I recently read this sentence in a New York Times article on telecommuting: “We know that those who work at home tend to put in longer hours and are often more productive.”

What? Is that the writer’s scientific conclusion? To me, it looks more like a note someone sends to his boss on why he isn’t coming in again today.

A lot of what I read about telecommuting assumes that it’s a good thing and that businesses should allow for more of it. The Times piece cites a survey by the Society for Human Resource Management that “found a greater increase in the number of companies planning to offer telecommuting in 2014 than those offering just about any other new benefit.”

We all hear lots of great anecdotes about productive people working at home in their pajamas or increasing their company’s performance over a latte at the local Starbucks. What’s missing here is data. So I asked Gallup’s best workplace scientists what they could find on telecommuting in our U.S. employee engagement database, which is the largest of its kind. The resulting discoveries offer a mixed picture at best.

On the plus side, people who work remotely less than 20 percent of the time are the most likely to be engaged of all employees: 35 percent of those employees are engaged, compared with an average 30 percent engagement in the overall U.S. workforce.

But active disengagement rises as employees spend more time off site. Among people who work remotely 20 percent to 50 percent of the time, 18 percent are actively disengaged. That number increases to 22 percent actively disengaged for employees who work remotely 51 percent to 99 percent of the time. And here’s a killer finding: People who spend all of their time working remotely are nearly twice as likely to be actively disengaged (23 percent) compared with those who telecommute less than 20 percent of the time (12 percent actively disengaged).

Pretty simple math here: Working remotely less than 20 percent of the time is very good for engagement, but doing so 100 percent of the time is very bad. That’s because actively disengaged employees aren’t just miserable, but they spread their misery among their colleagues. Remote employees may infect their colleagues via e-mail and phone calls, rather than by roaming the halls, but don’t kid yourself: They’re still doing damage to your company.

Yet people who work away from the office less than 20 percent of the time are, by far, the least likely to be actively disengaged— 12 percent vs. 18 percent for the U.S. workforce as a whole. Why is that?

My hunch is that people who can choose to work at home some of the time enjoy a culture of great workplace freedom — one where productivity trumps punching a clock. But my other hunch is that, while people love the freedom, they also draw immeasurable energy and inspiration from human interactions in the workplace. They feed off of being around their colleagues. And while working at home has many positives, the downside is isolation — no friends and no fun.

To many of us, sitting at our desks in our pajamas, going out for an extra-long workout, and then grabbing a really good coffee and logging on at Starbucks sounds like a pretty good work schedule. But when it comes to telecommuting, it’s possible to have too much of a good thing.

Jim Clifton is chairman and chief executive of Gallup. This column is adapted from a piece he wrote for Gallup’s the Chairman’s Blog.