As long as you go into the playoffs in the NBA with Big Core (3, or 4, or 2), you have a decent shot at going as far as you your team's talent should take you. In the NHL, there is an extra emphasis on the hot goalie, like birther Tim a few years ago. In the NFL, it definitely comes down to having a healthy roster. In baseball, it is roster health and quality of the pitching staff.
Somehow, with hitting being so difficult, it does seem feeling the pressure may impact baseball more than the other sports (except for free throw shooting).