The one question I am most often asked is “how about those Jazz?”
Okay, I live in Utah (and these questions from Jazz fans). And right now, there is some excitement about our local NBA team.
The Jazz currently sit on top of the Northwest division standings. And if the Western Conference playoffs began today, the Jazz would currently have the third seed (ahead of the LA Lakers!).
The team’s current record of 16-6 projects to a 60-22 mark across 82 games. If this pace continues, the Jazz will reach 60 wins for the first time since 1997-98. Last year the Jazz only won 53 games, so it would appear that the Jazz have improved. At least, this is the story I hear in Utah.
The Diminishing Jazz
When we look at efficiency differential, though, it is a somewhat different story. After 22 games the Jazz have scored 105.2 points per 100 possessions while allowing –again, per 100 possessions — 100.5 points. Therefore the team’s efficiency differential (offensive efficiency minus defensive efficiency) is 4.7. Such a mark is consistent with a team that will win 53 games across an 82 game season. Last season the team had a differential of 5.5, so the Jazz – contrary to the story told by the team’s current won-loss record – have declined ever so slightly from what we saw last year.
When we move from efficiency differential to Wins Produced [and WP48 or Wins Produced per 48 minutes], we can see that the Jazz are actually a bit better than the performance of these players last year would suggest (in other words, this team should have declined further). Performance last year suggests this team (given the minutes and position played this year) should be on pace to win 46 games. So the Jazz – when we look at the players employed this year (and again, the performance last year) – have improved.
And who is responsible for this seven game improvement? Well, Deron Williams and C.J. Miles are doing a bit more (while Andrei Kirilenko is doing less). But the big leap is seen in the play of Paul Millsap.
The Suprising Story of Millsap’s Improvement
It is of course easy to understand why Millsap has improved. Last year the Jazz employed Carlos Boozer, a player who led Utah in rebounding. As we can see at 82games.com, the four leading line-ups that employed Millsap last year also included Boozer. So with Boozer in Chicago, all those rebounds should now go to Millsap. And since
- diminishing returns are HUGE for rebounds in the NBA, and
- rebounds are THE PRIMARY determinant of a player’s Wins Produced
it makes sense that taking Boozer away would boost the WP48 [Wins Produced per 48 minutes] numbers of Millsap.
And you can see this when you look at Millsap’s numbers in 2009-10 and 2010-11. In 2009-10, Millsap grabbed 11.8 rebounds per 48 minutes. And this year he is grabbing…. okay, only 11.4. It turns out Millsap’s improvement this year isn’t about rebounds. The key for Millsap is that – relative to last year – he is hitting a higher percentage of his shots from the field (and free throw line) and committing fewer turnovers. Yes, despite a career high in usage, Millsap had increased his shooting efficiency.
The Diminishing Returns Story Again and Again and Again
Of course, the Millsap story is just an anecdote. To understand the issue of diminishing returns and what determines a player’s wins produced we need some systematic evidence. For diminishing returns, that evidence can be found in the academic literature (and a couple of books you might have heard about).
For example, four years ago Tony Krautmann and I published “Shirking on the Court: Testing for the Dis-Incentive Effects of Guaranteed Pay” in Economic Inquiry.This paper – which had originally been presented at the Western Economics Association meetings in 2005 – argued that a player’s productivity will fall as his teammates improve. And looking back at papers I have presented in the past; way back in 2001 I presented at the Western Economic Association that also noted that as a player’s teammates offer more the player will offer less (yes, I have been telling the diminishing returns story for at least ten years).
Given my history with this tale, it is not surprising that the diminishing returns story was also mentioned in The Wages of Wins (you might have heard about this book published in 2006). In fact, the diminishing returns story – or the argument that better players must make their teammates worse – was one of my favorite stories in this book (and yet – oddly enough – I have read that I deny the existence of diminishing returns).
