A winning team is one whose members all understand two things, above all else: "do what it is they do best to the best of their ability, and to always possess a great attitude in the process."
When we're selected to be a part of something, it's because we've done something that was deemed appealing to others. They don't expect us to show up and do something other than why we were selected, they expected us to do exactly what we were selected for. If something isn't broke, why try to fix it by doing something that's unnecessary. Not saying that we shouldn't think of ways to enhance our established appeal, but if said ways don't coincide with the established appeal, we should strongly consider not doing them.
A team is made up of several positions, so this means that it needs specify players to represent said positions. The best candidates are those who have had the most success, prior to the present opportunity. Success doesn't just represent accomplishment, but also attitude. A good performer, with a bad attitude, equates to a loser in the eyes of those who are truly out to win. A good performer + a better attitude = an excellent teammate.
So, in conclusion. To be deemed an asset, and not a liability, we must: do what it is we do best to the best of our ability, and always possess a great attitude in the process. This is not a complicated formula, in fact, it's the simplest one I understand to obtain success.