• Nobody, including this author, believes that these lists are the be all and end all.
• Age is as of the end of the 2005-06 season. Minutes are for the 2004-05 season.
• The overall rating tells us, for example, that if we replace an average defender with Ben Wallace, defense should improve by about 5.8 points per 40 minutes.
• Bigger standard errors indicate that the rating is more prone to error. (I have incorporated differences between the statistical and adjusted plus/minus rating into these standard errors. For that reason they are probably a little bigger than they should be.)
• The percentiles tell us what percentage of players at the same position have worse adjusted (or statistical) plus/minus ratings.
• Remember that in the last three columns, adjusted plus/minus ratings will vary more when players have not played a lot of minutes. In cases where players have played only a few minutes, we can get some extreme results.
• Don’t look only at the ranking or only at the rating. Look at the standard error. See how big it is. See if the adjusted and statistical plus/minus ratings are about the same. See if the adjusted plus/minus ratings vary a lot from year to year (beware of rookie ratings because we can’t see how they vary from year to year). Think about all of these things before coming to a conclusion about how much to trust any one given number.
• For those of you who think these ratings have no basis in reality, ask yourself this question – courtesy of Kevin Broom. If your favorite player isn’t rated highly enough, why are his defensive contributions not showing up on the scoreboard? And why isn’t the scoreboard what really matters?

Here are some points to consider.

• Defensive ratings, on average, are highest for centers, then power forwards, then small forwards, then shooting guards, and then point guards.  Offensive ratings go the other way.  This squares with the conventional wisdom that defense is anchored by big guys.
• Ben Wallace is rated highly on both the adjusted and statistical plus/minus ratings.  His contributions are picked up in these numbers.
• Dikembe Mutumbo had a phenomenal year last season on the defensive end, but his ratings bounce around a good deal from season to season, so we should be skeptical of exactly how good of a defender he will be next season.
• Jason Collins is a consistently great defender; I don’t remember ever hearing him discussed as an elite defender in this league, but only a select few players have been more effective defensively than he has been over the past three seasons.
• Jeff Foster is a very effective defender despite not having great defensive statistics.  Joel Pryzbilla is an effective defender who may be a bit overrated by his defensive statistics.
• There is a big dropoff after the top five defenders.  The difference between #5 (Foster) and #6 (Brendan Haywood) is the same as the difference between #6 (Haywood) and #15 (Shaquille O’Neal).  Thus, at the very least rankings #6-#15 should be considered to be about the same.
• The big drop in defensive effectiveness between Nazr Mohammed and Rasho Nesterovic is interesting.

Here are some points to consider.

• Again there is a big gap between the top five and everyone else.
• Remember rookies like Nick Collison, Al Jefferson, and Matt Bonner are more prone to extremes given the scarcity of data on them.  I would expect them to gravitate more toward the middle in the future.  That said, Collison subjectively seems like a very good defender to me, so this is not a big surprise.
• Players similar to Tyson Chandler have great adjusted plus/minus ratings.  Chandler’s ratings are so-so.  That to me is a red flag about exactly how effective his defense is.
• Interestingly, the list of least effective defenders has a number of high-priced players.  Championships may be won with defense, but it is offense that pays the bills.

Here are some points to consider.

• For those of you who are going to complain about Bruce Bowen, note that he has the highest adjusted plus/minus rating in 2003-04 among those in the top 10.  He is an elite defender and these numbers show that.
• Paul Pierce and Vince Carter are often criticized for not giving full effort on the defensive end, but their teams have played better defense when they are in the game.  Notice that both are brought up by the adjusted plus/minus ratings.  On the defensive end, they do not appear to be stat whores.
• Andres Nocioni is a curious case – great defensive stats but horrible defensive adjusted plus/minus ratings.  I’d like to see him for another year before coming to any conclusions.
• Wally Szczerbiak has been very inconsistent defensively.  Matt Harpring has been very consistent – in a bad way.

Here are some points to consider.

• Tony Allen, Ben Gordon, and DerMarr Johnson all have very large standard errors.  Take their ratings with an even bigger grain of salt.  In fact, of the top six players, only Gerald Wallace has a reasonably small standard error.
• Gordon and Tyson Chandler played a lot of minutes together.  Looking at 82games lineup data for Gordon and Chandler, it appears that the Bulls played very good defense in the few times when Gordon played without Chandler. When Chandler played without Gordon, the Bulls played pretty poor defense.  Statistically, this implies that it is Gordon who is the better defender and thus he is getting the lion’s share of the credit for the good defense played when both were in the game.  This does not square with anyone’s perception of who should get credit, but it will be interesting to see if this pattern continues into next season.  
• In my blog, I erroneously said the following: “Interestingly, [Raja] 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.” This is wrong. Well, that might be a little harsh. It is not quite right.  Bell has been an ineffective defender the past two seasons for Utah, but was effective for Dallas in 2002-03.  Thus, perhaps in a new environment in Phoenix he will be effective once again.
• Michael Redd is in a league of his own on defense at the shooting guard position.  The difference between Redd and the next lowest-rated shooting guard is three times as large as the difference between the 2^nd and 10^th lowest-rated shooting guards.  And Redd has been very consistently ineffective over the years.  Again, defense may win championships, but it does not pay the bills.

Here are some points to consider.

• Chris Duhon defensively is the highest-rated point guard both with the statistical and adjusted plus/minus ratings.  It would be good to see another year of data on him, but he appears to be an elite defender (and one who has gotten very little interest in the free agent market).
• Earl Watson also has consistently been a very effective defender, despite not having great defensive stats.  He also is a testament to the defense wins championships, but does not pay the bills theme of this piece.
• Note that because of injury or indifference Baron Davis’ defensive effectiveness has fallen rapidly over the past three seasons.
• Steve Francis has consistently been an effective defender.  He is a lightning rod for criticism but on two different teams he has consistently helped his team on the defensive end.
• Troy Hudson probably gets the award for the being the worst defender in the league.  He is dead last among point guards in both the statistical and adjusted plus/minus ratings and his adjusted plus/minus ratings are consistently horrible.  He is playing a game on the defensive end that is not remotely like anyone else’s in the league.   

Dan T. Rosenbaum is an economics professor at the University of North Carolina at Greensboro. Besides this statistical work, Rosenbaum has been cited in numerous publications for his expertise on issues related to the NBA collective bargaining agreement and especially the luxury tax. He is thankful to the many remarkable individuals who have helped him tremendously in better understanding the NBA.  See his blog for more of his writings on statistical and financial issues related to the NBA.