# The Surprising Leader of the Overpaid

Sean Deveney of The Sporting News wrote a column a few days ago listing the ten most overpaid players in the NBA. His list – which I reproduced below — focused on 2007-08 and excluded players who were bought out or are scheduled to make less than $7 million.

1. Kenyon Martin

2. Stephon Marbury

3. Andrei Kirilenko

4. Theo Ratliff

5. Antoine Walker

6. Raef LaFrentz

7. Malik Rose

8. Wally Szczerbiak

9. Ben Wallace

10. Kwame Brown

There is not much to quibble about Deveney’s choices. The average player on this list made $11.6 million last year. And these players only averaged 2.3 Wins Produced — and a 0.089 WP48 (Wins Produced per 48 minutes) – in 2006-07. An average WP48 is 0.100, so in general these players were both extremely well paid and below average performers.

**Measuring the Economic Value of an NBA Player**

Still, there are a few players that might have been better choices (in other words, for the purpose of my column I shall quibble). To see this, we need to establish a method for assessing whether a player is overpaid or not.

One might argue that all NBA players are overpaid. After all, these players are extremely well paid to play a game.

Economists, though, consider a worker overpaid if the wage the worker receives exceeds the revenue the worker generates for his employer. USA Today provides us information on each player’s wage (well, most players). All we need to do is determine how much revenue each player has generated.

Back in 1974, Gerald Scully published a study in The American Economic Review (perhaps the top journal in economics) outlining how a baseball player’s economic value could be measured. Scully’s method involved two steps. First he figured out the baseball player’s level of productivity. Then he figured out how much this production was worth in terms of revenue.

For basketball we can look at Wins Produced to measure productivity. So all we need to know is how much each win is worth to an NBA team.

The standard approach is to simply regress team revenue on wins (and other stuff). But I think there’s a problem with this approach for the NBA (a problem I wish to avoid getting in to for a blog entry), so I am going to estimate the value of a win differently. According to USA Today, NBA teams paid their players $1.818 billion in 2006-07. We know from our research on revenue and attendance [mentioned in The Wages of Wins, which is soon to be published as a paperback :) ] that players primarily generate value in the NBA via their ability to generate wins. And we also know that a player’s wage is only for the regular season. Consequently, we could say that the value of one win in the NBA is simply the amount of money the league paid its players divided by how many wins these players produced in the regular season.

Such an approach makes three assumptions. I am assuming that all players in the NBA are collectively paid what they are worth (which may be true if the union bargained effectively), players are only paid to produce wins (which is a reasonable assumption given the research cited above), and the value of a win is the same for all teams (okay, not true, but two out of three ain’t too bad).

According to the USA Today, players were paid $1.818 billion in 2006-07. And these players must have produced 1,230 wins (41 wins multiplied by 30 teams). So each win must be worth about $1.478 million (I would note that this is just a crude estimate, and if I were writing an academic article – which I am not – I would try harder to measure the value of a win).

Okay, we have all the numbers we need to figure out how much each player was overpaid (or underpaid). All we need is some criteria for who gets considered for the list.

Like Deveney, I am going to ignore players who made less than $7 million. I am also going to ignore people who received a buy-out last year (see Jalen Rose, Chris Webber, and Eddie Jones), but I will include those who got a buy-out this summer (hello Steve Francis). And although Deveney included players like Kenyon Martin and Theo Ratliff, who were each hurt last year, I am only going to include players who actually played. Well, at least those who played at least 1,000 minutes.

**The Most Overpaid**

Given all these requirements, there is a surprising name at the top of the list. Shaquille O’Neal was paid $20 million (only Kevin Garnett was paid more). He also only played 1,135 minutes (okay, Shaq was hurt, so maybe he should be skipped for this list). If each win is worth close to $1.5 million, Shaq would have had to produce 13.5 wins to justify his wage. With only 1,135 minutes played, O’Neal would have had to post a 0.572 WP48 to get to 13.5 wins. Shaq has been very good in his career, but he has never been this good.

What if Shaq hadn’t been hurt? He only played 40 games last year. Had he played 82 games, and his minutes per game was unchanged (28.4), his WP48 would have only had to be 0.279. This mark is below his career average of 0.331, but actually better than what he has done each of the past two seasons.

Two years ago his WP48 was 0.225. Last year his mark was only 0.128. Given his 1,135 minutes played, his WP48 mark in 2006-07 translates into only 3.0 wins. And given the value of a win, Shaq only produced $4.48 million in value. With a salary of $20 million, he was overpaid to a tune of $15.5 million. Such a mark does lead all overpaid players, which means that Shaq was the most overpaid player in 2006-07 (if we ignore some stuff that I will talk about tomorrow).

Now for Shaq’s career… wait, that story will have to wait until tomorrow as well.

Let’s talk about who else appears on the list of most overpaid players. Here is the top ten.

Table One: The Most Overpaid in 2006-07

Walker and Marbury appear on Deveney’s list as well as mine. And if we removed the 1,000 minutes played criteria, K-Mart, Ratliff, LaFrentz, and Szczerbiak would appear on my list as well (although I think Deveney, given his criteria, missed on Peja Stojakovic).

But if 1,000 minutes played is the cut-off, a few different names appear. Desmond Mason was only paid $8 million, but since his wins production wandered in the negative range, he was overpaid by $11.5 million. The same issue exists for P.J. Brown, whose productivity is nowhere near what it was when he was a younger player. Allen Iverson, Larry Hughes, Grant Hill, Steve Francis, and Jermaine O’Neal each produced a positive quantity of wins. But the production of each was not worth the immense salaries each received.

Including these players bumps Kirilenko, Rose, Wallace, and Brown from Deveney’s list. Wallace is the strangest choice by Deveney, since he was actually underpaid by $7.3 million last year (15.8 Wins Produced, $23.3 million in revenue generated, $16 million in salary paid).

Kirilenko, Rose, and Brown, though, were overpaid. None, though, were overpaid by enough to make the top ten. Rose, who played quite badly in only 810 minutes, was still only overpaid by $8.9 million. Brown only produced 1.7 wins, but was still only overpaid by $5.7 million. And although crying in the playoffs is bad, if we only focus on regular season production we see that Kirilenko was only overpaid by $1.1 million.

As noted, tomorrow I want to return to the subject of Shaq. And hopefully soon, I can review the list of players who were underpaid last year.

– DJ

Our research on the NBA was summarized HERE.

Wins Produced and Win Score are Discussed in the Following Posts