I never thought I’d say this, but the big winners of the latest Republican presidential debate weren’t seasoned politicians like Jeb Bush or Scott Walker, but outsiders with little political experience who made their bones in the business world: real estate developer and reality show host Donald Trump, and Carly Fiorina, the former Silicon Valley CEO who landed sharp jabs at Trump and evidenced keen knowledge of just about every issue thrown at her.

In the hunger games of the 2016 GOP nominating process, these two type-A personalities will now be battling every day for bragging rights over who was better at their old jobs as business leaders.

We saw some of that during the debate on Wednesday. Trump couldn’t resist the opportunity to point out that Fiorina’s business decisions led to the “destruction of the company” she once ran, Hewlett-Packard. Fiorina, without missing a beat, jabbed Trump with his own business failings, saying he “ran up mountains of debt, as well as losses, using other people’s money, and you were forced to file for bankruptcy not once, not twice—four times."

For the record, Trump has never filed for personal bankruptcy. But the conventional wisdom in the media is that when all is said and done, they both kinda sucked in business, and for a time I was in that camp.

Consider the following: Despite Trump’s own garish (and hard to confirm) descriptions of his net worth, he has reigned over failed (and, yes, bankrupt) casinos and real estate, and nearly went insolvent himself. This is all after inheriting a fortune from his real estate developer-father. The younger Trump made some money back, but mostly as a marketer of his name and a reality show star.

Fiorina’s business record is likewise uninspiring, if not downright scary, again according to this conventional wisdom. Yes, she started her career at the bottom as a management trainee, but when she got to the top as CEO of computer maker Hewlett-Packard, she whiffed big time with ill-advised acquisitions (Compaq) and declining PC sales, and then topped it off with massive layoffs and a decimated stock price.

Then she got fired and hasn’t run a major company since.

Sounds like a race to the bottom, right? Well, a deeper dive into both of their records shows that the conventional bearish view of the Trump-Fiorina record in business is superficial and largely inaccurate.

Let’s start with Trump. Yes, in the early 1990s he was nearly insolvent, he was involved in a messy divorce, and his casinos were heading toward bankruptcy. Not a great place to be, and based on my experience covering business and finance, executives in that position rarely rebuild both their wealth and their career.

But Trump did, and his pivot was brilliant: He understood that his best attribute wasn’t as a land speculator—in fact, that’s what got him in trouble. But as a showman and brand manager, he’s near genius. By utilizing those skills, he began to rebuild the Trump brand piece by piece, first through books and then through relentless hype on television. Yes, he can be a blowhard and a nasty chauvinistic prick. But a lot of people who got to know him also liked the image he began to cultivate: that of a man who spoke straight and exuded wealth even if he had lost nearly all of it.

This brand got his name on plenty of high-end buildings in New York City, even if he doesn’t outright own them, allowing him to collect a regular fee with almost no risk. This brand gave him a reality TV show, The Apprentice—successful thanks to Trump’s unique way of firing people. It’s why, for all his rhetorical excesses, he still leads in the polls, even if he doesn’t know the difference between the Kurds and the Quds.

Is he worth $10 billion, as he incessantly reminds everyone almost every time he opens his mouth? I think the number is closer to $4 billion, as estimated by Forbes, which I am told was derived after a fair amount of research. Still, that’s pretty damn good for someone who was basically broke about 20 years ago and didn’t rely on insider trading to make his fortune back.

The Fiorina story is a bit more complicated, because she was fired from her last business job as CEO of HP after massive layoffs and a controversial acquisition of Compaq. “Despite such carnage,” writes one of her fiercest critics, Yale University management school professor Jeffrey Sonnenfeld, “Fiorina pocketed over $100 million in compensation for her short reign—including a $65 million signing bonus and a $21 million severance.”

Trump cited Sonnenfeld’s criticism at Wednesday night’s debate, saying: “The head of the Yale business school, Jeffrey Sonnenfeld, wrote a paper recently: one of the worst tenures for a CEO that he has ever seen, ranked one of the top 20 in the history of business. The company is a disaster and continues to be a disaster. I only say this: She can’t run any of my companies, that I can tell you.”

Given a chance to respond, Fiorina said: “Jeffrey Sonnenfeld is a well-known Clintonite and honestly had it out for me from the moment that I arrived at Hewlett-Packard.”

Let’s consider the sources: Trump is running against Fiorina, and Sonnenfeld (whom I personally like) is a well-known Democrat and considered a supporter of party frontrunner Hillary Clinton (though he clarifies that he “votes for the person, not the party”).

In an email, Sonnenfeld responded to Fiorina’s criticism: “This is the pathetic maneuvering of a peevish, imperious person who does not like to be criticized. Instead of addressing the facts, she discredits the critic—and avoids addressing the public facts…She sliced shareholder wealth in half in five years and was paid over $100 million for this accomplishment.”

The S&P 500 was only down 7 percent those years, Sonnenfeld continued. The only stock pop under her reign was the 7 percent jump the moment she was fired. If the board was wrong, the employees wrong, and the shareholders wrong, why in 10 years has she never been given another public company to run?

Fiorina worked about six years at HP from 1999 to 2005, so she did indeed make a lot of money. But she is hardly the most overpaid CEO in corporate America, either then or now.

HP’s stock price did get hammered during the Fiorina years, as did those of dozens of technology companies because of the Internet bubble that burst just after she took over as CEO. In the face of that maelstrom, Fiorina had to cut jobs or else the company wouldn’t have survived—which it did.

I’m not trying to make light of Fiorina’s messy record at HP. She made mistakes like every other CEO I have met, and her mistakes did in fact get her fired. But again, some context here: HP didn’t need a government bailout because of horrible decisions made by managers, like those who ran Citigroup, where our current Treasury Secretary Jack Lew got some of his private-sector experience around the time of the 2008 financial crisis.

In fact, according to one of the board members who fired Fiorina, longtime venture capitalist Tom Perkins, it was Fiorina’s tenacity during a turbulent time that may have gotten her fired but also set the stage for HP’s future growth.

The problem with comparing the Trump-Fiorina business records is that Fiorina has the distinct disadvantage of running a public company that answers to public shareholders. Trump, meanwhile, runs a privately held personal fiefdom, the Trump Organization, that answers to The Donald and no one else.

They both have a lot to brag about. In fact, they would make a great ticket if they didn’t hate each other so much.