IF Bill Murray wasn’t a living, breathing movie icon, he might be mistaken for an especially ripe urban myth. Circulating on the web are dozens of accounts of the 63-year-old actor’s irascibility.

The time he turned up unannounced at a crowded restaurant in Austin, Texas, climbed behind the bar and started serving tequila. The evening he crashed a karaoke party in New York, spending several hours boozily dueting Sinatra songs with tourists. His 2007 golf buggy ride through Stockholm, where he offered lifts around town to strangers.

So far as can be ascertained these incidents — along with others of comparable far-fetchedness — actually happened. All share the same basic structure: Murray, motivated by boredom or fecklessness or who knows what, parachutes into a perfectly banal situation, his innate ‘Bill Murray-ness’ turning the everyday into the surreal.

Then, just as people are getting their heads around his presence, he’s out of there, leaving behind nothing but vapour trails of weirdness (in the case of a student bash graced by him in Scotland, he cleaned the dishes prior to exiting).

Why Murray — who is to have an entire day dedicated to his acting achievements at the Toronto Film Festival on Friday — should conduct his life in such a manner is a mystery on a par with the ending of perhaps his best movie, Lost In Translation, in which he whispers an inaudible farewell to Scarlett Johansson.

In the (very few) interviews he has given across the decades, the actor himself comes across slightly baffled at his eccentricities — leading you to wonder whether Bill Murray might not be a mystery to Bill Murray too.

“I live a little bit on the seat of my pants,” he explained to American interviewer Charlie Rose earlier this year. “I try to be available for life to happen to me. We’re in this life, and if you’re not available, the sort of ordinary time goes past and you didn’t live it … if you’re available, life gets huge. You’re really living it.”

Murray’s high-jinks probably goes someway towards explaining why he is one of the truly beloved actors working today. There are few movie stars at his level who do not divide opinion to some degree. Even certifiable treasures such as Meryl Streep and Helen Mirren have detractors. And yet, absolutely nobody can muster an unkind word for Murray. He’s made good films, average films, a few clunkers — regardless of the quality, at every moment he emanates an aura of bulletproof ‘Murray-ness’. You may loathe everything else about the film and consider Murray constantly watchable.

Mysterious in so many other facets, Murray has firm theory as to why he is regarded so highly, by Hollywood and audiences. It isn’t that he’s a heroic actor or a fantastic comedian. It is that, in contrast to the majority of his peers, he has an aversion to corniness. His performances, he believes, are bereft of sentimentality, imbuing even his most trivial parts with hard-won authenticity. From that perspective — and maybe it is ‘too soon’ to offer the comparison — he might be regarded as the anti-Robin Williams. Where Williams was always stoked, forever running at 150% capacity, Murray burns low and cool. On screen, he is the ultimate exponent of less is more.

“One thing I’ve tried not to do is be sentimental,” he told Rose. “I try to really squeeze the schmaltz out of everything. I try not to allow it. If someone has a script walking a tight-rope of sentimentality. I will be committed not to falling into the pit.”

Such an approach is evident in his best known roles. In Ghostbusters — shortly to celebrate its 30th birthday — he rolled his eyes as all about him flailed and mugged. Without anything to counter Dan Aykroyd’s boyscout exuberance and Ivan Reitman’s attention-deficient directing the movie might be unwatchable. Murray, though, injected endless deadpan. He won’t be starring in Ghostbusters III — so there may never be a Ghostbusters III (without Murray, Aykroyd has struggled to get it off the ground).

He similarly rescued Scrooged, a thoroughly creaky mid-80s revisiting of Dickens’s Christmas fable. Imagine how ghastly the film would be with anyone else in the lead. With his hangdog gaze and air of barely-contained boredom, Murray diverts a train-wreck. Look, he seems to say, I know you find this ridiculous. I find it ridiculous too.

The second act of Murray’s career has been one of the most intriguing in Hollywood. While generally regarded as a comic actor, he actually hasn’t done a straight-up comedy part in over a decade. Today, he’s the guy you call for rumpled pathos. Then he never thought of himself as a funny man exclusively. He may have emerged from Chicago’s Second City stand-up troupe — however, comedy was a passing phase, never a destination.

“Being funny, you’ve got to be able to play straight, which sounds like a paradox, but it’s not. So, if you can play straight to play funny, playing straight isn’t a big thing at all. I started making comedies because I came out of SNL [Saturday Night Live] and those were the things I’d get asked to do. Now I get all kinds of straight parts, and people say, ‘Oh, you’ve made a change in your life,’ and I go ‘no, this is what I get asked to do.’ Lately, people ask me to do straight things, or straight things that have a little bit of humour to them.”

A constant in the work of Wes Anderson, on screen nowadays Murray projects a sort of stifled zaniness — the perfect counterpoint to Anderson’s fustiness as director. And, of course, he was the best thing in Sofia Coppola’s Lost In Translation, haunting as a sad, middle-aged man so barnacled with ennui he cannot recognise the husk his life has become.

“If you don’t make a fool of yourself early on, people will trust you later,” he told Rose. “If you don’t make movies that should have been burned, people feel they can [believe in] you. They say ‘Well this guy didn’t sell his soul’.”