicting evidence.

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: 5:00 AM, August 2, 2005


Anonymous Anonymous said...

How did Larry Hughes do in this?

8/02/2005 11:12 AM  
Blogger KnickerBlogger said...

It's surprising to not see Prince & Kirilenko on these lists. I'm also a bit shocked with Ariza's ranking. While I know that he's a rookie, so you have less data to judge him on.

Watching him, he seemed to be a good team defender, but a poor one on one guy. Kobe Bryant just lit him up one night, blowing past him at will. In light of Tayshaun's absense and Ariza's inclusion is it possible that we're still seeing some residual effect from team play? (IE Prince plays with the Wallaces, while Ariza plays with the Crawfords & Marburys)

8/02/2005 11:13 AM  
Anonymous Jason Napora said...

Well, this certainly points out as to why the Wolves did so badly last year, with representatives on SF, SG, & PG worst lists..

Incidentally, how does Trenton Hassell rank? It's a subject of much debate among Wolves fans. It did seem like he defended worse last year, particularly in the first half, but it's always hard to tell, even watching most of the games, how much of the overall decline in team D was any one player's fault.

8/02/2005 11:21 AM  
Blogger Dan Rosenbaum said...

Remember Kirilenko was near the top of the power forward list. I used the positions in Doug Steele's data with a handful of changes. There are still a number of players out of position.

Hughes and Hassell are just below this top group. Hassell was better in the 2003-04 and probably would have been listed near the top during that season.

Rookies in the past have improved a lot from the first season to the next, so I estimate that improvement and include that in the projections for next season. But this group of rookies came into the league immediately doing the "little things" and so maybe we will not see the improvement out of them that we have seen with past rookies. That would mean that I am tending to overrate rookies, which I suspect might be the case.

That said, I don't think the Ariza and Prince situations are that comparable. The problem with estimating the effectiveness of Prince is that Detroit uses a pretty fixed substitution pattern which makes it hard to separate Prince from the two Wallaces.

8/02/2005 11:38 AM  
Anonymous Anonymous said...

Where did Vince Carter rank? I realize it's a tossup as to whether he's considered a SG or SF. The NBA always lists him as a forward for all-star balloting purposes, but his position has been more predominantly SG for several years.

I feel that, when motivated and focussed, he plays excellent defense, certainly better than he's been given credit for in "expert" circles. On the other hand, there's no denying that he can slack off on that end of the floor, and so his defensive performance is inconsistent. Am curious as to what the rankings show, particularly after the trade to NJ.

8/02/2005 12:23 PM  
Blogger fanerman91 said...

Do you have (or plan on making) complete lists available? I'd like to see where a number of players not on that list are.

8/02/2005 12:34 PM  
Anonymous NickS said...

I'm surprised to see Paul Pierce rate to highly. I have always thought of him as an abover-average defender but not an elite defender.

Harpring is also interesting. I knew that he was terrible on defense this year (along with the rest of the Jazz) but I thought that he had a better reputation than that before his injuries.

8/02/2005 2:39 PM  
Anonymous Anonymous said...

How did Steve Nash rate? The big knock on him is always his defense … does the knock hold up statistically?

8/02/2005 3:10 PM  
Anonymous Kevin Broom said...

One interesting pair of names is Tony Allen and Ricky Davis. According to 82games, the two combined to play 69% of the Celtics' SG minutes last season. How much of their ratings are the push-pull of subbing for each other?

8/02/2005 4:02 PM  
Anonymous Jason said...

Wow, tons of surprises on the top SG and SF lists.

If Prince's non-admission into the Top 7 could be because of a rigid substitution pattern, would it not apply to several other players as well? How can you adjust for something like that statistically?

Ben Gordon's admission really does not pass the smell test either.

But to be honest, I haven't fully grasped the method here. I know how you get pure adjusted +- : Y=margin, X=vector of 400+ player categories, read off the coefficients. I know you use some kind of efficiency rating based on pp100. But I don't know what rating that is or how you combine it with the adjusted +-.


8/02/2005 4:14 PM  
Blogger Joël Janssens said...

Where is T. Prince en Kirilenko? There must be something wrong with your system.

8/02/2005 5:00 PM  
Anonymous Anonymous said...

i liked a lot of the hacking the refs let Detroit get away with in games 3 and 4 of the finals (blow outs?). does this make ben wallace a game changer while he is karate chopping tim duncan's arm off to give up a transition hoop? or is he a game changer in the loss when theyre actually calling fouls?

and its funny that redd is at the bottom of the SG list but their point guard Mo Williams isnt found anywhere since he is the a huge reason their team defense as a whole crumbles and makes everyone look like crap. run a pick and roll on the kid and the opposing PG is in the paint in less than a second. the defense is consistently forced to quickly collapse and rotate. the entire team is bad at it.

this doesnt say much for individual physical factors on why someone succeeds as a defender and why someone fails. its just 'objective' numbers mashed together to get some numerical ranking system and sheds no light on the subjective feel of the game and a teams defense (or lack of) as a whole. its just short-sighted math.

numbers arent everything

8/02/2005 9:43 PM  
Anonymous Anonymous said...

