Fred and Barney get into trouble coaching Pebbles and Bamm-Bamm --now shown as pre-teens-- who are playing on rival teams.
The story begins with Fred's jealousy over Barney's new position as Bamm-Bamm's little league coach causing a rift between the friends. Things get hairier when Mr. Slate asks Fred to coach the opposing team. On his way home from the quarry, Fred manages to get out of a speeding ticket by agreeing to let the officer's son pitch for his team --- who turns out to be awful. Meanwhile, Pebbles wants desperately to be involved in the activity with her father, but Fred feels that baseball is not for girls.
As the rivalry between the Flintstones and Rubbles escalates, Fred starts to realize that his team is in real trouble ---- until he accidentally discovers that Pebbles is a pitching sensation.
Not trusting each other, Fred and Barney decide to stick to each other like glue until the big game, but Fred gets into more trouble with the officer and Judge Shale after he is forced to bench their kids --- who are awful players. When the boys get stuck in court (and then in traffic) and don't show up for the game, Wilma and Betty are forced to take over as coaches --- knowing nothing about baseball.
After 30 scoreless innings, Bamm-Bamm is finally able to hit a pitch off of Pebbles, but the ball goes straight up ---- never coming down. Not sure how to score it, both teams call it a tie, and sing a song about being a good sport.