A short time after he takes the inaugural oath at the White House Sunday (a private act to be followed by the public ceremonies the next day), President Reagan will get on a TV hookup with athletes, officials and dignitaries assembled on a football field in Palo Alto, Calif. Hugh McElhenny, a former great running back, will relay to Mr. Reagan via ABC-TV the word on whether the captain of the Miami Dolphins has called heads or tails, and Mr. Reagan will then flip a coin to determine who kicks off and who receives in the Super Bowl.

Mr. McElhenny might wonder how the game ever got so complicated. When he was playing in the 1950s, football supremacy in the Free World was decided in a fairly simple way. The National Football League had two divisions of six teams each. The teams played 12 games in a season, at the end of which the two that led their divisions played a single game to decide the championship. They met on a Sunday in late December at the home park of one of the contestants. Usually this was in a northern industrial city, and the setting was gray and cold.

With the increasing popularity of the professional game in the '60s came more teams, longer regular seasons, playoff games, and then Super Bowl I. The Roman numeral signified the beginning of a new era. (Sunday we will reach XIX. Eventually this may produce the first generation of American schoolchildren in modern times that knows how to use the "L" in Roman numerals). The Super Bowl is played in a Sun Belt city or, occasionally, a northern domed stadium. It is separated from the mundane regular season and the playoffs by a two-week interval filled with frantic scurrying for tickets and a mass migration of private jets toward the host city.

Because it is such a major event, all of the lesser occurrences associated with it assume an importance of their own: The Introduction of the Players, The Kickoff, The Pre-Game Variety TV Show, The Pageantry, The Press Conferences, The Press Conferences, The Press Conferences, The Singing of the National Anthem. And now this year The Official Presidential Flip of the Coin. This business of doing an oath-taking and Super Bowl coin toss on the same afternoon has never been tried before. It will probably work out all right if the president doesn't wind up pledging to preserve, protect and defend the north goal.

Will it be the final element in making the Super Bowl the supreme event it strives to be? Probably not. Ask a football fan of almost any age what was the greatest game ever played, and he will skip over all XVIII of the Super Bowls and say it was the championship game in Yankee Stadium in 1958 between the New York Giants and the Baltimore Colts. He might add something about how the tough, rowdy big-city crowds and the chill weather seemed to spur the players on to greater heroics in those days the likes of which we shall not see again. Then he will probably ask if you know anybody who has tickets to the Super Bowl.