When you listed Josh Smith as the 3rd best shooting guard, did you mean Josh Childress? I think Smith played more small forward and power forward.

8/02/2005 10:18 PM  
Blogger Dan Rosenbaum said...

First of all, it would be preferable for these questions to be at the APBRmetrics message board.


Complete lists are unlikely to be available anytime soon as I am letting a situation develop. I am sorry.

Vince Carter (Steve Nash) is near the top (bottom) of the defensive ratings for small forwards (point guards).

KevinB, having two players (Davis and Allen) share 69% of the time at a position does not sound unusual. I am sure there are many cases where that percentage is much higher.

I hope that I have not overstated the case for the rigid substitution pattern for Prince. My belief is that his results are a little more prone to random error because of the substitution pattern, but that will not explain his mediocre defensive rating. I think part of the problem is that qualitatively we have a tough time evaluating him as a defensive player. It is hard to know how much playing with the Wallaces makes him look pretty good.

Now Gordon is another story. We have only one year of data on him, so I think a conclusion that he might be a good defender but there is a lot of uncertainty around his rating does pass the smell test. The thing about his rating is that the two parts of it - the statistical and adjusted plus/minus ratings - are very different (with the statistical being lower). This raises more reason to be skeptical about his result. For the other rookies, their ratings are more consistent across the two measures, so I think we can have relatively more confidence in those ratings.

8/02/2005 11:43 PM  
Anonymous jeremiah cole said...

I seems to me that if your team's second string is better than most other teams' second strings, that hurts the plus/minus of your starters. And if your team has a pretty set substitution pattern in which the second stringers pretty much spend all their time on the floor with their second-string teammates, it would be very hard to make adjustments using the very small number of minutes that each starter would get playing with the second-stringers, and each second-string player would get playing with the first string.

Am I wrong about this?

8/03/2005 1:05 AM  
Blogger KnickerBlogger said...

Is 'opinions aren't everything' the official response to 'numbers aren't everything'?

8/03/2005 7:35 PM  
Anonymous Anonymous said...

yes i think it is

8/03/2005 9:21 PM  
Blogger Dan Rosenbaum said...

Jeremiah, your first point is true of unadjusted plus/minus ratings, but not adjusted plus/minus ratings. Rigid substitution patterns do lead to less precise estimation, but as more and more data becomes available, that becomes less of an issue.

8/03/2005 11:40 PM  
Anonymous Kevin Broom said...

Dan: I'm sorry I wasn't clear -- I didn't find the 69% percent being shared by Allen and Davis unusual in the least. What I'm interested in is the fact that Allen showed up at the top of the SG list while Davis was near the bottom. And, what I'm wondering is whether a good defender subbing for a poor defender (or vice versa) may serve to "exaggerate" the ratings of each.

8/04/2005 12:58 PM  
Blogger Dan Rosenbaum said...

Kevin, as long as the substition pattern is not too rigid resulting in imprecise defensive ratings, then this should not be a problem. Chris Duhon, Kirk Hinrich, and Ben Gordon played a large fraction of the minutes at 1 and 2 for the Bulls, but each of them have good or very good adjusted plus/minus ratings.

8/04/2005 2:09 PM  
Anonymous Anonymous said...

Interesting list, but Miles isn't even the best defensive small forward playing for the Blazers: Ruben Patterson is by a large margine.

8/04/2005 2:17 PM  
Anonymous Kevin Broom said...

Thanks, Dan. That actually makes sense to me. I guess that the adjustments you make for lineup, etc. would reduce the effect that I'm thinking of.

To "anonymous" who thinks Ruben Patterson is a better defender than Darius Miles -- according to what? Why is Patterson so much better than Miles? What does he do on the court that makes him better defensively? And why isn't it showing up on the scoreboard?

8/04/2005 2:27 PM  
Anonymous Anonymous said...

re: Ruben Patterson. While a criminal headcase, he might be the best defensive small forward in the league. Few play with the intencity and tenacity that he does in limited minutes. He's fast and quick and takes pride in defence, something that very few players (most notably Darius Miles) do. To say it doesn't show up in the stats is to look at the wrong stats.

8/04/2005 4:18 PM  
Anonymous Kevin Broom said...

All right, I'll bite. If we're looking at the wrong stats for the Patterson vs. Miles question, which ones should we be looking at?

8/04/2005 4:35 PM  
Anonymous Anonymous said...

yeah... good question. I don't know. have you seen games with the two of them? maybe espn classic runs games from last year? last year was a pretty good test of that, with patterson playing extended minutes consistantly. I'm not saying he's a great player, I'm just saying when I watch him play (which happens to be quite a bit) I'm amazed at the effect he has on the defensive end. wild claims about kobe-stopping aside, watch some tape of him covering kobe. I don't have a tried-and-true metric for you though. the point I'm making is, if your system tells me that d miles is better than r patterson then your system is broken.

