Albert Pujols signs autographs for fans after a public news conference introducing newly signed Angels players Pujols and C.J. Wilson at Angel Stadium. (Stephen Dunn/GETTY IMAGES)

In baseball free agency, only one rule has emerged over the last 35 years: You overpay for quality because the rest is junk.

Even with quality, you often get burned. But at least you had a chance.

However, this week, the game’s classic offseason maxim has finally been pushed to a new breaking point. All over baseball, teams are wondering, “How much is finally too much?” That’s why the hunt for Prince Fielder, the pursuit of Japan’s Yu Darvish and the Nationals’ so-far-indecisive courtship of Roy Oswalt will be wracked with so much tension.

The stakes were always high. Now they may finally be nuts.

This week, Albert Pujols, Jose Reyes, C.J. Wilson, Mark Buehrle and Heath Bell signed $509 million in free agent contracts, all with either the Los Angeles Angels or Miami Marlins. At first glance, all five deals look idiotic. Pujols was overpaid by about $100 million, the rest by a total of maybe $75 million, if you apply conventional stats for guesstimating player value.

For a generation, the wisdom in baseball has been that if you find a player who fits your team’s need — in the clubhouse, with young players and with your fan base — then go for the proven star, even though he’ll always seem to cost too much.

Specifically, try to focus on those few players who will someday be in the Hall of Fame, such as Pujols, or who are virtually certain to appear on the Hall of Fame ballot, an honor granted to players with long, distinguished careers, even if they aren’t really of Cooperstown caliber. With any normal baseball progression, Reyes and Buehrle (161 wins) will fit the latter description.

In fact, in 2010 the only monster-money star that didn’t pass the Hall-ballot litmus test was Jayson Werth. This year, Wilson, 31, is the exception.

The Angels’ deal with Pujols shows just how deeply the “pay up” mantra has sunk into the game. Before the ’08 season, Alex Rodriguez signed a $275 million, 10-year extension with the Yankees at the same age Pujols is now. This year, A-Rod had only 16 homers and 62 RBI in 97 games. His career slide seems irreversible — with six seasons left on the deal.

Over and over we hear “Pujols is unique.” But he isn’t quite. At the same age, Frank Thomas had a 1.013 career OPS, a hair behind Pujols now, and a career .320 batting average. But the Big Hurt faded fast. Before ’08, A-Rod had higher home run and RBI totals than Pujols does now.

Yet the Angels weren’t alone. The Marlins and Cards reportedly went to $220 million. It’s time for some historical perspective. Look at the accompanying chart of 15 of the greatest hitters ever: Babe Ruth and Ted Williams “down to” Frank Robinson and Ken Griffey Jr. As a group, they had an OPS+ of 170 when they were Pujols’s current age (he will turn 32 in January). By a nice coincidence, Pujols also has a career OPS+ of 170.

(OPS+ is just OPS — on-base-plus-slugging-percentage — but adjusted for the league offensive norm in a particular year as well as home ballpark.)

Pujols also has been just as durable — 1,705 games played so far — as the average of these 15 superstars.

As a group, what happened to our 15 icons? Over the remainder of their careers, their OPS dropped to 154, down about 10 percent. They stayed great — when they played. But they averaged only 944 games apiece for the rest of their lives. Stan Musial played the most (1,502 games), Jimmie Foxx the least (483). Pujols could fall anywhere on the spectrum.

But, in this Moneyball era, you analyze the average outcome — the most likely scenario — before you ink a vast 10-year contract. All teams have their own proprietary models. But how much different from this one can they be?

Here’s the proposition the Angels accepted: They’ll probably get (average case) 944 games from Pujols — the equivalent of six full seasons, though probably broken up by injuries over more years. And he’ll hit about 90 percent as well as he has in the past. I think I just felt myself shudder.

In effect, the Angels are willing to pay $42 million a year ($252 million divided by six years of production) for a 90-percent version of the old Albert.

For me, this is pushing the “pay-up-for-quality” maxim to the breaking point. But the Angels have as many extra factors in the picture as a team could. After 80- and 86-win seasons, Pujols plus Wilson will probably haul the Halos back above 90 wins and into the playoffs. Instant payback.

By the time the Dodgers are bought by a group led by Magic Johnson or a sheik or Stan Kasten (his group’s been formed, funded and lurking for months), the Angels may be the top mouse in Southern California with a fresh, fatter regional-cable TV deal due up for negotiation in ’15.

Every team is in its own smaller version of the Pujols dilemma. How much do we pay, and how soon must we jump, in a rising market?

So far, the Nationals have been shut out. They wanted Buehrle but wouldn’t offer him a fourth year. Their only other logical play, besides a trade for a center fielder (perhaps Angel Peter Bourjos, 24) is Roy Oswalt. He fits the “pay-up for a star” mold, except he’s tarnished. Temporarily.

Oswalt (159-93, 3.21 ERA) has been an even better pitcher than Buehrle, but he had an injury (back) that limited him to 23 starts (3.69 ERA) in ’11. If Oswalt were provably healthy, the Nats would offer him their $35-$40 million Buehrle deal in an instant. But if Roy were in mint condition, he might still be a Phillie. This is where a team needs a theory of free agency. You can’t always be right but you can always try to play the best odds.

The Oswalt type is where you want to lay your bet. In happy moods, the Nats say, “Jordan Zimmermann could become another Oswalt.” On stats through 33, Oswalt most resembles Roy Halladay, Jimmy Key, Jim Bunning, Bret Saberhagen, Tim Hudson, Mike Mussina, Kevin Brown, John Smoltz and David Cone. Nice company. Most aged well, some didn’t. Oswalt lost a foot off his fastball last year and threw more change-ups. Will the speed come back? With all his other stuff, how much does he need it?

Maybe the Nats should think back one year. Baseball overlooked Lance Berkman, after the first poor season of his life, in favor of first basemen with lesser careers: Carlos Pena, Derrek Lee and Adam LaRoche. The assumption: Berkman, a sure Hall-ballot player, must be old or hurt. But he wasn’t.

The Cardinals signed Berkman for half the guaranteed money that LaRoche got from the Nats. The “healthy” LaRoche got hurt. The “injured” Big Puma, 35, after taking a 45-percent pay cut, moved to the outfield, hit 31 homers, eerily duplicated his career slash line and starred in the World Series.

Just because one ex-Astros star can bounce back doesn’t mean another one will. How’s Roy’s back? Ask a doctor. But if you want him, don’t insult him. Give him what you offered Buehrle. If that’s not enough, let him go.

Remember, in free agency, you pay up for quality because the rest is junk; that is, unless you find Roy Oswalt marked down by accident.

Hey, compared with $126 million for Werth, he looks like a bargain.