Euro 2004 was the latest episode in the long history of American indifference to the world's favourite sport, which continues despite strenuous efforts to put the game on the same footing as America's three major team games: baseball, American football and basketball. Why have these efforts failed?

One reason has to do with the existing popularity of the big three. Even in as large and wealthy a country as the United States, where the national appetite for playing, and even more so for watching, games is enormous, the cultural, economic and psychological space available for sport is limited and that space is already taken. Baseball, American football and basketball have long since put down deep roots, claimed particular seasons of the year as their own (although they now overlap) and gained the allegiance of the sports-following public.

A fourth team sport, ice hockey, is widely played across the northern tier of the country and has a professional league with teams located across the border in Canada and throughout the United States, even in cities whose climates are so benign that ice has never formed in them: indeed, the franchise in Tampa, Florida, won this year's championship. The presence of four major team sports - more than in any other country - has made the barrier to entry in the competition for the affections and the dollars of American sports fans extraordinarily high, so high that even the world's most popular game has not been able to surmount it.

One in particular of those three sports - basketball - poses a singular obstacle to the national acceptance of football. The two are too similar for them both to succeed. Each belongs to the family of games whose object is to put a ball (or similar object) in a goal.

Because the two games are similar, they have the same kind of appeal. Both are easy to follow; you can immediately understand the point of each one. The rules and strategies of cricket, baseball, rugby and American football, by contrast, are less straightforward. The action of a basketball game and of a football match are easier to follow than that of other team sports as well because the ball is larger than in cricket and baseball and is never hidden in a tangle of bodies or a scrum, as it is in American football and rugby.

Football and basketball are also easier to play than the other team games. They do not require elaborate equipment and satisfactory informal games can be staged without the full complement of players. And both football and basketball players can perfect their skills practising entirely alone.

Spectators see the same thing in the two games: episodes of spontaneous coordination, with players devising and implementing schemes for scoring. They see, that is, acts of creation. If architecture is, as is sometimes said, music set in concrete, then football and basketball may be said to be creativity embodied in team sports.

The two games are both played partly in the air. Basketball players spring off the floor to launch shots at the basket and soar to capture missed shots as they bounce off the rim, even as football players leap upward to intercept a kicked ball with their heads to control it, tap it to a team-mate, or redirect it into their opponents' goal. Football and basketball are therefore the team sports that most vividly evoke a common human fantasy: to leave the ground and fly through the air.

This is why, perhaps, football and basketball are the team sports with the widest global appeal. It is no surprise that each of the two has established a beachhead in the last great expanse of unoccupied sports territory, the People's Republic of China. Their marked similarities, however, also mean that the two sports duplicate each other. They provide the same satisfactions. For spectators they are, in a sense, alternatives. North Americans don't need football because they already get what it has to offer from basketball.

There is, too, the problem of the frequency with which football matches end in a draw. Americans want conclusive results from their games. Baseball and basketball have rules forbidding draws: the two teams must play until one of them wins. Draws were more common in American football until two decades ago when, responding to the national irritation with them, the managers of the sport changed the rules. Now collegiate games cannot end in draws and professional contests very rarely do.

Most American sports fans would regard the method used for deciding international championship matches that end in a draw even after extra time - the penalty shoot-out - as absurdly arbitrary and no more fitting a way to determine a winner than flipping a coin.

There is a remedy for what is, in American eyes, football's gravest defect. The game's rules could be changed to make scoring much easier, which would mean that even if the match were drawn at the end of 90 minutes, one or the other team would almost certainly score in extra time.

Altering the rules to encourage scoring is an old and well established practice in American sport. In the course of the 20th century, baseball, American football and basketball each did so several times. The changes helped to sustain, and indeed to expand, the popularity of all three, since, as one astute student of baseball put it, 'offense [scoring] is making things happen. Defense is keeping things from happening. People would much rather watch things happen.'

To do the same thing for football might well require dramatic modifications in the way the game is now played - the abolition of the offside rule, for example, or awarding points that count in the final score for corner kicks, which, as in prize fights that do not end in knockouts, would give an advantage to the side that makes the most determined efforts to score.

Why has this not happened in the US? One possible reason is that such changes would make the American version of football substantially different from the game played everywhere else, and here Americans are reluctant to be out of step with the rest of the world. If that is the case, then the failure of the world's most popular sport to gain full acceptance in the world's most sports-obsessed country suggests that there are, after all, limits to American unilateralism.

· Michael Mandelbaum is one of America's leading authorities on US foreign policy and international relations and the author of The Ideas That Conquered the World: Peace, Democracy and Free Markets in the Twenty-First Century (Public Affairs