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.

Male/female wage gap reversed for “unmarried, childless women under 30 who live in cities”

The gap between male and female earnings has been a persistent feature in American society for decades. However, recent research suggests that a certain group of women are now outearning men:

[A]ccording to a new analysis of 2,000 communities by a market research company, in 147 out of 150 of the biggest cities in the U.S., the median full-time salaries of young women are 8% higher than those of the guys in their peer group. In two cities, Atlanta and Memphis, those women are making about 20% more. This squares with earlier research from Queens College, New York, that had suggested that this was happening in major metropolises.

Here’s the slightly deflating caveat: this reverse gender gap, as it’s known, applies only to unmarried, childless women under 30 who live in cities. The rest of working women — even those of the same age, but who are married or don’t live in a major metropolitan area — are still on the less scenic side of the wage divide.
The article discusses the main causal factors identified by authors: “a growing knowledge-based economy, the decline of a manufacturing base and an increasing minority population.”
At first glance, this may not be that surprising considering the number of women enrolling in and earning degrees at college. Additionally, the restructuring of the American economy away from manufacturing jobs and toward a service/knowledge economy has hit male dominated fields hard.
This bears watching.