Spend a day with any leader in any organization, and you’ll quickly discover that the person you’re shadowing, whatever his or her official title, is actually in sales. These leaders are often pitching customers and clients, of course. But they’re also persuading employees, convincing suppliers, sweet-talking funders or cajoling a board. At the core of their exalted work is a less glamorous truth: Leaders sell.

So what kind of personality makes the best salesperson – and therefore, presumably, the most effective leader?

Most of us would say extroverts. These wonderfully gregarious folks, we like to think, have the right stuff for the role. They’re at ease in social settings. They know how to strike up conversations. They don’t shrink from making requests. Little wonder, then, that scholars have shown that managers select for this trait when assembling a sales force.

But there’s one teensy flaw: There’s almost no evidence this view about extroverts is true.

When social scientists have examined the relationship between extroverted personalities and sales success they’ve found the link to be, at best, flimsy. For instance, one of the most comprehensive investigations, a meta-analysis of 35 studies of nearly 4,000 salespeople, found that the correlation between extroversion and sales performance was near zero.

Does this mean instead that introverts, the soft-spoken souls more at home in a study carrel than on a sales call, are more effective? Not at all.

The answer, in new research from Adam Grant, the youngest tenured professor at the University of Pennsylvania’s Wharton School of Management, is far more intriguing. In a study that will be published this year in the journal Psychological Science, Grant collected data from sales representatives at a software company. He began by giving reps an often-used personality assessment that measures introversion and extroversion on a 1-to-7 scale, with 1 being most introverted and 7 being most extroverted.

Then he tracked their performance over the next three months. The introverts fared worst; they earned average revenue of $120 per hour. The extroverts performed slightly better, pulling in $125 per hour. Neither did nearly as well as a third group: ambiverts.

Ambiverts are people who are neither extremely introverted nor extremely extroverted. On Grant’s scale, ambiverts aren’t 1s or 2s, but they’re not 6s or 7s either. They’re 3s, 4s and 5s. They know how to assert themselves, but they’re not pushy.

In Grant’s study, ambiverts earned average hourly revenues of $155, beating extroverts by a healthy 24 percent. In fact, the salespeople who did the best of all, earning an average of $208 per hour, had scores of 4.0, smack in the middle of the scale.

What holds for actual salespeople holds equally for the quasi-salespeople known as leaders. Extroverts can talk too much and listen too little. They can overwhelm others with the force of their personalities. Sometimes they care too deeply about being liked and not enough about getting tough things done.

But the answer – whether you’re pushing Nissans or leading a major corporation – isn’t to lurch to the opposite end of the spectrum. Introverts can be too shy to initiate, too skittish to deliver unpleasant news and too timid to close the deal. Ambiverts, though, strike the right balance. They know when to speak up and when to shut up, when to inspect and when to respond, when to push and when to hold back.

Here’s the best part, however. Some of us are heavy introverts. Some of us are stalwart extroverts. But the vast majority of us are ambiverts.

The good news, then, is that in some sense we are all born to sell and equipped to lead. And that means a hidden but urgent challenge for organizations of every kind is to shatter the stereotype of who’s an effective leader. When we choose leaders, as when hiring managers choose salespeople, we’re understandably drawn to the gregarious, friendly types with their comfortable patter and ready smiles. But are they really the best?

We’d be far better off with those who take a more calibrated approach – who can talk smoothly but also listen keenly, who know when to turn on the charm but also when to turn it off, who combine the extrovert’s assertiveness with the introvert’s quiet confidence. In other words, in picking leaders, perhaps we should look for people a bit more like us.