As to the greatest female never to win a SINGLES slam...
It would be hard to overlook Andrea Jaeger - two slam finals before age 18 - before being forced out due to injury and perhaps a little craziness... she had huge talent that never came to fruition.
Rosie Casals is tied for first in 'top 10 index' in the open era among non-slam winners. 'Top 10 index' is the sum of top 10 yearend rankings a player achieves in their career - 10 points for #1, 9 points for #2... etc... 1 point for #10. So her 50 pts in 'top 10 index' represent something like 10 years in the top 10.
Tied with her is Pam Shriver, who is also worthy of mention here. However, she only ever made the one slam final... at age 16.
Next up in a tie for 3rd place at 32 pts are Wendy Turnbull and Caroline Wozniacki. All these players have logged some serious top 10 time without bagging a slam, especially Wozniacki who finished yearend #1 twice... and her career is not over...
Helena Sukova should also be mentioned. She has the dubious distinction of making 4 slam finals without ever claiming a title - a unique feat in the open era - 1984 AO, 1986 USO, 1989 AO, 1993 USO.
She was matched by one player in the pre-open era, Jan Lehane, who made 4 consecutive Aus finals, losing them all to Margaret Court. Lehane played in the much more limited fields in the AO than did Sukova or the other players I've mentioned, and never really made that much of a mark on the international stage.
One of the greatest players never to win a singles slam was Elizabeth Ryan who played mostly in the 1920's and was a contemporary of GOAT candidates, Suzanne Lenglen and Helen Wills. When Lenglen (who only lost once between 1919 and 1926) turned pro to play a tour with Mary Browne, Hotchkiss (I believe) said that the tour wouldn't be too exciting, but if Lenglen were playing E Ryan, she would pay to see it. Ryan won 19 Wimbledon doubles titles, and the Irish open, which was almost a major in those days. She lost 3 singles slam finals, and was definitely a top player of her day. There's a great story about her fleeing Russia at the start of the 1917 revolution, after playing a series of tournaments, and trading away her trophies for her life so she could escape.
Rose Payten was a brilliant Australian player at the turn of the 20th century... she played in the pre-slam era and won a raft of Australian (NSW, QLD, etc) titles before the Aus Open was established for women in 1922. Karoly Mazak ranks her in the world top 10 for 7 or 8 years, reaching a high of #3. She probably would have won slam titles given the opportunity.
And no list of 'best without a slam' can be complete without mention of the great Irish player, Louisa Martin. She was ranked in the top 10 something like 19 years, including 2-6 years as #1 (depending on who you ask). She won 9 titles at the Irish championships which would have been about as important as a slam in those days (1880's - 1900's), but of course, doesn't show up in most record books - they didn't really have slams then... Indisputably Martin was one of the greatest players ever...
So my vote is with Louisa Martin, and in the open era, Andrea Jaeger.
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