Ever heard of Richard Paul Pavlick? I'm sure you haven't.

Because if you had, you would most certainly never have heard of Lee Harvey Oswald. Pavlick was a retired New Hampshire postal clerk with a big grudge against John F Kennedy, victor of the 1960 presidential election. He went down to the Kennedy winter home in Palm Beach, Florida, with a car loaded with dynamite. On 11 December 1960, he was in place and ready to push the button when JFK appeared at his front door with his wife and three-year-old daughter Caroline. Pavlick decided he couldn't kill Kennedy in front of his family, so he held off. A few days later he was picked up by the police. No harm done, nobody noticed. But what if...?

I must confess to being an addict of alternative history. It is, of course, as no one knows better than this sports devotee, an utterly pointless exercise. The wrongly disallowed goal, the LBW that wasn't, the erroneous line call that changes a Wimbledon final. So what, these things happen. The past can't be undone. Get a life.

But then try reading Then Everything Changed, an enthralling trio of novellas by Jeff Greenfield, a veteran American political reporter. The first deals with what might have happened if JFK had been assassinated, not in November 1963 but by Pavlick, at a moment when the electoral college had not even met to ratify his win.

The second imagines that his brother Robert had not decided to take a short cut, unprotected, through the kitchen of the Ambassador Hotel in Los Angeles on 4 June 1968. Then maybe a second Kennedy in the White House, a speedy end to the war in Vietnam, and no President Nixon. The third supposes that Gerald Ford hadn't made that idiotic remark about Poland not being under Soviet domination, during a debate with Jimmy Carter in 1976.

Ford wins a second term by a hair's breadth, and the political landscape is transformed. In 1980, after 12 unbroken years of rule by Republicans, the country is fed up with them. So no Ronald Reagan. Instead Gary Hart, a young reformist outsider, recaptures the White House for the Democrats.

Alternative history, of course, is nothing new. Philip Roth wrote a book supposing that the US national hero Charles Lindbergh, isolationist and Nazi-sympathiser, was president as the Second World War broke out. Robert Harris produced Fatherland based on the premise that Hitler won the war. And what if the Confederacy had broken away in 1865, or if Britain had stamped out the American rebellion in 1776?

The problem with such themes, however, is that they are simply too vast. The joy of Greenfield is that he takes small, highly comprehensible alternative events as his starting point, and then follows through with the main players – RFK, Lyndon Johnson, Nixon, Ford, Ted Kennedy and Reagan – behaving exactly as they did in real life. Greenfield is the keenest of students of US politics. His "history" is as credible as the real thing. These novellas read like fact, not fiction.

Of course, America is wonderfully fertile soil for such fantasising, with the unending presidential campaigns to choose the most powerful man in the world ever shadowed by the risk of random violence, and studded with tiny events that can change – and have changed – the course of history.

What if incumbent George H W Bush hadn't glanced at his watch during his 1992 debate with Bill Clinton and Ross Perot, signalling disastrously to voters that he was bored stiff? And what if someone had designed a better voting form in Palm Beach County, Florida, in November 2000? Thousands of elderly voters, many of them Jewish and Democratic, mistakenly voted for Pat Buchanan, the paleo-conservative who once described Congress as "Israeli-occupied territory". A clearer form and Al Gore would indubitably have won Florida and the White House. No George W Bush, therefore, and almost certainly no Iraq war. Rarely has so much hinged on so little.

But we've had such moments in Britain too. Suppose back in 1605 that Parliament hadn't been postponed a month, that Guy Fawkes's plot had not been revealed and his gunpowder was in working order. King James I would have been blown to smithereens, and Catholic plotters might well have seized power, instead of being hanged, drawn and quartered. What then?

Or what if, in May 1940, Lord Halifax had not demurred when the prime ministership was within his grasp, after Chamberlain decided to resign? No Churchill, at least not for a while, when many were measuring Britain's survival in weeks. Or what, more prosaically, about the random purchase of a couple of jumbo jets that swelled the monthly trade deficit, announced on the eve of the June 1970 general election?

The poor figures dented Harold Wilson's claim to have turned the economy around, and may well have cost him victory. And had Wilson won? Very possibly a smooth handover to Roy Jenkins, no need for the Lib Dems, and the arrival of New Labour a generation early. And talking of New Labour and Tony Blair, what if John Smith had not been struck by a heart attack on 12 May 1994, three years at most before an election there was no way Labour could lose?

Is it as futile to rewrite history as to rewrite a football match after the final whistle blows? Alternative history, even within as scrupulously researched a framework as Greenfield provides, is impossible to plot precisely. Events breed events, in a chain reaction that could lead anywhere. But what the hell. It's fun.