Using statistics in basketball: the bar is higher

By Dan T. Rosenbaum

David Leonhardt in his Sunday New York Times "Keeping Score" column has been a pioneer in describing the ways in which statistical analysis has affected sports. (He writes about economics during the week, so, of course, everything he writes is gospel.) This week David writes that baseball "has found itself in the equivalent of a theological dispute about whether [it] is a game of mystery or of data, of statistics and analysis or of intuition and human instinct."

David points out while teams using statistical analysis, such as Oakland and Boston, have achieved a great deal, there is no denying the success of "traditionalist" teams, such as Atlanta and St. Louis. The article is fairly even-handed, but this passage appears to betray the author's feelings.

"Academic research, however, is pretty much on the side of statistics. Whether diagnosing patients or evaluating job candidates, human beings vastly overestimate their ability to make judgments, research shows. Numbers and analysis almost always make people better.

'There have been hundreds of papers on subjects from picking students for a school to predicting the survival of cancer patients,' said Richard Thaler, a University of Chicago economist who uses sports examples in his class on decision-making. When a computer model is given the same information as an expert, the model almost always comes out on top, Thaler said."

This last sentence begs the question, however, because traditionalists would argue that the "computer model" never has the "same information" as the scout or coach. And they would be right. The real question is whether the benefits of more data (often collected and analyzed in a more objective manner) outweighs the costs of a simplified model that necessarily ignores some aspects of reality. Thaler argues above that in most circumstances the answer appears to be yes. And in baseball, I believe the argument in most cases is yes.

But in basketball, I am not so sure. Recently, I received an e-mail from a friend who argues that "basketball stats are a really interesting challenge."

"There's a sense in which [basketball stats are] much more related to economics than baseball stats are, which I always found a bit boring although incredibly accurate and powerful as a game predictor. Baseball is mostly about a small number of repetitive hand/eye coordination tasks, while basketball involves constant maximizing interaction between optimizing actors on the court."

Tabulating statistics may very well be the best way to form predictions about the "repetitive hand/eye coordinating tasks" of baseball, but applying those same techniques to the game of basketball which "involves constant maximizing interaction between optimizing actors" may not prove to be as useful. The costs of a simplified model may be too high.

But do not interpret me to be saying that statistical analysis has no place in basketball. Instead the point I am trying to make is that basketball people are right to be skeptical of statistical analysis, because analyses based upon an overly simple model of the game of basketball often can be more misleading than useful.

A good example of this is the "possession usage vs. offensive efficiency" debate over at APBRmetrics. Dean Oliver, author of Basketball on Paper and consultant for the Seattle Supersonics, makes the following argument.

"Implying that all these high percentage, low usage shooters can ramp up their usage without penalty implies that the people running the NBA are not just a little wrong. It implies also that the fundamental nature of basketball is poorly understood. It implies that any sort of linear weights rating is wrong. . . .

It implies that pretty much every rating method is wrong, because the context in which players are being used is incorrect. [Dan Rosenbaum's] method, which is totally different from others here, has to be wrong because it is flawed by the decision to not let Fred Hoiberg shoot 25 [times] per game. This is not just a matter of a tiny little assumption that has to be proven. This is a principle that really underlies the game of basketball. It very much distinguishes it from baseball, where players take turns being on offense."

This argument by Dean highlights how important a solid understanding of the game of basketball is to good statistical analysis in basketball. But a solid understanding of statistics - perhaps moreso than what is necessary in baseball - is also critical in making the right judgments when using basketball statistics.

I have heard reports of a Western Conference general manager that is heavily using basic unadjusted plus/minus data in his evaluation of free agent acquisitions. I probably understand the nuances of working with plus/minus data about as well as anyone, and I am one of the biggest advocates for plus/minus data. But I shudder when I hear about this general manager.

