The problem with using averages as illustrated by the average salaries of NBA players

In negotiations between NBA owners and players, the topic of the “average player salary” has come up. This discussion illustrates some of the issues involved with  using averages and medians:

Here is the “average player salary” for each of the major U.S. professional team sports, based on a variety of sources using the most recent data available:

NBA: $5.15 million (2010-11)

MLB: $3.34 million (2010)

NHL: $2.4 million (2010-11)

NFL: $1.9 million (2010)

From the public’s view, these numbers are high in all four sports. But players and agents argue that these averages obscure important distinctions including the value of certain positions over others (the quarterback in the NFL versus the punter) and the size of the roster (fewer NBA players, more NFL players).

One common solution to problems with averages is to instead use a median. Here is how this might change the discussion in the NBA:

“It’s the median salary that’s more important,” NBA agent Bill Duffy said. “Look at the Miami Heat as an analogy here: You’ve got three guys making $17 million and probably six guys making $1.2 [million]. So that’s a little misguided, that average salary.”…

It is not unlike, Duffy said, news stories that cite the “average” U.S. household income as opposed to the median. The latter figure, according to the most recent U.S. census, was $50,233. If you were to average in the dollar amounts pulled down by Wall Street bankers, Ivy League lawyers, certain public-union employees and yes, professional athletes, that number would jump considerably.

Curiously, neither the NBA nor the NBPA seems to make much use of a median player salary.

“We use [average] because it’s the most commonly used measure and best reflects the amount of compensation that the NBA provides to players across the league,” an NBA spokesman said this week. “In addition, it’s the measure that both we and the union agreed upon in the CBA.”

In the NFL, the median salary is approximately $770,000 — about 40 percent of the average.

In the NBA, using USA Today salary figures for the 2009-10 season, the estimated median salary was about $2.33 million. That’s still about 46 times what the median U.S. household earns, but it is less than half what the max-salary-bloated “average” is.

What happens in these sports is this: a small number of star athletes make huge amounts of money, pulling the average for all athletes up. If you use the median instead, where 50% of the players make more and 50% more make less, it suggests that more of the athletes in each sport make less. Particularly in the NFL which has bigger rosters, the difference between the average and the median shows that many players make very little.

It is interesting that the NBA spokesman said the two sides had agreed in their Collective Bargaining Agreement that they would use the average salary figure. Was this really a point of contention negotiations or did no one really think about the consequences? What was the thinking behind this for the players? If the union was focused on helping all of their members, perhaps they would focus on the median, suggesting that they are strongest when all of their members are well taken care of. This lower figure might also look more palatable to the public though it is unclear whether public perceptions have any influence on such negotiations. However, if the union was more interested in making sure that individual athletes could receive the biggest possible payouts because of their athletic exploits, then perhaps the average is better.

Two takeaway points:

1. Averages and medians are both measures of central tendency but they are open to different interpretations. People need to be clear about which they are using and which interpretation their number interprets.

2. It will be interesting to see if the new CBA is based on average or median salaries.

Do NBA players really make a difference in their community?

In the course of watching the NBA playoffs, I’ve seen a lot of commercials about how NBA stars are active in their communities. While this might be good PR, do we know anything about whether these efforts have any effect? Perhaps the NBA doesn’t care as long as they portray the image that they desire…but I suspect many of these occasional forays into the neighborhood are just that.

I suppose people could cite particular athletes that are active in the community. They do exist. But on the whole, do these professional sports leagues really care about structural inequalities and the average citizen’s daily fate? Perhaps a more foundational question is to even ask whether they should even as the commercials try to suggest that they do.

The conservative musical selections at Chicago Bulls games

While I think this Chicago Tribune piece about the DJs at Chicago Bulls games was supposed to provide a behind-the-scenes look at how musical selections are made, the real crux of the story seems to be that the music selections are quite conservative:

Every Bulls game at the United Center has its own soundtrack. Just as each game is different, roller coasters of emotions and shifting fortunes, the music and sound effects roll with the changes. A team of about 20 technicians plays DJ each night at the United Center, accenting the ebbs and surges on the floor.

The head DJ is Jeff Wohlschlaeger, the Bulls’ senior director of game operations, who sits courtside and communicates on a headset to music and scoreboard operators to wed sounds and game action. There are cavalry-charge bugle calls and countless ways of imploring “De-Fense,” but there are also more than 1,000 songs and song snippets available to enhance every movement and mood…

When the home team has the ball, just about anything goes. Nothing is explicitly banned, but all teams know they’re programming for a family-friendly event, so songs deemed the least bit salacious or provocative won’t be tolerated, the NBA says. Teams that bend the rules often end up paying for it. The NBA’s “Game Operations” department monitors every game; one source in the office said that at least two NBA franchises were fined in the last month for inappropriate sound and video while the visiting team was on offense.

