From the beginning the XIV Winter Olympics were Sarajevo's show, and it appears history will remember them that way. Most of what happened on snow and ice took a back seat to one overriding fact: Sarajevo did it. With almost no previous background in hosting winter sports - nor even the facilities needed to do so until recently - Sarajevo brought the world to its mountainous doorstep and managed to stage a successful Olympics - and the largest of its kind with 1,590 athletes representing a record 49 nations.
This isn't to say there weren't moments of athletic brilliance, because there were. The most memorable of these came in, of all things, ice dancing, where British virtuosos Jayne Torvill and Christopher Dean pushed out the barriers of their event with a flock of perfect scores. And with their scintillating interpretation of Ravel's ''Bolero,'' they placed their names alongside those of Jean-Claude Killy, Eric Heiden, and Sonja Henie in the pantheon of all-time Olympic greats.
The most highly decorated individual athletes were Finnish cross-country skier Marja-Liisa Hamalainen, who collected three individual gold medals plus a relay bronze, and East German speed skater Karin Enke, who took home two golds and two silvers.
In Alpine skiing, a sport heretofore dominated by Europeans, the United States came out well on top with three gold medals and two silvers. Debbie Armstrong and Christin Cooper finished 1-2 in the women's giant slalom, Bill Johnson won the men's downhill, then on the final day twin brothers Phil and Steve Mahre captured the gold and silver respectively in the men's slalom to complete by far the best-ever American showing in this traditional glamour sport of the Games.
The Zetra Arena also was a scene of high drama, topped by the tense duels in which East Germany's Katarina Witt edged US and world champion Rosalynn Sumners for the women's figure skating crown and America's Scott Hamilton just held off Canada's Brian Orser for the men's gold. It was in this rink too, of course, that the Soviet hockey juggernaut rolled through all opposition to regain the gold medal it had lost at Lake Placid.
These efforts gave the Games some of their texture, yet Sarajevo's hospitality, unstinting efforts, and warm, engaging inhabitants are what those who were here will talk about in the years to come.
The Yugoslavs took pride in their role as Olympic innkeeper, and never seemed burdened by the task. Many Westerners undoubtedly went away surprised that things worked as well as they did in only the second Olympic competitions held in Eastern Europe, the others, of course, having been the Moscow Games in the summer of 1980.
With full government cooperation, things got done. One priority was to provide a workable transportation system. This was accomplished by assembling a fleet of touring buses and restricting traffic within this city of 450,000.
The organizers had many hands on deck at the sports venues. They were particularly needed at the Alpine skiing runs, where slopes had to be groomed repeatedly due to weather postponements. But like the mail, the Olympics were eventually delivered within the framework of their Feb. 7-19 timetable despite various problems with heavy snow, raging winds, and dense fog.
All this isn't to say there weren't any glitches, but the overall report card was good. And though Sarajevo may not become the ''unavoidable tourist destination'' organizers hope, the city, by daring to host the Games, has definitely leaped years ahead with new roads, buildings, and sports facilities, and a fesh new identity.
As for the competition, East Germany and the USSR always seem to divide up the lion's share of medals, and they did so again here. The East Germans won the battle for gold, 9-6, but the Soviets edged them overall, 25-24. Finland was a distant third with 13, followed by Norway, 9, and Sweden and the United States, 8 each - the Scandinavian countries doing well in the Nordic disciplines as always, while the Americans collected their entire total in Alpine skiing and figure skating.
The most prolific haul by any country in a single sport occurred in women's speed skating, where Enke led her East German teammates to a virtual sweep. The GDR's strapping frauleins let only three bronze medals slip through their skate blades, finishing 1-2 in three of the four distances and 1-2-3 in the other.
East Germany has developed into a high-yield athletic factory that plays only to its strengths, refusing, for instance, to develop Alpine skiers, who would have to train elsewhere because of the country's lack of mountains, and reportedly keeping its Olympic-caliber hockey team home because it wasn't a medal threat.
