run (someone or something) close

To nearly match or surpass someone or something in one's performance, skill, or ability. While he is still the undisputed master of filmmaking in my opinion, there are a few directors who run him close. She finished first to retain her championship title, but the favored newcomer ran her very close—just half a second behind her.

run someone close

1 almost defeat a person or team in a contest. 2 almost match the same standards or level of achievement as someone else.