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RaptorsHQ Talks With "The Wages of Wins," David Berri

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To kick off our season previews here at the HQ, we post a long-awaited chat with the Wages of Wins' David Berri as we talk about "Wins Produced," the Raptors' prospects for the upcoming season and of course, everyone's favourite topic of conversation, Andrea Bargnani...

Back in May 2005 when we first launched the HQ, there wasn't much in the line of analytics in basketball.

You had the box score and...well...that was pretty much it.

However there were some folks who were interested in more than that, and had been working behind the scenes to develop basketball's version of Sabremetrics.

Within a few years, names like John Hollinger, Dean Oliver and David Berri became well known for their parts in the basketball statistics revolution, and at present, it's tough to find an NBA blog that doesn't spend some time focusing on the more analytical points of the game.

We've always bent a bit in that direction, and in particular, D Stance and myself here at the HQ have been big fans of the work of Mr. Berri and his website, The Wages of Wins.

This past off-season, Berri and co-author Martin B. Schmidt released "Stumbling on Wins," their newest book on the subject of wins in professional sports, and the flaws in traditional thinking behind achieving them.  It's an amazing read, and one that lead us to follow up with the man behind it, resulting in the following interview touching on his career, the Toronto Raptors, and of course, Andrea Bargnani...


RaptorsHQ - So let's kick things off with a biggie - how on earth did you get interested in not only the field of sports economics, but in developing the metric you're most well-known for, "wins-produced?"

David Berri:  My interest in the economics of sports began as a graduate student at Colorado State.   And it began somewhat by accident.  In the process of looking for a research topic I came across a reference to a paper measuring the economic value of a baseball player.  Prior to seeing this reference I did not know someone could use economics to study sports.  Once I found this paper - and others in the same area - I decided to write a paper on the economics of the labor market in baseball.  From there, I began my own research program in the economics of sports.

Because most economists had focused on baseball, I decided to start examining the economics of professional basketball.  That research, though, had a significant road block.  In baseball, productivity can easily be measured with OPS, Runs Created, etc...  These measures have already been established, generally capture accurately a hitter's contribution to wins, and are fairly easy to explain in an academic article.  When I started research in the NBA - around 1994 or 1995 - the only measures that were generally available were something akin to NBA Efficiency.  The NBA Efficiency measure (which is similar to Dave Heeran's  TENDEX measure and Robert Bellotti's Points Created model) is quite easy to calculate and explain.  But it is not highly correlated with team wins.  So it is not a particularly good measure of player performance.

A better approach is to determine how the statistics tabulated for NBA players statistically relate to wins.  But this is easier said and done.  As I recall, Stacey Brook (my co-author on The Wages of Wins) came up with somewhat convoluted four equation system back in 1996 (for a paper we presented at the University of Colorado).  Upon seeing the model a person in the audience said, "I take it this is not your first guess."  And I think I replied, "And it won't be our last."

These four equations were eventually reduced to two equations for a paper Stacey and I published in 1999.  And these two equations were further refined for a paper I also published in 1999.

Dean Oliver and I had many discussions concerning this two equation system.  Dean had also developed a measure of player performance, a measure that I questioned on theoretical and practical grounds (the issues raised were briefly discussed in The Wages of Wins).  But although I was not willing to fully accept Win Shares (by the way.... Win Shares is a model that I prefer - as a forthcoming paper I have written argues - to the Player Efficiency Rating and Adjusted Plus-Minus), that doesn't mean that what I had done so far couldn't be improved upon.  And with Dean's urging me along, the model I had published was made better.

In 2006, Tony Krautmann and I published a paper (a paper originally presented in 2004) that offered a simple one equation model that connected much of what a player did on the court to team wins.  This approach was improved upon - and labeled Wins Produced -- for The Wages of Wins.

So the Wins Produced model began back in the mid-1990s.  After much discussion (with various academics -- including Dean Oliver), it was gradually transformed into what people can see today (in Stumbling on Wins and other publications). 

Let me close by noting the basic lessons the Wins Produced model teaches. 

