I've been saddled with a poor performer in the group I'm managing, and I can't get rid of him because he's related to one of our top executives. He's really dragging us down, though. What, if anything, can I do about it?
First of all, you need to find out where you can get the most out of this person. And this means doing a full inventory of his strengths and weaknesses and figuring out where his strengths can best be used and his weaknesses least exposed. Even though he may come with a certain reputation or track record, try to look clearly at your needs and where he might fit in; you might be surprised at how well he performs in the right role.
Secondly, though, you need to be careful to manage your superior's expectations of your group's performance based on the strengths and weaknesses of your team, and this person in particular. You might say something like 'Here's what we're getting out of my team, but I don't have the full horsepower I need' so that you can prepare your bosses for where you might falter.
Over time, this can also be your opening to getting rid of the deadweight by emphasizing how critical the role is that this person is performing, and how much more you could accomplish with someone else. You could even frame it to your bosses in terms of a tradeoff, as in, if it's really so important to us that we do X well, then we need to get someone else in there. It's important, though, to discuss this in terms of your needs versus your problems so it doesn't seem like you're just complaining -- emphasize the additional results you could achieve if you could get person A or B.
I once worked with a director at a large consumer products company who was in a similar situation with an employee who was being protected by a higher-up. I advised him to try to trade this person out, but it wasn't something he could get done immediately. So this director made an ongoing case for why he needed someone with more skills in that person's role and why it was so important. He further identified two people within the organization who he thought would do a much better job and explained to his bosses why. After about six months, he finally managed to get his poor performer moved to a less critical job outside of his group, and one of his desired people into it. It took time and some finesse, but he got it done and that's the way you should approach your problem as well.
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