Two really obscure players -- Glenn Burke (who died of AIDS in 1995) and Billy Bean (not the celebrated "Moneyball" general manager of Oakland -- that's Billy Beane) -- came out of the closest, but that's it for admitted homosexuals in the history of big league baseball. (In contrast, AIDS claimed the lives of numerous male figure skaters).
But what about famous players? Maybe 1,000 ballplayers in history would be more or less "famous" and thus would be subject to constant reminiscences and research.
The only rumor I've heard about about a prominent player of the past being gay reflected desperation more than evidence. A New York gossip columnist claimed Sandy Koufax was gay, which would be a surprise to his live-in girlfriend (who is First Lady Laura Bush's old college roommate), his two ex-wives, and his neighbors in all the small, conservative rural towns the Jewish, Brooklyn-bred Koufax has chosen to live in in Idaho, Maine, North Carolina, and Oregon since he retired from the LA Dodgers in 1966. Koufax denounced the rumor, then had to put up with a lot of tsk-tsking about how backward baseball players are not to come out of the closet.
What about famous players who displayed traits that correlate to some degree with homosexuality? There aren't many.
For example, I looked up the life story of Earl Averill, one of the lesser Hall of Famers, who played centerfield for the 1930s Cleveland Indians. Why? Because he hadn't played baseball professionally until he was 24. Instead, among other jobs, he'd worked as a florist, a job with an above-average concentration of gay men. Maybe flower-arranging was his true passion and hitting a ball with a stick was just something he did to make money?
But, it appears that he'd been a florist mostly because he'd married young and he needed a sure paycheck. He and his wife were married for half a century and after he retired together they long ran the Earl Averill Motel in his hometown of Snohomish, Washington. His son Earl Jr. played in the majors, too. I can say with a high degree of certainty that Earl Averill wasn't gay.
Now, you are probably saying, "Okay, but what do we really know about individual ballplayers of long ago?" Actually, we know quite a lot. At least since Jim Bouton's 1971 bestseller Ball Four, there's been a big market for tell-all baseball books. Reporters constantly interview cranky old retired baseball players, who often love to gossip maliciously about their contemporaries.
Compare baseball to a more obscure sport, tennis.
In contrast, we know that the greatest tennis player of the 1920s, Bill Tilden, was a homosexual pedophile. He was arrested twice in the 1940s for corrupting minors and served a prison term, so it was in all the papers at the time. He is a minor character in Vladimir Nabokov's 1955 novel Lolita, where Bill Tilden is called "Ned Litam:"
Also, Baron Gottfried von Cramm, the leading German tennis player of the 1930s, who played a famous match against American Don Budge in the 1937 Davis Cup, was so publicly flaming in manner that Hitler couldn't make up his mind whether to promote the tall blond von Cramm as the perfect Aryan hero or arrest him for his affair with a Jewish male actor.
I'm not saying there have not been any famous gay baseball players, but I am estimating that less than 1.0% of the top 1000 players of the past were homosexual.