A few years later the story was told again when I published (with Michael Leeds, Eva Marikova Leeds, and Michael Mondello) “The Role of Managers in Team Performance” in the International Journal of Sport Finance. As part of a study looking at how NBA coaches impact player performance it was shown that player productivity declines as the quality of his teammates increases. Again, that is diminishing returns.
And that story was told again in Stumbling on Wins (you might have heard about this book). Stumbling on Wins also explored diminishing returns with respect to each of the individual statistics. What was reported – in a study of 30 years of player data (in a model that controlled for a number of other factors that determine player productivity) – is that a player’s points, field goal attempts, free throw attempts, defensive rebounds, assists, and blocked shots all decline as their teammates do better with respect to these statistics. Offensive rebounds, turnovers, shooting efficiency, and personal fouls are not related to the productivity of teammates. Of these, the biggest effects were seen with respect to points and shot attempts. Yes, scoring definitely comes at the expense of your teammates – and yes, that is one more reason why scoring is overvalued in the NBA.
The big issue is the size of the diminishing returns effect. A few weeks ago I wrote a post discussing the departure of Carlos Boozer in Utah. This post presented evidence that the impact of diminishing returns (across all statistics) – on a player’s per-minute performance [or WP48] – appears “small”. Specifically, the following was observed with respect to Al Jefferson:
What does it mean to move from a team where the players are quite bad to a team with much better teammates? For an answer we turn to our study of NBA coaches. This study considered the impact a variety of factors (beyond coaching) had on player performance. The list of various factors we considered included the productivity of a player’s teammates, or more precisely, teammate WP48. This study – across 30 years of data – indicated that teammate WP48 had a statistically significant and negative impact on player performance. The coefficient on this factor was -0.300. And this tells us that the Jefferson’s WP48 should decline by 0.025 as he moves from Minnesota to Utah [-0.300 * (0.109 – 0.025)].
If we look back at Jefferson’s ADJ P48 in 2009-10 and 2010-11, we see that Jefferson has actually declined by 0.025. Is all of that decline diminishing returns? Probably not, since other factors do play a role in determining changes in player productivity. But once again, the impact of diminishing returns on per-minute performance appears “small”.
What Determines WP48?
What about the role rebounds play in WP48? To answer this question we need data. Well, how about more than 8,700 player observations from 1977-78 to 2007-08? Across this data WP48 was regressed upon the following statistics: Points per field goal attempt, free throw percentage, rebounds, turnovers, steals, assists, blocked shots, and personal fouls. These statistics were adjusted for position played and measured on a per-minute basis.
Estimating the regression doesn’t actually answer the question (at least, it doesn’t if you estimate a linear model). What we want to know is the relative importance of each statistic, or the responsive of WP48 is changes in each statistic. Another name for “responsiveness” is “elasticity” (a concept you may remember if you ever took Microeconomics). More specifically, we need to look at how a 1% change (or a 10% change or whatever percentage change you wish) in each factor impacts WP48.
The elasticity results – derived from the aforementioned regression and reported below – might prove surprising to some:
- Points per field goal attempt: 5.2%
- Rebounds: 3.2%
- Free throw percentage: 1.2%
- Personal fouls: -1.1%
- Assists: 1%
- Turnovers: -0.9%
- Steals: 0.7%
- Blocked shots: 0.2%
Rebounding certainly matters. After all, getting and keeping possession of the ball is important; and rebounds are the primary way a team gains possession (without letting the other team score). But WP48 is more “responsive” to shooting efficiency from the field. A 1% change in points per field goal attempt (or adjusted field goal percentage times two) leads to a 5.2% change in WP48.
And that result re-enforces a story that has been told again and again. Scoring totals – by themselves – are not what matters in the NBA. What matters is the ability to put the ball in the hoop. In sum, shooting efficiency is important and players who score inefficiently are not really helping. Furthermore, metrics like Player Efficiency Rating and NBA Efficiency – which do not properly capture the importance of shooting efficiency, do not properly capture a player’s impact on wins.