The Bulls don’t push the envelope by design, Wohlschlaeger says. The music selections are “conservative,” reflecting a mix of classic rock and contemporary pop hits that is determined by audience surveys. During Game 2 of the Hawks series, songs leading out of timeouts designed to get the crowd pumped included the Beastie Boys’ “(You Gotta) Fight for Your Right (to Party!),” AC/DC’s “Thunderstruck,” John Mellencamp’s “Authority Song” and Mitch Ryder and the Detroit Wheels’ “Devil With a Blue Dress On.”…

Mostly, it’s about what the paying customers want, Wohlschlaeger says, “tried and true stuff that you or I would never listen to in a car, but that gets a positive reaction from the fans.”

On one hand, the article suggests that the DJs have a lot of music and sound effects at their disposal and try to respond to the action on the floor. On the other hand, it sounds clear that the actual music/effects played is quite limited in order to please the NBA and the fans. I can’t quite say why I find this depressing: it still sounds like an intriguing job but at the same time, much of it sounds scripted. For example, the article mentions the playing of U2’s “Where the Streets Have No Name” which every Bulls fan who has watched a game this year or in recent years knows is played during a timeout with about 4-6 minutes left in the game. So all of this is simply canned, fan-friendly entertainment?

I wonder if there are any pro sports teams who are known for pushing the envelope a bit more in their musical selections. Does everyone play the same stuff that the DJs “would never listen to in a car” but they think is safe for fans? Having attended a number of San Francisco Giants games over the last 10 years or so, I know they play a lot more salsa music, fitting in with the atmosphere of the Bay Area. Some baseball stadiums have music for individual home team players when they come up to the plate. There may not be the same opportunities for other sports though perhaps music could be introduced in situations when they make a reception or step up to the free throw line or at other points.

Of course, perhaps this is just good business: don’t alienate your fan base that can afford to go to NBA basketball games. Change up the music too much or make it too edgy

Grant Hill, Jalen Rose, and race and class

ESPN recently aired the documentary The Fab Five which earned the network its highest ratings for a documentary (though its unclear how this stacks up against their typical Sunday night programming). One part of the documentary that has drawn attention are the comments Jalen Rose made regarding Grant Hill, Duke, and race. Here is what Rose said in a short segment:

I hated Duke and I hated everything Duke stood for. Schools like Duke didn’t recruit players like me. I felt like they only recruited black players that were Uncle Toms … I was jealous of Grant Hill. He came from a great black family. Congratulations, your mom went to college and was roommates with Hillary Clinton. And your dad played in the NFL — a very well-spoken and successful man. I was upset and bitter my mom had to bust her hump for 20-plus years. I was bitter that I had a professional athlete that was my father that I didn’t know. I resented that more than I resented him. I looked at it as they are who the world accepts and we are who the world hates.

Hill responded to Rose’s comment on the New York Times website. Here are a few relevant points:

In his garbled but sweeping comment that Duke recruits only “black players that were ‘Uncle Toms,’ ” Jalen seems to change the usual meaning of those very vitriolic words into his own meaning, i.e., blacks from two-parent, middle-class families. He leaves us all guessing exactly what he believes today…

This is part of our great tradition as black Americans. We aspire for the best or better for our children and work hard to make that happen for them. Jalen’s mother is part of our great black tradition and made the same sacrifices for him…

To hint that those who grew up in a household with a mother and father are somehow less black than those who did not is beyond ridiculous. All of us are extremely proud of the current Duke team, especially Nolan Smith. He was raised by his mother, plays in memory of his late father and carries himself with the pride and confidence that they instilled in him…

I caution my fabulous five friends to avoid stereotyping me and others they do not know in much the same way so many people stereotyped them back then for their appearance and swagger. I wish for you the restoration of the bond that made you friends, brothers and icons.

While this appears to be a conversation about race, I wonder how much of this might be about social class. While Rose used terms that invoked race (particularly the reference to “Uncle Toms”), what also might have been describing differences in social class: Grant Hill grew up in more of an upper-class family where his dad was a known athlete and his mom had connections. Rose did not have the same opportunities that Hill’s family provided and felt bitter about Duke, a private school known for its wealth (according to the National Association of of College and University Business Officers, Duke is #15 in its 2010 endowment with over $4.8 billion).

In the long run, both men have done well for themselves: Hill is still playing in the NBA while Rose is an analyst for ESPN and also played 13 years in the NBA. But these discussions about opportunities and race and class are ongoing in sociology: is it race that is the primary issue or is it social class? A sociologist like William Julius Wilson has written about this, most recently here, invoking a lot of discussion over the last few decades. How this particular discussion ends up between  Rose and Hill remains to be seen but there will be plenty of ongoing talk about these larger issues.

