Thankfully, running the bases works well. Using the control stick, just hold it down in the direction you want your player to run. When you have multiple baserunners to worry about, tapping the Z button allows you to switch among them; although, the game will automatically run players forward as you control whatever player is at bat.
In the end, The Bigs will live or die on its controls. From what we've seen, its Wii incarnation should be able to survive with awesome batting and pitching mechanics; however, fielding could be an issue. Hopefully it gets sorted out before the game ships; 2K Sports is going to have to hurry though, as The Bigs will be taking the field on June 25.