Mrs. Fiorina tries to obscure these harsh realities with a blizzard of her own “facts.” On the campaign trail, for example, she speaks of having doubled her company’s revenues. However, most of that increase came from adding in Compaq’s sales, which is a misleading way to calculate revenue growth.

While some of the intricacies of Mrs. Fiorina’s performance may elude voters amid the dust storm that she has kicked up, her compensation won’t. She banked $21 million in severance payments as part of the more than $100 million in compensation she received during what one critic called her “destructive reign of terror” (which included pushing for H.P. to acquire five corporate jets.)

In the course of her losing Senate run in 2010, she was also attacked for the 30,000 layoffs that occurred at H.P. during her tenure. That’s not entirely fair — the entire technology industry was going through a downsizing and H.P.’s total employment ultimately climbed back up — but it was deadly effective politics that could doubtless be repeated in 2016.

Less attention has been paid to her time at Lucent Technologies, where she rose through the marketing ranks, learning the sales techniques that she is now putting to good use on the stump.

Soon after she left, Lucent veered off a cliff, and while she was never the chief executive, part of the company’s collapse stemmed from overly aggressive sales and loans to financially shaky customers made under her supervision.

Strikingly few former colleagues have come to Mrs. Fiorina’s defense. And her most prominent advocate, the venture capitalist Tom Perkins, has his own challenges; last year, he compared the criticisms of wealthy Americans to the attacks on Jews during Kristallnacht.

In a recent essay, Mrs. Fiorina noted that many other successful business leaders — Steve Jobs, Oprah Winfrey, Walt Disney and Michael Bloomberg — were all fired at one point in their careers.