It is easy to misinterpret what can be learned from plus/minus data, and I see mistaken analyses using these data more often than not. Teams do not play their players randomly. Match-ups matter. Roles matter. And trying to isolate the contribution of a player or two when ten players are on the floor at a time is a tough statistical feat. Hearing a general manager without extensive experience with statistical analysis is making heavy use of these data sounds to me like a recipe for disaster. Without a strong understanding of statistics, as well as a strong understanding of basketball, it is just too easy for statistics to be more misleading than useful.

Another example is Dallas who has for several years made use of adjusted plus/minus ratings in their coaching/front office decisions. And the consultants who do this work for the Mavericks - Wayne Winston and Jeff Sagarin - are unquestionably skilled data analysts. But they have never interacted much with the wider basketball statistics community, and I think this has made it more difficult for them to place their work in the proper perspective. (I cannot begin to describe how the APBRmetrics community has been influential in my thinking.)

In addition, my understanding is that these adjusted plus/minus ratings are largely treated as "raw data" and the coaches/front office are pretty much left to their own devices in interpreting/analyzing the data. This, in my opinion, is a huge mistake, which very well could result in very useful data produced by skilled analysts being more misleading than helpful for the Dallas coaches/front office.

Given all of this, I think it is very much an open question how useful statistical analysis can be in basketball decision-making. Done poorly, I think it can hurt teams. Done well, I think it can be a valuable asset. My sentiments are summed up pretty well in this passage by NickS at APBRmetrics.

"The reason to use stats in any field is because humans are poor at evaluating probability. We tend to see patterns where there aren't, overestimate the probability of low frequency events and, most importantly, have a tendency towards comfirmation bias -- looking for evidence that confirm our preexisting beliefs.

One of the things that's said in defense of stats in baseball is that you can't tell the difference between a .260 hitter and a .280 hitter by watching one game or one series. The difference amounts to one extra hit every 2 weeks. Similarly is there any way to tell just by watching whether Eddy Curry is more or less prone to turnovers than Yao Ming?

Similarly I think that one of the best uses of stats is to provoke questions and try to map out ways in which questions can be answered. How can we tell if a team is shooting 'too many' or 'too few' three-pointers? Do shot-blockers have an 'intimidation' effect? How valuable are 'scoring' point guards compared to 'traditional' point guards? Are specialists more or less valuable than generalists? How valuable is it to have guards who can rebound or big men who can pass? What separates a good shooter from a great shooter? Stats can't answer all of those questions but they can rule out some wrong answers that have intuitive appeal and focus attention on possibilities that are more likely to be correct."

Statistical analysis can play a critical role in basketball decision-making, but it can also be misleading if the complexities of the game of basketball (and the statistical issues generated by those complexities) are not well understood. In other words, the bar is higher for statistical analysis in basketball than it is in baseball. Ultimately this will greatly benefit the teams that incorporate skilled statistical analysts in the right way, because the greater complexities in basketball will mean that it will be harder for other teams to ever catch up with the first teams that get this right. It will be fascinating seeing how this all plays out over the next few years.

Last updated: 4:00 AM, August 29, 2005

A Mea Culpa by Mark Cuban

By Dan T. Rosenbaum

Mark Cuban in his blog presents a fascinating discussion of how the financial realities of the NBA, along with his misunderstandings of these realities, eventually resulted in him waiving one of his best friends - Michael Finley. This blog entry should be required reading for every NBA front office executive. It is a textbook example of why teams need more than a "capologist" who understands the ins and outs of the collective bargaining agreement. Teams need to understand how the details of collective bargaining agreement, trends in revenue across the league, and the structure of team salaries and player contracts will come together to form a market for trades and free agency. Seeing how that market will develop and how it can be exploited is worth millions (if not tens of millions) to teams.

I have had the good fortune of having dozens (and maybe hundreds) of e-mail exchanges with Mark over the years, as well as meeting him for lunch last Spring. He is a very impressive person - friendly, smart, insatiably curious, and always thinking.

