Geena Davis has always had self-confidence. She'll be the first to say so. Moviegoers got their first glance of her in the hit comedy "Tootsie." She portrayed a bit player in the film's "General Hospital"-type soap opera, and when her character shared a dressing room with Dustin Hoffman's, he almost forgot he was supposed to be a woman. That was 10 years ago. Since then, she has won an Academy Award (for "The Accidental Tourist"), starred in a landmark film (last year's "Thelma & Louise"), is the major player in a hot summer movie ("A League of Their Own," opening tomorrow) and will be seen later this year in "Hero" (again with Mr. Hoffman, but this time as a co-star rather than as a supporting player). "I always thought it would turn out this way," she says, with more honesty than arrogance. "I've been blessed with overconfidence, you might say. I think to survive in this business, you have to feel that way about yourself. Maybe I'm overcom-pensating about something, but I don't know what. Even when I was working with Dustin in that small part in 'Tootsie,' I felt that one day I would work with him on equal footing." Self-confidence can be either healthy or unhealthy. Ms. Davis seems to be completely healthy. She laughs a little at herself, thinking about the flamboyant dress she wore to the Oscar ceremony last spring. "Remember how that dress just turned up where you didn't expect it to? It was intentionally flamboyant, which I tend to think is very, very chic. And when I found out I had offended [self-appointed fashion arbiter] Mr. Blackwell, I was delighted. Who wants to be conservative?" Ms. Davis wears no fancy dresses in "A League of Their Own." Her role is that of the star player on one of the all-female baseball teams organized during World War II to raise the morale of the country, keep the sport alive while the men were off at war and, of course, make a little money for the backers. Ms. Davis, fresh from the success of "Thelma & Louise," was called in to replace Debra Winger in a cast that includes Tom Hanks, Madonna, Lori Petty, Jon Lovitz and Rosie O'Donnell. Penny Marshall is the director. "I don't know why Debra left," she says. "I just got this call, telling me to come to Chicago and meet Penny. Filming was to start in three weeks. I had never played baseball in my life. I rehearsed on weekends and after hours. I feel like I could play in the majors now." She considers the film to be a tribute to the real members of the All American Girls Professional Baseball League. "One of the most important things to me is that when the surviving members of the AAGPBL see it, they like it and feel we did right by them. In a humorous way, the movie speaks out against the sexism of the time. And that sexism still exists. We don't have women's baseball today. It was important for us to be directed by a woman. Penny is a feminist, and she has a great sense of humor." At the core of the screenplay is the sibling rivalry between Dottie (Ms. Davis), who excels at athletics and everything else she attempts, and Kit (Ms. Petty), who has lived in the shadow of her older sister. "I get to play this strong, heroic, athletic character. I would much rather play that than play the bouncy cheerleader who cheers on the strong, heroic, athletic male hero. But beyond that, I think I responded to Dottie's sense of resolve. During the course of the film, she has to make several important decisions. She has the strength to move on rather than to cling to something, and I think that's admirable. She recognizes when a stage of her life is over. She's able to say to herself, 'I've done this; now it's time to move on.' "And she recognizes that she and Kit are better off apart, which is very difficult for family members to realize. She lets go of the idea that they're going to be an incredibly close pair of sisters," says Ms. Davis, who has only one sibling -- an older brother, with whom she has had "very little" rivalry through the years. The shooting of "A League of Their Own," with summer heat and the intense physical action, was the most difficult she had experienced. "And, much as I love Penny, I have to say she requires a lot of takes. But all of us got along great. I kept reading that we weren't supposed to be getting along, that the set was divided into two distinct cliques. Those rumors started because there were two big trailers that we used as dressing rooms, and each cast member was assigned to one of those two trailers. So you got to know the women in your trailer better."