Can the NFL over-hype itself?

As the NFC and AFC title games slowly approach, I wonder: can the NFL over-hype its product?

On one hand, it appears not. NFL television ratings have been excellent this year (regular season stats here). The league has a number of stars that draw a wide range of attention, from the good (Tom Brady, Peyton Manning) to the bad (Brett Favre, Michael Vick’s sage in recent years). Particularly at this time of year, talk about the NFL dominates the airwaves – a number of other sports are mid-season. The final four teams remaining in the playoffs are historic franchises that have passionate fan bases. Even with Bill Simmon’s recent claim that there is “there’s at least one great [NBA] game” each night, other sports can’t match the popularity of the NFL. The NFL even thinks it can sell $200 tickets for a “party plaza” outside of the Super Bowl.

On the other hand, it is A LOT of talk. In the weeks between playoff games, it seems that ESPN can’t stop talking about the next match-ups. In Chicago, everyone has been talking Bears-Packers. The teams already have played twice so how much more is there to discuss? Could it get to the point where fans tune out the week before and are just happy to get the game over with? And interestingly, it only gets worse for the Super Bowl: then we get the infamous “Media Day.” Though the Super Bowl gets tremendous ratings, how often does the game match the hype? In my lifetime of watching Super Bowls, I distinctly remember being disappointed by most of them. (A couple stand out in memory: the Giants-Bills match-up in 1991, Rams and Titans in 2000, the Bears-Colts in 2007, Patriots-Giants in 2008, Steelers-Cardinals in 2009.)

From a broader perspective, there is no guarantee that the popularity of the NFL will be maintained over the years, let alone continue to increase. (Gregg Easterbrook, ESPN’s Tuesday Morning Quarterback, points this out.) The first non-sports comparison that comes to mind are presidential elections. Yesterday, the New York Times reported how President Obama is getting his next campaign in order and plans to formally declare his candidacy in two months. From now until November 2012, this is what we will hear about in the news: who will challenge Obama, how much money will be raised, what are the issues, who has the best image, what do the latest polls say, etc. Don’t voters, at least some of them, get burned out by all of this by the time the actual election takes place? The idea that some countries have of holding more defined election seasons, typically announced by the current leader and lasting for a few months, seems preferable to this endless, over-hyped presidential election season.

I am sure someone has done research on over-hyping. For the NFL, the question is when will it saturate its market. Of course, one way around this is to expand your market and head overseas. (They are trying to do this with games in Toronto, London, and Mexico City in recent years. But the NBA is way ahead of them.) In the meantime, the sporting public will get heavy doses of talk, analysis, and replays. I, for one, will be very happy when it finally gets to 2 PM Sunday afternoon and we can actually see whether the Bears and Packers will win.

The NBA, referees, Malcolm Gladwell, and race

Henry Abbott at Truehoop reexamines an issue that emerged a few years ago with a paper written by several economists: do NBA officials exhibit implicit race bias when calling fouls? Here is Abbott’s take on the findings and implications of the original study:

Basically, the more black referees on the court, the better the calls for black players. And the reverse is true for white players. The entire combined effect is fairly limited, around 4 percent, but the pattern is certainly there.

All of this means not all that much about NBA referees, other than that they’re human. The research was about human decision making in the workplace, and the referees were just a handy group to study.

And nothing about these findings do much to undermine the NBA’s position as one of the most successfully race-blind organizations on the planet.

Abbott writes that the NBA essentially lost the scientific battle as experts pored over the economists’ paper as well as the NBA’s study and found the NBA’s study to be lacking. (It is also interesting to note that the economists made all of their data available online, making it open for scrutiny from others.)

Malcolm Gladwell enters the picture because of his book Blink where he looks at how people make quick decisions. In instances where race matters, such as calling fouls or making a decision about whether a suspect is about to pull a gun, a person making a decision nearly instantaneously makes judgments based on knowledge or associations they make about different races. Abbott sums up this research on race and judgments (read more about it at the Project Implicit website):

The lesson Gladwell, Winfrey, Harvard researchers and others took from this was about environment: We may have reached a point where a lot of explicit racism (the kinds of things we’d associate with hate speech, the klan, segregation and the like) is largely behind us. But our brains are still bombarded with images of “bad” black people and “good” white ones, which affects our quick reactions to white and black faces.

More broadly, this lines up with sociological thinkers who have suggested that in recent decades, racism and discrimination has become less overt and more covert. But just because racism appears less present doesn’t mean that the problem has been solved or that we have entered into a color-blind world. Gladwell and others suggest that it is even built into our snap judgments.