(As an aside, my wife who is better at judging this than me was impressed by how down-to-earth he was. As an example, he remembered details about my wife that I had briefly mentioned to him in an e-mail several weeks before. This despite the fact that he handles hundreds of e-mails a day. Also, he generously offered to assist on a personal matter that we never in a million years would have thought about asking his assistance with.)

Mark also has as good or better an understanding of the collective bargaining agreement as anyone that I have run across in the league or the player's association, for that matter. This is especially true when thinking about the implications of the rules as Mark is a damn good economist. (He is also a very good stats person.)

That said, Mark has so many irons in the fire that sometimes he just does not have the time to think carefully through the implications of every last detail. Combined with his aggressive decision-making justified by his remarkable life story, this can lead to mistakes - especially as new realities start to unfold. He alludes to this in his blog.

"The model for success in the NBA has changed over the past 6 years I have been in the league. When I first got to the Mavs, there was no luxury tax, revenues from TV and the league went up every year, as did the salary cap. That changed dramatically with the leagues new TV deal and it changed even further with this years new collective bargaining agreement. Rather than an environment where salaries could go up because the cap and revenues were going up, we entered an environment where trades were made almost exclusively for financial reasons and rarely for basketball skill reasons.

The Mavs tried to take advantage of the situation. When the annual league revenue increases stopped and a luxury tax loomed, teams adjusted their financial profiles. To get under the tax threshold, they offered good players packaged with horrible contracts. We took them. We hoped the talent would get us a championship before the number of bad contracts we took on in trades caught up with us.

It didn't happen."

In the end trying to buy a championship is too expensive in the NBA. It may occasionally work for the Yankees in baseball, but in the NBA the salary cap and luxury tax make it prohibitively expensive to go that route. Trying to buy a championship also tends to lead to teams with too many scorers and too few role players, another point Mark now realizes.

"More importantly we have gone from just trying to acquire talent to have assets that in turn might be traded for better talent, to making sure we have players that fill a role for Coach Johnson’s vision of the team. Today, and for the future with young players that we can develop to fill those roles on future Mavs teams."

The problem with the idea of "acquiring talent to have assets" is that too often these "assets" have large contracts. But if a player produces less than his contract is worth, he is not an asset to the Mavs or any other team that he might be traded to. This reality becomes more important in a league with a luxury tax that doubles (or more than doubles) the costs of adding a player. In essence, we get back to the principle that a player is an "asset" only if his marginal productivity exceeds the marginal cost he adds to the team.

And players who don't fit into a role on a team, i.e. don't have high match quality, to use an economics term, run the risk of seeing their asset value fall over time. Players who are poor matches often are not going to be happy in their roles. This leads to reduced productivity for the team and the perceived value of that "asset" starts to fall. Putting players into roles where they can succeed probably is THE most important task of coaches and front offices. It leads to more wins and increased asset values for player contracts.

To that end, I have one final suggestion for Mark Cuban. Last year Seattle exceeded all expectations not because they got better players (very little change from the previous year) or got a new coach (the coaching staff stayed about the same), but because they did a better job putting players into roles where they would succeed. Part (but not all) of the reason for that is because they added Dean Oliver. Dean is a great stats expert and good basketball person and his specialty is helping coaches and front offices put teams together that best utilize their players' talents.

I know that Mark is not a big fan of Dean's book, but that is somewhat beside the point. Look at the evidence. Seattle improved by 15 games without significant changes in personnel or in the coaching staff. Historically, spending more on players has on average cost about $3 or $4 million for every extra win. Even if Dean had only a one tenth probability of being responsible for a third of those extra 15 wins, he would be worth $1.5 million a year. Wouldn't it make sense to take a tiny chance and spend one tenth of that and have Dean helping you?

Last updated: 3:00 PM, August 17, 2005

Update: how will the new NBA collective bargaining agreement and new luxury tax rules affect the free agent market?

By Dan T. Rosenbaum

Shortly after the new deal was announced between the players and owners, I declared it a big victory for the players. But with a caveat. We shouldn't pretend that the fat lady was singing until the fat lady was indeed singing.