In men's speed skating, while no one could approach Heiden's historic five gold medals at Lake Placid, Canada's Gaetan Boucher emerged as the top performer this time with golds in the 1,000 and 1,500 meter races and a bronze in the 500. Now he's contemplting sticking around for the 1988 Calgary games, by which time Canada will have its first outdoor speed skating oval.
In hockey, the fact that the Soviets came prepared to make amends for their loss at Lake Placid was no surprise. Mildly jolting, however, was the vanishing act of Team USA, which was hardly expected to duplicate 1980, but was thought to have a chance for a medal.
Instead the United States was beaten by Canada and eventual silver medal winner Czechoslovakia in its first two games and was out of contention almost before things were under way.
The Soviets, meanwhile, skated circles around everybody else, raising the perennial questions about the inequities and hyprocrisy in the sport's eligibility code. The Russians are as professional as players from other countries declared ineligible before the Games because of brief stints in the National Hockey League. Sentiment is growing to remedy the double standards before 1988.
Another concern should probably be the rough play and flareups that too often marred the hockey competition.
If the hockey was at times too ''chippy,'' there was always the grace and beauty of figure skating to enjoy.
Torvill and Dean skated with arresting elgance and originality in copping Britain's only medal. And Hamilton and Sumners led what was probably the most glittering array of American skaters ever, with the brother-sister tandem of Kitty and Peter Carruthers winning a silver in the pairs competition; Judy Blumberg and Michael Siebert barely missing a bronze as they finished fourth in ice dancing; and 16-year-old Tiffany Chin skating spectacularly in both the short and long programs to pull herself from far back to also just miss a bronze while stamping herself as a top prospect for the women's gold four years from now in Calgary.
Alpine skiing produced a mixed bag of results, with many established stars absent from the awards podium while several new ones crashed the party - especially on the women's side.
Swiss teen-ager Michela Figini had already made enough of a splash on the World Cup circuit that the experts knew she was a contender, but her name was still new to the public when she won the downhill to become the youngest Alpine gold medalist in history. Meanwhile the other two women's winners - Armstrong in the GS and Italy's Paoletta Magoni in the slalom - were surprises to everybody, as was Olga Charvatova, who won a downhill bronze for Czechoslovakia's first-ever Alpine medal.
On the men's side things came out a bit more predictably. The Mahre twins were among the favorites, of course, while giant slalom winner Max Julen of Switzerland was also an expected contender, and Johnson, though little known until recently, had raced and trained so well in the last few weeks that he had become the man to beat by the time the downhill was run. Still, the names of the winners, except for that of Phil Mahre, were hardly of the household variety. And here too there were some surprises among the other medalists, topped by the most significant event of all to local fans - Jure Franko's giant slalom silver for Yugoslavia's first medal in any Winter Olympic sport.
Meanwhile such stars as America's Tamara McKinney, the reigning world cup champion, and Switzerland's Erika Hess and Pirmin Zurbriggen, two of the top skiers on the 1983-84 circuit, all went home empty-handed. The traditionally strong Austrian team also was far below par on the slopes, with Anton Steiner's bronze in the men's downhill the country's only Olympic keepsake.
If there was one event that epitomized the Yugoslavs' enthusiasm for the Games it was ski jumping, which drew one of the largest crowds in Olympic history to the 90-meter competition. Finland's Matti Nykannen didn't disappoint the cheering throng, either, practically soaring into tomorrow to win, with American Jeff Hastings just missing a rare US medal in the sport with a fourth-place finish.
Yes, the athletes gave Sarajevo plenty to relish, and the city reciprocated with what International Olympic Committee President Juan Antonio Samaranch called ''the best organized games in history.'' And perhaps the experience here has helped spark renewed interest elsewhere in hosting the Winter Games.
There was a time not long ago when basically no one wanted them. But now six communities have already thrown their ski hats into the ring for 1992 - Lillehammer, Norway; Falun, Sweden; Berchtesgaden, West Germany; Cortina d'Ampezzo, Italy; Albertvill, France; and Sophia, Bulgaria. The IOC will make its final decision on the site two years from now.