One of the tools, and I emphasize the words “one of”, that we use to better understand how the Mavs are performing is

an advanced Plus Minus and Impact analysis. Similar to traditional plus minus systems, we also add a special sauce

that also defines the impact of the plus or minus. A simple way to look at it is that scoring or giving up a score

when you are down 30 with 2 minutes to play is far different than when then when its tied with 2 minutes to play.

We take this information by player and combine it into lineups to determine not just our best lineups, but our

best lineups against the lineups against us. The information is useful as one component of many more. (It doesn’t

take into account the impact of coaching, so its worthless as a stand alone tool. IE, a smart coach knows what

matchups put a player and lineup in the best position to succeed.They know once a player hits 15,20 mins,

whatever, their ability to impact a game is reduced. They know a guy can only succeed in a zone or against a zonet,

etc.)

Where it becomes very useful is in the playoffs, after you have played a team 4 times in the regular season, and

they have played 82 games. Then the data has more validity in team on team matchups, and in understanding which of

the other teams lineups work best or worst. (If they play their worst lineups unknowingly, we may keep matchups to

keep those guys on the floor.)

This isn’t something that Nellie keeps in his pocket to look at during a game, but its something our assistant

coaches know going into games and review for any edges we can get. Sometimes it can help give us an edge a couple

possessions in a playoff game. On the other hand, if we don’t execute, it wont help a bit.

In any event, it’s relatively early in the season, so the numbers are far from conclusive. It is far enough in for

the anamolies to have fallen out relative to the top players. Given some of the things I have been reading in the

basketball media, I wasnt going to, but I decided to post this just for the fun response it would create.

Have fun and no,I won’t post the rest of the scores. And no, I won’t explain everything to you. If you can

figure out what each number means, more power to you. AllI will tell you is that the points on the left is the

index, a plus for offense is good and a minus for defense is good.

******

POINTS= OFFENSE-DEFENSE IMPACT% MINUTES

Z-SCORE PT_WINS ZS_WINS PSALARY$ ZSALARY$ SALARY$ TEAMIN AGE

POS

HT ALGEBRA +/-

1 NYK Stephon Marbury 25.32 19.36 -5.96

68.07% 1179.04

3.2308 20.17_w 19.46_w 27.359$ 26.397$ 0.000$ 1450

(27.86) G

6-2 { 15.66} [ 2.89]

NYK last 3/ 30 24.03

21.59 -2.44 63.30% 123.95

NYK last 5/ 30 27.64

23.90 -3.74 62.95% 204.33

NYK last 8/ 30 20.28

18.28 -2.00 70.14% 327.70

NYK window 6/ 6 tm 22.25 21.55

-0.71 58.36% 238.12

NYK varies 30/ 30 ( 12.98)( 9.21)(

10.54)( 39.97%) 1179.04

2 DAL Dirk Nowitzki 18.66 12.16

-6.50 45.96% 1117.65

2.3013 15.75_w 14.96_w 21.367$ 20.292$ 0.000$ 1450

(26.54) F

7-0 { 20.67} [ 11.77]

DAL last 3/ 29 21.15

20.59 -0.56 40.28% 129.01

DAL last 5/ 29 21.98

21.83 -0.15 32.07% 195.82

DAL last 8/ 29 15.20

14.52 -0.68 29.65% 311.61

DAL window 5/ 5 tm 21.98 21.83

-0.15 32.07% 195.82

DAL varies 29/ 29 ( 16.58)( 12.77)( 11.27)(

37.72%) 1117.65

3 MIN Kevin Garnett 16.96 10.55

-6.41 61.72% 1107.26

2.6772 15.80_w 17.37_w 21.436$ 23.558$ 0.000$ 1354

(28.62) F

6-11 { 11.82} [ 6.50]

MIN last 3/ 28 22.59

9.55 -13.05 85.70% 115.75

MIN last 5/ 28 15.84

7.03 -8.81 62.94% 196.15

MIN last 8/ 28 16.67

7.53 -9.14 57.17% 314.15

MIN window 5/ 5 tm 15.84

7.03 -8.81 62.94% 196.15

MIN varies 28/ 28 ( 12.80)( 10.43)(

9.56)( 37.76%) 1107.26

4 LAL Kobe Bryant 14.23 8.17

-6.06 32.10% 1217.44

1.7088 15.77_w 14.86_w 21.388$ 20.153$ 0.000$ 1354

(26.36) G

6-6 { 20.66} [ 4.34]

