The economics of the N.B.A. dictate that there are only two ways to build an elite team:

1. Acquire players who produce above-average value relative to the salaries they are making. 2. Exploit the loopholes in the salary cap so that you spend more money than other teams.

This is not merely a rule of thumb; it’s a mathematical axiom. At least one of these two things absolutely must be true for a team to be better than its competition.

So when a team makes a franchise-altering trade, as the New York Knicks did last night for Carmelo Anthony, it’s worth considering whether it’s part of a strategy that allows them to accomplish either of these two objectives.

Let’s start with the first question: have the Knicks acquired players who are worth significantly more than the salaries they will make?

It’s actually pretty easy to build an equivalency between salary and value on the court. Collectively, the 30 N.B.A. teams will spend a hair over $2 billion on player salary this year. For this, they will “purchase” 1,230 wins — that is, 41 wins per team, or half of the games in an 82-game season. That means that the price of a win is about $1.63 million dollars.

Yes, it really is (almost) that simple. If we were looking at baseball instead of basketball, the analysis would be more complicated, because even a team full of players making the league minimum salary — what stat geeks like me refer to as replacement-level players — would probably luck its way into winning about 50 ballgames. Basketball, however, is much less forgiving of mediocrity, and a roster full of 12-players signed from the D-League would have trouble winning any games at all. (Consider that the Cleveland Cavaliers — who are on pace to win just 15 games this season — nevertheless have a couple of decent players like Antawn Jamison and Mo Williams.)

The other thing we need is an estimate of how many wins any given player’s contributions are worth on the court. There are several different statistical systems that do this, each of which have their detractors. But my favorite is probably the Estimated Wins Added statistic developed by ESPN’s John Hollinger.

Mr. Hollinger’s statistic, for instance, estimates that Amar’e Stoudemire has produced 12.0 wins for the Knicks thus far this season. Projected over the full, 82-game year — and assuming that Stoudemire’s performance remains constant — that works out to 18.2 wins. At a value of $1.63 million per win, that means that Stoudemire will produce the equivalent of almost $30 million in value to the Knicks this season. Since he is “only” making $16.5 million this year, however, that means that Stoudemire has so far produced a strong return on investment for the team. (Although note that Stoudemire’s salary will increase in subsequent seasons while his performance may decline.)

Stoudemire, however, is not the only Knick who scored well by this metric. So did three of the players they traded: Wilson Chandler, Raymond Felton, and Danilo Gallinari. All are roughly league-average players, but they are comparatively cheap — Chandler, for instance, is making just $2.1 million this season, although he was due for a raise next year. Mitigating against this is that the Knicks also traded another player, Eddy Curry, who was making $11 million to sit on the bench.

Here, by contrast, are the players whom the Knicks acquired. In general, they are worth about what they are being paid:

Anthony does come out with a positive valuation — about $5.7 million in excess value. But keep in mind that there are significant debates about what he is worth — and although I tend to side with Mr. Hollinger’s statistics, they are more optimistic about Anthony than most other systems. Also, as part of the deal, Anthony will sign an extension that will pay him an average of $21.7 million over three years — almost exactly the same as the $22.8 million that Mr. Hollinger’s numbers say he is worth this season.

So, is Anthony a ‘superstar’? That is a matter of semantics, of course. But one reasonably meaty way to define a superstar in the N.B.A. is this: a player who is worth significantly more than the maximum salary, which depending on the circumstances is usually on the order of $20 million per year for a veteran player. A player that contributed the equivalent of $25 million to his team’s performance, for instance, would unambiguously be worth more than the veteran maximum contract and would be wholly deserving of the superstar label.

Very few players in the NBA, however, meet this definition. If we average the players’ Estimated Wins Added over the past 3 seasons (including this one, with current totals extrapolated out over 82-games), and then convert it to cash at our $1.63 million exchange rate, we find that just 10 players qualify: LeBron James, Dwyane Wade, Dwight Howard, Kevin Durant, Chris Paul, Kobe Bryant, Blake Griffin (based solely on his performance this year since he is a rookie), Dirk Nowitzki, Pau Gasol and Tim Duncan.

The list, of course, would change somewhat if we were projecting performance over the next three years, rather than looking at it retrospectively: Chicago’s Derrick Rose and Oklahoma City’s Russell Westbrook would probably need to be part of the group, for instance, while veterans like Duncan and Nowitzki would drop off the list. Nevertheless, it is a select group; probably not more than a dozen players at any given time are worth significantly more than the maximum salary.

There is also another group of players who are valued at somewhere between $20 and $25 million per year — that is, they are deserving of the maximum salary, but do not produce a significant return above and beyond it. Their teams still need to fill out their rosters with cost-effective players to win a championship with them, or to spend significantly more than the league’s ‘soft’ salary cap of about $58 million. (The Los Angeles Lakers, for instance — although they do have two superstars — also have a payroll of about $92 million by having exploited various loopholes in the league’s salary structure, which would be worth the equivalent of 56 wins even if all players were just average from a cost-efficiency standpoint.)

