The ferocious December snow in Springfield, Massachusetts, can lie 50 centimetres deep. Confined to indoors for days and days, idle hands can – to borrow a phrase – provide work for the devil. At the local School for Christian Workers, the natives were getting restless in the frozen winter of 1891.

“And they’re beginning to be a problem,” Jim Naismith attests. The ingenious solution, devised by his grandfather James, was meant to provide a temporal distraction. Instead, the creation initially notarised as Basket Ball became a phenomenon which travelled further and wider than its inventor could ever have imagined.

An unlikely consequence of the decision to furnish James’ father, John, with a one-way trip from The Gorbals to the other side of the Atlantic before he had reached the age of 10. “There were family there already and they felt this young man would have a better chance in Canada than he’d have in Scotland,” Jim confirms. “That’s not an uncommon story.”

Caledonian emigrants and their descendants have provided Canada with prime ministers and prominent achievers but few have made the lasting impact of the second-generation Naismith, who lived just long enough to see his brainchild become an Olympic discipline in Berlin in 1936 but not to see it become the global behemoth that it is today.

Back in his great-grandfather’s home city this week, Jim – the last survivor of his generation – took a first trip down memory lane through the streets that spawned his branch of the clan, a timely visit ahead of a documentary which he has narrated on the ascent of the Scottish game, entitled ‘Making It Rain’, which gets its world premiere tonight.

Now in his 80s, he only latterly pursued an association with a sport birthed by a grandparent who died when he was just three. “Part of what I was not told was anything that should make me feel special because of what anyone else did,” he reflects. “That was down to my Dad.”

It was his elder brother Ian who was the keeper of the flame for many decades, a custodian of the heritage and a trustee of the Basketball Hall of Fame that bears his name and which is located, appropriately, in Springfield, not far from the YMCA where the very first trials of this once-brave new experiment were staged.

Naismith was a PE instructor who was asked to find a means to divert his students away from mischief. A thoughtful soul, he spent two weeks throwing ideas off the wall. “Some gymnastics wasn’t going to work,” Jim reports. “So he thought about sport. He started with rugby and modified it so they could play four-a-side.”

Modifying what already existed was a dead end, he felt. So it became a brand-new concoction. “He specified that firstly, there had to be a ball, not a small one but one big enough not to hide, Then you’d think the goal would be next. Hockey, a vertical goal, soccer, he went through them all. He felt force would be better. So what came up next was the path of the ball and having to chuck it has hard as you can.

“He played a game as a kid called Duck on a Rock and the shot that works best was an arc shot. And it would land with little force. So he went a-ha, ‘what kind of goal would I talk about?’ He thought a box 18 inches square. He asked the maintenance guy whose name was Stubbins. He comes back and says ‘I can’t find any boxes but I got a couple of peach baskets, would that work?’

“He took a couple and attached them to the street level which is where the 10 feet came from. So he’s got the ball, he’s got the baskets. There is a recording of his voice, where he said the aim was to get this ball in the other man’s goal. That’s all he told them. Then the first game began.”

The 13 original rules were transcribed in a notebook. Nine years ago, the family – seeking funds for their foundation – sold the document at auction for $4.3m (now £3.3m), acquired by a benefactor to reside at the University of Kansas where Naismith later coached the game which he had imagined.

It spread quickly. “It almost immediately went to China, to Japan, to France,” Jim outlines. “It went into Canada. He was Canadian. He was still a Canadian citizen at that point. Some people say it is an American sport. No way. It was invented by a Canadian. Who was also Scottish.”

The documentary, produced by the NBA, chronicles the emergence of a brand of Tartan hoops in the 1960s, with Scotland teams touring North America before a contra-flow of traffic brought names like Alton Byrd and Bobby Kinzer and illuminated a rivalry between Edinburgh’s Murray International and Falkirk’s Team Solripe that packed the rafters for a decade.

In Glasgow, Naismith was reunited with the FIBA World Cup trophy that bears the family name but also witnessed another crop of youths given a distraction through one of the many junior NBA competitions which act as feeders to the billion-dollar league now seen around the world, one whose Eastern Conference Finals features a head coach who played for a Scottish League team (the Milwaukee Bucks’ Mike Budenholzer) facing another (the Toronto Raptors’ Nick Nurse) who won regularly north of the border during his lengthy stint in the British Basketball League.

From humble origins, the Naismiths birthed a goliath. The labours of Dr James – deeply instilled with his Scots heritage – are now to be found in every corner of the world. “I think he would be amazed at the growth of the sport,” Jim grins. “But I think he’d ask how this relates to a better life for young people. Because that was his passion.

“Not ‘how much money did you make?’ Clearly no. If we’d followed that, I might be drunk and dead. Or I could be inviting you in my Rolls Royce. That’s nonsense to me. It’s not the assets or the money. It’s about a man who loves people and the most effective way to reach then as early as possible.

“As I’ve got older, I’ve realised the power of reaching young people. We have four of our own and 24 grandchildren and great-grandchildren. It’s teaching them life skills and that ought to be No.1 on most people’s lists.”

Making It Rain screens on Sky Sports Arena on Wednesday at 6.30pm