DRAKE BAER

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A career doesn't move linearly,LinkedIn founder Reid Hoffman famously advised — it can ratchet up suddenly with one critical insight, meeting, or opportunity.

You call it a big break.

Every success story has one.

Even luminaries like Sheryl Sandberg, Steve Jobs, and Howard Schultz had a moment where the path of their future clicked into focus.

Here are the big breaks that helped these execs build 10-digit fortunes.

Richard Branson discovered a singer who became a huge success.

Courtesy of Richard Branson via LinkedIn

When Richard Branson was 16, he started a magazine called Student. But his big break came six years later when he opened a recording studio and brought in a singer named Mike Oldfield.

Oldfield released "Tubular Bells," a mega-single that would stay on the U.K. chartsfor 247 weeks.

"On the back of that, we built a record company," he told us, "and one thing led on to another from there."

Henry Ford impressed the mayor of Detroit.

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In 1898, Henry Ford won the loyalty of Detroit mayor William C. Maybury after he built a carburetor, for which Maybury awarded him a patent.

Maybury would prove instrumental in helping Ford become an automobile maker.

"Maybury's support, combined with Ford's bold ideas and charisma, helped assemble a group of investors who contributed some $150,000 to establish the Detroit Automobile Company in early August 1899,"says History.com.

That allowed Ford to quit his day job at the Edison Illuminating Company — and found the companies that would make the first mass production cars.

Bill Gates landed an IBM contract.

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In 1980, Bill Gates had dropped out of Harvard and was leading a tiny company called Microsoft that was trying to worm its way into the nascent personal computer industry.

He — and the company — soon got a giant break, in the form of IBM.

Big Blue wanted to bring a cheap personal computer to market fast. It contracted Microsoft to provide the operating system. At the time, it didn't have one to sell, but soon cobbled one together.

Steve Jobs got the idea to start Apple from a computer shop owner.

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In the fall of 1975, a spiritual wanderer/aspiring techie by the name of Steve Jobs noticed that his Californian friends were getting excited about model-kit computers that you build for your at-home use.

He asked his buddy Steve Wozniak if he'd like to build a circuit board for the computer kit enthusiasts, making them for $25 and selling them for $50.

Then he went to the electronics shop — and things got interesting.

Cal Newport describes the scene:

Steve arrived barefoot at the Byte Shop, Paul Terrell's pioneering Mountain View computer store, and offered Terrell the circuit boards for sale. Terrell didn't want to sell plain boards, but said he would buy fully assembled computers. He would pay $500 for each, and wanted fifty as soon as they could be delivered.

Jobs jumped at the opportunity to make an even larger amount of money and began scrounging together startup capital. It was in this unexpected windfall that Apple Computer was born.

So without Terrell's beckoning, we wouldn't have Apple.

Jim Koch found a "wasteland of beer."

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Jim Koch founded Boston Beer Company, brewer of Sam Adams, in 1984.

By 2013, he was a billionaire.

The break that enabled Boston Beer to become a $600-million-in-annual-revenue company was an insight.

Back in the '80s, American beer was "basically a wasteland," he says, with beer drinkers having to quaf one of two beverages — fizzy, weak-tasting mass-produced American beers or imports that grew stale by the time they got over here.

"There really wasn't an alternative that was rich, flavorful beer delivered fresh," he says.

So, as an entrepreneur does, he made one called Sam Adams.

Larry Page learned how to make money on search.

Getty / Justin Sullivan

Before 2002, Google was barely bringing in any revenue.

Then Larry Page and Sergey Brin learned of Goto.com, a search company founded by serial entrepreneur Bill Gross.

Gross had what Page and Brin didn't: cash flow.

He "introduced a twist" to the business model, says Slate writer Will Oremus. "[P]aid search. Like the way companies bought ads in the Yellow Pages, websites could pay for top placement on the GoTo.com results page for a given keyword. This would push down spam results, Gross reasoned, because companies would have an incentive to buy ads for search terms that were actually relevant to their products."

So the Google guys made their own version of the mechanic — called AdWords Select — and revenue took off.

Sheryl Sandberg took a seat on a rocket ship.

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In 2001, Sheryl Sandberg had just moved to Silicon Valley after working in the public sector. She made a spreadsheet of qualities she wanted in possible jobs.

When she met with then-CEO of Google Eric Schmidt, she told him that Google didn't fit any of her spreadsheet's listed qualities.

His reply: "Don't be an idiot."

And then: "Get on a rocket ship."

As she explained in a Harvard Business School commencement speech, she did.

"When companies are growing quickly and they are having a lot of impact, careers take care of themselves," she told the grads. "If you’re offered a seat on a rocket ship, don’t ask what seat. Just get on."

Howard Schultz learned what a cafe was for.

Starbucks used to be a Seattle-based high end coffee supplier — until Howard Schultz ducked out from an industry conference in Milan in 1983.

Everywhere he went, he ran into cafés.

"There were 1,500 alone in the city of Milan, a city the size of Philadelphia," he said. "They were on every street corner, and all were packed."

Why were they packed? Not just because of the latté — which Schultz dubbed the "perfect drink" — but because he realized coffee was supposed to be enjoyed communally.

Starbucks, he realized, would be a place people could gather.

"It was like an epiphany," he said.