In a letter to a friend in 1961, Samuel Beckett spoke, with a characteristic blend of sadness and nostalgia, of seeing the great prewar England cricket all-rounder Frank Woolley in the bar at Lord's cricket ground. Woolley was escorting the legendary 84-year-old Wilfred Rhodes, perhaps the greatest England cricketer ever. By that time, wrote Beckett, Rhodes was totally blind. Woolley he had admired as a boy, and this was his predominant memory of that day, as well as a summation of Beckett's perspective on life: you can't and mustn't ignore eventual pain, suffering and illness.

At first glance, sport seems out of place in Beckett's world. His characters emerge as physical derelicts, down-and-outs, failures ("Fail again, fail better"). In his Waiting for Godot monologue, Lucky speaks of "sports of all sorts autumn summer winter winter tennis of all kinds, hockey of all sorts", only to point out that "in spite of the tennis" man still "shrinks and dwindles". Beckett looks beyond the exhilaration and triumph to the decline and debility that awaits us all, even record-breakers.

At the first international Beckett festival, which begins in Enniskillen tomorrow, there will be some half-dozen sporting events (races, a cricket match) alongside the prose, the theatre and the events devoted to music and art. Beckett attended the town's Portora Royal School, from 1920 to 1923. And, while good at English and French, he was even better at sport: he played cricket and rugby for the first teams; won medals for swimming and boxing (researching my biography, I found a man in his 80s who remembered being knocked clean out of the ring by Beckett the light-heavyweight champion; he never boxed again). Beckett played golf and tennis, ran, cycled and motorcycled. He loved diving from high rocks.

He followed many of these sports with interest, even passion throughout his life. Cricket was his strongest sport (he remains the only Nobel prize winner to feature in Wisden as a player). He left the game behind when he went to live in France in 1937, a more or less non-cricket-playing country, but as an old man was remarkably well informed. He continued to read the sports pages of English newspapers (The Guardian or The Times), as well as the French daily L'Équipe. And he enjoyed chatting about the exploits of various players. We once talked about Ian Botham, or "Beefy" as Beckett knowingly called him, soon after Botham had scored that brilliant 149 not out against Australia at Headingley in 1981, setting up a possible victory for England. (The original odds stood at 500-1.)

On another occasion, we dined at the Îles Marquises restaurant in Monparnasse, and Beckett glowed with pleasure as he pointed out on the wall above our table photographs of the great boxers: Joe Louis, Georges Carpentier and Jack Dempsey. We usually talked about rugby and cricket; with other friends, it was golf.

After Beckett's graduation from Trinity College Dublin, sport was overtaken by his more cerebral interests, and by his growing sense of vocation as a writer. He played no cricket or rugby after 1930 but in the 30s still played tennis in Paris, and, later, on visits to Ireland, snatched the odd game of golf with his brother or nephew, renewing his intimate acquaintance with the Carrickmines golf course in County Dublin. Had he been alive today, he would have been glued to his TV for the 100 and 200m Olympic sprints, the cycling and the swimming, but, above all, cheering on Katie Taylor to the first gold medal for Ireland at boxing. He might have lived in Paris, but he always supported Ireland against France in the rugby. One quickly learned never to attempt to make an appointment with him for a Saturday afternoon when the rugby was on.

Beckett's work has a strong vein of vitality and verbal athleticism and, although some of his late plays move slowly towards stasis, there is a strict concern with physicality, establishing rigorous order, shape, pacing and precision in movement reminiscent of the top flights in sport. As a director of his own plays, he counted out steps and coordinated movements like the most demanding coach or ballet master. In his late TV play Quad, the figures move along across the diagonals of a square in rapid, complex permutations.

Beckett made astonishing demands of his actors. Not I is an extended sprint: the central Mouth becomes a unique stage "thing", a spotlit "organ of emission", spewing words in an unstoppable flood. Delivering it, Jessica Tandy was too slow, according to Beckett, at 20 minutes; Billie Whitelaw, the Roger Bannister of 1973, delivered the text in 14 minutes flat; Lisa Dwan, in Enniskillen this weekend, rehearsing at 9 mins 40 secs, is likely to again break the 10-minute barrier.

"You can't go fast enough," Beckett said to Billie, who described the experience as being "like an athlete crashing through barriers". Dwan says she has had to train her mouth, work on her breathing, go for a run to loosen up her chest and neck muscles. With Lucky's Godot monologue, Beckett created a spectacular kind of athletic event, building gradually from a slower pace to a Usain Bolt sprint: its performance often leads to spontaneous applause, for its physical energy and endurance more than for its desolate content.

Double gold-medallist Mo Farah recently said of his training programme: "It's all hard work. It's been a long journey, grafting and grafting." Obsessively, almost maniacally dedicated to his work, Beckett grafted away as much as any athlete. Every year, only one gold medal is awarded in each of the Nobel prize categories. Beckett achieved his own gold in 1969.

• James Knowlson appears at the Happy Days Enniskillen International Beckett festival, 23-27 August. Details: happy-days-enniskillen.com