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There is a key scene near the end of “Moneyball” when Oakland Athletics’ general manager Billy Beane (played with great energy and charm by Brad Pitt) watches as his whiz kid statistician Pete Brand (Jonah Hill) shows him a video of a hulking minor league player afraid to run the bases who wallops a long fly ball, rounds first, trips and scrambles back to the bag.

 “He doesn’t realize he’s hit a home run,” says Mr. Brand. It is a metaphor he offers his boss, too driven to enjoy the amazing success of a team that’s broken the record for successive victories and amassed a won-loss record equal to the New York Yankees, on a payroll about 75 percent smaller.

But Mr. Beane, as played by Mr. Pitt with toothy smiles and gum-chomping folksiness that barely mask a high-wire intensity, is not able to see the fun of it, “the romance of baseball,” as he mockingly says. He can only fault himself, flashing back on his own failed baseball career, when the team is eliminated in the playoffs. “None of it matters if you don’t win the last game,” he says. He is Vince Lombardi on speed.

The movie, based on the book of the same name by Michael Lewis, focuses on the A’s amazing 2002 season in which Mssrs. Beane and Brand, forced by the loss of key players and hamstrung by a paltry payroll, attempt to reshape the national pastime by developing a winning team with a roster of cast-offs and has-beens, “an island of misfit toys,” as Mr. Brand explains. Their formula? “We’re card counters at the blackjack table,” Mr. Beane says. They pore over data and use statistics to help them spot diamonds in the rough, the promising players the other teams do not want. Beane wheels and deals to assemble his odd cast of characters, firing his chief scout (Ken Medlock), going toe-to-toe with his stiff-necked manager (Philip Seymour Hoffman) and playing head games with his players to get them to see baseball the way he does. “Everyone wants to attack,” he tells them. “Let the game come to you.” But mostly it comes down to getting on base and scoring runs – nothing else matters, not bunting, stealing or fielding.

At times the movie, like Icarus, overreaches, spinning into a classic Greek drama played out on a baseball diamond. Mr. Beane is the tragic hero, too superstitious to attend his team’s games, too flawed to appreciate their incredible victories. TV announcers and opposing players and coaches are a chorus of voice-over critics, castigating Mr. Beane’s methods and mocking his results. “They call it money ball, I call it a ticket on the Titanic,” says one.

If most of the hidebound baseball world dismisses Beane’s methods, the Boston Red Sox get it. The Sox offer him the GM job at the end of the 2002 season, and later hire the uber-statistician Bill James. Utilizing Beane’s methods, Boston goes on to win its first World Series in 86 years.

“How can you not be romantic about baseball?” Mr. Beane finally concedes at the end, sounding not quite convinced.

And then over the closing credits, we learn he’s still at it, still trying – and failing – to win the last game of the season for Oakland. Hey, Billy, want to try your luck somewhere else? Wrigley Field and the Cubs are romantic losers too.