To his admirers, Spectacular Bid did not have to do anything else to prove that he is the best American thoroughbred since Secretariat. His greatness was fully established in his 3-year-old season.

But on Sunday at Santa Anita, Bid ran the kind of race that should finally convince the doubters and the dunderheads what kind of horse he is. He won the prestigious Charles H. Strub Stakes by running a mile and one-quarter in an unbelievable 1:57 4/5, shattering the American record of 1:58 1/5 that had stood for three decades. The time was also a world record for the distance for a race run on the dirt.

Until that race, Bid had never quite achieved the superstar status that had been accorded such inferiors as Seattle Slew and Affirmed. When he ran his best races last season, he never happened to be running over tracks fast enough to produce dazzling times. As a result, Bid's detractors said he was merely beating the best of a bad lot.

When Bid lost to Affirmed in their showdown last fall, his reputation was further tarnished. Yet Affirmed had so many advantages in that confrontation at Belmont Park -- the distance, the pace, the timing of the race -- that for Bid to come within three quarters of a length was really a heroic effort.

In one respect, Spectacular Bid's loss to Affirmed was a blessing. If he had won, his reputation would have been so secure that owner Harry Meyerhoff could have syndicated him for more than $15 million and retired him to stud. Having lost, Bid got to race as a 4-year-old this season.

Santa Anita would be an ideal showcase for his talents, just as it was for Affirmed last winter. The ranks of top-class horses are a bit thin on the West Coast; Bid would be facing only one formidable challenger, Flying Paster. The conditions of the races would enable him to run without carrying oppressive weights. And Santa Anita is so fast that Bid could finally run times everyone could understand.

Bid was facing only three rivals in the Strub, but one of them, Flying Paster, was good enough to force him to run his best. Bid trailed while the leaders set a blistering early pace covering the first three-quarters of a mile in 1:08 2/5. When the field hit the one-mile mark in 1:32 4/5, Bid drew abreast of Flying Paster and Valdez, and trainer Bud Delp told Meyerhoff, "The world record is ours."

He was right. Bid's 1:57 4/5 broke by two-fifths of a second the world mark that Noor set in 1950 for 10 furlongs on the dirt. But just how great was his performance?

The Santa Anita track was so fast on Sunday that one might have thought Huntington Drive had been rerouted down the home stretch; $25,000 claiming horses ran the first race in a sizzling 1:09.

Bid scored by 3 1/2 lengths over Flying Paster, a horse who has not yet fully established how good he is. A better point of reference was the third place finisher, Valdez. A reliable colt trained by the brilliant Laz Barrera, Baldez won tour stakes last year and earned $440,000. He was one of the six best 3-year-olds of 1979. Yet Bid demolished him by nearly 13 lengths on Sunday.

Spectacular Bid's performance in the Strub was not a great one-race explosion, in the manner of Secretariat's Belmont Stakes or General Assembly's 15-length triumph in the travers Stakes last summer. It was a normal performance for Bid, perhaps slightly better than his victories last season.

By the end of this year, Spectacular Bid should prove to everyone's satisfaction that such great efforts are his norm. By then, there will be no doubters left.