Football fans take it on faith that the San Francisco 49ers, who hold the first pick in the NFL’s annual draft on April 24, have the best chance to improve of any team. The team, after all, has its pick of the best and brightest, and should emerge with the most talented and promising amateur player in the world.

But two business professors who have studied the draft extensively say the big contract given to the first pick is a millstone that actually puts San Francisco in the worst position of all in the first round.

The professors, Cade Massey of Duke University’s Fuqua School of Business and Richard H. Thaler of the University of Chicago’s Graduate School of Business, analyzed every selection, every trade, and every player in every NFL draft since 1988. They published their findings last month in a paper titled “The Loser’s Curse: Overconfidence vs. Market Efficiency in the National Football League Draft.”

The professors’ conclusions centered around the exorbitant cost of players chosen early in the draft. The NFL’s salary cap dictates that every dollar spent on a high-priced rookie is a dollar that can’t be spent on improving the rest of the team. The player taken with the first pick typically costs four times what the last first-round pick costs and, therefore, is actually of less benefit to his team.

So while the Giants were delighted to acquire Eli Manning last year, their young quarterback’s six-year, $54 million contract is exorbitant compared to the production teams typically get out of the first player selected. Ben Watson, the tight end who went at the end of the first round to the Patriots, may actually end up a better pick because he comes with a contract of only $13.5 million for six years.

Because of the salary cap, a better way to judge players than “who is the best?” is “who is the best per dollar?” And by that measurement, every selection in the second round is better than the first pick in the first round. It turns out that the most valuable pick in the draft in terms of getting a good player without breaking the bank is the 43rd overall, which is the 11th pick in the second round.

Last year, that pick belonged to the Dallas Cowboys, who took running back Julius Jones out of Notre Dame. Jones ran for 819 yards and scored seven touchdowns in just eight games and cost Dallas only $4.37 million on a six year contract. The professors’ graph shows peak value at pick no. 43 and then a steady decline through the rest of the draft, with one small blip toward the end caused by a single outlier, Patriots quarterback Tom Brady, who was selected with the 199th overall pick in 2000. Brady aside, top picks are better players than later picks – but not by a wide enough margin to justify their significantly higher salaries.

Teams often target a specific player and trade picks to move up in the draft order because they’re sure other teams want the same player. This is another instance of misperception, Massey and Thaler argue; teams wrongly assume they won’t be able to select the player they want unless they trade up.

Cleveland Browns coach Butch Davis illustrated that classic mistake last year. Davis coveted University of Miami tight end Kellen Winslow so much that he shipped his team’s second round pick to the Detroit Lions solely so he could move from the seventh pick to the Lions’ sixth and take Winslow.

Davis was afraid the Lions would take Winslow for themselves or trade the pick to another team. But reports since then have indicated that the Lions’ intention all along was to take Texas receiver Roy Williams with the sixth pick. So the Lions got a free second-round pick for moving down and taking Williams, who they wanted anyway, while the Browns sacrificed their all-important second-round pick to move up and grab Winslow, who would have been available anyway. And the reversed order meant the Browns had to pay more for Winslow than the Lions had to pay Williams.

Every team knows the market for picks; a widely used chart gives a numeric value to every pick in the draft, and Massey and Thaler have found that the chart closely approximates the actual value that teams have spent in trades. But that chart overvalues the highest picks, and in some cases, like the Browns’ draft-day trade last year, teams overpay even compared to what the chart suggests.

Though the professors’ research is new, it corresponds with the innovative draft strategies employed by the Washington Redskins in the 1980s. General Manager Bobby Beathard felt strongly that trading out of the first round and getting lower-priced players in the second round was the best choice. Beathard traded away first-round picks seven straight years in the 1980s; the team he built won three Super Bowls.

The best illustrations of the professors’ line of reasoning come from the actual results NFL teams have had. The Arizona Cardinals’ recent draft history has been filled with players such as Andre Wadsworth, a defensive end selected third overall from Florida State whose career was marked by major injuries (knee problems limited him to only eight sacks in his Cardinals career) and major paychecks (Arizona paid him more than $12 million).

Even young players who look promising, like the Cardinals’ first-round pick (no. 3 overall) in 2004, Larry Fitzgerald, exact a heavy financial toll. Fitzgerald’s six-year contract gives him $20 million in guaranteed money. Meanwhile, Michael Clayton, the receiver Tampa Bay selected with the 15th pick, got only $6.2 million in guarantees on his six year deal. And Clayton had a better rookie year than Fitzgerald.

On the flip side are the Patriots, who have had only two top-10 picks in the last 10 drafts. One of those picks, Terry Glenn, has long since departed, while the other, Richard Seymour, remains an integral part of the team. But the absence of high picks has given the Patriots the leeway to spend money on other players, and that wise spending has made them the best team in the league.

One reason teams overvalue high picks is that they’re overconfident of their ability to pick the best players. Every team makes lists of all the available players and sorts them by position, ranking, for instance, the top 50 offensive tackles. Although teams are accurate in the general assessments, such as which player deserves a first-round grade and which deserves a second round grade, they do badly when picking within those general assessments.

Scouts and general managers (who use hours of film study and reams of data to determine which player is, say, the 12th-best at his position and which is 13th) fare about as well as they would if they flipped a coin. Take any player chosen in the draft, and there’s a 49% chance that the next player chosen at his position will make as many or more Pro Bowls and a 47% chance that he’ll start as many or more games.

The ideal strategy for the 49ers would be to call every team and offer to trade down. If they could find enough trading partners, the 49ers could get six mid-second-round picks – even though all six of those picks are actually more valuable than the first overall.

That strategy illustrates just how bad a move it was for the Giants to give up the rights to Philip Rivers, a third round pick in 2004, and first- and fifth round choices in 2005 in exchange for Manning.

“We thought it crazy for the Giants to give up so many picks for the opportunity to move up from the fourth pick to the first one,” the professors write. “Rather than a treasure, the right to pick first appears to be a curse.”

Mr. Smith is a writer for FootballOutsiders.com.