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Staturday: Market Value

Free agency has been underway for a couple days, and players and money are already flying in every direction. That's, of course, given us the opportunity to make fun of the Rudy Gay, Darko Milicic, and Drew Gooden to various degrees (though I've (somewhat?) successfully defending the Amir Johnson deal to a couple people). Of course, it's all fun and games during the week, but come Saturday, it's time to put the hammer down and bust out the hard figures.

With max deals being thrown at guys like Rudy Gay, A'm''a*re Stoudemire, and Joe Johnson (in addition to the usual suspects, LBJ and Wade), now's as good a time as ever to ascertain "true market value."

For starters, a little history lesson. As with the burgeoning statistical revolutions in footballsoccer, and hockey, a good amount of current analytical NBA work has its roots in baseball and sabermetrics. Market analysis is no exception. For the average fan, Moneyball was one of the first mainstream works to delve into sabermetric concepts; instead of stressing a particular statistic, it explored how the market could be (and was being) exploited for underrated skill sets and the immense value in avoiding overrated and expensive skills.

Importantly, the book explained the value of "marginal wins," a concept pioneered by Doug Pappas, and one that will be of utmost importance in this post. One of Moneyball's critical passages describes this concept's applicability in Major League Baseball:

"A leading independent authority on baseball finance, a Manhattan lawyer named Doug Pappas, pointed out a quantifiable distinction between Oakland and the rest of baseball. The least you could spend on a 25-man team, if everyone was paid the minimum salary, was $5 million, plus $2 million more for players on the disabled list and the remainder of the 40-man roster. The huge role of luck in any baseball game, and the relatively small difference in ability between most major leaguers and the rookies who might work for the minimum wage, meant that the fewest games a minimum-wage baseball team would win during a 162-game season was something like 49. The Pappas measure of financial efficiency was this: How many dollars over the minimum $7 million does each team pay for each win over its 49th? How many marginal dollars does a team spend for each marginal win? Over the past three years Oakland has paid about half a million dollars per win. The only other team in six figures has been the Minnesota Twins, at $675,000 per win. The most profligate rich franchises--the Baltimore Orioles, for instance, or the Texas Rangers--have paid nearly $3 million for each win, or more than six times what Oakland paid. Oakland seemed to be playing a different game from everyone else."

For a small market team like Oakland, the concept of marginal wins is absolutely imperative. The applicability to a market like New Orleans and a team like the Hornets is unmistakable. We, as fans, often think about on-court production in absolute terms, but as APBRmetrician Kevin Broom remarked in 2005:

Most fans don’t care much whether the owner makes money — the fans just want their team to win. But, the [NBA] has placed limits on how much teams can spend in pursuit of wins, and is seeking to impose even further limits in the ongoing collective bargaining agreement discussions.

Economic considerations and sound fiscal management are essential for a good front office. Money spent unwisely has a ripple effect on the team for the duration of the contract. It siphons resources and hinders future moves that might help the team achieve more wins. The best run teams understand this, and manage their teams accordingly.

If you follow that above link, you can see Broom's calculations of marginal dollars per win for the 2005 season. Similar calculations are available for the 2004 season at HoopsWorld (Kevin Pelton), and the 2009 season at Basketball Reference (again, Kevin Pelton). The key to understanding marginal value and marginal wins is the idea that every team in the NBA has a baseline dollar amount that it must shell out, at minimum, per season. According to the latest CBA, in terms of operating costs associated purely with player salary, that's 75% of the annual cap. And with that minimum comes a floor amount of player production. Essentially, we've got two floors- a floor on minimum player costs and a floor on minimum player production. Marginal analysis refers to studying any wins produced and any dollars spent above their respective baselines. 

