If you fill-up the bases, then every single hit of a bat-based attack will earn you a run. If your opponent blocks one of your attacks, that is considered a ball. The opposite is not true, as every attack you land with a bat in a combo will count as a base hit (though multi-hitting special attacks, such as his Super Spin Swing will only count as a single hit).
Though, thankfully, combos only count as a single out, no matter how long they are. Miss three times, and you will strike out. If you swing the bat and miss, you will earn a strike. If you hit the opponent with a bat-based attack, you will take a base.
At the bottom of the screen, there is a little baseball diamond and a counter that will track strikes, runs, balls, and outs.