Wins in the NBA are determined by the ability of a team to gain and keep possession of the ball (so rebounds and turnovers are important) and the ability to turn possession of the ball into points (so shooting efficiency is also important).  Players who are not particularly efficient scorers and/or have problems gaining and maintaining possession of the ball, tend not to be very productive.  And that is true, even if the player takes a large number of shots.  In sum, scorers who are not outstanding with respect to shooting efficiency (and/or the possession factors) really don't help their respective teams win many games.


RHQ - It's interesting to see how the theoretical models used to evaluate a player's impact on the court have evolved. Do you know of anyone working on further advancements to your "wins produced" metric and in any one direction? Is there anything you would say your metric leaves out, or undervalues?

DB:  Let me start with the explanatory power of the Wins Produced model.  The model essentially connects everything in the box score to wins.  And we find that a team's aggregate box score statistics explain about 95% of a team's wins.  Why not 100%?  The missing 5% reflects the fact that teams do not carry their statistics from game to game.  So if you win a game by 20 points, the extra 19 points are not carried to the next contest.   Across a season the excess statistics (i.e. statistics not needed to decide a contest) tend to even out.  But that process is not perfect, hence we don't explain 100% of a team's total wins in a season with their aggregate statistics.  And I would add, I don't think we are going to be able to change the model in any substantial fashion to close this 5% gap.  So I do not see changes in the future along these lines.

That being said, it is possible to offer variations on Wins Produced to address various topics.  This list of topics includes on-the-ball defense, diminishing returns, and the value of replacement players.

Incorporating Defense

There is a sense that focusing on the box score statistics means we are completely ignoring defense.  In fact, I have seen people argue that the box score statistics only capture 50% of the game.  That is not actually true. There are defensive factors in the box score.  So the box score does capture much of what is going on.  What is missing, though, is a method to credit a player who is an exceptional on-the-ball defender. 

The approach taken in calculating Wins Produced is to treat defense as a team activity (this is essentially the same approach taken by Dean Oliver and Win Shares).  In other words, if you are on a team that is very good at preventing the other team from scoring, Wins Produced gives you credit for this outcome.  And if your team is bad at defense, then your Wins Produced is lower.  Because so much of defense depends on teammates working together, this approach does make sense.  But it is not the only approach one can take.

Another approach to incorporating defense was offered back in 2007.  Specifically, I looked at allocating the team defensive factors (i.e. opponent's field goals made, opponent's turnovers that are not steals, etc...) according to the individual defensive measures reported at  The results didn't appear much different for the one team I examined.  But this is something that might be expanded upon the future.

Ty Willihnganz -at the Courtside Analyst - takes a different approach.   Ty calculate "Marginal Win Score" which "attributes wins produced on the basis of the Player's Win Score and the Win Score he and his team allow opponents who play the same position to produce."  The difficulty with Ty's approach is that the counterpart defensive numbers don't appear to be very stable over time.  So we are not sure you are getting at the performance of the individual player.  That being said, Marginal Win Score is an interesting alternative and Ty's analysis is always a worthwhile read.

Diminishing Returns

Beyond defense is the issue of diminishing returns.  As noted in The Wages of Wins, the more productive a player's teammates the less productive the player will be.  Although the effect is real, it is overall rather small (an observation illustrated in Stumbling on Wins). 

In Stumbling on Wins we also looked at diminishing returns with respect to specific statistics.  For example, the more points and field goal attempts a player's teammates accumulate, the fewer points and field goal attempts a player will have.  In fact, this effect is quite large.  It really appears to be the case that most of a player's shot attempts come at the expense of his teammates.

For defensive rebounds (but not offensive rebounds) we also see an impact (although not near what we see for points and field goal attempts).  Given the diminishing returns effect with respect to defensive rebounds, we thought it would be interesting to see what would happen to our player rankings if the value of a defensive rebound was reduced.  In Stumbling on Wins we summarized our analysis:

When people see a player like Ben Wallace (a player known for rebounding) lead the league in Wins Produced in 2001-02, then questions are raised.  To address these concerns, two versions of Position Adjusted Win Score (PAWS) were constructed.  The first only counted half of a player's rebounds. Re-ranking the players with this adjusted version of PAWS revealed that Ben Wallace was still the top ranked player in the game in 2001-02. This is because the revised version of PAWS per-minute and WP48 have a 0.95 correlation.  One can also construct PAWS by giving offensive rebounds a weight of 0.7 and defensive rebounds a weight of 0.3 (following Hollinger's lead).  With these values Ben Wallace was still the top ranked player in 2001-02.   This is also not surprising since this version of PAWS per minute and WP48 still has a 0.95 correlation.

