It’s not what you know. It’s who you know.

Conventional wisdom says that high-status mentors—star connections—help you get ahead at work. From CEOs to sports coaches to (yes) academic researchers, the protégés of titans have a disproportionately easy time advancing in their careers.

But do connections to stars help you stay ahead?

Our research (Buffered by reflected glory? The effects of star connections on career outcomes) suggests that the answer isn’t straightforward. Using data from the National Basketball Association (NBA) coaches and a follow-up lab experiment, star connections indeed helped candidates get jobs. And, once in those roles, the star-connected were less likely to be punished when performing poorly than those lacking star connections. That’s consistent with the idea that prestigious connections help you get ahead.

The surprise came when we looked at overperformance. When exceeding expectations, these protégés of industry titans were more likely to be fired and less likely to be promoted than their peers without star connections. In other words, the star-connected were buffered from the consequences of their own performance—they suffered less when performing poorly but benefited less when performing well. This buffering effect proved sticky—even nine years after having worked for a star, protégés were still more likely to get fired compared to their non-connected peers. If you are a manager who is hiring or evaluating talent, here’s the takeaway: Beware of overweighting star connections! Our research showed no evidence that the star-connected are better performers than anyone else. Evaluating the star-connected differently may be an irrational bias you want to avoid. Look carefully at the knowledge, skills, and performance of candidates and avoid being blinded by the radiance of past star connections.

If you are one of the lucky few to have a star connection, be cautious about emphasizing it. You may benefit by publicizing your connection to greatness when things aren’t going your way. However, when things are going well, it’s probably better to let your work speak for itself. Your star connection may be both a blessing and a curse. It helps you get a job and protects you when you aren’t meeting expectations. But it may also create a bar so high that you constantly struggle to reach it.