The units considered to be elite in their times were not necessarily the ones most effective in combat.........I mean like it's been said, the people with higher ranks and status were elites even if they sucked at combat.
In medieval times, all barons/knights, were elites. In this instance they were actually very effective on the battlefield too.
Another example cited before, the Pretorian guard, they were chosen on the basis of their social status, not fighting ability.