LAL last 3/ 28 25.08

17.21 -7.87 59.41% 132.25

LAL last 5/ 28 16.94

8.42 -8.51 39.13% 221.87

LAL last 8/ 28 15.46

11.25 -4.21 34.97% 358.18

LAL window 5/ 5 tm 16.94

8.42 -8.51 39.13% 221.87

LAL varies 28/ 28 ( 13.03)( 11.96)(

7.78)( 39.51%) 1217.44

5 LAC Elton Brand 13.91 7.12

-6.79 50.74% 1044.84

2.1976 12.60_w 13.75_w 17.090$ 18.644$ 0.000$ 1437

(25.81) F

6-8 { 10.87} [ 4.23]

LAC last 3/ 28 21.22

10.08 -11.14 65.04% 113.51

LAC last 5/ 28 11.68

6.65 -5.03 43.51% 166.33

LAC last 8/ 28 8.35

4.66 -3.69 25.17% 282.75

LAC window 6/ 6 tm 10.78

6.51 -4.28 34.89% 215.37

LAC varies 28/ 28 ( 15.32)( 10.00)( 10.74)(

39.15%) 1044.84

6 BOS Paul Pierce 13.29 4.72

-8.58 15.18% 1084.76

1.1507 12.57_w 10.26_w 17.054$ 13.915$ 0.000$ 1460

(27.22) G

6-6 { 6.17} [ 2.04]

BOS last 3/ 30 -0.95

11.70 12.66 -8.52% 109.96

BOS last 5/ 30 3.85

8.97 5.12 -1.00% 174.15

BOS last 8/ 30 9.23

9.77 0.53 32.07% 286.32

BOS window 7/ 7 tm 5.22

9.14 3.92 7.80% 240.88

BOS varies 30/ 30 ( 13.33)( 10.08)( 12.90)(

49.39%) 1084.76

7 DEN Carmelo Anthony 13.19 9.44

-3.74 47.60% 881.31

2.0720 10.28_w 11.16_w 13.941$ 15.133$ 0.000$ 1445

(20.59) F

6-8 { 7.79} [ 1.20]

DEN last 3/ 24 15.12

13.04 -2.07 62.11% 109.40

DEN last 5/ 24 9.93

11.94 2.02 39.74% 191.11

DEN last 8/ 24 16.53

14.89 -1.64 53.23% 307.86

DEN window 2/ 6 tm 13.02 10.75

-2.27 55.28% 80.93

DEN varies 24/ 24 ( 17.31)( 12.31)( 10.56)(

43.15%) 881.31

8 SAS Tim Duncan 11.89 3.44

-8.45 29.66% 1115.16

1.5323 11.62_w 11.37_w 15.762$ 15.427$ 0.000$ 1536

(28.68) F C

6-11 { 15.11} [ 16.36]

SAS last 3/ 32 15.34

4.52 -10.81 41.03% 102.63

SAS last 5/ 32 18.45

7.05 -11.40 51.52% 164.97

SAS last 8/ 32 13.34

2.62 -10.72 40.55% 268.32

SAS window 7/ 7 tm 14.79

2.15 -12.64 45.36% 241.42

SAS varies 32/ 32 ( 14.43)( 10.98)(

9.02)( 39.25%) 1115.16

9 CLE LeBron James 11.86 7.50

-4.35 61.01% 1185.03

2.1339 13.41_w 15.61_w 18.191$ 21.167$ 0.000$ 1412

(20.00) F

6-8 { 10.10} [ 5.39]

CLE last 3/ 29 1.23

9.14 7.91 44.65% 108.38

CLE last 5/ 29 6.50

10.71 4.21 51.01% 194.20

CLE last 8/ 29 7.16

8.16 1.00 41.72% 316.95

CLE window 5/ 5 tm 6.50 10.71

4.21 51.01% 194.20

CLE varies 29/ 29 ( 14.99)( 8.48)(

11.53)( 45.83%) 1185.03

10 SEA Ray Allen 11.74

8.68 -3.06 24.52% 1125.46

1.3775 13.27_w 12.44_w 17.999$ 16.875$ 0.000$ 1349

(29.45) G

6-5 { 13.96} [ 9.43]

SEA last 3/ 28 4.24

11.07 6.83 -3.32% 112.84

SEA last 5/ 28 12.68

12.83 0.15 21.32% 194.79

SEA last 8/ 28 10.48

9.97 -0.52 9.30% 316.27

SEA window 5/ 5 tm 12.68 12.83

0.15 21.32% 194.79

SEA varies 28/ 28 ( 12.58)( 10.83)( 11.06)(

35.29%) 1125.46

Theodoros Plakadopoulos is a Greek American professional basketball player. His Nicknames are TPlay and Toro.

