SARATOGA SPRINGS — Every time Songbird runs, the script is the same. Glide swiftly as overmatched opponents strain to keep up, then kick clear to win by daylight. Not once has Mike Smith asked her for her best.

She’s 8-for-8, all runaways, by a total of 42½ lengths, and it could have been twice that if she’d been pushed. Perfection is glorious, yet it can be disturbing, too.

“It scares me to think of how good she is,’’ Smith said. “I try not to think of it.”

The racing world has obsessed about Songbird since last fall, when it became clear she was special. On Sunday, she’ll make her East Coast debut in Saratoga’s Grade I, 1 1/8-mile Coaching Club American Oaks for 3-year-old fillies. Will she dazzle as usual or become the next victim of the “Graveyard of Champions”?

The New York Racing Association convinced owner Rick Porter and trainer Jerry Hollendorfer to fly Songbird cross country by raising the Oaks purse from $300,000 to $500,000 as long as she runs. Even if she crushes her four challengers, she’ll still enrich their connections. Like the winner’s share, the also-rans’ payoffs will increase, with second worth $100,000 instead of $60,000 and third 50 grand, not 30. Now that’s trickle-down economics at its best.

Songbird got a feel for the Saratoga dirt by galloping 1½ miles Friday morning, and Hollendorfer called it “a good trip. She likes the track.”

Songbird tuned up for the Spa in a minor stakes June 18 at Santa Anita. It was her first race since a low-grade fever canceled a start in the Kentucky Oaks, run the day before the Derby. Many handicappers rated her above all the colts, citing she ran 1.06 seconds faster Oct. 31 in the Breeders’ Cup Juvenile Fillies than eventual Derby winner Nyquist did in the Juvenile that day.

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A week later, Porter ruled out the Derby, saying, “Maybe when Songbird is a little older we may take a shot against the boys in a big Grade I.”

Many thought Porter’s real reason stemmed from the traumatic 2008 Derby, in which his filly, Eight Belles, suffered a fatal breakdown after finishing second to Big Brown. Porter said the horrific incident wouldn’t keep him from running a top female against males, and three years later his mare Havre de Grace beat the boys in the Woodward on the way to becoming Horse of the Year.

Like Porter, Songbird’s trainer and jockey have world-class status. Hollendorfer has more than 7,100 wins, third all-time behind Dale Baird and Steve Asmussen. Among his stars were champions Shared Belief and Blind Luck, and he has three Kentucky Oaks trophies.

Smith has exceeded 5,300 victories, including a record 22 in the Breeders’ Cup; a Derby, a Preakness and two Belmonts. Twice he’s been the regular partner of a female Horse of the Year, Azeri (2002) and Zenyatta (2010). Zenyatta was a deep closer who finished 19-for-20 and became an international cult figure. Songbird has done nothing to suggest she can’t emulate her, even though their running styles are a 180.

If you believe parents’ names can hint at the future, you figured Songbird would excel. Her sire is Medaglia d’Oro, Italian for “gold medal.” Her mother is Ivanavinalot.

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“A lot of the great fillies I was blessed to ride earlier in my career didn’t have the career Songbird has had at 3,’’ Smith said. “A lot of them didn’t get good until they were 4. So I would say right now she ranks above them as a 3-year-old, anyway. I would have to say that includes the boys as well.’’

Porter is 76, Hollendorfer is 70 and Smith turns 51 next month. None of them could have anticipated having a horse this brilliant so late in the game. Smith admits he’s more her passenger than her pilot.

“She’s just incredible,’’ Smith said. “She does it with tremendous ease. I feel so blessed to be a part of it and I keep pinching myself, having to remind myself that I’m the one that gets to keep the weight on her. That’s really all I do.”

Hollendorfer was asked if there was pressure training a perfect superstar. “No,” he said, smiling, “the pressure is if you don’t have one.”