Among the players in this latter group are Anthony and Stoudemire (who is playing better this year than in the past couple and may revert to the mean some as he ages). They are very good players, but they’re in a different league from those like Orlando’s Dwight Howard — who is worth about $34 million per year — or Miami’s LeBron James, who is worth $47 million.

The Knicks now have two of these players — but not a whole lot else. They have the point guard Chauncey Billups, but he is worth roughly the $14.2 million that he would be due to make next year if the Knicks pick up his option and not more. They do also have the rookie Landry Fields, a second-round draft pick who is owed only $788,872 next year but who is worth many times that; he isn’t the best Knick, but from an economic standpoint, he is probably the most valuable one. Beyond that, however, the roster is now very thin.

If the Knicks pick up the options on Billups and Toney Douglas, and Ronny Turiaf accepts his player option, they would have nine players under contract for next season for a collective $62 million, accounting for the raise that Anthony will receive. And those players would be worth 51 wins according to Mr. Hollinger’s statistic assuming that they matched their performance from this year — an assumption that is arguably optimistic since the Knicks have suddenly gone from being a young club to a middle-aged one and since these players have generally avoided injury this year.

A team winning 51 games would have been the No. 4 seed in the Eastern Conference in each of the past three seasons. By the standard of recent Knicks seasons, that would count as quite a lot of progress — the Knicks would host a playoff series at Madison Square Garden — but they would be underdogs to advance past the second round.

And one thing the Knicks will not have is a whole lot of flexibility to improve their roster further. The $62 million that they will owe to these nine players is close to the $58 million salary cap from this season — and that cap may well decrease if and when the league and its players sign a new collective-bargaining agreement this summer. Nor, other than Fields — who would be hard to improve upon from an efficiency standpoint — do the Knicks have much in the way of either draft picks or appealing young players, since they traded so many away in the deals with Denver and Minnesota.

So the lineup that you’ll see when Anthony makes his debut at the Garden on Wednesday is basically the one you’ll get for the next year and a half. The Knicks might have some upside if Stoudemire, Anthony and Billups gel especially well together, if they get a steal with their first-round draft pick, or if it’s a down year for the other teams in the conference. But they are very probably not a championship-caliber team as currently constructed.

What about 2012-13? That winter, several star players — including Dwight Howard, Chris Paul and Deron Williams — will become available. The Knicks, meanwhile, will be obligated to only three players — Anthony, Stoudemire and Renaldo Balkman, who will make about $44 million between them. Depending on how the collective-bargaining agreement turns out, they might be able to afford one of them.

But that team, also, could be a step behind the best in the league. Collectively, Stoudemire, Anthony and Paul have produced an average of 47 wins between them, according to Mr. Hollinger’s statistic.

Getting 47 wins out of just three players gives a team a huge leg up if it can surround them with any sort of talent at all. But the Knicks might have a lot of trouble doing so. Signing a player like Paul or Howard would almost certainly squeeze the salary cap down to the last penny, if it could be accomplished in the first place. Fields, for instance, will be a restricted free agent after 2011-12 and the Knicks probably could not keep him if they were clearing space to sign a player like Paul instead.

It’s tempting to cite the Miami Heat as a favorable comparison; they are succeeding with a roster of three stars and nine scrubs. The nine players who fill out Miami’s roster, other than LeBron James, Dwyane Wade and Chris Bosh have combined to produce negative value this season by Mr. Hollinger’s numbers.

James, Wade and Bosh, however, have combined to produce an average of 69 wins per season over the last three years, according to Mr. Hollinger (they are somewhat underachieving this year), as compared to 47 for the Knicks’ would-be Big Three.

None of this means that the Knicks will be unwatchable. Far from it, they will be one of the most exciting teams in the league, which is one of the reasons that the share price for MSG group is trending upward. And merely good teams sometimes find ways to back into having great seasons.

What the Knicks really needed to do, however, was to find some better way to exploit the assets that were already on their roster. The salary cap is relatively permissive about allowing teams to re-sign their own players, at least under the current rules. So, although players like Chandler, Gallinari and Randolph would have become more expensive after their current deals expired, the Knicks could hold onto them simply by spending well in excess of the ‘soft’ cap.

Instead, the Knicks seem to have put themselves into a situation where, on the one hand, the players on the roster aren’t quite good enough to contend for a title, but on the other, they have little flexibility to add others without making significant sacrifices.

The trade is being billed as a high-risk move. But in some ways it is just the opposite, seeming to lock the Knicks in to roughly 50 wins over the next handful of seasons — not a lot more, not a lot less — under most of the more realistic scenarios.

What might the Knicks have done differently? One thing might have been to insist that the Nuggets’ center, Nene, was among the bounty of players they were receiving from Denver. A starting five of Billups, Fields, Anthony, Stoudemire and Nene could well be a 60-win team, even with almost no depth.

No, the Nuggets might not have made the trade. But no one was forcing the Knicks to make their deal either. And the trade that they did make was extravagant from the perspective of opportunity cost.