to gain an advantage over someone, especially in a discussion or argument
Your daughter deserves two parents who can be civil to each other - not parents whoconstantly score points against each other.
We can see our leaders looking shifty in close-up every night on television. Thereis no frankness, only point-scoring.
to do something that impresses someone or makes them admire you
Again, Laine paused, clearly confident in his arguments. He was scoring points withthe judge and the spectators. The judge kept nodding in agreement.