Yes. And it's not that they can't function, but it's the sense of the moment, the close game, that allows them or fuels them to achieve that heightened level of performance that insulates them from the excitement or pressure building about them and separates them from their teammates.

You made a good point about relievers and closers, in particular,being a bit strange and bizarre, which is like a built in mechanism that helps them cope with the daily pressures of their job, and is reflected in their appearance, often a hair or beard style that sets them apart from others. Of course, the rule isn't absolute, but the prototypical closer is very introspective and usually, despite his quirkiness, has limited interaction with his teammates. Closers also have relatively little to say to the press.

Because of this specialized and conditioned focus and tunnel vision, there aren't many closers in the coaching ranks after the careers are over. You'll always see former catchers rise fastest in the managerial ranks and in tv commentary. They are the natural extroverts, the link between the pitching staff and position players, the interpreter between management and players, the field leader.

The closer's trsits, I'd argue, are shared by kickers in football. They exist in their own world until called upon to perform, often in high pressure.