Comment by Biggest Dirk Fan -

To put some of these numbers in context, it is possible to use the z-scores above to compute 95% confidence intervals for the player ratings given above. Now since we don’t know the units, I am going to guess that the units are points per 48 minutes relative to replacement players (players who barely play).

The 95% confidence interval for Stephon Marbury is between 10 and 41 points per 48 minutes. In other words, if Marbury played 48 minutes per game, we are 95% certain that replacing Marbury’s minutes with minutes from a replacement player (such as Moochie Norris) would cost the Knicks between 10 and 41 points per 48 minutes. Over the approximate 40 minutes that Marbury actually plays, the effect would be between 8 and 33 points.

That is a pretty big interval, but it is not completely useless because we are to rule out (with 95% confidence) that Marbury in his role with the Knicks is only marginally better (or worse) than replacement players. That is worth something.

The 95% confidence intervals (per 48 minutes) for the other players are as follows.

Dirk Nowitski: 3 to 35 points per 48 minutes

Kevin Garnett: 5 to 29 points per 48 minutes

Kobe Bryant: -2 to 31 points per 48 minutes

Elton Brand: 2 to 26 points per 48 minutes

Paul Pierce: -9 to 36 points per 48 minutes

Carmelo Anthony: 1 to 26 points per 48 minutes

Tim Duncan: -3 to 27 points per 48 minutes

LeBron James: 1 to 23 points per 48 minutes

Ray Allen: -5 to 28 points per 48 minutes

As is pretty obvious, some of these intervals are so wide that they are not particularly useful. For example, I am sure most of us would have been willing to peg the effect of Paul Pierce between -9 and 36 points per 48 minutes before ever looking at the data.

As the season progresses, those intervals will get smaller as more data is available for estimation. This lack of precision is one of the drawbacks of the WINVAL or DanVal methodology. It captures practically everything that is relevant but at the cost of being very noisy, especially with small samples.

Comment by Dan T. Rosenbaum -

Ok, so does Nellie have a PDA that takes the live statistical feed, adjusting for injuries, obvious mismatches (based on objective size, strength, and quickness ratings) fouls, and give him a live read on his optimum lineup against the opponents on the floor? I mean, if NBA live can do it on an Xbox, why can’t somebody at a real NBA team geek up a program to advise the coaching staff- or at the least point out a matchup that might not be intuitive? Realtime AI aided coaching? Can we get it for the ref’s too?

Good lord, can someone please do this and send it to Maurice Cheeks?

Comment by Mike -

her’s what made me go “hmmmmmm….”: what point does it serve to publish virtually context-free statistics that compare such a small sample size of players as to be rendered completely irrelevant for drawing any sort of reasonable conclusions? we don’t really know how the scores are calculated (and you tauntingly refuse to divulge that info), so there’s no way to know how meaningful these numbers are. we don’t know the scores for the other 200+ players in the league, so we don’t know where these fall along that spectrum. and we don’t know why these specific players were chosen, which further biases any comparison to be made.

are we supposed to simply marvel at how good Marbury is or congratulate you for coming up with the measuring stick? and how can anyone take this seriously when you take each players age out to 2 decimal points? using insignificant figures isn’t going to endear you to many statisticians.

Comment by jamie -

It’s sad to see #1 and #3 on that list on opposite teams. They could be working on their third or fourth championship by now. guess we have no one to blame, but Stephon and his ego. Money and fame over wins, that’s the kid to a “T”.

Comment by Matt -

Do not ever worry about “monopolizing” the comments about statistics, Professor Rosenbaum. As the academic authority on NBA statistical analysis, we appretiate your contributions to the conversation greatly.

Also, good numbers Mark. Marbury is definately a big surprise. He’s a guy I always thought of as a Me 1st, Team Last, kind of guy. Maybe things are turning around for him this year.

Comment by Scott Griffith -

Mark Cuban, along with Wayne Winston and Jeff Sagarin, deserve a lot of credit for their work on developing this WINVAL system. It really does a great job isolating the contributions of individual players. At times in the press they have oversold how precisely they can isolate these contributions, but all in all I think Mark and Wayne and Jeff have done a lot to advance statistical analysis in the NBA.