Of course, one should add that this isn’t just about performance metrics. The importance of shooting efficiency also reminds us that the emphasis placed on scoring totals in the NBA – which we can see in the study of free agents, the voting for post season awards, the allocation of minutes, and the NBA draft – is misguided. Inefficient scorers may be rewarded by decision-makers. But these players do not contribute much to wins.
Let me close with a brief comment again on diminishing returns. Again, I think this effect is quite real (and makes for a very interesting story about how “great” players make their teammates worse). But I also think it is a “small” effect. Even if it is “small”, though, why can’t we just play with the coefficients used to calculate Wins Produced to take this into account?
My answer is twofold: First, we actually did this and reported the results in Stumbling on Wins (I don’t think it made much difference). And secondly… well, read what the Sport Skeptic had to say about this last weekend. It is a very interesting read.
And one last note… I am going to post in the next few days (or few weeks?) at stumblingonwins.com a document that reports my answers to frequently answered questions. Most (if not all) of these questions have been addressed (in this forum, in articles, or in books). But it might be good to have one place where people can look for answers. So hopefully I can get that done soon.
– DJ
Wages of Wins Journal 
JChan
December 8, 2010
Thanks for this writeup. I think we’re going to see the Jazz end up at about the same spot they were last year. There’s something to be said for experience playing together, and I think Jefferson will improve somewhat from where he is now. I believe any diminishing returns will be offset by the fact that Jefferson is playing with an elite point guard for the first time in his career. Getting the ball in good position should help with his shooting percentages. As far as the team as a whole, I would guess that the efficiency differential will end up around 5.5, like last year.
That being said, they’ve certainly had some good luck pulling games out this year. They could easily be 12-10 rather than 16-6, and no one would be talking about them at all.
Cheech Cohen
December 8, 2010
How ’bout another question, Dr. Berri? How about the Cavs? I know you didn’t expect them to be good but I recall that your model predicted a playoff appearance Do you still see that happening?
All best,
Cheech
kevin
December 8, 2010
Yeah, the Cavs have reallly cratered. I think they came out breathing fiore, wanting to show everyone they didn’t need LeBron but I think they’re starting to be confrotned with the ugly reality they don’t have a leader and a legit go-to guy and the opposition has figured them out.
arturogalletti
December 8, 2010
Prof.,
Fantastic post. I had to print this one out and read it. Love that Jefferson’s numbers behaved exactly as predicted.
Daniel
December 8, 2010
I would have posited that blocked shots and steals are independent of a player’s teammates– with the Spurs, their individual players have always had similar per-minute numbers in blocked shots and steals.
When the Spurs stopped employing shot-blocking big men in favor of better rebounding big men, the remaining individuals did not pick up the slack in blocked shots. The one constant over the past 14 seasons is Duncan– his blocked shots have never decreased due to the presence of other shot-blocking big men, nor have they increased due to the lack of shot blockers on the team. Apparently other players and teams are different.
dberri
December 8, 2010
Daniel,
The blocked shot effect appears very small.
Shawn Ryan
December 8, 2010
Excellent post Dr. Berri. I love the long, deep ones (err… articles that is).
Also, I think that a definitive FAQ would be tremendously useful.
Westy
December 8, 2010
Prof. Berri, you note, “After all, getting and keeping possession of the ball is important; and rebounds are the primary way a team gains possession (without letting the other team score).”
I certainly agree with this at the team level, but still struggle with how it gets translated to the individuals involved. I guess I’d ask that you further discuss the distribution of this possession gained entirely to the rebounder in your FAQs. (And thanks for providing that.)
brgulker
December 8, 2010
Yay FAQ! Yay points!
Seif-Eldeine
December 8, 2010
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Alvy
December 8, 2010
Arturo actually suggested the same finding when he JUST started his blog when concerning the elasticity of effective FG%
dberri
December 8, 2010
Sorry to interupt the conversation… but “some dude” is going to have to send me an e-mail (berri@suu.edu) if he wants to post comments in this forum anymore.
