Can my pitcher finish the batter after reaching the pitch limit?

Yes. If a pitcher reaches their limit while facing a batter, they may keep pitching until:

• the batter reaches base,
• the batter is put out, or
• the third out ends the half-inning or the game.

They can't start a new batter once they've reached the limit.

For rest days, the pitch count is taken at the first pitch to each batter. So if a pitcher starts a batter on pitch 64 and finishes them on pitch 67, their rest is based on 64 (three days, not four), as long as they don't pitch to another batter.