If the home crowd is the ''12th man'' for a football team, then you have to say that Mikhail Gorbachev is bidding to become ''the 13th man'' in the American presidential campaign. Like a noisy cheering section, the Soviet leader is the presence that can change the dynamics of the game.
We have just seen the first intimations of his potential impact. NBC News gave him an hour for a prime-time interview with anchorman Tom Brokaw on Monday night, then divided two hours on Tuesday night among the 12 Republican and Democratic aspirants for the White House. By my calculation, that gave Gorbachev approximately six times as much exposure to the TV audience as any one of the men who may be our next president.
Everything we know about Gorbachev and his approach to politics and diplomacy suggests that he will use his first trip to Washington next week to sell himself and his ideas to the American people. As important as signing the intermediate-range nuclear forces agreement with President Reagan may be, his top priority will be a public-relations offensive aimed at prepositioning the next president as a prospective partner for further deals on arms, trade and other matters.
He will do that by emphasizing the ''three Rs'' of his glasnost policy, appearing to be reasonable, realistic and reformist. Those are the recurrent themes of his book, ''Perestroika: New Thinking for Our Country and the World,'' published this fall by Harper & Row.
The more Gorbachev comes across as a ''modern man,'' unencumbered by the ideological fixations of his aged predecessors in Kremlin power, the more he encourages the American people to select a president who has the same qualities.
The situation is almost made to order for him. Every poll shows many Americans are growing weary of the rising cost of military competition with the Soviet Union. Voters already have signaled their desire for a cessation of partisanship and the achievement of political consensus on important domestic issues such as the budget deficit, health care costs and welfare reform, which have remained intractable problems for too long. Gorbachev, it is clear, will seek to nurture the notion that a similar meeting of the minds is possible when it comes to the U.S.-Soviet competition.
Over the years, Americans have learned that it is always wise to be wary of the Soviet smile; it can change in an instant into a teeth-baring threat. One hopes we will not be so naive as to make Gorbachev a new pop hero. But the worst mistake we could make would be to underestimate the man.
He has been extremely impressive in his public diplomacy. While his mind and political resources have been focused on securing power at home and launching his ambitious overhaul of the Soviet economy, he has played a smart, effective game on the world scene. As a relative newcomer, years behind Reagan, he nonetheless has established strong personal relationships with almost all the European leaders and with many in this hemisphere, in Asia and in Africa.
He has shown his skill in political public relations, charming Margaret Thatcher even before he came to power and playing artfully on mass opinion almost everywhere he has been on both sides of the Iron Curtain.
With the advice of that consummate Washington politician, the longtime former ambassador Anatoly Dobrynin, Gorbachev and his wife, Raisa, have given substantial thought to the ways he can influence American domestic politics on the eve of the presidential election.
He already has gained some leverage on the next president simply by achieving an arms-control agreement with Reagan. He and Reagan are de facto partners in pushing for Senate ratification of the INF pact. And they well may seek together to bring a strategic-arms agreement along fast enough that it could be ready for ratification in 1989 if not in 1988.
If the next president seeks to slow down or reverse that process, Gorbachev can certainly use Reagan's example as a stick to beat him in American public opinion.
But he has other leverage as well. The stock market break has focused attention on the economic costs of the arms race. Most Americans would welcome relaxation of the pace of the buildup. Big business -- an important constituency for the Republican Party -- hankers to supply the technology and capital the Soviets need to modernize their economy and make themselves a market for the world's goods.
The traditional view is that the Russians prefer to deal with Republicans, finding them more predictable and in a sense ''practical.'' Gorbachev's special attention to Vice President Bush on his announced schedule does nothing to diminish that view.
But his larger aim is to influence American opinion in ways that will make it harder for anyone who succeeds Reagan to impose unwanted choices on the Soviet Union. It will be fascinating to watch Gorbachev go about his work. He is very good. So keep your eyes open -- and your hand on your wallet.