Incorporating Defense

Posted on March 26, 2007 by


The Wins Produced model begins with a simple idea.  Wins are a function of offensive and defensive efficiency.  This idea can be found in the work of John Hollinger and Dean Oliver.  And with a bit of math, you can show that wins are indeed a function of these efficiency metrics.

Once we see that wins are a function of offensive and defensive efficiency, a simple regression (of wins on the efficiency metrics) allows us to determine the value, in terms of wins, of the following statistics tracked for a player: three point field goals made, two point field goals made, free throws made, field goals attempted, free throws attempted, missed field goals, missed free throws, offensive rebounds, defensive rebounds, turnovers, steals, and personal fouls. Now the efficiency metrics are not only comprised of these player statistics.  From the wins regression we can also derive the value for the opponent’s three point field goals made, opponent’s two point field goals made, opponent’s turnovers (that are not steals), and team rebounds.  For the most part, these team factors are associated with defense.  Before I get to these team defense statistics, let me review two basic lessons from this wins model.

Wins are a function of offensive and defensive efficiency.  This is not only what theory tells us, but also the empirical evidence. The efficiency metrics explain 95% of wins and hence provide an accurate depiction of the quality of a team.

Each element in the efficiency metrics is linked to actions taken by the players on the floor.  It is the players who are responsible for made shots, rebounds, turnovers, team defense etc.. Thus, our wins model – because it accurately links these actions to wins – allows us to accurately value the contributions of an individual player. In sum, Wins Produced links all the elements of the wins model back to the players. Hence, Wins Produced also explains 95% of team wins.

For the player statistics, evaluating the player’s contribution in terms of wins is easy.   We simply need to multiply a player’s statistics by the corresponding value. The result of this calculation is then compared to the average performance at the player’s position.The team variables, which are associated with team defense, are not tracked for individual players.  So how can we incorporate these factors? Here is what we say in the book:

…we have constructed what we call the team’s statistical adjustment. We then follow a convention we have observed and personally employed in the economics literature. Specifically we allocate the impact of the team statistical adjustment according to the minutes each player was on the court.

The convention we followed was originated by Frank Scott, James Long, and Ken Sompii. In 1985 these authors published an article in the Atlantic Economic Journal examining the link between salary and performance in the NBA.  For the team factors employed in their model these authors simply allocated each factor across the players according to minutes played.   

What does that mean?  We don’t have a measure of defense for each player.  What we do have, though, is knowledge about how good the team played defense.  We argue that if a player played 15% of the team’s minutes, then he is responsible for 15% of the team’s defense [or specifically, the opponent’s made field goals, opponent’s turnovers (that are not steals), and team rebounds accumulated].

And this makes some sense.  Defense, especially in today’s NBA, is a team effort.  If your team is good at this, you should receive credit.  If not, you should be penalized.  The Wins Produced metric, by allocating the opponent’s made field goals, opponent’s turnovers, and team rebounds across the players, thus takes into account the quality of a team’s defense.So as one can see, the infamous team statistical adjustment is simply a measure of team defense.  Despite its simplicity, there has been a bit of confusion regarding what this is and how it impacts our results.  Let me try and answer these questions.

1.  Is this a “giant fudge factor”?

In simple terms, no.  Wins are a function of offensive and defensive efficiency.  The factors comprising what we called the team statistical adjustment are the opponent’s field goals made, opponent’s turnovers (that are not steals), and team rebounds.  In essence, this is the quality of the team defense. The players are the individuals playing defense, so they should get credit if a team does well or poorly with respect to this aspect of the game.

This factor has been described as an addition to our wins model designed to increase its accuracy.  That charge is false.  The opponent’s statistics are part of defensive efficiency, not an addition to the model.

People have also said that you could take points scored and a “team adjustment” and predict wins just as accurately as we do.  I do not know what the author of this statement means by a “team adjustment.”  If you employ the team factors listed above, this statement is false.  To demonstrate this point, I regressed wins on points scored, opponent’s three point field goals made, opponent’s two point field goals made, opponent’s turnovers (that are not steals), and team rebounds.  These five factors explained 79% of team wins, not the 95% that is explained by offensive and defensive efficiency.

Again, the team statistical adjustment is not some random factor we yanked out of our ass.  It is simply team defensive factors that must be accounted for in the measurement of defensive efficiency and player performance.

2. How does this impact our evaluation of players?

What I have mentioned, more than once, is that these team defensive variables do not have much impact on our evaluation of players.  PAWSmin, which is position adjusted win score, does not consider these team variables.  WP48, or wins produced per 48 minutes, does have these team variables.  The correlation between these two is 0.994.  So the team defense measures do not matter much in our evaluation of players.

