Alcott, King Have Eyes on a Bigger Prize : Women’s golf: A victory in the Dinah Shore tournament this week will qualify either for the LPGA Hall of Fame.

Amy Alcott and Betsy King, two of the long-lasting stars of women’s golf, have something else in common. Both are knocking on the door of the toughest hall of fame to enter--the LPGA.

If either wins the $700,000 Nabisco Dinah Shore, a 72-hole major that starts today at Mission Hills Country Club, she qualifies for the exclusive group.

A vote of the media determines who enters most sports halls of fame, but the women who make it in golf earn it on the course. It takes a minimum of 30 victories in LPGA tournaments to qualify, providing the golfer wins at least two of the major events. If she wins only one of the four majors, she must win 35 and, if no majors, 40.

Only 13 golfers have been inducted. Alcott and King have 29 victories each, including numerous majors. They face one of the best fields in the history of the tournament. Included are defending champion Helen Alfredsson, newest hall of famer Patty Sheehan, Nancy Lopez, Pat Bradley and recent tour winners Laura Davies and Dottie Mochrie.

King, who was the player of the year in 1993, appears to be a cinch to win her 30th title this year. She is at the peak of her career and has won at least one tournament every year since 1984.

Although Alcott says she is certain she will get at least one more victory, she has struggled in recent years. Her last victory was in 1991, her record third in the Dinah Shore. She and Shore celebrated by jumping into the lake in front of the 18th green. Alcott’s record score of 273 still stands. Her best effort last year was a tie for sixth, and she missed the cut in two of her three events in 1994.

“I know I’ll win again,” Alcott, 38, said Wednesday. “It would really be wonderful to do it here in this tournament. I’m playing well, I just need more consistency. I have to put four rounds together, and that will do it. I don’t really think about it anymore. I just know it will happen.”

There was no rancor when Alcott said she thought the qualifications for the hall were out of date.

“I’m not sure what the changes should be,” Alcott said, “but it is going to get tougher to qualify for several reasons, not the least of which is that there are so many good golfers.

“There won’t be any more 25-or more-year careers like JoAnne Carner and Kathy Whitworth have had.

“Soon, 10 victories will be a lot, 12 or 13 a great career. I’m not saying that should be enough to make the hall of fame, but 30 victories will just be almost impossible to achieve.

“I think it should be difficult to get in, but changes need to be made. Maybe, a major should be worth more than other events. I don’t know.”

Alcott listed several reasons why women’s golf has become so competitive in recent years.

“For one thing,” she said, “there is the training. Not even the men went on an exercise program years ago. The players now are younger and stronger. Then, too, they have psychological training. It has played an important part.

“Another thing is equipment. The improvement in clubs and balls has made it possible for some women, who would not have made it several years ago, to compete. Another reason is that there’s a lot more money out there, and that has made potential tour players interested.”

Beth Daniels, who tied for second last week at Phoenix, is another veteran nearing 30 victories. Daniels has 27. She needs one more major and two other victories.

Although she has never won the Dinah Shore, she appeared to have the 1983 event won until she knocked a ball into the water on the 18th and allowed Alcott to slip in for her first victory in the event.

Alcott’s prize that year was $55,000. The winner in the 23rd tournament will earn $105,000. In another tribute to Shore, the tournament course, the Old Course, has been renamed the Dinah Shore Course.