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“I think Mitt wants to maximize opportunity while at the same time avoiding disaster,” Mr. Stemberg said. “Say you want to open a new store. Mitt would say, ‘Well, if it succeeds, how good will it be? Really big? That’s great.’

“Then, he’ll have you think through if things don’t go well. ‘What could happen here?’ If you are investing the entire capital of your company to make things work, for instance, that’s too much of a downside.”

When Mr. Romney entered politics and ran against Edward M. Kennedy for a U.S. Senate seat in 1994, his candidacy appeared audacious, if not downright quixotic: Ted Kennedy was a longtime Democratic incumbent in a liberal-leaning state, the surviving scion of a political dynasty and a larger-than-life fixture in national politics.

Once again, however, Mr. Romney had done the math. Mr. Kennedy had testified in the much-publicized 1991 rape trial of his nephew, William Kennedy Smith. He had publicly apologized for drinking and womanizing. He seemed diminished, with pollsters detecting a lessening of public support they labeled “Kennedy fatigue.”

Mr. Romney ultimately lost the race — but not for a lack of confidence. He later said that he figured Mr. Kennedy “was going to be kind of a doddering old fool. I’d be able to crush him like a grape.”

Time and again, a former business associate said, Mr. Romney follows a three-step pattern when taking on major challenges: first, pooh-pooh and stress-test the idea; second, crunch data to come up with the best possible plan; third, attack the problem with stubborn determination.

In high school, Mr. Romney ran cross-country. He was more tortoise than hare. As his biographers recount, he once failed to pace himself during a 2.5-mile race held during halftime of a football game.

Cramping and falling down repeatedly, Mr. Romney finished dead last. He crawled across the finish line. He did not give up.

Mr. Romney’s successful turnaround of the scandal-ridden Salt Lake City Olympic Games — and his ongoing, six-years-and-counting bid for the White House — could be viewed as variations on the same theme.

“I think he’s very self-assured,” Mr. Helman said. “He believes strongly in his own abilities. He loved to say, and his dad loved to say, too, ‘The Romneys were built to swim upstream.’ He’s wired to tackle tough problems, and to think, ‘If not us, who?’

“So it’s part of his duty to step in. But he has two counterforces. On one hand, he’s a risk-averse person who has been very, very cautious. On the other hand, he feels destined to accomplish big things. It can be hard to reconcile both.”

A ‘natural diplomat’

One gaffe was all it took. During a 1967 television interview, presidential candidate George Romney said he had been subjected to “the greatest brainwashing” by American generals and diplomats during a visit to Vietnam.

George Romney’s campaign never recovered. Among political observers, it’s an article of faith that Mr. Romney — who adored and idolized his father — has vowed to avoid the same mistake.

Mr. Romney’s sister, Jane, concurs.

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