As far as I know, I am the only other person to have computed plus/minus statistics that adjust for home court advantage and who a player shares the floor with. Like with WINVAL, I also give more weight to clutch time performances and less weight (or no weight) to garbage time performances. So for those of you really interested in all of this, you can check out my quite detailed account of my “DanVal” ratings (http://www.uncg.edu/bae/people/rosenbaum/NBA/winval2.htm).

In addition to computing adjusted plus/minus ratings like the WINVAL ratings, I have related these adjusted plus/minus ratings to the statistics available in box scores. Box score statistics are far more stable from game-to-game and season-to-season than are plus/minus statistics.

In fact, I have computed the part of the adjusted plus/minus ratings that are not predicted by the box score statistics, i.e. those contributions not picked up in the box score.

Interestingly, when I do so there is very little correlation of this “residual” from season to season for a given player. What this tells me is that box score statistics are able to capture most of what is in these adjusted plus/minus ratings – IF they are calibrated well. But one has to be careful. Even something somewhat sophisticated like the NBA.com efficiency formula does not do a very good job of capturing what is in these adjusted plus/minus ratings.

Well, I do not want to monopolize these comments, so I will quit. I would like to add that the best group of NBA statistical analysts, including Dean Oliver, John Hollinger, and Kevin Pelton, congregate at APBR Analysis(http://sports.groups.yahoo.com/group/APBR_analysis/) and Kevin is beginning a new more user-friendly site at Sonics Central (http://sonicscentral.com/apbrmetrics/).

Comment by Dan T. Rosenbaum -

I’m disappointed my previous comment got wiped. So I’ll re-post in kinder language.

So, at a glance, what you’re saying is that Steph is an above-average player on paper, but games don’t get played on paper. His numbers don’t help his teammates and therefore Isiah made a dumb move about a year ago. Correct?

I agree.

Comment by Swade -

Sounds like an advanced web site statistics package for rating user sessions a buddy of mine developed. Nice to see there are some smart folks working behind the scenes with NBA data.

Comment by Jason Dowdell -

Basketball HAS something like SABR, it’s called the Association for Professional Basketball Research (http://www.apbr.org) and Mr Cuban is on the e-mail list.

Comment by Gabe Farkas -

Interesting post. The weighting of the plus/minus in interesting. But if the coach still needs to take into account things like amount of time played, etc isn’t that a sign that the algorithm could still be tweaked more. A proven metric, sabermetrics style, for a players impact on a game could be really useful for the game. Mark, what are your thoughts of the achieving something like baseball has with sabermetrics and the A’s (give Moneyball a read if you haven’t already).

http://www.mjberger.com/archives/2005/01/basketball_stat_2.html

Comment by Mikel Berger -

Basketball could really use something like http://sabr.org/ I look forward to further statistical exegesis from you.

Comment by rone -

we don’t really know how the scores are calculated (and you tauntingly refuse to divulge that info), so there’s no way to know how meaningful these numbers are. we don’t know the scores for the other 200+ players in the league, so we don’t know where these fall along that spectrum. and we don’t know why these specific players were chosen, which further biases any comparison to be made.

Comment by runescape money -

As far as I know, I am the only other person to have computed plus/minus statistics that adjust for home court advantage and who a player shares the floor with. Like with WINVAL, I also give more weight to clutch time performances and less weight (or no weight) to garbage time performances.

Comment by wow powerleveling -

Wow.

Comment by Paul -

I think this is fantastic, and really not necessary for the top 10,20 players in the league. At the end of the game, you KNOW that Dirk, KG, Kobe, LeBron or Marbury is going to be out on the floor. The question is which teammates can help him out the most.

So, I would think that the key with this formula is to look for the top 60 to 120 range of players, and try to see if any of your guys fit in there better than others.

Comment by Dark Munkin -

The Mavs, I assume, must be the Dallas Mavericks? Sorry if I sound stupid, but what kinda team is that? What sport do they play?

Oh and the ‘confirm comment thing’ is horribly complicated – the emails end up in my junk mail folder!

Comment by apples -

Yes that is exactly what I wanted. Thanks Kevin.

Comment by Mark Powell -

Mark: If you’re talking about the NBA’s efficiency formula, it’s — pts + rebounds + assists + steals + blocks – missed FGA – missed free throws – turnovers. Then they divide by minutes played and multiply by 48.

Comment by Kevin Broom -

Does anyone know the formula for figuring a players EFF rating?