3. Can you predict wins without the team defensive factors?

People have asked: Can you predict well without the team variables?  And my answer is “I don’t think so, but then again, I haven’t looked.”  Without the opponent’s field goals made, the opponent’s turnovers, and team rebounds, the wins model is mis-specified (in other words, you have left out relevant variables, which introduces a number of statistical issues for your model). 

Nevertheless, since people have been clamoring to know, I thought I would look.  Without the opponent’s field goals made, opponent’s turnovers, and team rebounds, we are explaining wins with the following variables: three point field goals made, two point field goals made, free throws made, field goals attempted, free throws attempted, missed field goals, missed free throws, offensive rebounds, defensive rebounds, turnovers, steals, and personal fouls. A regression of wins on these factors reveals that 84% of wins can be explained without opponent’s field goals made, opponent’s turnovers, and team rebounds. 

Of course the model is mis-specified and the results cannot really be used to evaluate individuals.  The easy fix to this problem is to specify the model in a fashion that is theoretically correct, which we did in The Wages of Wins. 

Getting Rid of the Team Adjustment

Is it possible, though, to do “better”? Maybe we can change how we allocate opponent’s field goals made, opponent’s turnovers, and team rebounds. has several measures of how well a team’s opponent does when each player is on the court.  If we use one of these measures, we can scrap the team statistical adjustment (which allocates defense in terms of minutes played), and allocate the defensive variables across each player according to their ability to play defense.

I did this for the Washington Wizards.  82games. com reports how well the opponent scores with each player on the court.  The team surrenders about 104 points per game.  From we see that when Jarvis Hayes is on the court the team gives up 106.2 points per game.  So by this measure he is a relatively poor defender.  In contrast, Brendan Haywood gives up 100.6 points, so he appears to be a relatively better defender.  Previously we are allocating the opponent’s field goals made and opponent’s turnovers in terms of minutes played, so each player – on a per-minute basis – was evaluated the same on defense for each team. There were differences across teams, but on any one team it was the same.

Now we have a measure that differentiates players on a team. What happens if we allocate the opponent’s statistics with the measure of defense? The results reveal a difference, but not very big.

Table One: Examining the Impact of Team Defense with the Washington Wizards

Brendan Haywood improves, posting a WP48 of 0.133 when we treat every player the same and a mark of 0.142 when he is credited for his defensive ability.  Jarvis Hayes looks a bit worse.  In general, though, the results are very similar.This should not surprise.  There are apparently large differences in the defensive abilities of teams.  And these differences across teams are incorporated in the evaluation of players with Wins Produced.  Yet we found that with or without adjusting for these factors our evaluation of players was essentially the same.  Now when we do this for an individual team, we tell the same story.

The research at, if it accurately measures individual defense, allows us to get rid of the team adjustment. The model still explains 95% of wins. It is also still tells the same story about player performance.  And what is that story?  The primary factors in evaluating a player are shooting efficiency, rebounds, and turnovers.    

A Comment on Baseball

The box score statistics in basketball are often discredited because these do not account for on-the-ball defense.  We can see defensive ability at the team level, but without the work at we cannot get at the individual’s contribution.  Does the inability of the standard box score statistics to measure on-the-ball defense really matter in our evaluation of players?

I want people to step outside basketball for a moment and think about baseball.  In baseball there is the issue of fielding.  OPS and linear weights are measures of performance in baseball.  They both ignore fielding entirely.  Yet, very often (not always, but often) people discuss the merits of a player strictly in terms of his offensive output.

Of course there is also the issue of evaluating pitchers.  A pitcher cannot strike everyone out.  Pitchers depend on fielders.  Yet in evaluating pitchers, I often see people reference statistics (ERA, Wins, etc…) that do not separate the pitcher from his fielders. 

Imagine if we regressed wins in baseball on a team’s ability to hit, pitch, and field.  We would be able to explain about 90% of wins, which is what happens when you regress wins on runs scored – your ability to hit — and runs surrendered – your ability to pitch and field. 

Now let’s say you isolated a pitcher’s contribution from his fielders.  Then you regressed wins on runs scored (what the hitters did) and just the pitcher’s contribution.  How well would explain wins now?  I do not know the exact answer, but without any measure of fielding your explanatory power would have to be a good deal less.

Despite this issue, traditional measures of hitters and pitchers do not consider fielding. Is this a problem?  Should we throw out all the traditional box score statistics in baseball because they ignore fielding, a factor that must have some ability to explain wins?

