Who was the best player in 2006-07? The MVP was Dirk Nowitzki. The scoring leader was Kobe Bryant. And the leader in Player Efficiency Rating (PER) was Dwyane Wade.

Of course, voting by the sportswriters is problematic. Sports writers tend to pick the leading scorer – or in the case of Steve Nash, leading contributor to offense – on one of the best teams.

Looking at scoring alone is also a problem, since it completely ignores all other facets of the game. Plus, scoring alone is not highly correlated with team wins.

And then there is PER. The problems with the PER were detailed in the following two posts:

Marvin Williams Makes a Hypothetical Deal (December 16, 2007)

A Comment on the Player Efficiency Rating (November 17, 2006)

Each of these posts highlighted how an inefficient scorer could dramatically increase his PER and Game Score (Game Score is John Hollinger’s simple version of PER) value by simply taking more inefficient shots. Certainly inefficiency shooting is inconsistent with winning basketball games.

Well, if we are not going to rely on the sports writers, scoring, or PER, what else can we look at? Surely I am not going to once again suggest Wins Produced?

**The Best in Player Winning Percentage**

Although I like Wins Produced, let’s look at something else. Here are the top ten players in 2006-07 in Player Winning Percentage [PW%].

1. Dikembe Mutombo

2. Alan Henderson

3. Brent Barry

4. Chuck Hayes

5. Dirk Nowitzki

6. David Lee

7. Manu Ginobili

8. Ira Newble

9. Tim Duncan

10. Shawn Marion

Well, that’s interesting. Alan Henderson, Chuck Hayes, and Ira Newble are all better than Tim Duncan. Wow.

Okay, what’s PW%? Is this a new WoW Metric designed to torment sports bloggers?

Here is how PW% is described at Basketball Reference

*Player winning percentage; the formula is ORtg ^{14} / (ORtg^{14} + DRtg^{14}). *

What is ORtg and DRtg? Again we turn to Basketball Reference.

*ORtg: *

*Offensive rating (available since the 1977-78 season in NBA); for players it is points produced per 100 posessions, while for teams it is points scored per 100 possessions. This rating was developed by Dean Oliver, author of Basketball on Paper. I will point you to Dean’s book for complete details.*

*DRtg: *

*Defensive rating (available since the 1977-78 season in NBA); for players and teams it is points allowed per 100 posessions. This rating was developed by Dean Oliver, author of Basketball on Paper. I will point you to Dean’s book for complete details.*

Yes, PW% comes from the work of Dean Oliver and his wonderful book, Basketball on Paper. And the results of this work seem to defy conventional wisdom.

**A Look at Adjusted Plus-Minus**

Of course, Oliver’s work – like The Wages of Wins – is based on box score statistics. What if we turn to adjusted plus-minus? Will this give us a measure that is consistent with common sense?

In the spirit of The Wages of Wins quiz posted by Ballhype, please take the following test. Specifically, which of the following players is better?

Anthony Parker or Vince Carter

Dwight Howard or Brian Cook

Allen Iverson or Rajon Rondo

Dan Dickau or Steve Nash

Anderson Varejao or Chris Bosh

Hedo Turkoglu or Carmelo Anthony

Rudy Gay or Brandon Roy

Jason Richardson or Rafer Alston

Tracy McGrady or Bobby Jackson

Corliss Williamson or Carlos Boozer

Looking strictly at the Adjusted Plus-Minus per 40 minutes rankings of Steve Ilardi (posted at 82games.com), the answers are

Parker, Cook, Rondo, Dickau, Varejao, Turkoglu, Gay, Alston, Jackson, and Williamson.

Well, that hardly fits conventional wisdom. Is Parker a more effective player than Carter, Iverson, or Melo? Is Dickau really a better point guard than Nash? Should the Orlando Magic let Brian Cook play more than Dwight Howard? Was Rudy Gay a better rookie than Brandon Roy – the player named Rookie of the Year?

**Learning How to Evaluate Models**

The purpose of the above exercise was not to attack the work of Dean Oliver or the adjusted plus-minus approach created by Wayne Winston and Jeff Sagarin (yes, these are Ilardi’s numbers but this basic method was originated by Winston-Sagarin).

Nor was this exercise designed to tell us that there is much to be learned in creating advanced statistical measures for basketball, and until this is learned, let’s stick with conventional wisdom.

No, the purpose of this exercise is to show that there is still much to be learned when it comes to *determining the value* *of a particular model*.

A few weeks ago I offered a column that was designed to help. In A Guide to Evaluating Models, I identified several issues one should think about when looking at a model. This list of issues included the model’s theoretical foundation, robustness, explanatory power, out of sample forecasting power, and simplicity. I emphasized that this was but a partial list. Furthermore, and this is perhaps most important, although my list was not all inclusive, a complete list would not argue that we should evaluate a model in terms of its ability to confirm what we already believed.

Models are designed to test theories. If you reject a model because your theory was not confirmed, then you simply don’t understand why you created the model in the first place.

Turning to basketball, this means we do not become unhappy when a model tells us that Andrew Bynum is more productive on a per-minute basis than Kobe Bryant. Or as PW% indicates, Dikembe Mutombo is more effective than Yao Ming. Or as Adjusted plus-minus says, Anthony Parker is more effective than Carmelo Anthony.

**Learning from these Models**

When we look at Wins Produced, PW%, and Adjusted plus-minus, we see some similarities. And we see some differences. Certainly, for reasons stated in The Wages of Wins, I prefer Wins Produced. But regardless of my preference (or your preference) one result is clear from each of these advanced metrics.

