Facebook’s Sheryl Sandberg, author of the new book, “Lean In.” (Laurent Gillieron/AP)

Forbes magazine just released its annual list of the world’s billionaires, calling it a “record-setting year for women on the Forbes Billionaires list.”

I was cheered by this news. A record 138 women are now billionaires.

Then, I became a bit less cheery. Although 138 is a big number relative to the 104 women billionaires who made Forbes’ list last year, it’s a small number relative to the 1,426 billionaires that Forbes found around the world this year.

My mood spiraled down when I saw why many of these women made the list. They’re billionaires because of who they married or what they inherited, not what they did. Whether it’s Jobs, Mars, or Walton — two Walton women, Christy ($28.2 billion) and Alice ($26.3 billion), are the second and third richest women in the world — they didn’t make it on their own.

While a billion is a billion no matter how it came about, a billion earned is different from a billion inherited.

Among the 138 female billionaires, just 24 of them started her own business and only nine started her business without the help of someone else, as Forbes pointed out. Forbes also noted that, by contrast, most male billionaires are entirely self-made.

On the positive side, American woman are five of those nine self-starters: Oprah Winfrey (#503, $2.8 billion), Judy Faulkner  (#736, $2.0 billion), Meg Whitman  (#792, $1.9 billion), Sara Blakely (#1,342, $1.0 billion) and newcomer Tory Burch  (#1,342, $1.0 billion). Winfrey made her fortune in media and through her Harpo production company. Faulkner founded Epic Systems, an electronic health records software company. Whitman, who is now chief executive officer at Hewlett-Packard, earned her wealth largely as CEO of eBay. Blakely invented Spanx, a line of body-shaping undergarments, whose mission is “To help women feel great about themselves and their potential.” Burch is a fashion-designer and creator of the famous “Reva” ballet flats.

These lists, whether it’s of 138, 24, 9 or 5 women, made me think of a Ted talk by Sheryl Sandberg, Facebook’s chief operating officer, who noted the great advancements that women have made in absolute numbers, but how unremarkable those advancements are in relative terms. “The numbers tell the story quite clearly: 190 heads of state — nine are women. Of all the people in parliament in the world, 13 percent are women. In the corporate sector, women at the top, C-level jobs, board seats — tops out at 15, 16 percent,” Sandberg reported in December 2010.

The figures also made me think of Sandberg’s book “Lean In” where she writes about what women need to do to succeed in the office. In short, women must promote themselves and stay engaged — Sandberg phrases it as sitting at the table, raising your hand and leaning in — while on the job. (The Wall Street Journal put together a list of perspectives on the book.)

Thinking about Sandberg’s advice drew me to the stories of these self-made American billionaires and what lies behind their success. Being smart and not afraid to take risks helps. In other cases, getting noticed makes a huge difference.

On this point, a remarkable fact stands out — the influence of Oprah Winfrey. Blakely says that her big break came when Oprah called Spanx one of her “Favorite Things.” As Blakely, who has created a foundation called “Leg Up” to help women entrepreneurs, says, “Everybody needs a leg up in starting a business.” A similar success came to Tory Burch after Oprah called her “the next big thing in fashion” in 2005. Burch established the Tory Burch Foundation “to support the empowerment of women and families.”  As for Sandberg, she interviewed Oprah at Facebook, calling her “an example to everyone that anything is possible” and has created the “Lean In Foundation” to encourage and support women to “lean in to their ambitions.”

Sandberg’s been criticized for placing too much blame on women, but she appears to be trying to change that through her work on the boards of two nonprofit organizations, Women for Women International and V-Day, that work to improve the lives of women around the world. (I became a donor to Women for Women International three years ago after seeing that Sandberg was on its board of directors.)

Maybe Sandberg sees these efforts as a way to help women around the world “Lean In” in their own way, just as Oprah may have seen her support for Burch and Blakely as helping  them succeed. What’s also seems to be true about these five billionaires and Sandberg, whose wealth is estimated to be $500 million, is that they may be self-made, but they know they didn’t succeed all by themselves.