IF THINGS KEEP going the way they are, it will be tempting to change the name of the sports assembly to be held in Moscow this summer to the Allied Games. According to the list of participants announced yesterday, every ally of the Soviet Union will be sending a team of athletes. So will most allies of the United States -- with notable and honorable exceptions. The majority of the nations who athletes will be at home are in Africa and the Islamic world.

No doubt this will be taken by the Russians as a major defeat for the American effort to organize a boycott. The Russians will also inevitably interpret it -- and this should be more troubling to America's allies and to Third World nations than any reaction in Washington -- as an endorsement, or at least a toleration, of the invasion of Afghanstan.

A more correct interpretation, it seems to us, is that various governments in the West -- Great Britain and Italy are prime cases -- have failed to get one simply truth through the heads of their athletes. It is that international sports and international politics have become entricably mixed largely through the efforts of the Soviet Union. The Kremlin has actually published a document for its own citizens stating that the decision to hold the Olympics in Moscow was a recognition of the "legitimacy" of the regime. Athletes, submerged in striving for an edge of a hundredth of a second or a tenth of a point, may not comprehend that. Politicians have no excuse not to.The Italian government's policy of not opposing the decision of its athletes to go to Moscow but barring them from taking along the flag and the national anthem is particularly lame.

The numbers game -- who's boycotting and who's not -- will go on right up to the final day of the events in Moscow. The organizers, both there and in Lausanne, seem prepared to forget their rules about deadlines and welcome any athletes who want to come. (Unless, of course, they happen to be from Taiwan or another of the excluded nations.)

But it is obvious that the summer Games this year will be no more than a shadow of past Olympics. Without Americans, a swimming or track meet, not to mention a basketball tournament, hardly qualifies as world-less competition. The same is true of gymnastics without the Japanese or cycling without the West Germans. Competition in some of the less publicized sports -- archery and the equestrian events, for example -- may, by decision of each sport's international governing body, not be at all.

It is unfortunate that some nations, particularly those that count themselves as friends of freedom, have chosen to give in to short-term pressure. But others have been willing to put principles above gold and silver medals and the adulation of the crowd. What is likely to be most remembered about this summer's sporting events in Moscow is not who was there but who was not.