Koufax, 80, has been a regular attendee of Dodgers postseason games since Guggenheim Baseball Management bought the club. The Dodgers have reached the postseason each of the last four years.
"It's almost an honor to have him around, but he doesn't look at it that way," said Dodgers chief marketing officer Lon Rosen. "He carries that sense of the Dodgers history with him. The players really enjoy talking to him."
Charlie Culberson, who slugged the walk-off home run to clinch the NL West title, said he asked to have his picture taken with Koufax.
"Obviously, it's Sandy Koufax, but another thing is that he's a genuinely nice guy," said Culberson. "For someone of his stature and what he's done in the game, to come up to you like you're his best friend, it's pretty special. When Sandy Koufax walks into the clubhouse, you stop. It's a different feeling when he's there."
Known for treasuring his privacy, Koufax, who has a home in Florida, participated in the Dodger Stadium tribute for Vin Scully's retirement two weeks ago.
Ken Gurnick has covered the Dodgers since 1989, and for MLB.com since 2001. This story was not subject to the approval of Major League Baseball or its clubs.