Leaders don’t matter. That might seem hard to believe. Any large group needs a leader to function, right? How good can an orchestra be without a conductor? From Zubin Mehta to Leonard Bernstein, great conductors seem an integral component of great classical music. Someone needs to make sure the woodwinds don’t come in too early and the percussionists don’t drown everyone else out. The Orpheus Chamber Orchestra, though, has received multiple Grammies and is regarded as one of the finest orchestras in the world — without a conductor. It turns out that professional musicians can organize themselves without a formal leader just fine.

That’s all well and good for an orchestra, but surely a company the size of GE couldn’t function very well for very long if it didn’t have a CEO. That’s true. But the fact that GE needs a CEO doesn’t mean that it matters who the CEO is. There are three reasons — first laid out in a classic article by sociologists Stanley Lieberson and James F. O’Connor — why the identity of the leader probably matters less than you think.

1. External Constraints. Most organizations have competitors. The United States, for example, is the world’s most powerful country, but other countries always make themselves felt. They can and will counter many of the things the United States might want to do. In the corporate world, the strongest company in any industry almost always has competitors who are close to being peers. Unless you’re a monopoly, you can’t set prices at whatever level you want, for example. So whatever a leader, be it a president or CEO, might want to do, her options are limited by external pressures.

2. Internal Constraints. Large organizations also have internal politics that can limit a leader’s freedom. Whatever President Obama wants to do, what he can do is limited by Republican opposition in the House and Senate. Most CEOs have more authority over their companies than the President does over the government, but no matter how determined she might be to make radical changes, a CEO usually needs to take into account the internal dynamics of the company she leads.

3. Leader Selection Systems. Despite internal and external constraints, we can all think of situations where a leader has plenty of room to make choices. That’s why successful companies put so much effort into choosing their leader and why directors often describe choosing a new CEO as their most important job.

The problem is that it’s precisely all the effort that goes into picking leaders that makes any individual leader’s identity unimportant. Let’s say your company spends years evaluating candidates to be its next CEO. It observes every one of them closely in their positions, it interviews all of them over and over again, it even asks the candidates to rank each other. All that effort means that you should be confident that whoever gets picked will be good at the job. If she isn’t very capable, how did she pass all those tests?

But let’s take a look at the candidate who came in second. If your second choice almost made it to the top during the rigorous review process, how different could he be from your first choice? Your system for selecting leaders was looking for something particular, and even though the second candidate didn’t fit as well as the first one did, if you’re drawing from a large enough pool of candidates, he is almost certainly pretty close.

So the difference between the person who got the job and the person who almost got the job is probably pretty small. Throw in external and internal constraints, and the marginal difference in outcomes for your organization, depending on which one you chose, is tiny. The leader you choose might be enormously skilled, but, most of the time, that leader is also quite replaceable. With some exceptions, researchers from organizational behavior to economics to political science have come to this conclusion.

If leaders don’t matter, though, how do we explain people who really do seem to have changed history? From demonic politicians like Adolf Hitler to dazzling executives like Steve Jobs, we can all think of people who reshaped the world and were not, in any sense, replaceable. That will be the topic of my next blog post.