The chestnut horse stands and gazes over the fence of his paddock, then suddenly breaks into a gallop, moving with long, fluid strides. Even at the age of 13, he is powerful, graceful, resplendent.

John Sosby, general manager of Claiborne Farm, watches him with admiration. "This," he says to a visitor, "is what the all-American horse is supposed to look like."

The sight of Secretariat stirs such vivid memories that it seems hard to believe a decade has passed since the spring when he rewrote racing history and set a new standard of thoroughbred performance.

In May 1973, he made his electrifying move on the turn at Churchill Downs and won the fastest Kentucky Derby in history. A month later, he completed his sweep of the Triple Crown with his 31-length victory in the Belmont Stakes that was probably the greatest single performance in the history of the sport. After it, Daily Racing Form columnist Charles Hatton wrote, "His only point of reference is himself."

He came to Claiborne Farm at the end of that season, and no prospective stallion has ever generated such interest, such expectations.

"He had everything a reasonable breeder could want," said racing historian Kent Hollingsworth. "He had perfect conformation and pedigree, and he was the greatest racehorse I ever saw."

When an offspring of Secretariat won a race for the first time--in late 1975 at Laurel--the event was considered so significant that all the television networks covered it. The world waited for Secretariat to alter the future history of his species.

But it didn't happen. And now that he has stood at stud for a decade, it is safe to say that it won't happen. Secretariat has sired many stakes winners, including General Assembly, who finished second in the 1979 Derby, but his performance as a stallion has been an undeniable disappointment.

Racing Update, an industry newsletter, calculated the average earnings of all the progeny of all the 86 stallions who had their first foals in 1975, and found that Secretariat ranked 15th on the list. One of the horses ahead of him was Sham, the arch rival he trounced in each of the Triple Crown races.

Why hasn't Secretariat lived up to the expectations for him?

Bill Oppenheim, the editor of Racing Update, offers the theory that for many years Secretariat was bred to the wrong type of mares. Since he was a son of the brilliantly fast Bold Ruler, breeders assumed that Secretariat should be mated to mares who were distance runners with classic pedigrees.

Secretariat eventually proved to be a stallion whose offspring had more stamina than speed, and mating him to similar mares tended to produce plodders. His most successful runners came from breeding him to mares with speed.

But other aspects of Secretariat's performance at stud remain a genetic mystery. Unlike many great stallions, he doesn't produce a definite physical type the way his own sire did; as the breeders say, he doesn't stamp them.

"You could walk into a field of yearlings," Sosby said, "and pick out the Bold Rulers with that good shoulder and rump. Secretariat doesn't stamp them that way."

Hollingsworth offers another interpretation of Secretariat's stud record.

"The basic law of genetics tends to the norm," he said. "When you get horses who are freaks, it's very unlikely they're going to reproduce themselves. Look at the greatest horses of this century--Sysonby, Colin, Man o' War, Citation. None of them reproduced themselves."

Hollingsworth points out that Secretariat ranks in the top 1 percent of all stallions. His record looks bad only because our expectations were impossibly high, because we hoped Secretariat the stallion would be as great as Secretariat the racehorse.