And not a peep was heard from the fat lady until more than a month later when the final details were hammered out. Based upon what I am hearing, the owners did quite well. This deal is pretty even for both sides and the ultimate outcome will depend largely on what happens to revenue growth over the life of the deal.

The initial details suggested that the teeth were taken out of the luxury tax, but that does not appear to be true. The luxury tax is guaranteed in every season of the deal at a lower threshold than used in 2004-05. Perhaps most importantly, teams not paying luxury taxes will likely continue to get larger luxury/escrow tax distributions than teams paying the tax. The new luxury/escrow tax system will be different, but it may deter spending just as much as the old system.

The increases in the salary cap were not extended to maximum salaries, which for owners takes a bit of the sting out of that change. Also, changes in the formula for the salary cap and for salary cap holds will, in effect, make the increase in the salary cap smaller than it appears. In addition, changes in the formula for the Mid-Level Exception (MLE) will result in it growing more slowly than it otherwise would.

Another important detail not known last month was that basketball related income (BRI) increased to $3.037 billion in 2004-05 - a 10.2% increase over 2003-04. That is a marked change from the 1.7% average growth over the previous two seasons. Part of the increase is due to the expansion Charlotte franchise and some accounting quirks, but some of it appears to reflect real growth. If so, the players may regret allowing maximum raises to decrease. It could be the case that revenue growth comes close to outstripping these maximum raises.

Before continuing, let me lay out the major provisions of this new deal. The provisions in green should significantly increase the overall compensation of the players, while those in red should decrease them. There is a lot in here that I believe is not reported anywhere else at this time, so I hope that this can serve as a resource for what this new deal looks like (at least until Larry Coon is able to update his FAQ). I think I have pretty good information on most of these provisions, but as new information becomes available, I will update this material.

