JMoff’s got it right. There’s a lot of little things in the scoring rules that can easily trip someone up, and this is one of them. In this case, the rules make whether the batter/runner reaches 1st on the uncaught 3rd strike the determining factor.
Ordinarily, if a runner advances because of a WP of PB, that’s how the movement to the new base is accounted for. But 10.12(f) changes the definition of a WP/PB slightly to make it dependent on whether or not the batter/runner reaches 1st safely, and 10.13’s comment reinforces that thought.
The thinking is a lot like a hit not being scored if there’s a force out on the ball. Thankfully that’s not a situation that comes up very often.
10.12(f) The official scorer shall not charge an error when a runner or runners advance as the result of a passed ball, a wild pitch or a balk.
(2) When the catcher recovers the ball after a wild pitch or passed ball on the third strike, and throws out the batter-runner at first base, or tags out the batter-runner, but another runner or runners advance, the official scorer shall score the strikeout, the putout and assists, if any, and credit the advance of the other runner or runners on the play as a fielder’s choice.
10.13(a) The official scorer shall charge a pitcher with a wild pitch when a legally delivered ball is so high, so wide or so low that the catcher does not stop and control the ball by ordinary effort, thereby permitting a runner or runners to advance. The official scorer shall charge a pitcher with a wild pitch when a legally delivered ball touches the ground or home plate before reaching the catcher and is not handled by the catcher, thereby permitting a runner or runners to advance. When the third strike is a wild pitch, permitting the batter to reach first base, the official scorer shall score a strikeout and a wild pitch.
Rule 10.13 Comment: The official scorer shall not charge a wild pitch or passed ball if the defensive team makes an out before any runners advance. For example, if a pitch touches the ground and eludes the catcher with a runner on first base, but the catcher recovers the ball and throws to second base in time to retire the runner, the official scorer shall not charge the pitcher with a wild pitch. The official scorer shall credit the advancement of any other runner on the play as a fielder’s choice. If a catcher drops a pitch, for example, with a runner on first base, but the catcher recovers the ball and throws to second base in time to retire the runner, the official scorer shall not charge the catcher with a passed ball. The official scorer shall credit the advancement of any other runner on the play as a fielder’s choice.
