In MLB free agency, teams face the Albert Pujols dilemma: How much is too much?

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.

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First baseman Albert Pujols and pitcher C.J. Wilson made their first public appearances with the Angels Saturday at a raucous pep rally outside Angel Stadium. The two free agents signed deals for a combined $331.5 million. (Dec. 10)

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.