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For baseball fans who have suffered through a harsh winter, spring training couldn't have arrived soon enough. Once pitchers and catchers start soft-tossing, you know that warmth is on the way.

Warmth — and this year, as it turns out, endless talk about Albert Pujols' contract.

As players report to Arizona and Florida, the future of Pujols, the first baseman for the St. Louis Cardinals who has won three MVP awards and is arguably the best player in baseball, has dominated spring-training discussions. Pujols is entering the final season of the eight-year, $111 million contract he signed in 2004. He set a deadline to sign an extension — Wednesday, Feb. 16, at noon — that came and went. Pujols is reportedly seeking to top the 10-year, $275 million deal Alex Rodriguez, then 32, signed with the New York Yankees in 2007. In his mind — and in the minds of many baseball fans — Pujols is just as good, if not better, than A-Rod. According to some reports, Pujols wants $300 million for 10 years, though he has called those numbers "way off." He has said he does not want to negotiate during the season, so unless St. Louis unexpectedly ponies up, he'll test the free-agent market come fall.

There is no denying how great Pujols has been. He is the only player in major-league history to hit 30 or more home runs in each of his first 10 seasons. He is the face of a storied franchise — the Cardinals have won 10 World Series titles, second only to the Yankees' 27 — and a generous, community-minded guy who causes no trouble.

And yet the Cardinals should absolutely call Pujols' bluff. After all, like any other athlete, Pujols, 31, is a depreciating asset. (Barry Bonds, who allegedly took performance-enhancing drugs to extend his career, is the notable exception. No evidence has emerged linking Pujols to banned substances.) That the Cardinals would even consider giving a 31-year-old player an exorbitant raise, when the odds of his replicating his past feats over the next 10 years are infinitesimal, highlights the irrational economics of pro sports.

One Cardinals-centric website, Viva El Birdos, has projected how Pujols might decline. Through the age of 30, the careers of Jimmie Foxx, Frank Robinson, Ken Griffey Jr., Lou Gehrig, Hank Aaron, Mickey Mantle, Mel Ott and Manny Ramirez most resemble that of Pujols, according to baseballreference.com, a respected statistics site. That's pretty impressive company: these players are all current or future Hall of Famers. Using a measurement of overall player value called Wins Above Replacement (WAR), which calculates how many wins a given player, as opposed to a minor leaguer or bench player, is responsible for, Viva El Birdos showed that these Hall of Famers retained just 52% of the value they generated during their prime years (ages 27 through 30) by the time they reached 35. At 38, they retained just 15% of their value.

If there's a reasonable chance that a player would be 85% less valuable in eight years, why would you give him a 10-year contract with any kind of raise, especially one that costs you $300 million? Pujols is like a beautiful, trusted car that hasn't broken down in a decade and still runs extremely well. If you were to sell that 10-year-old car now, would there be any chance you'd fetch a premium above the newest, hottest model? Even the best used-car salesman couldn't pull that one off.

You could even argue that Pujols is already paid too much. According to fangraphs.com, another respected statistics site, among position players, Pujols finished third in WAR in 2010, behind Josh Hamilton of the Texas Rangers and Joey Votto of the Cincinnati Reds. Hamilton received a $3.25 million salary last season; having generated 8.0 wins above replacement, each of Hamilton's wins cost the Rangers $406,250. Votto was a true steal: at a $525,000 salary and 7.4 WAR, he cost the Reds just $70,946 per win. Pujols, on the other hand, cost the Cardinals close to $2 million per win ($14,595,953 in salary; 7.3 WAR). In fact, among the top 10 leaders in WAR, Pujols ranked ninth in cost per win. Cardinals outfielder Matt Holliday, who signed a seven-year, $120 million contract with the club last off-season, was 10th, at over $2.3 million.

Like any smart negotiator, Pujols is using the inflated free-agent market as leverage. Outfielder Carl Crawford, for example, signed a seven-year, $142 million deal with the Boston Red Sox this off-season. In 2010, Crawford generated 6.9 WAR for Tampa Bay. If he matches that total in 2012, when he will make $19.5 million, Crawford, 29, will cost Boston over $2.8 million per win, comfortably above Pujols' $2 million rate. And as Pujols looks to capitalize on market inefficiencies, A-Rod is the ultimate negotiation gift. Rodriguez, 35, made $33 million in 2010 and had 3.9 WAR. He's costing the Yankees a ridiculous $8.46 million for each extra win. If I'm now the best player in baseball, Pujols is maybe telling the Cardinals, give me A-Rod money.

But A-Rod's case should actually help the Cardinals make theirs. Since Rodriguez signed his extension after a monster 2007 season, his WAR has declined each year, from 9.2 in 2007 to 6.0 in 2008 to 4.5 in 2009 to 3.9 last season. The clear lesson owners have continued to ignore: Beware of long-term deals for players plunging into their 30s. Plus, just because teams like the Yankees and Red Sox regularly overpay for talent, why should St. Louis? Since 2000, the franchise has thrived — the Cards have won six division championships, the 2004 National League pennant and the 2006 World Series — with, on average, the 10th highest payroll in the majors.

This off-season, the Yankees gave fading shortstop Derek Jeter, 36, a three-year, $51 million contract. But keeping legacy players in pinstripes, at any price, is part of the Yankees' global branding strategy. The Cardinals have never concerned themselves with this kind of exposure, and they shouldn't.

Yes, Pujols is popular, and his departure would hit the fan base hard. But if any franchise could withstand the loss of a single player, even one with the all-time credentials of Pujols, it's the Cardinals. The team has drawn loyal fans — decked in red — from multiple Midwestern states, even during losing seasons. And Cards fans don't hold grudges. After St. Louis got swept by the Red Sox in the 2004 World Series, Cards fans celebrated alongside delirious Red Sox fans, who could at last die in peace because their belawved Sawx finally won one.

So if the Cardinals don't make Pujols a $300 million man, fans won't flee their beloved team. In fact, the high ticket prices needed to cover Pujols' inflated salary would be more likely to tick them off. Let the New York Mets — if Bernie Madoff's legal fallout doesn't bankrupt them — put in the ludicrous bid for Pujols. It was Madoff himself who showed that an investment's return is never as good as you think it will be.

Gregory is a staff writer at TIME. Keeping Score, his sports column for TIME.com, appears every Friday. Follow him on Twitter at @seanmgregory.

• Sean Gregory