NEW YORK -- Because Alysheba has scored decisive victories over most of his Belmont Stakes rivals, logic suggests he can do it again and capture the Triple Crown on Saturday.

But the lessons of history say otherwise.

History says that it takes a genuinely great horse to sweep the Kentucky Derby, the Preakness and the Belmont. The only colts who have done it in the last 40 years -- Citation, Secretariat, Seattle Slew and Affirmed -- rank among the best thoroughbreds of all time.

The Triple Crown almost always has eluded 3-year-olds who are less than great. Only Omaha, the winner in 1935, had a record as weak as Alysheba's.

It is somewhat surprising that the Triple Crown series has proved such a difficult test. In theory, an unexceptional horse ought to be able to get hot for a few weeks in the spring and win three races in a row, especially if his opposition is weak. But this hasn't happened. The 11 Triple Crown winners are such a select group that the three-race series has to be considered the most definitive test of greatness in American racing.

Nobody planned it this way. In fact, if it had been conceived in a logical fashion, the Triple Crown should have tested horses over a wider range of distances. (England's elusive Triple Crown includes races from a mile to 1 3/4 miles). But instead of being designed, the Triple Crown evolved over the decades into its present form.

Sir Barton, in 1919, was the first horse to win all three races, but there was no recognized Triple Crown then. In fact, the Derby and the Preakness were sometimes run on the same day; that's why Man o' War couldn't sweep it.

In the 1930s, Daily Racing Form columnist Charles Hatton started referring to the three races as the Triple Crown, borrowing the idea from English racing. By 1941 Hatton's phrase had taken hold and newspaper headlines said, "Whirlaway Wins Triple Crown."

In 1950 the Thoroughbred Racing Association made the idea official by creating a Triple Crown trophy. Starting this year, a horse who wins all three classics gets a lot more than a trophy; he will earn a $5 million prize.

Why has the Triple Crown been so difficult to win? The main reason, surely, is the timing of the races. The pampered thoroughbreds in Europe almost never would be asked to run in three classic races during a five-week period, as America's 3-year-olds are. (And the schedule used to be even tougher; in Sir Barton's year, the Derby and the Preakness were only four days apart.)

The sheer stress of the series has taken a toll on many horses who otherwise might have won the Triple Crown. As many as a half-dozen horses won the Derby and Preakness but missed a sweep for physical reasons: Bold Venture bowed a tendon in 1936. Tim Tim fractured a sesamoid in 1958. Majestic Prince was ailing in the 1969 Belmont.

Of the horses able to survive the three-race series, many missed a bid for the Triple Crown because of a lack of versatility. In particular, habitual stretch-runners have trouble. They are apt to encounter heavy traffic in the Kentucky Derby (as Little Current did), or to fall short on Pimlico's speed-favoring surface (as Twenty Grand, Needles and Chateaugay did). And, contrary to popular mythology, a stretch-running style isn't necessarily an edge in the Belmont -- as Pleasant Colony and Spectacular Bid demonstrated in recent years. The only pure stretch-runner able to sweep the Triple Crown was Whirlaway in 1941.

To win the Triple Crown, too, a horse must have the innate ability to go the Belmont's 1 1/2 miles. And he may need a little luck as well.

The early Triple Crown winners weren't necessarily precocious; some (such as Alysheba) didn't really blossom until the Kentucky Derby. Sir Barton and Assault were lightly regarded before the Derby, but both went on to distinguished careers that verified their Triple Crown success was no accident.

Only Omaha can be considered a fluky Triple Crown winner. Racing historian William Robertson wrote that he "was condemned in some quarters as a lucky colt who owed his . . . success to inept competition."

Of course, that was a much different racing era; Omaha was one of only about 5,000 thoroughbreds foaled in his year; now the annual foal crop is more than 40,000. As the thoroughbred population has grown, the Triple Crown has become tougher and tougher to win; during the 25-year hiatus between Citation and Secretariat, racing people wondered whether any horse would be able to do it again. The answer, seemingly, was that only a truly exceptional horse could.

Citation, Secretariat, Seattle Slew and Affirmed were brilliant throughout their careers. Each was the champion of his generation as a 2-year-old and the horse of the year at 3; those who raced at 4 were champions yet again; each has been enshrined in racing's Hall of Fame.

Even Alysheba's most ardent fans would not claim that he belongs in this exalted company. Before the Triple Crown series he had never won an important race; his best performance was his third-place finish in the slow Breeders' Cup Juvenile. When he won the Derby and the Preakness, his times were slower than those of even mediocre colts who had won in recent years; at Churchill Downs he was a full four seconds (20 lengths) slower than Secretariat's track record.

Yet the obstacles that commonly have stopped other colts from winning the Triple Crown seem unlikely to stop Alysheba. He is sound and robust, and unless his need for the drug Lasix is a key factor in the Belmont, physical problems won't stop him. Although he won the Derby and the Preakness with rallies in the stretch, he is versatile enough to stay close to the pace. Both his running style and his pedigree suggest that he will be an effective runner at 1 1/2 miles.

And although it is impossible to predict the kind of racing luck he will have on Saturday, he already has been lucky in one sense. No new challengers have emerged for the Belmont who look any more formidable than those he has beaten; one who would have given him a run for his money, Java Gold, was injured.

The only argument against Alysheba is that he is simply not a good enough racehorse to join the ranks of Secretariat, Citation and the others. If he does succeed, the Triple Crown will be worth $5 million, but it also will seem slightly devalued.