This concept can, and has, been extended from the team level to the individual level. There's been lots of work done on establishing exactly what a "replacement level" player is in baseball; Doug Pappas' work with marginal team wins use .300 as a baseline winning percentage in baseball. Not too much work has been done in establishing replacement level in basketball (it's definitely a bigger task, because what truly comprises "zero" value? There's no basketball equivalent to going up to the plate and striking out every time, especially when defense is factored in). But this 2004 story by Kevin Pelton is a start, and replacement level value in recent studies at the APBRmetrics forums have used .025 WP/48 as a baseline, a quarter of the ~0.1 WP/48 league average. Thus, for the sake of this article, I'll be defining replacement level as 25% of a league average player (in this case, production being defined by win shares). 

We can then find what minimum production is purchased by a team's mandated minimum player costs. The NBA median for player win shares this year was 2.0 (which makes sense in context, given that there are a total 30*41 wins per league, per year, and that there are approximately 13-15 players for each of the league's 30 teams). A quarter of that is 0.5, or a rough approximate of the win shares a replacement level player provides per season. I'll leave the minimum player salary as the veteran's minimum, ~1.1 million (even though there are contracts that run lower). At the end of all this, the crude (but sort of not too crude) methodology indicates that each marginal win should be worth approximately 2.2 million dollars. 

Let's toss some caveats on here: (1) This doesn't account for defense, really. But in a way, not having defense kinda, sorta doesn't make a difference in the big picture because teams very, very rarely pay exclusively, or even primarily, for defensive ability. Teams pay for guys that can put the ball in the bucket or guys that are big (and can rebound). So even if we did have an absolutely perfect way of quantifying defense, it ironically wouldn't affect this valuation too much. (2) This is a rough estimate. Yes, there's logic and some math behind the process, but there are uncertainties associated with all the following numbers. (3) Obviously, certain positions may be weighted more towards one end of the spectrum than the other. But that's a decision made on a team-by-team basis: ie, do we build around a center? a guard? is a forward the missing piece, and therefore more valuable to us than any other team? 

One other issue should immediately jump out here: the NBA caps how much a team can pay a player. For example, Kobe Bryant was worth approximately $27.9 million in 2008-2009, by this method. However, the NBA's maximum allowable contract was $21.6 million for the year, which was what he received. Clearly, the Lakers "saved" a good chunk of cash (as did Cleveland with LeBron, New Orleans with Chris Paul, etc).

This gives credence to the idea that the most efficient way to construct a team is to surround a superstar player (surplus savings since the player produces much more than he is paid) with players on rookie contracts (exceptionally good savings, given good drafting). Remind you of anyone? (The San Antonio Spurs!) Thank you, Captain Obvious. S.A.'s a small market, but they surrounded a superstar talent (Duncan) with solid young guys (notably Parker and Ginobili), and essentially became the NBA's version of the Oakland Athletics. 

And so now that that's all out of the way, we're ready to dive into this year's free agency. 

LeBron James, Dwyane Wade: easily worth the max, right?

Right. LBJ is the least brainy no-brainer of the current generation of players. He's never missed more than 6 games in a single season, and has averaged almost 15 win shares per year for seven years. His "dollar" values for the last two years translate roughly to $45 and $40 million dollars. Whichever team nabs him will significantly improve their marginal dollars/win figure. And they'll be getting LeBron James. 

In May, Christopher Reina of RealGM took a look at how much LeBron James would command this summer in a true open market, without a cap. One of the methodologies he used- inflation adjusting max contracts from the 1990's before the maximum contract concept was mandated- arrived at the following conclusion:

Jordan earned $33.14M in the 97-98 season, his final campaign with the Bulls.

Adjusting for inflation, that would put LeBron's contract at approximately $44.1M for the 10-11 season. Even if the contract was a flat rate and did not include raises, a six-year deal would be worth $264.6M, more than twice the figure he is expected to sign for this summer.

The fact that the inflation adjusted estimate of $44 million falls in my predicted range of $40 to $45 million is rather interesting. Dwyane Wade, though, I'd contend wouldn't be worth quite as much on an open market. The past two seasons, he's been worth about $28 and $32 million dollars. Even when you toss in Wade's injury history, those figures easily warrant the maximum contracts he's received, but they're certainly not in James' territory.  

How about Chris Bosh? Amar'e Stoudemire? Joe Johnson? ... Rudy Gay?