Michael
December 9, 2010
Why what did he do?
Also, I just had to add to the sentiments of others that this was a great post.
These longer posts really help to highlight the logical and systematic methodology you apply to these issues, and honestly I found the elasticity results very illuminating (I have to admit I did not expect that result).
scott
December 9, 2010
I was rereading parts of Bill Simmons’ Book of Basketball and there was a hilarious footnote where he relays a conversation he had with John Hollinger about PER where Hollinger allegedly said someting to the effect of “PER is OK but it places too much emphasis on rebounding and field goal percentage”. Immediately made me of wins produced.
Evan
December 9, 2010
Seif-Eldeine has now left a few spam comments without them getting deleted.
Tom Mandel
December 9, 2010
Interesting of course, but I’m not sure what is being demonstrated here. I may very well be wrong, but it looks like “elasticity” is a more or less direct function of the original contribution of a given statistic to WP48 and of nothing else.
Much more of overall WP48 is contributed by rebounds than by steals — because there are so many more rebounds than steals — hence, it is certainly not surprising that a 1% increase in rebounds should result in a much greater change to WP48 than a 1% increase in steals.
Nor is it a surprise that a 1% increase in shooting efficiency should have more impact on WP48 than a 1% increase in rebounds. There are by definition more shot attempts than rebounds (some shots do go in!). But in a world in which 1% more of shot attempts went in the basket, there would also be a decrease in rebounds. Actually to estimate “elasticity” we would have to know how this increase and decrease affected the *calculation* of WP48.
Moreover, does this elasticity not occur over *a range* — imagine a player who averages exactly 20 shots per 48 minutes and shoots exactly 50%. Imagine as well that this player averages exactly 10 rebounds per 48 minutes. Will a 1% increase in points per shot have the effect on WP48 that you cite above; will a 1% increase in rebounds?
Will these effects on WP48 be the same for someone who takes 10 shots rather than 20 and shoots 40% — while averaging 15 rebounds? What if each of these example players raises both statistics by 1%? Will both their WP48 measures rise by 8.4% (the sum of the 2 effects per the above)?
Perhaps I’ve misunderstood something — in fact, probably I have. What have I misunderstood?
bduran
December 9, 2010
Tom,
I’m not sure if I’m thinking about this correctly. It would seem that while there are more FGA then rebounds, there are not more FGM then rebounds. Just looking at the 2010 Spurs it looks like you would have to increase your FGM by about the same number as your rebounds to achieve both a 1% increase in PPS and a 1% increase in rebounds.
Tom Mandel
December 10, 2010
Yes, that’s true — that was a gaffe on my part. But the main point I’m making is that I don’t see any measure of “elasticity”; I see only a direct function of the influence of a particular stat on WP48 in the first place. Hence I’m not sure what is being demonstrated.
By no means am I asking this in order to question WP48. It’s clear that the Dave Berri Five (or whatever the right number is) have devised the best overall measure of player productivity so far. If FG% and rebounding have preponderant influence, that reflects reality. If a team shoots a higher FG% than its opponent and also outrebounds the other team, it really is hard to lose! :)
Michael
December 10, 2010
“I see only a direct function of the influence of a particular stat on WP48 in the first place. ”
Exactly. I think the point was to demonstrate to those of us who thought WP overvalued rebounding that the fact that a 1% increase in shooting efficiency is worth 2% more than a 1% increase in rebounding is a straight forward way to show that isn’t really true.
Tom Mandel
December 10, 2010
Well, I never thought it was true — but how does this show that it isn’t true?
Or, to be frank, no it doesn’t show that at all. It shows that in WP48 shooting efficiency is weighted higher than rebounding, but to do that no “sensitivity” analysis was required. Moreover, the fact that shooting efficiency “weighs more” than rebounding in WP48 doesn’t itself say that rebounding isn’t overvalued (or undervalued for that matter).
Michael
December 12, 2010
That is why context is important.