Pick the Best Players - No, not exactly!

You have an important project at work.  You need to assemble a team to complete the critical task.  Who do you select?  Pick the best people, of course.  Well, perhaps not.   As  Tara Nicholle Nelson   writes in Fast Company, 

"A-players Don’t Always Make Great Team Players. Motivated by credit, praise, promotions, and raises, Superstar employees are often amazing individual contributors. But they are not always amazing to work with.  When multiple A-listers are on one team, unless the culture aggressively fosters collaboration and cooperation, they can become competitive with each other, hoard resources, and spend way too much time focusing on what each other is doing, versus focusing on beating your company’s actual competitors in the marketplace."

I have always argued that team creation should involve picking the right players, not simply the best players.  Picking the right players means thinking about how they will complement one another.  Can they fit into certain roles on the team?  Do they have personalities that will enable them to collaborate effectively?  Are they all willing to put the organization's goals above their own personal or departmental interests?