In sum, when we try and take into account diminishing returns and defensive rebounds, our analysis remains essentially the same. 

Value Above Replacement

A more recent proposed change to the Wins Produced calculation comes from Arturo Galletti (of Arturo Silly Little Stats).   The Wins Produced calculation compares each player's production to the average seen at his position.  Arturo wondered what would happen if a player was compared to the productivity of a replacement player.  In other words, Arturo wished to re-formulate Wins Produced so that it was consistent with the VORP (Value Over Replacement Player) measure seen in baseball.

JC Bradbury - of Sabernomics - has raised some legitimate questions regarding VORP in baseball.   I also think there are some questions about how one defines the productivity of a replacement player.  And I am not sure the VORP calculation actually tells you something beyond the study of standard deviation of performance (from The Wages of Wins) tells us.  All that being said, Arturo's work with VORP is interesting and another approach worth reading about. 

I would also add that we now have Wins Produced numbers for the past five years posted on-line (courtesy of Andres Alvarez).  And soon we will have numbers back to 1977-78.  As these numbers are made available, more and more people will be offering research using Wins Produced. In fact, we already have a group of blogs I have called "The Wages of Wins Network."

§  Arturo Silly Little Stats

§  Courtside Analyst

§  Miami Heat Index

§  NBeh?

§  Nerd Numbers The Blog

§  NYK Mistakes

§  Roblog

§  The NBA Anti-Expert

So everyone should look for more and more research along these lines.

Let me close this very lengthy answer by noting that the discussion of defense, diminishing returns, and VORP doesn't change the fundamental message of Wins Produced.  Wins in the NBA are driven by a team's ability to secure and maintain possession of the ball (i.e. get rebounds and steals, avoid turnovers) and the ability to hit shots (i.e. shooting efficiency).  The ability to take shots -- shots that are often taken at the expense of a teammate's shot attempts - is not a skill that should be rewarded.  We certainly shouldn't think that a player who takes many shots, but can't shoot efficiently (i.e. Allen Iverson) is really helping a team win many games. And furthermore, a player like Andrea Bargnani, who can't secure possession of the ball (i.e. can't rebound well) is not a player who helps either.  In other words, no matter which of the above approaches you like, none are going to change the basic Bargnani story (he really isn't a productive NBA player).


RHQ - The Bargnani debate is one that rages on a near daily basis at the HQ, and while we've reached a bit of an "agree to disagree" point amongst our readership, there's no question that he's the most polarizing Raptor since Vince Carter.

The book on Andrea via your work has been twofold; he's an unproductive player and based on the average NBA player's development curve, it's highly unlikely we'll see him take that proverbial "next step" to develop into a very productive one.

However, there's a huge contingent that believes that with Bosh now gone, this is Bargnani's year.

What's your take on this?  Is it possible that with Bosh gone we see Andrea vault into All-Star consideration? Or are the same issues that drag down his number of Wins Produced (rebounding etc) always going to be present regardless of what team he's on and what situation he's placed in? 

DB:  Unfortunately for fans of Bargnani, these questions are fairly easy to answer.  Here is what Bargnani has done so far in his career:

  • 2006-07: -0.8 Wins Produced, -0.024 WP48
  • 2007-08: -4.2 Wins Produced, -0.109 WP48
  • 2008-09: -0.3 Wins Produced, -0.006 WP48
  • 2009-10: -1.1 Wins Produced, -0.018 WP48
  • Career: -6.4 Wins Produced, -0.035 WP48

As one can see, Bargnani has always offered a level of production in the negative range.  And that is - as Devin Digham notes at NBeh? - because Bargnani can't rebound.  Now diminishing returns does exist in the NBA.  So playing with productive players can diminish a player's statistical output.  But that effect is not that large. Furthermore, although Bosh is good, he is not exactly LeBron James (Bosh produced 11.7 wins last year, James produced 27.2 wins).  In other words, it is hard to believe that Bosh's production is the reason why Bargnani played so poorly.  I think fans of the Raptors are just going to have to accept the fact that Bargnani is not really a productive big man.  And at the age of 25 (players tend to peak in their mid-20s) he is probably never going to be as good as his draft position suggests.


