In the more than two decades we’ve spent advising boards, investors, and chief executives themselves on CEO transitions, we have seen a fundamental disconnect between what boards think makes for an ideal CEO and what actually leads to high performance. That disconnect starts with an unrealistic yet pervasive stereotype, which is shaped in large part by the official bios of Fortune 500 leaders. It holds that a successful CEO is a charismatic six-foot-tall white man with a degree from a top university, who is a strategic visionary with a seemingly direct-to-the-top career path and the ability to make perfect decisions under pressure.

Yet we’ve been struck by how few of the successful leaders we’ve encountered fit this profile. That realization led us to embark on a 10-year study, the CEO Genome Project. Its goal is to identify the specific attributes that differentiate high-performing CEOs (whom we define as executives meeting or exceeding expectations in the role, according to interviews with board members and majority investors deeply familiar with the CEOs’ performance). Partnering with economists at the University of Chicago and Copenhagen Business School and with analysts at SAS Inc., we tapped into a database created by our leadership advisory firm, ghSmart, containing more than 17,000 assessments of C-suite executives, including 2,000 CEOs. The database has in-depth information on each leader’s career history, business results, and behavioral patterns. We sifted through that information, looking for what distinguished candidates who got hired as CEOs from those who didn’t, and those who excelled in the role from those who underperformed.

And when we compared the qualities that boards respond well to in candidate interviews with those that help leaders perform better, the overlap was vanishingly small. For example, high confidence more than doubles a candidate’s chances of being chosen as CEO but provides no advantage in performance on the job. In other words, what makes candidates look good to boards has little connection to what makes them succeed in the role.

But our most important discovery was that successful chief executives tend to demonstrate four specific behaviors that prove critical to their performance. We also found that when boards focus on those behaviors in their selection and development processes, they significantly increase their chances of hiring the right CEO. And our research and experience suggest that when leaders who aspire to the CEO’s office—87% of executives, according to a 2014 survey from Korn Ferry—deliberately develop those behaviors, they dramatically raise the odds that they’ll become high-performing chief executives.

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