8/04/2005 4:59 PM  
Anonymous indocat said...

i did not see Suns' Shawn Marion who finished 5th overall on 2004/05 NBA Defensive Player of the Year results. I could not find him on your PF list either.

any explanation?


8/06/2005 2:35 AM  
Anonymous Kevin Broom said...

Not to beat this Miles vs. Patterson thing to death, but... I'm interested in the "tenacity" and "intensity" comment. While it may be true that Patterson plays with greater intensity, tenacity and effort, it does not necessarily follow that he plays with more effectiveness. No one plays with more effort, intensity and tenacity than Michael Ruffin, for example, and while he has his uses, many more players are more effective.

John Wooden cautioned at some point or another against confusing activity with achievement, and it's a warning I try to take seriously. Fans, media, coaches -- heck, players too -- like those hustle/effort guys. But playing hard doesn't always mean playing well.

One factor in why Miles may have better defensive results than Patterson (according to Dan's in-depth look at scoreboard effects) despite Patterson playing harder and with more tenacity, etc. could be in some physical attributes. Miles is several inches taller, he leaps well, and has long arms. Those attributes could help with stuff like forcing misses and turnovers, that could *result* in better scoreboard performance despite Patterson's superior effort.

Last season, for example, Miles blocked 2.2 shots per 48 minutes while Patterson had 0.5 blocks. Patterson had more steals -- 2.6 to 2.1 per 48 minutes -- but Miles' steals are a pretty good number. Add in Miles' defensive rebounding edge (about 2.8 additional defensive rebounds per 48 minutes), and what we're seeing is box score evidence of Miles getting more defensive stops per minute than Patterson. My guess is that height and length are key factors in those additional stops.

Note -- I'm not saying that the observation that Patterson plays with more effort etc. than Miles is incorrect. It probably is an accurate observation. My point is that effort does not always equate to achievement.

8/08/2005 1:14 PM  
Anonymous Anonymous said...

To add to your point Kevin,

A team that rotates well and plays good team defense in general can be much more effective than 5 individuals expending much more energy but not playing together as a cohesive unit (not trapping on the baseline when a teammate forces him into the corner, etc). The observation that Darius helps the team more than Ruben on defense using the metrics that were used could mean that Darius contributes more to a solid "team" defense. This could be because he talks more on defense, helps out with trapping, rotates well, etc.

8/08/2005 3:31 PM  
Blogger The Zoner said...

I live in Chicago and I agree with Dan's assessment that Chandler (and even AD) helped him onto this list. The reason he did not start and play more minutes last year was based primarily on his poor defense, according to Skiles. And also, as noted, Duhon's tremendous defense. I also think Hinrich is overrated defensively. He is definitely a good team defense player and he puts forth maximum effort, but there are many PGs in the league who can dust him.

This is a great blog.

8/11/2005 12:47 AM  
Anonymous Anonymous said...

Where is Josh Howard?? He has become Dallas' whole D? That kid is mean and will definitly be there next yr.(he lost some PT to others as well.)
As for the Wallace's hacking TD.... I guess you didn't see TD hacking in them, or see him bellyache EVERY time he was touched. I lost some respect for him watching him turn to an official evertime he misses.
Oh, this could go on forever, but as someone said "numbers arent everything"!
Nice props on T.Allen the C's will be reinging on these lists for yrs w/ he, Jefferson and Pierce.

8/11/2005 11:24 AM  
Anonymous Anonymous said...

you fucking fuckers. Peja Stojakovic is better than all of you dumbshit!!!!!!!! Ur just jealous cuz he WAY more awesome than any of YOU...... and don't be racist.... sons of bitches........just cuz he's a different race or religion or w/e...that is bullshit. it's discrimination and im pretty sure anyone else would say so.........

9/29/2006 4:51 PM  
Anonymous Anonymous said...

you dumb fuckers. Peja Stojakovic is AWESOME. ur just jealous cuz ull never be as good as him...... and dont be racist just cuz hes different race or religion or w/e that's bullshit and it's discrimination.......and fuckers.......im pretty sure ANYONE else would agree.......u lazy *** *

9/29/2006 4:54 PM  
Anonymous Anonymous said...

U dumb assholes. Peja Stojakovic is AWESOME in what he does for his team. u motherfuckers are just jealous cuz ull NEVER U HEAR ME NEVER BE AS NEARLY AS GOOD AS HIM. u dumbshit dont know the first thing about basketball..........u dont even know who tha hell Peja is.................... and what the hell he does. and its discrimination................im PRETTY sure ANYONE would agre...............

9/29/2006 4:56 PM  

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