Bill Murray: Is he doing some of his best work off-screen?

Ever since Bill Murray rebooted his career with “Rushmore” in 1998, delivering the canny mix of humor and melancholy that would become his trademark, he has built a reputation as one of Hollywood’s most interesting and idiosyncratic leading men.

In addition to starring in well-regarded films like “Lost in Translation” and “Broken Flowers,” the 63-year-old actor has cultivated a real-life mystique unlike any other celebrity — mostly by both being as unavailable within Hollywood as any celebrity in recent memory as well as participating in seemingly random acts of merrymaking with ordinary people.

In recent weeks, for example, Murray has made headlines for spontaneously joining a stunned couple’s engagement-photo session and delivering an impromptu bachelor-party speech for a group of strangers.

It’s getting to the point where Murray’s off-screen escapades are threatening to match — or even surpass — his movies. After all, Murray’s recent films have been something of a mixed bag. His last prominent roles were in George Clooney’s World War II movie “The Monuments Men,” released this year, and Roger Michell’s FDR biopic “Hyde Park on Hudson,” released in 2012. Both films received mixed to negative reviews.

Fortunately for Murray fans, he’s set to return to the big screen in a number of roles, including comedy “Rock the Kasbah,” the animated movie “B.O.O.: Bureau of Otherworldly Operations” and an untitled Cameron Crowe movie.

Most imminently, there’s the comedy “St. Vincent,” in which he plays a misanthropic war veteran who becomes an unlikely mentor to the kid next door and learns a few lessons of his own.

When the Weinstein Co. showed footage of “St. Vincent” at the Cannes Film Festival last month ahead of its Oct. 24 release, it drew a lot of comparisons to “About a Boy,” the Nick Hornby arrested-adolescent novel that has had life as both a film and, more recently, a TV show, with Murray’s old-coot quirkiness folded in.

Time will tell if “St. Vincent” will be as well received as, say, his slow-motion video walk with a few stoked fans, his crashing a kickball game in New York or his sly tribute to “Ghostbusters” co-star Harold Ramis at the Oscars. Here’s hoping.

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