A Nation Pins Its Title Hopes on Davenport : Tennis: Highest-seeded American woman is 6-1, 6-1 first-round winner over Maria Grossi of Italy.

At the moment, the future of women’s tennis in the United States is an 18-year-old who stands 6 foot 2, hits tennis balls like Babe Ruth used to hit baseballs and is feeling a bit out of sorts because some of her recently graduated high school friends have just headed off to college.

Meet Lindsay Davenport of Murrieta, Calif., the highest-seeded American woman in this year’s U.S. Open draw at No. 6, and the possible heir to all the fame, fortune and foolishness that comes with that territory.

Where Davenport is today there once was:

--Martina Navratilova, currently ranked No. 4 but not even playing in the U.S. Open this year and within months of ending her masterful 21-year singles career.

--Monica Seles, No. 1 until the stabbing incident in April 1993 that has placed her career in limbo.

--Jennifer Capriati, a Wimbledon semifinalist at 15, an Olympic gold medalist at 16 and a possible burnout victim at 18.

--Others such as Mary Joe Fernandez, Zina Garrison Jackson and Lori McNeil, each never quite sustaining the success it takes to be this country’s fair-haired girl.

While age and defections have played a huge role in the quick emergence of Davenport, her physically imposing game might have been enough to get there, anyway. In her first-round match, she handled Italian Maria Grossi, a low-ranking player and a first-time entrant in the U.S. Open. The score was 6-1, 6-1, and the match was so one-sided that Davenport hit 23 winners to four for Grossi and converted all six of her break-point opportunities.

Davenport’s first serve hovered in the 100-m.p.h. range, and her ground strokes, struck with the power of many of her male counterparts on the pro tour, landed consistently deep in her opponent’s court. If the WTA kept a slugging percentage category as in baseball, Davenport would lead it.

After dispatching Grossi in 44 minutes, Davenport said she was happy to get the first match behind her because it is always a nervous moment in Grand Slam tournaments, and she showed that she has a sense for where she is, even though it happens to be only two years removed from her high school tennis team.

“I’m the highest American seed, so it is a little bit more pressure than before, because last year, I wasn’t even seeded here,” she said. “So I don’t think the public necessarily expects me to win because I’m still pretty new.”

Public patience for sports heroes is not always a safe bet. There are always those who look ahead on the draw sheet, and a peek at Davenport’s path shows a quarterfinal meeting with Steffi Graf. Davenport peeked, too.

“I’m playing well right now,” she said, “and if I keep going through the rounds, then, obviously, I’d love to play Graf.”

Davenport remains somewhat amazed at even being able to talk and think about things such as showdowns with the likes of Graf.

“I’m really happy how far I’ve come in a year or two,” Davenport said. “I never thought I’d break the top 10, and then all the way to No. 6 so fast. So I don’t know what to say where I want to be next year, because this is a great position to be in now.”

The fast rise doesn’t mean she doesn’t occasionally look back at what she gave up. A June graduate of Murrieta Valley High, she regrets that life as a tennis pro means no life as a college student.

“I was fine with (turning pro) for two years,” she said, “but then, this past summer all my friends are entering college and three of my friends moved in this week, so, now it’s like, kind of, I’m here and they’re there, and . . . “

For American tennis boosters, heartened last year when Davenport made it to the fourth round, the question is whether she will be at the U.S. Open long enough to contend for the title.

“I think the women have three or four good bets that are probably going to be there,” she said, “plus a couple of floaters. I consider myself a floater.”

At the moment, U.S. tennis fans consider her Miss America.