Middle managers don’t get lots of respect in the workplace. And for a variety of reasons, scholars have mostly studied the worth of CEOs and the efficacy of various management practices. But a new study suggests that frontline supervisors are far more important than many have thought.

In fact, replacing a poorly performing boss with a top-notch middle manager is roughly equivalent to adding one more worker to a nine-member team, the study concludes. “These bosses do matter, and they earn their pay,” says Kathryn Shaw of Stanford’s Graduate School of Business, co-author of a paper titled, “The Value of Bosses,” along with Stanford GSB’s Edward Lazear, and the University of Utah’s Christopher Stanton.

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