1. The luxury tax will be dollar-for-dollar on spending above the 61.0% of BRI luxury tax threshold (just below that used prior to 2004-05), except that the new deal guarantees that the luxury tax will be triggered in every season of the deal. [Note that in 2004-05 the threshold was at 63.3% of BRI.]
2. All teams (including those who pay tax) under the new deal will receive a full share of the escrow tax collections. The most likely distribution of the luxury tax appears to be a full share to teams below the luxury tax threshold with the remainder being split evenly among all teams. This is likely to result in teams losing about $3 million in distributions in 2005-06 (more in later seasons) if they end up being taxpayers.
3. Luxury Tax Amnestry Provision (Allan Houston Rule): Up through August 15, teams will be given a one-time opportunity to waive one player and eliminate the luxury tax on any future contractual payments to that player. The salary will still count towards the salary cap, and payment will still have to be paid to the player according to the contract, but the team will not be subject to tax on that player’s contract. This provision will also apply to previously waived players, but not players traded for after June 21st.
4. For all minimum salary players, teams above the luxury tax threshold will pay luxury tax equal to the amount for a minimum salary player with two years of experience. This is also true of minimum salary players with zero or one year experience, whose salary for luxury tax purposes will be bumped up to that for players with two years of experience. Edit: This is how it reads in the CBA, but according to league sources this rule will be changed to only apply to free agents with zero or one year of experience who earn up to the minimum for a second year player.
5. The salary cap and luxury tax exceptions for players who are deemed ‘permanently injured’ will begin after one year rather than two, but can only be applied by the team on which the player played at the time of injury. [Teams will not be able to trade Terrell Brandon to a team looking to create salary cap space and/or avoid the luxury tax.]
6. The escrow tax on player salaries will be reduced from 10% in year one, to 9% in years two through five, and to 8% in year six of the agreement.
7. The players will be guaranteed a total of 57% of BRI each year. My understanding is that, contrary to earlier reports, this percentage will not increase during the life of this agreement.
8. The escrow tax will only be retained by the owners to offset salary costs when total salaries exceed 57%, just like in the last season of the prior deal, but in the new deal that threshold will be raised to 57.5% if BRI is 30% higher than in 2004-05 and to 58% if BRI is 60% higher than in 2004-05.
9. The salary cap will be set at 49.5% iof BRI in 2005-06 and 51% thereafter, up from 48.04%. Maximum salaries will continue to be tied to the old 48.04% of BRI percentage.
10. Gilbert Arenas Provision: Restricted free agents in their first two seasons can be offered contracts above the MLE by teams with salary cap room, but in the first two seasons of such deals players will be paid the MLE and 108% of the MLE. After the second year of the contract, the contract can increase to the maximum allowable salary for that player. For example, with no restrictions a player in their first two seasons could be offered a maximum deal of $69.6 million over five years ($12M, $12.96M, $13.92M, $14.88M, and $15.84M.) But this provision will limit that to $55 million over five years ($5M, $5.4M, $13.92M, $14.88M, and $15.84M). For the team offering this contract, the salary cap hold will be equal to the average value of this contract over each of the five years of the contract - in this case $11 million. Thus, the offering team would need to have $11 million in space under the salary cap in order to offer this contract. The original team can match if it has its MLE or early Bird exception available and for the original team the salary cap hold will be equal to the value of the contract in each year ($5 million in the first year, $15.84 in the last year).
11. A team will have 7 days to match an offer for a restricted free agent (down from 14).
12. The maximum length of a new contract will now be 6 years for a player who signs with his current team (down from 7), and 5 years for a player who signs with another team (down from 6).
13. The maximum annual raises on a new contract will now be 10.5% of the first-year salary (not compounded) for a player who signs with his current team (down from 12.5%), and 8% for a player who signs with another team (down from 10%).
14. First-round picks will be given standard contracts with two years guaranteed (down from 3), followed by two years of team options (up from 1). The contract amounts will remain standardized. [The option for year 3 will have to be picked up prior to year 2. This is very early to give up on a rookie, so it is likely that teams will rarely decline this option.]
15. In general, there are no changes being made to the general salary cap exception mechanisms which allow teams to exceed the salary cap to add players, such as the Bird Exception, Million Dollar Exception (renamed the Bi-annual Exception), Mid-Level Exception (MLE), etc. However, the average NBA salary will be computed assuming 13.2 players per team (up from 12.5), which will result in the MLE being about five percent smaller than it would otherwise be.
16. For teams over the salary cap, trades will be allowed as long as they trade away as much first-year salary as they receive within 25% (up from 15%) + $100,000.
17. Gary Payton Rule: Players will have to wait 30 days in the regular season (20 days in the offseason) before being allowed to sign with the team that traded them away.
18. Alonzo Mourning Rule: The league will have more discretion to fine players who refuse to play for a team they are traded to.
19. Base-year compensation (BYC) rules (for trades involving players who just received a sizable raise) will expire on the later of (a) June 30 of the following year or (b) six months following the commencement of base year compensation player status.
20. Minimum salary levels will be increased by 3.5%.
21. Teams will be required to have 13 players (up from 11) under contract with the maximum staying at 15. Related to this, teams will have a salary cap hold for every roster spot under 12 (up from 11). The league has guaranteed that teams will have an average of 14 players and will be fined if that average is not met.
22. The active roster will still be limited to 12 players, but the designation for the others will now be ‘inactive’ rather than ‘injured.’
23. The NBA age limit will be 19, and one year past high school for Americans, based on calendar year. [There is likely to be a related league rule implemented that prohibits NBA scouts and personnel from scouting any high school games.]
24. The NBA Developmental League (NBDL) age limit will be 18, down from 20.
25. Teams will be able to send players with less than two years experience to the NBDL for needed development during the year, while still retaining full rights, with the ability to recall any such player at any time as desired. Such players will receive their full NBA pay.
26. Teams will be able to send an assistant coach to their associated NBDL team to work with and monitor the development of their players.
27. Players will be subject to as many as 4 random drug tests per year (up from 1), with penalties increasing for failing a test on a 4-strike system (5-10 games, 25 games, 1 year, lifetime).
28. Suspensions for on-court misbehavior will be subject to arbitration if the penalty exceeds 12 games (formerly there was no arbitration regardless of length).
29. More money will be added to pension payments for the older retired players, pending approval under IRS regulations. [I am not sure what happened with this. I certainly hope this made it into the final deal.]

