The influence of your birthday—certainly something outside your control—may be small in the grand scheme of subsequent wealth and success. But even the most talented people in the world can point to coincidences that gave them a crucial edge. Frank cites the 60-year-old Gates: Despite growing up in the 1960s, the co-founder of Microsoft Corp. happened to attend the rare school that offered students unlimited access to computers.

Or consider the actor Bryan Cranston. After decades as a well-respected performer on television and film, the series “Breaking Bad” made Cranston, 60, a true star. But, Frank notes, Cranston almost didn’t get to play the show’s central character, Walter White. Both John Cusack and Matthew Broderick turned down the role before producers agreed to offer it to the less famous Cranston. “You can have talent, perseverance, patience, but without luck you will not have a successful career,” the actor has said.

Could Cranston or Gates have achieved wealth and fame without these lucky breaks? Of course it’s possible. But Frank’s thesis is that our economy is changing in ways that amplify the role of luck in making the difference.

Winner-take-all markets

For more than 20 years, Frank has been studying the rise of winner-take-all markets—fields of fierce economic competition where only a few top performers take home the bulk of the rewards. More and more of the economy is starting to look like sports or music, Frank says, where millions of people compete and the winners are paid thousands of times more than the runners-up.

Another example he gives is the humble neighborhood accountant. In the 20th century, the typical accountant was competing against nearby rivals. If you worked hard, there was a good chance of winning over the most lucrative clients in town. Today, neighborhood accountants face much more competition: Sophisticated global accounting firms can swoop in and sign up their biggest clients. Tax preparation, an accountant’s bread-and-butter, has been mostly swallowed up by two large players—H&R Block for storefront preparation and TurboTax online.

“Technology has enabled people who are best at what they do to extend their reach geographically,” Frank says. TurboTax was initially just one of a number of tax software programs on the market. But, as happened with search engines and social media sites, it was able to win over customers early and its competitive advantage snowballed. TurboTax now dominates online tax preparation—thousands of local accountants replaced by one company.

In these winner-take-all markets, luck can play a huge role. A simulation conducted by Frank shows how: Imagine a tournament in which every contestant is randomly assigned a score representing their skill. In this simple scenario, the most skilled person wins. The more competitors there are, the higher the score the winner will likely have.

Now, introduce chance by randomly assigning each participant a “luck” score. However, that score can only play a tiny role in the ultimate outcome, just 2 percent compared with 98 percent allotted to skill. This minor role for chance is enough to tilt the contest away from the top-skilled people. In a simulation with 1,000 participants, the person with the top skill score only prevailed 22 percent of the time. The more competition there is, the hardest it is for skill alone to win out. With 100,000 participants, the most skilled person wins just 6 percent of the time.

Frank writes:

Winning a competition with a large number of contestants requires that almost everything go right. And that, in turn, means that even when luck counts for only a trivial part of overall performance, there’s rarely a winner who wasn’t also very lucky.