People who feel healthy in body and mind tend to feel happier about their jobs. And people who hate their jobs are less likely to feel very good about their lives.

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These are hardly shocking revelations, but perhaps they are factors of employee engagement managers should consider more regularly, according to a new report by Limeade, a wellness consulting group that has an interest in promoting well-being initiatives.

According to the report, employees who say they enjoy very little support from their organization are much less likely to assess their overall well-being as high.

Nearly all employees who reported high levels of well-being and a high level of organizational support as high say they expected to be working for the same employer in a year, while those who reported less support and low well-being were significantly more likely to anticipate leaving.

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Surprisingly, perhaps, the percentage of those in the latter group who expected to remain in jobs despite reporting very little support and low well-being is high — 79 percent. Similarly, 65 percent of the same group said that they would recommend their current organization to others as a good place to work.

But whether employers are losing out through less-engaged workers or higher turnover, they need to do more to make their employees feel supported.

Limeade argues that support from supervisors, particularly mid-level managers who interact most regularly with employees, is more important in driving a sense of worker well-being than other popular targets of engagement initiatives, such as the physical work environment and social media.

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Although many wellness programs were originally developed as a way to get employees to become healthier and therefore reduce employer health costs, there is very little evidence that they have succeeded in that regard. As a result, wellness vendors and employers have increasingly shifted their attention to employee engagement, arguing that helping workers become healthier will make them happier and more productive.