From the beginning, I have argued that the big enchilada in this deal is the change in how luxury and escrow taxes are distributed back to the teams. In the old deal the bulk of the $300 million or so a year (in luxury and escrow taxes) went to teams below the luxury tax threshold. This resulted in the first $3 to $4 million spent above the luxury tax threshold costing teams $3 to $4 million in luxury taxes and $8 to $10 million in lost distributions. That, in effect, was a 300 to 400 percent effective tax rate for spending just above the luxury tax threshold. That got teams attention and for some teams made the luxury tax threshold a "hard cap."

The new deal results in the escrow taxes being distributed evenly to all of the teams. Non-luxury tax payers also get 1/30th of the luxury taxes and mostly likely all teams will get about 1/30th of what is left over. That would mean that the first dollar of luxury tax would cost teams $3 to $4 million in lost luxury tax distributions. It is not the $8 to $10 million in the last deal, but if teams might lose all of that money with their first dollar of luxury tax it might result in many teams treating the luxury tax threshold as a "hard cap."

This is bolstered by the the luxury tax being guaranteed to be triggered in every season and the luxury tax threshold being known prior to the season (at a level below that of 2004-05). I suspect this might result in more teams treating the luxury tax threshold as a "hard cap."

On the other hand, as soon as teams take the $3 to $4 million hit, the effective tax rate will be just 100 percent, which is lower than it was in the old deal. Also, the luxury tax teams will be richer because they will be getting a higher share of the distributions. This could result in more spending. The luxury tax amnesty provision, in essence, redistributes income from low-spending to high-spending teams, which likely will result in more spending, especially since it puts more players into the free agent market.

So the luxury/escrow tax system will be different, although it is possible that it may deter spending as much as the old deal. (Note also that the players will be paying less in escrow tax at the end of this deal. That is a clear benefit for the players.)

As mentioned above, the salary cap increase is a benefit to the players. But it is phased in (starting at 49.5% in 2005-06 and rising to 51% thereafter) and the salary cap hold for the 12th roster spot will in effect make the increase a bit smaller. Also, the welcome changes in how projected BRI is calculated will likely result in the salary cap being a bit smaller than it otherwise would have been. Finally, not allowing maximum salaries to rise with the increase in the salary cap is a big deal, because maximum salary players account for a significant share of total player compensation. All told, the increase in the salary cap is good for the players, but not as much as it appeared a month ago.

And finally, if the over 10 percent increase in BRI is the start of a new trend, the legislated reduction in maximum raises could result in players not being able to keep pace with BRI growth. Potentially that more than anything could result in this being a great deal for the owners.

This author initially claimed that the players may have taken the owners to the cleaners with this new deal. Well, about the only thing that needs to be taken to the cleaners is perhaps my mouth for suggesting that the league may have negotiated a bad deal. (I expressed a lot of caveats, but should have been more skeptical of those initial details.) So if the league would like to send a bar of soap down here to Greensboro, I promise to oblige them by sticking it in my mouth.

Last updated: 11:59 PM, August 26, 2005

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

By Dan T. Rosenbaum

I have updated my defensive ratings and provided more detail in an article posted at 82games.com.

We can debate about what plus/minus statistics tell us about future defensive effectiveness (especially if a player changes roles), but there can be no debate about what they tell us about past defensive effectiveness. Like a free throw percentage statistic that records who was the most effective free throw shooter, plus/minus statistics can be used to record who was the most effective defender. The calculation is more complicated, especially when we account for the other players on the floor, but the concept is the same.

Nobody, including this author, believes that these lists are the be all and end all.

Last updated: 9:30 AM, August 5, 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