Johnny Carson didn’t invent late night. Nor did he invent late-night talk shows. He didn’t invent their desk-and-couch format or the opening monologue, or the game of golf, which inspired the golf swing he mimed to finish his own monologue each night. Carson didn’t invent the talk-show host’s sidekick, or the obligatory house band. Even many of his most popular comic characters were lifted brazenly from other performers, such as Jackie Gleason and Jonathan Winters. So what made Carson a trusted, enduring, influential and altogether likable presence unmatched by anyone in the history of the medium except, arguably, Walter Cronkite and Oprah Winfrey? Finding out is the mission of “Johnny Carson: King of Late Night,” a two-hour “American Masters” portrait premiering at 9 p.m. Monday on PBS (check local listings). A few stats gathered for the film begin to tell the tale: With his debut as host of NBC’s “The Tonight Show” 50 years ago this October, until his exit on May 22, 1992, he was seen by more people on more occasions than anyone else in American history. Carson reigned for nearly 30 years, hosting 4,531 episodes and receiving 23,000 guests. For most of his run, he had no competition, or none that mattered. His nightly viewership, averaging as much as 15 million, was more than the current audience of “Tonight” successor Jay Leno and CBS rival David Letterman combined. Hired to replace the departing Jack Paar on “The Tonight Show,” Carson made his first appearance on Oct. 1, 1962. No video exists of his debut, just an audio tape that finds him sounding cool and confident even as he jokes about his jitters. “King of Late Night” follows Carson from there all the way to his retirement from the show (and, as it turned out, his total withdrawal from the public scene) in 1992, and his death, at age 79, in 2005.