As Abbott suggests, how the NBA responds to this remains to be seen. The initial response of strongly denying the economists’ research appears no longer tenable. For a league that aspires to become global (involving even more ethnicities and races) and also wants to gain a larger audience in America (fighting football and baseball as the big sports), recognizing that this issue exists and also demonstrating a willingness to work at reducing the effect may matter quite a bit.

Again trying to link the fate of Cleveland with LeBron James

With LeBron James returning to Cleveland, ESPN has another story about how Cleveland has suffered. But let me take a few pieces of this story and offer an alternative explanation of what has happened to Cleveland:

The issue is not really sports – LeBron James is just the symptom. The real issue is similar to that of many Rust Belt cities – manufacturing jobs left, the population shrunk, and the city’s glory disappeared. The city has tried some various tricks: funding new sports stadiums and building the Rock ‘n’ Roll Hall of Fame.

So when LeBron James, a local kid become star, joined the Cavaliers, the city perked up. Having James meant recognition, new money, and a chance for lasting glory with championships. When James left without bringing the championships, it turned into a cruel joke – the city is still recognized but as the place with terrible luck.

Having James for as long as they did masked the true problems of Cleveland. In fact, if James hadn’t played for the Cavaliers, there may be no one writing anything about Cleveland at all. For almost a decade, Cleveland could dream of sports and glory rather than thinking about what should be done to turn the city around. It won’t be easy: some of the ideas associated with reviving Detroit, which has drawn its own share of attention, are pretty drastic. Some other ideas that could be tried: developing park land along the water, building upon academic institutions, or trying to attract or develop newer industries.

Ultimately, the losing sports teams aren’t the issue. Sure, most cities would like to win championships. But the bigger issue is coping with or reversing the Rust Belt decline. LeBron wasn’t the answer – and Cleveland is still searching.

The presence of error in statistics as illustrated by basketball predictions

TrueHoop has an interesting paragraph from this afternoon illustrating how there is always error in even complicated statistical models:

A Laker fan wrings his hands over the fact that advanced stats prefer the Heat and LeBron James to the Lakers and Kobe Bryant. It’s pitched as an intuition vs. machine debate, but I don’t see the stats movement that way at all. Instead, I think everyone agrees the only contest that matters takes place in June. In the meantime, the question is, in clumsily predicting what will happen then (and stats or no, all such predictions are clumsy) do you want to use all of the best available information, or not? That’s the debate about stats in the NBA, if there still is one.

By suggesting that predictions are clumsy, Abbott is highlighting an important fact about statistics and statistical analysis: there is always some room for error. Even with the best statistical models, there is always a chance that a different outcome could result. There are anomalies that pop up, such as a player who has an unexpected breakout year or a young star who suffers an unfortunate injury early in the season. Or perhaps an issue like “chemistry,” something that I imagine is difficult to model, plays a role. The better the model, meaning the better the input data and the better the statistical techniques, the more accurate the predictions.

But in the short term, there are plenty of analysts (and fans) who want some way to think about the outcome of the 2010-2011 NBA season. Some predictions are simply made on intuition and basketball knowledge. Other predictions are made based on some statistical model. But all of these predictions will serve as talking points during the NBA season to help provide some overarching framework to understand the game by game results. Ultimately, as Gregg Easterbrook has pointed out in his TMQ column during the NFL off-season, many of the predictions are wrong – though the makers of the predictions are not often punished for poor results.

Comparing greatness of players past and present an enjoyable part of sports fandom

As the NBA season approaches, discussion this week has centered on the relative status of several players: Kobe Bryant, Kevin Durant, LeBron James, and Michael Jordan. While the first three players in this list were involved in a question about who is the best current player and potential MVP, Jordan also has been inserted in the discussion due to his starring role in NBA2K11 and comments he made about the number of points he could score if he played today when more fouls are called.

Several quick thoughts come to mind:

1. The new era of statistics in sports offers more opportunities to make comparisons of players across different eras, particularly if you can control for certain features of the game at each time period (like the average pace in basketball).

2. I wonder how much current players think about issues like these. Fans seems to like these discussions. It allows the average guy sitting on the couch to say, “my guy, whoever that may be, can match up or beat your guy.”

3. Jordan, like some other old players, still likes to be part of these discussions.

4. All of these discussions are magnified by the non-stop media attention for sports these days. I can hear it on local sports talk radio which all sound like the CNN of the radio airwaves; stories are repeated all day long with slightly different interpretations.

American sports leagues eye $155 million income for sponsorships on uniforms

It was recently reported that English Premier League teams earn about $155 million a year from the sponsorships on their uniforms. How much longer before American sports leagues follow suit and try to benefit from such a ready-made revenue stream?