The answer is of course not.  Yes, fielding matters.  But our evaluation of players will generally not change very much if we ignore this factor.  Barry Bonds and Manny Ramirez will still be great players.  Greg Maddux will still be a great pitcher. 

I think the same thing can be said for defense in basketball.  Yes some players are better at on-the-ball defense than others.  But if it truly mattered a great deal we would see vast differences in our evaluation of players when defense is included and when it is not.  We would also see that rebounding totals fluctuate for players dramatically depending on who their teammates were.  When we look at the data, though, we see none of this.

Perfect Models?

I want to return to a statement I made a couple of weeks ago.  Models are not supposed to be “perfect” (whatever that means).  When I and my colleagues construct models, we are trying to construct a simplified version of reality that allows us to focus on what is important (and answer the various questions we pose in our research).That is what I think Wins Produced does. It is a simple and accurate measure of performance, based on the theoretically sound idea that wins are determined by a team’s offensive and defensive efficiency.  This model ultimately tells us that wins are primarily determined by shooting efficiency, rebounds, and turnovers.  Yes, other issues matter.  But players who do not score efficiently, who fail to rebound (given their position), and/or turn the ball over excessively, will not help you win games.

Let me repeat what I said a few days ago:

Now it’s not the case that factors like blocked shots, assists, and personal fouls don’t matter. But none of these factors are as important as shooting efficiency, rebounds, turnovers, and steals. And once we see this, we can understand the outcomes we observe.

For example, the Rockets lost Yao Ming to a devastating injury, yet managed to maintain their winning percentage. Once we see the importance of rebounding, though, we can see how having an extraordinary rebounder like Dikembe Mutombo come off the bench mitigated the loss of Yao.

We also see why the 76ers improved after Iverson departed. Iverson has problems hitting shots and avoiding turnovers, so despite his scoring totals, our model tells us he does not produce as many wins as his star power suggests. In other words, we should not have expected a team that replaced Iverson with Andre Miler to get worse (as many people who focused on scoring predicted).

And on Collaboration

I have written a paper entitled “A Simple Measure of Worker Productivity in the National Basketball Association.”  An earlier working version of this paper – which details the math behind the Wins Produced metrics — was referenced in The Wages of Wins.  Later this year this paper should finally be published.  Although I am the solo author on this paper, one should not think that Wins Produced and the related models are only the results of my efforts.  As noted in The Wages of Wins, many conversations with Dean Oliver clearly impacted my thinking.   

In addition, a collection of co-authors also should be credited (or blamed, depending on your perspective).  At the top of this list are Martin Schmidt and Stacey Brook (co-authors on The Wages of Wins).  The Wins Produced metric has also been employed in papers I have written with Anthony Krautmann, Aju Fenn, Bernd Frick, Erick Eschker, Young Hoon Lee, Rod Fort, Michael Leeds, and Michael Mondello. 

This is how I described my tendency to collaborate at my website in April of 2006: Beyond my publication rate, we can also see that virtually all of my work is co-authored. Over the course of my career I have published research with eleven different writers, with Martin Schmidt being my most frequent collaborator.  In all, Marty and I have published twelve papers together.  One can look at this as I work well with others, or lack the skills to complete projects by myself.  I like the “works well with others” story, although my many co-authors might play up the “lacking skills” angle. 

Almost all of my work is a collaboration with someone else.  All of these c0-authors are accomplished researchers who have the corresponding list of academic publications as evidence of their abilities.  But even with their help, academic research still requires the help of more people.

My list of co-authors leaves out the various editors and referees who review our academic papers.  Research in academia is never a solo effort.  Other people comment and critique your work constantly, and these efforts improve the final product. Hence when people argue that I do not “collaborate” I am left very puzzled.  Academic research – be it in journals or at academic conferences – is always a collaboration.  And anyone with an understanding of academic research would see this point.

The Future

We are on the quarter system at California State University – Bakersfield.  This is a good deal in the fall, since we don’t begin until late September and finish around Thanksgiving. In the spring, though, it’s a bit of drag. Today we begin the Spring Quarter, which does not end until June.  This quarter I am teaching three classes. I also have a paper to complete for the Western Economic Association and several other research projects to finish.

All of this means that over the next 10 weeks, postings in this forum will be less frequent.  I will simply not have time to post as often as I have across the last year.  Hopefully this summer I will have time to resume posting on a daily basis. Thanks to everyone who makes this a part of their day.  Unfortunately, for a few weeks at least, this will no longer be a part of each day for me.

– DJ