The players who score the most are not always the players who contribute the most to wins. This is the lesson that The Wages of Wins seeks to teach about basketball. And when I look at these different advanced methods, it’s this lesson I think you learn.

**One Final Thought**

Let me close this column by repeating something I said a couple of weeks ago.

*I would note that there is nothing “magical” about the Wages of Wins models, or even adjusted plus-minus (or the models of Dean Oliver). Each of these models are just ways of looking at performance in basketball. And each has their pluses and minuses (pardon the pun)*

*I sense, though, that people become frustrated with these metrics because they expect “magic.” In other words, people want a number that answers all questions and reduce the cost of thinking to zero. Models, though, help us explain the world we observe. Models are not “magical”, nor do they remove the need to keep thinking. And that is something to think about when you look at basketball measures, or any other models researchers offer to improve our understanding of our world.*

– DJ

Our research on the NBA was summarized HERE.

The Technical Notes at wagesofwins.com provides substantially more information on the published research behind Wins Produced and Win Score

Wins Produced, Win Score, and PAWSmin are also discussed in the following posts:

Simple Models of Player Performance

What Wins Produced Says and What It Does Not Say

Introducing PAWSmin — and a Defense of Box Score Statistics

Finally, A Guide to Evaluating Models contains useful hints on how to interpret and evaluate statistical models.

*Basketball Stories*

Huey

December 18, 2007

Nice post!

Vivek

December 18, 2007

Well Written Post !

dustin

December 18, 2007

Every stat blog should reference this entry. Models are supposed to provoke thought, not replace it.

firebird

December 18, 2007

Nice post!

Kent

December 18, 2007

Excellent post. Pointing out a single anomaly to a model is not enough to overthrow it. All models are arbitrary simplifications of reality that don’t capture every element.

Tep

December 18, 2007

I enjoyed the post Mr. Berri! It’s a nice rebuttal to the ballhype quiz

Tim

December 18, 2007

“Furthermore, and this is perhaps most important, although my list was not all inclusive, a complete list would note argue that we should evaluate a model in terms of its ability to confirm what we already believed. ”

You mean “not argue,” right? I only point out the typo because you call it the “most important” point, and I want to make sure everyone understands.

Thanks for the quick response!

dberri

December 18, 2007

Thanks Tim. It’s fixed.

Jason

December 18, 2007

That was a very, very lucid column.

Ben Guest

December 18, 2007

The best model will be the one that can most accurately predict what is going to happen…

JChan

December 18, 2007

I really hope Henry puts this one in his links today. It’s funny to me how so many people think it has to be one way or the other. There is nothing wrong with using advanced stat models AND conventional basketball wisdom.

Oh wait. Preaching to the choir.

TG Randini

December 18, 2007

dberri,

That PW% formula at basketball reference.com is non-sensical. It doesn’t even correlate to player wins and player losses and how the PW% SHOULD be calculated, or IS, in fact, calculated when you look at an individual player’s stats on that site.

Example: Michael Jordan 1990-1991

PW is 15.8

PL is 0.8

ORtg is 125

DRtg is 102

The sites formula says Michael’s PW% according to their formula and the way you reproduced it is…

125/(125+102) = .551 or 55.1%

But the site shows .950 or 95.0% in his stat line which is close to 15.8/(15.8+0.8).

So the site’s formula doesn’t even come close to the way he is actually calculating it.

I don’t think Oliver would calculate it that way either.

Are you using that site’s wacky formula in your rankings? … or doing the formula the way Oliver intended it to be done… and the way it appears his stat lines are doing it?

It sure is a whacky formula in that guy’s glossary (who runs that reference site)… and it makes no sense that he would put a non-sensical formula in his glossary when he doesn’t even use it to calcuate his PW%’s in his stat lines.

Either I’m senile and have forgotten math, or the quality control over at that site is abysmal.

Hopefully, you weren’t using that guy’s whacky formula… I’m sure it isn’t Oliver’s.

TG Randini

December 18, 2007

Mea culpa: … then, again, I’m 82 and I might be getting a little senile…

Check it out and let me know. I’d like to see if I still have something on all these young whipper-snappers running all these sites.

Jason

December 18, 2007

Randini, you left out the exponent in your computation. The formula is 125^14/(125^14+102^14)=.95.

That’s the formula basket-reference and Dave both use and it’s clear here and there. You just made a math error. I think the QC error is yours.

mrparker

December 18, 2007

Its the same formula used to estimate team wins based on point differential.

IMO it comes the closest to approximating player production.

I guy like Matt Bonner might have a pedestrian wp48 but have a high pw%. This shows that Bonner might be able to give some quality minutes without taking anything away from his teammates wp48.

Steve Kerr had a great win % while with the Bulls. He’s a good example of this type of player.

TG Randini

December 18, 2007

Thanks… senility it is. I thought the exponent was a footnote referencing the description of the term being used!

Westy

December 18, 2007

Good post.

Joseph

December 18, 2007

This was very interesting.

BasketballGuy

December 19, 2007

Very good post.

dragonsi55

December 20, 2007

TG Randini

“I thought the exponent was a footnote referencing the description of the term being used!”

Isn’t this the same problem you had in the ‘how many economists does it take to get a joke’ section of ‘evaluating models’?

I thought your rant there was excellent, by the way. The extra complexities of time (specifically, owners wanting high-priced players to play, and also the competitive levels of garbage time) might take a supercomputer. ‘Entertainment value per dollar’ may be the force determining opportunity for a player to amass stats.