As the game goes on, players get tired and their effectiveness can decrease. Atrocious or pitiful stamina usually won't cut it for a starter. I've heard it's good to have a guy with inept (4) or mediocre (5) stamina.
The reason for this is that they won't play too many minutes (assuming there are no foulouts, injuries or OT). In my experience, player with respectable (7) stamina or higher tend to get overplayed.