The Effects of N.B.A. Minimum Wage and Salary Cap Rules

Earlier this month, the prolific and now controversial economist Justin Wolfers put forth some reasons for why so much economic research is devoted to sports.

Here's one I will draw upon for justifying this post:

Sports shapes broader national debates. Sports is a microcosm of our broader society and our national narrative on the important issues, from drugs, to race, to cheating, to sexual harrassment often play out on our sports pages. In honor of a particularly compelling example, let's call this the Jackie Robinson defense.

And perhaps another reason that Wolfers left out of his list was the vast amount of publicly available -- and crunchable -- numbers that pro sports throw off at every at-bat and fast break.

With those two pieces of information in mind, let's turn to an interesting piece of research by Chad Turner of Nicholls State University and Jahn Hakes of Albion College.

In the 1990's the N.B.A. owners and the union representing the players agreed to two collective bargaining agreements. The first important change was the rookie-scale, a new system that defined the boundaries for how much a rookie player could earn over the first three to four years of his career.

So for example, Carmelo Anthony of the Denver Nuggets was second in the league in scoring last year behind Kobe Bryant. But Anthony only had four year's of experience while Bryant was in his 11th year. That meant Anthony still got paid scale ($4,694,041) while Bryant's salary was something closer to a market wage ($17,718,750).

The second important change was the introduction of the "Larry Bird exception" to the league's salary cap rules (which had existed in some form since 1984) that allowed teams to go over the cap by signing their star players to mega contracts.

To see what effect these changes had on pay-for-performance, the researchers looked at performance and salary data over a two decade period (1985-86 season to 2005-2006 season).

The first interesting result is that players' salaries peak about 3 years after their performance peaks. So just like investors who buy hot stocks after they've climbed as high as they're going to go, N.B.A. teams are also paying for past performance. (There is another interpretation: that a star player's pay reflects ancillary benefits for the team like ability to attract fans and sponsors.)

Here are a couple of graphics from the paper to illustrate this point. They are very cluttered, but you can ignore most everything except for the thick black line which shows (after some statistical manipulation) how one measure of ability (in this case the IBM score plotted on the vertical axis) changes for the average player over his career.

The second chart shows the same thing except an adjusted measure of salary is plotted instead of ability.

The two important points are
- After they become free agents, players' salary paths are much flatter than their ability paths.
- The high point in the salary curve happens later than the high point in the ability curve.

The other interesting result from Turner and Hakes' research is that although somebody like Carmelo Anthony is receiving much less than he would if he was getting paid a market wage, in general the impact of the rookie scale has been that the average rookie is getting paid more than his performance justifies. And since N.B.A. teams operate under a salary cap, that means many veteran players are probably getting underpaid.

Going back to Wolfers' point on the relationship between sports and broader society, the researchers make a case for a wider impact of their findings:

"Given the difficulties involved in the appropriate measurement of productivity in basketball, our conclusions should be viewed cautiously pending further exploration and verification using alternative methods. If the results hold, the finding that salary inefficiencies exist in two dimensions in basketball -- both between high- and low-experience players and between ability cohorts of veterans - leaves interesting public choice questions over how union priorities are formed prior to collective bargaining".

Related:

• A Starting Point for Analyzing Basketball Statistics