Leaders know this intuitively: Quality time makes people feel more engaged. But how much time should you spend with each person who reports to you? Is there a magic number?

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It turns out there is: Six hours per week. That’s the result of a new survey of 32,000 people from research firm Leadership IQ. As part of a broader poll, respondents estimated how many hours per week they spent with their direct leaders. They also answered questions about how inspired they felt at work, how likely they were to recommend their organization to others, whether they were coming up with new ideas, and how interesting they found their jobs. As people rose from one to six hours spent with their direct leaders, they became 29% more inspired about their work. The study found a relationship between time with the boss and engagement. But the relationship is more complicated than more time always being better. The results also have interesting implications for corporate structures in general. In most cases, more time with the boss is a good thing. As people rose from one to six hours spent with their direct leaders, they became 29% more inspired about their work, 30% more engaged (that is, likely to recommend their company as a great place to work), 16% more innovative, and 15% more intrinsically motivated (finding something interesting in most of their tasks).

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But then, above six hours per week, all of these measures flattened out, or even declined. “I’m not exactly sure why six is the magic number,” says Mark Murphy, the CEO of Leadership IQ. “That could be how long it takes to get through some of the basics.” At that point, people say, “I can actually see there is some purpose to what I’m doing,” but beyond that, people feel, “I’ve got it now.” That’s the point where micro-management kicks in. Every study has its limits, and despite this one’s size, it has its flaws too. First, people are estimating how much time they spend with their leaders, adding up face time, phone calls, and emails (rather than keeping a time diary during a work week). Most of us have no real sense of how much time we spend emailing any one individual. Second, engagement is a function of many things. People who like their bosses may naturally spend more time with them, though Murphy’s analysis did try to control for this. People who ranked in the lowest quartile on their answer to “I feel that my work is valued by my direct leader” still reported more engagement when they spent six hours with their bosses, vs. one hour, and the rise wasn’t that far off the rise for the overall sample. Working From Home Can Still Work There are several interesting implications to this six-hour finding. One is that the backlash against work-from-home arrangements has missed the mark. “There really is a point of diminishing returns here,” says Murphy. “Sitting with the boss for 20 hours a week doesn’t help.” People start to think, “There’s only so much classroom time I can take. Now I need to go do some homework,” he says. Working from home one to three days a week will still leave space for six hours of face-to-face interaction, and since being on the phone counts too, employees could be remote most of the time. Of course, “if you are leading remote employees, don’t think you can get away with zero,” Murphy says of interactive time. But you need not be hovering over someone’s desk 10 hours per day to keep her engaged.

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You Can’t Really Manage More Than Seven People The second interesting implication is that organizations may have become too flat. To be sure, some interaction can involve multiple team members, but not all of it. In follow up questions, Leadership IQ found that a lot of this interactive time was, in fact, one-on-one. If managers need to interact with direct reports for six hours per week, they can’t really manage more than six or seven people. “You can have 50 employees, but you’re not really managing 50 employees. You can monitor them, but you can’t really manage them,” says Murphy. “There are limits on span of control.” It also calls into question the idea that people can handle both manager and individual contributor roles simultaneously. This only works if such “player-coaches” manage just three or four people and have corresponding limits on their expected individual productivity. The good news, however, is that those six hours need not be formal, nor do they need to be manager-driven. “If you try to instantly go from zero to six, it’s kind of hard and a little weird,” says Murphy. Blocking six hours per employee on the calendar “feels very contrived.” But if you focus on having “one really good, meaningful conversation this week,” then team members will start coming to you whenever they have questions or want feedback. These team member-initiated conversations are much more valuable for making people feel like you truly want them to succeed.