WHEN film historians look back at the latter half of Bill Murray’s career, they may well decide that his on-screen performances are less significant than his off-screen ones. It has been a while since Mr Murray starred in a bona fide comedy classic to rank alongside “Ghostbusters” (1984) or “Groundhog Day” (1993). Now he shambles up to people he doesn’t know, puts his hands over their eyes, and murmurs: “No one will ever believe you.”

This anecdote might have the clunking ring of an urban legend, but numerous videos and photographs back it up. Mr Murray really does make a habit of joining in strangers’ karaoke sessions and football games, washing dishes in their kitchens or proposing toasts at their stag nights, before slouching off into the night like some kind of crumpled superhero. Many of these tales are chronicled in “The Bill Murray Stories: Life Lessons Learned From A Mythical Man”, a delightful documentary co-written and directed by Tommy Avallone. Compiling a wealth of phone-footage and pictures, as well as the awed reminiscences of those people who have brushed with greatness, Mr Avallone has made a film almost as entertaining as the ones Mr Murray stars in for money.

On one occasion, we learn, he recited poetry to a group of bemused construction workers on a building site. On another, he took the wheel on a long taxi journey so that the driver could do some saxophone practice in the passenger seat. The film’s centrepiece recounts how Mr Murray bumped into a rock band at the South by Southwest festival in Austin, Texas, went with them to a house party, carried in their guitar amps, served lasagne to his fellow guests, accompanied the band on the tambourine and sweet-talked the police who responded to noise complaints. It is all there on video for us to see.

Mr Murray, it seems, treats other people’s social events just as he treats the films he graces with cameos, whether he is hiding in a hollow tree in “Get Smart” or demanding painful dental work in “Little Shop of Horrors”. That is, he turns up, pours out the patented Murray cocktail of hipster cool and potential chaos, and then vanishes. The people who have tasted this cocktail rhapsodise about how warm and generous he was, and how similar he was in reality to the laidback imp he portrays on screen: mischievous, effortlessly funny, so relaxed that he’s nearly asleep, and with the half-devilish, half-cherubic smile of someone who has spotted something that everyone else has missed. One eyewitness describes him as a human scented candle: “You light it and the room smells great.”

But what does Mr Murray get out of these interactions? Are they Andy Kaufman-esque performance-art pieces? Are they attempts to burst the Hollywood celebrity bubble around him? Mr Avallone links Mr Murray’s antics to the actor’s improvisational comedy training in Chicago, the theory being that in “improv” you have to go along with whatever the other participants suggest, and that Mr Murray applies the same principles of playfulness and spontaneity to everyday life. Elsewhere in the documentary, various critics and commentators laud him as a Zen master. He is “teaching us how to live”; reminding us to go with the flow and to be in the moment.

Far-fetched as that might sound, Mr Avallone points out that there are traces of such philosophy even in some of Mr Murray’s earliest films. An obvious example would be “The Razor’s Edge” (1984), a W. Somerset Maugham adaptation in which he plays a first world war veteran searching for enlightenment. (It was not a hit.) A less obvious example would be “Meatballs” (1979), a raunchy comedy in which Mr Murray’s camp counsellor subverts the standard inspirational speech given by big-screen sports coaches by concluding that “it just doesn’t matter” whether his team wins or not.

But maybe there is something else going on. Mr Avallone doesn’t acknowledge it, but a big part of what makes Mr Murray’s hit-and-run escapades so fascinating is that, at 68, he tends to be a generation older than the people he is hanging out with, and he is always on his own rather than with friends or relatives, two factors which hint at the isolation and melancholy that darken so many of his screen roles. Mr Murray’s personal life has been untidy, to say the least, and in Jim Jarmusch’s “Broken Flowers” (2005) and Sofia Coppola’s “Lost in Translation” (2003), among other films, he plays a loner, far from his family, more at home with strangers than with loved ones. But Mr Avallone, like the starstruck people he interviews, is too much of a fan to peer behind that particular curtain. He prefers to see his idol as a benign enigma. If that preference results in a light and superficial documentary, you can hardly blame him.

Perhaps the key to Mr Murray’s unorthodox hobby can be found in “Zombieland” (2009), Ruben Fleischer’s undead comedy. Playing a fictionalised version of himself, Mr Murray explains why it is that he potters around a post-apocalyptic Los Angeles, disguised as a reanimated corpse, instead of staying barricaded in his mansion. “Suits my lifestyle,” he shrugs. “You know, I like to get out and do stuff.”

“The Bill Murray Stories: Life Lessons Learned From A Mythical Man” is showing at the London Film Festival on October 10th, 11th and 20th. It will be released in America on October 25th