My friend wants to play basketball with us but I'm not going to invite him.
Why don't you want to invite your friend to play basketball?
He's an awful player and he'll just hold the game back
It's not nice to exclude your friends from something. If he isn't a good player, you should work with your other friends to help improve. That way no one's feelings will be hurt.
His feelings won't be hurt, he enjoys being the worst.
I highly doubt it's not going to hurt his feelings. I would recommend splitting up the teams so that people skill sets will make it even. This will prevent your friend from getting upset with you.