As Election Day approaches, President Obama is sharing a few important things about himself. He has impressive musical pitch, he told an Iowa audience. He is "a surprisingly good pool player," he informed an interviewer - not to mention (though he does) a doodler of unusual skill.

Barack Obama is a voraciously competitive perfectionist. Aides and friends say so in interviews, but Mr. Obama's own words of praise and derision say it best: he is a perpetually aspiring overachiever, often grading himself and others with report-card terms like "outstanding" or "remedial course" (as in: Republicans need one).

As he faces off with Mitt Romney, the Republican nominee, Mr. Obama's will to win is in overdrive. He is cramming for debates against an opponent he has called "ineffective," raising money at a frantic pace to narrow the gap with Mr. Romney and embracing the do-anything-it-takes tactics of an increasingly contentious campaign.

Mr. Obama's obsession with virtuosity and proving himself the best are remarkable, those close to him say. (Critics call it arrogance.) It is a core part of his worldview, friends say, formed as an outsider child who grew up to defy others' views of the limits of his abilities. When he speaks to students, he emphasizes living up to their potential.

"He has a general philosophy that whatever he does, he's going to do the very best he can do," Marty Nesbitt, a close friend, said.

When Mr. Obama was derided as an insufferable overachiever in an early political race, some friends were infuriated; to them, he was revising negative preconceptions of what a black man could achieve.

But even those loyal to Mr. Obama say that his quest for excellence can bleed into cockiness and the charge that he tends to overestimate his capabilities. The cloistered nature of the White House amplifies those tendencies, said Matthew Dowd, a former adviser to President George W. Bush, adding that the same happened to his former boss.

For someone dealing with the world's weightiest matters, Mr. Obama spends surprising energy perfecting even lesser pursuits. He has played golf 104 times since becoming president, according to Mark Knoller of CBS News, who monitors his outings, and he asks superior players for tips that have helped lower his scores. He decompresses with card games on Air Force One, but players who do not concentrate risk a reprimand.

His idea of birthday relaxation is competing in an Olympic-style athletic tournament with friends. The 2009 version ended with a bowling event. Guess who won, despite his history of embarrassingly low scores? The president, it turned out, had been practicing in the White House alley.

When he reads a book to children at the annual White House Easter Egg Roll, Mr. Obama seems incapable of just flipping open a volume and reading. In 2010, he began by announcing that he would perform "the best rendition ever" of "Green Eggs and Ham."

"He's shooting for a Tony," joked Arun Chaudhary, his former videographer. (Mr. Obama has already won a Grammy, in 2006, for his reading of his memoir, "Dreams From My Father" - not because he was a natural, said Brian Smith, the producer, but because he paused so many times to polish his performance.)

Asked if there was anything at which the president allowed himself to just flat-out fail, Mr. Nesbitt gave a long pause. "If he picks up something new, at first he's not good, but he'll work until he gets better," he said.

Mr. Obama's fixation on prowess can get him into trouble. Not everyone wants to be graded by him. Mr. Dowd said he admired Mr. Obama, but added, "Nobody likes to be in the room with someone who thinks they're the smartest person in the room."

Even some Democrats have been irritated by his tips on topics ranging from how to shake hands on the campaign trail (look voters in the eye) to writing well ("Think three or four sentences ahead," he advised).

While Mr. Obama has given himself high grades for his tenure in the White House, many voters don't agree, citing his handling of the economy, his unfulfilled pledge to unite Washington, and his claim that he would achieve Israeli-Palestinian peace.

Those were not the only times Mr. Obama may have overestimated himself: he has also had a habit of warning new hires that he would be able to do their jobs better than they could.

"I think that I'm a better speechwriter than my speechwriters," Mr. Obama told Patrick Gaspard, his political director, at the start of the 2008 campaign, according to The New Yorker magazine. "I know more about policies on any particular issue than my policy directors. And I'll tell you right now that I'm going to think I'm a better political director than my political director."

Though he never ran a large organization before becoming president, he initially dismissed internal concerns about management and ended up with a factionalized White House and a fuzzier decision-making process than many top aides wanted.

Now Mr. Obama is about to receive the ultimate judgment on his performance from the American people. It is a moment, aides say, he has been craving: during some of the darker days of his tenure, he told them he wanted the country to evaluate him not in isolation, but in contrast to the Republican alternative. The tough, often successful attacks from the right have hardened and fueled him, aides say, driving him to prove that "we're right and we're better," as one ally put it.

As far back as 2008, Mr. Obama's assessment of Mr. Romney was scathing. On the day Mr. Romney dropped out of the presidential race that year, Mr. Obama told reporters the former governor was a weak candidate who made "poorly thought out" comments.

This February, in an otherwise placid meeting with Democratic governors, Brian Schweitzer of Montana asked Mr. Obama if he had what it took to win the 2012 race.

For a moment Mr. Obama looked annoyed, a White House aide said. Then he came alive. "Holy mackerel, he lit up," Mr. Schweitzer said.

No matter what moves Mr. Romney made, the president said, he and his team were going to cut him off and block him at every turn.

Mr. Obama has been working at a furious pace, headlining three times as many fund-raisers as George W. Bush in his 2004 re-election campaign, according to Mr. Knoller.

At one of his farewell meetings for White House interns, Mr. Obama dispensed some life advice.

"When you all have kids, it's important to let them win," he said with a smile. "Until they're a year old. Then start winning."

Kitty Bennett contributed research.

The New York Times