Chris Bosh is an interesting case, too. Over the past five seasons now, he's been remarkably consistent: right at 70 games played every year, and right around the 10 win shares mark. There are obviously questions about his defense and "passion" for the game, but pretty much any team has to take that gamble when pitching offers to him. I'd contend that the max is actually a very accurate representation of Bosh's value- he's a 20ish to 25ish million dollar a year value kind of player, where guys like Wade and James are technically worth way more than the maximum. 

Stoudemire has even more questions about his defense, and infinitely more health issues. But at his peak, he represents significantly more value than Bosh. In 2004-2005 and again in 2007-2008, he was worth approximately $32 million. He's a riskier max contract than Bosh, but that's not to say his play doesn't warrant it.

Joe Johnson? As you might've guessed, definitely not worth that much. Since becoming Atlanta's primary weapon, he's been a ~7 win shares a year player. While he did scratch out a career high 8.4 mark this year, I don't see him exceeding that too often over the course of his next contract. If we go conservative and peg him to produce 6-8 win shares a year for the next five seasons, we see that he's really a 15 million type player. 

Rudy Gay is in a similar boat, but he has the advantage of youth. Where Johnson just turned 29 last week, Gay will be 24 in the fall. That said, Gay is still a significantly worse player than Johnson. For all his physical skills and shot making ability, Gay is still not the most efficient player (104 points/possession, career), and his floor percentages, passing, rebounding, and foul drawing have all stayed relatively static for three consecutive seasons now. Gay's 2009-2010 effort was worth around 14 million dollars, so he will have to step his game up. Fortunately for Memphis, he's on his first max deal, not his second, so if he can push his overall value to 16-17 million per year (not entirely implausible, I don't think), they can still come out on top. For some reason, I'd assumed that the Gay deal was far worse than the Johnson one, but given the figures, I don't think that's necessarily true. 

Richard Jefferson and Peja Stojakovic

Jefferson's curious decision to opt out of $15 million this week made many people wince anew at Peja's last year. Interestingly, my system doesn't find Jefferson's contract that much of an overvaluation of his production. As a Spur last year, Jefferson produced 6.0 win shares, the equivalent of about a $13.2 million dollar contract. Given that he'd hit $14.5 million and $16.5 million the two previous years, in addition to $25.4 million in 2004-2005 with New Jersey, the precedent was certainly there. 

Peja Stojakovic? He's been good for a total $34.1 million dollars in his four years in New Orleans. In that time, he's made an actual total in excess of $48 million dollars. That actually doesn't sound as bad as I thought it would (his 2007-2008 value of $17 million really saves him), but that's still a rather inefficient distribution of salary for a team that can use all the money it can get.

The Future of Chris Paul

CP3 has produced around $138 million dollars worth of wins in his five seasons in the league, which comes out to an average of $27 million a year. Now, if he can return to 2007-2009 form and health, that would certainly help matters. In those two seasons alone, he produced nearly $80 million dollars worth value. Essentially, a Chris Paul of questionable health is easily worth the maximum, and a healthy Chris Paul is in LeBron territory.

This has serious implications in regards to keeping him or trading him. As I mentioned earlier, New Orleans needs to maximize its marginal dollars/win in any way they can. The ownership has been an issue for a while now, and New Orleans isn't the nation's biggest media market- the team must be efficient if it reasonably expects any sort of sustainable success. The move towards youth is all well and good, but Chris Paul represents, far and away, the Hornets' best chance of remaining financially stable.

We already knew this in one sense- he puts fans in seats, and a trade would ensure a vicious backlash. But it's true in terms of basketball economics, too. Put in its simplest terms: CP3 provides wins the team can't afford to pay for. If the team wants to stay in New Orleans and win games, it needs Chris Paul. Period. 


I hope y'all enjoyed this Staturday- easily the most time consuming one for me, thus far. I'm hoping to go through several further refinements of the replacement level value, but I'm happy with the way this ended up. I'm out like an Asamoah Gyan penalty kick.