Soccer is the beautiful game, and basketball is the city game, but here's what hockey calls itself:

A game of mistakes.

No other sport has such a negative, reductivist self-image, and hockey people reiterate it constantly. When a goal is scored, the first reaction in press boxes is not to admire the shot, but to identify which player blew the coverage. The red light is still flashing, and TV analysts are already scolding forwards for turning over the puck or defencemen for changing at the wrong moment.

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Mistakes, mistakes, mistakes – coaches drill the idea into players from atom to pro, and the players, indoctrinated, repeat automatically what they have learned. A search of North American newspapers using the keywords "hockey" and "a game of mistakes" turned up 100 hits in the past year, each instance negating hockey's beauty and inventiveness in a slightly different way.

Blue Jackets defenceman James Wisniewski: "Hockey is a game of mistakes. The game would be 0-0 if there weren't any mistakes. If nobody made a mistake on the ice, there wouldn't be any goals."

Islanders goalie Jaroslav Halak: "Hockey is a game of mistakes. Whoever makes more mistakes will lose most of the time."

Bruins forward David Krejci: "It's a game of mistakes, and as long as there were fewer mistakes than last game, then we're going in the right direction."

The coaches are even drearier. Flames coach Bob Hartley proclaims hockey a game of mistakes after practically every loss – but he has yet to achieve the pinpoint concision of the Lightning's Jon Cooper.

"This is a game of mistakes," Cooper said last season. "Gosh, I make mistakes coaching."

In soccer, the rhetoric is all about joy. A goal triggers an explosion of admiration for the genius of invention and the beauty of execution, an effusion of praise from the announcers, an extended celebration on field and in the stands.

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But in hockey, the idea that a goal might actually result from a player's ingenuity or a team's brilliant collaboration is so inimical to the sport, rooted as it is in dour Victorian notions of work ethic and stiff upper lip, that even celebrating a goal can be a suspect act. Alex Ovechkin pantomiming that his stick is too hot to handle? Shameful, and entirely too … European.

I spent much of last year searching for an alternate view of hockey, but with little luck. For great, thoughtful players such as Henrik Lundqvist, Martin Brodeur and Patrik Elias, hockey is still a game of mistakes – they all said so, even when I prompted them to consider that it might be something more. You want to minimize the number of mistakes, they said; otherwise, you give the other team scoring chances.

Well, sure, but that's true of any sport. Why must hockey dwell on mistakes when so many amazing, positive things happen on the ice all the time?

"If I was to try to describe hockey in the way that soccer people like to describe soccer, I would think that hockey is the Magic Game, or the Impossible Game," Hall of Famer Ken Dryden told me one afternoon in New York.

That was more like it.

"The essence of it is the impossible skill of skating on ice, and of being able to fly, virtually, and do things," he said. "Wearing sneakers and on dry land, most of these things are impossible. Well, guess what? Try them with blades on your feet. And on ice. And moving three times as fast.

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"Anyone who is new to the game, and by a stroke of luck is able to sit in the first 10 rows or so, can see just how fast it is, to see just how impossible it seems to be with people who are so big, and where there is no space and no time to do anything. And yet somehow, they do. That is a miracle."

Sometimes when the Leafs are playing – and every time the Sabres play – it is hard to see hockey as anything other than a game of mistakes. But there's no getting around it: At the elite level, the game is something miraculous.

"Look at them – these 40 guys who are out there on the ice," Dryden said. "Look at them – can you believe it? The passes, stick, stick, stick, at speed; 100-mile-per-hour shots – that's quite unbelievable. That's the essence of it."

It would be a refreshing change to hear coaches and TV analysts expressing that sense of wonder. More refreshing still would be to hear an NHL game called by Werner Herzog, the inimitable German filmmaker.

Herzog does not follow hockey; he didn't even encounter it until his adolescence. But he produced Red Army, the documentary about the great Soviet teams (which opened in Toronto and Vancouver this week), and in a recent conversation he marvelled at what those teams did on the ice.

"They played in a way that is almost ethereal, almost bodyless in its perfection and in its speed," Herzog told me. "When you think about ice hockey, you immediately think about body checks and clashes and fistfights. This was contactless. It was so perfected and so grandiose that they eluded any physical contact.

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"We have never seen anything like this before or since," Herzog said, "this kind of elegance – the grace and speed and precision and intelligence and intuition."

Grace, speed, precision, the accomplishment of the impossible while practically in flight – these are hockey's true qualities. It's time we stopped seeing hockey as a game of mistakes, drab and repetitive, and started seeing it for what it really is: a magic game, an impossible game, a beautiful game.