Comment by Mark Powell -

Dan: Thanks for the information. I don’t know a ton about WinVal’s methodology, because they’ve kept it private. (As I would if I was making money with it.) I’ve read your DanVal ratings stuff, and I think it’s very good.

Comment by Kevin Broom -

Kevin, what you are saying is true about raw plus/minus data, such as those on Roland Beech’s http://www.82games.com, but it is a bit off the mark for adjusted plus/minus ratings like WINVAL (or DanVal) that account for the quality of the players that a given player plays with and against.

Adjusted plus/minus ratings are just as valid as any other summary statistic for player comparisons or for saying which player is “better.” But it is difficult with any statistic to say that one player is “better” than another, since “better” is so context-specific. So this is a problem for all summary statistics, not only for adjusted plus/minus ratings.

The bigger problem with plus/minus ratings, both raw and adjusted, is that they are very noisy. A whole season’s worth of games generates plus/minus ratings about as precisely estimated as do about 20 to 30 games for box score statistics-based ratings, such as PER or TENDEX. Thus, the biggest enemy of plus/minus statistics is the age old enemy of statisticians – sampling variation.

The tradeoff is as old as statistics – variance versus bias. Adjusted plus/minus ratings capture practically every contribution a players makes and thus is as closed to unbiased as any ratings system can be. But its higher variance means that more care than usual needs to be taken in extrapolating from partial-season or even full-season samples. It is this tradeoff between bias and variance that has led me to some hybrid approaches combining adjusted plus/minus and box scores statistics-based ratings.

Best wishes,

Dan

Comment by Dan T. Rosenbaum -

The variability of bench quality is exactly what makes +/- worthwhile. The goal of +/- isn’t to determine that Kobe is better than Marquis Daniels (just to pull a couple names out of the air), but to show the value of an individual player to his own team.

The +/- data can be used to say reliably that Dirk is more valuable to the Mavericks than Stackhouse or Alan Henderson. It can also be used to make comparisons between players on different teams, but not “Dirk is better than Larry Hughes” comparisons. Rather, a better way of stating what +/- offers is that Dirk has more value to Dallas than Larry Hughes has to Washington.

Comment by Kevin Broom -

So I was talking with a coach of the local high school that I do stats for and we both agreed that a modified plus/minus system for basketball would be interesting, not in the form of match-ups, but in the form of a player affecting the game. What I can draw from these stats is that, if you have a matchup pitting (let’s say) Danny Fortson against Shaq, Shaq is in a better position to affect the game than Fortson. If that formula could be broken down for high school, then that might help my team somehow get a couple extra points. Good work, Mark.

–Keith

Comment by Keith Chambers -

Dan R, i think the factor that you aren’t seeing is bench contribution.. Some team’s bench’s contribute more, so a standout player’s pp48 effect is marginalized

Comment by ian -

Who cares???

Comment by Scott -

First, I like the new features of this blog (latest enteries)…Secondly do you have correlation data between the transition points and Dirk (and other players) bring the ball up the court?

Additionally, do you keep any data which breaks down each drive that Steve Nash, Jason Kidd, and other point guards makes against opposing players? Maybe you could use that data help your point guards know what stastically works against opposing guards, players, and teams.

Finally,do you keep any data which shows how often and where gaps are open on the floor according to ball placement and movement on the court?

Interested Fan……

Comment by Sterling -

DM Hatcher: I think the system does take into account intangibles like Magic Johnson’s leadership, or a players strength and conditioning. At least, it would seem to take into account the net effect that all of a certain players contributions have on the team winning. I’m assuming, that if the system does measure the effectiveness of a player relative to substituting in a replacement player, that it shows more than just offensive points scored directly by a player. That would explain why there are negative point values included for the range of some players. Obviously Paul Pierce can’t score negative nine points, but the total effect of him being in the game, vs. someone from the bench, could be within that range. At least that’s my interpretation from Dan Rosenbaum’s explanations. Speaking of which, thank you Dan for the information about how a system like this works. It is very interesting, I for one would like to hear more about this or other systems the mavericks use from Cuban, I’d also like to see more numbers, but I doubt we’ll get any more…

I do wonder though, are these systems common enough in the NBA that all teams use them?

Comment by Tim -

Its good to use statistics as a general guide for the game of basketball, but how do you measure the value of Magic Johnson’s leadership skills in his prime? How do you measure his words in the huddle that motivated his teammates to play harder (causing their numbers to rise-while Magic’s do not)?

Because of the element of fatigue in this game usually those with the strongest human will eventually become winners.

Comment by D M Hatcher -