RHQ:  Andrea aside, let's look at the Toronto Raptors this coming season seeing as the season beings Wednesday.  I remember a post from NB'EH back in mid-August that projected the team to finish the season with 36 wins.

That seems extremely high compared to what most "experts" and fans are projecting.

Myself I have the bar set at 30 based on a number of factors, including subtracting Chris Bosh's nearly 12 wins produced, and very few positive wins produced additions. 

But what's your take on this team next year?  Is it possible in fact that fans will see 2009-10 New Jersey Nets levels of losing?

DB:  Although losing Chris Bosh doesn't help, it's important to remember that Bosh is the weakest member of the "SuperFriends" (Bosh is more like Robin, while Wade and LeBron are Batman and Superman).   Last season Bosh produced 11.7 wins (as the following table indicates).  Meanwhile LeBron produced 27.2 wins (Wade produced 17.9 wins).  So the departure of Bosh is not quite the same as the loss of King James for the Cavaliers.

Raptors 2009-10


Wins Produced

Chris Bosh



Jarrett Jack



Amir Johnson



Jose Calderon



Hedo Turkoglu



Sonny Weems



DeMar DeRozan



Reggie Evans



Marco Belinelli



Marcus Banks



Rasho Nesterovic



Patrick O'Bryant



Pops Mensah-Bonsu



Andrea Bargnani



Antoine Wright






Consequently it is possible for the loss of Bosh to be overcome.  To see this, let's look the 2009-10 productivity for the veterans currently on the Raptors depth chart (this depth chart is from, WP48 calculated with last season's data and this year's position assignment, minutes per game are my guess):

Projected Starters

Jose Calderon: 0.137 WP48, 5.6 Wins Produced (24 minutes per game)

DeMar DeRozan: 0.054 WP48, 2.6 Wins Produced (28 minutes per game)

Linas Kleiza: 0.081 WP48*, 3.9 Wins Produced (28 minutes per game)

Amir Johnson: 0.173 WP48, 8.3 Wins Produced (28 minutes per game)

Andrea Bargnani: -0.061 WP48, -3.6 Wins Produced (34 minutes per game)


Jarrett Jack: 0.139 WP48, 5.7 Wins Produced (24 minutes per game)

Leandro Barbosa: -0.013 WP48, -0.4 Wins Produced (20 minutes per game)

Sonny Weems: 0.039 WP48**, 1.3 Wins Produced (20 minutes per game)

Reggie Evans: 0.120 WP48, 4.1 Wins Produced (20 minutes per game)

David Andersen: -0.050 WP48, -1.2 Wins Produced (14 minutes per game)

* - Kleiza's numbers are based on what he did in 2008-09

** - it appears Weems spent more time at shooting guard last year, so his WP48 will be lower if he switches to small forward.

If we add up the Wins Produced of these players we get 26.3 wins.  Last season the team's wins produced was 36.2 (the team actually won 40 games).  So there is a drop-off. 

But it won't take much to close this gap.  Here is one way that gap can close.  If Jose Calderon [0.239 WP48 in 2008-09] and Leandro Barbosa [0.159 WP48 in 2008-09] return to what we saw two years ago - and all the minutes and positions stay exactly the same as they are listed above - the Raptors would win ten more games.   

The Raptors can also win more games if DeMar DeRozan improves (young players tend to get better) and Joey Dorsey [0.183 WP48 in limited minutes last season] sees more playing time (which also might mean that Bargnani and Andersen play less).  It might also help to get more minutes to Ed Davis (the team's lottery pick in 2010).  Davis was one of the more productive players drafted out of college last year, and it is likely that he could help more than Bargnani and Andersen (again, these players need to sit more).

To summarize... I don't see this team as bad as the Nets were last year.  The Raptors are not likely to be serious playoff contenders.  But I think there is a chance they will be about as good as last year.