I don't know what fractions of rape charges are false, or what fractions of rapes get reported. I know many women (ten or so) who claim to have been raped at least once, always by somebody they know; none of them reported the rape. I believe them. I know one guy who says he has been falsely accused. I assume that most real rape cases don't get reported, and that some significant minority of reported cases are false.
I believe that Mike Tyson did not rape his accuser; I believe she changed a slutty, groupie action on her part into a rape charge, probably triggered by loutish behavior by Mike. I believe something similar happened to Kobe, probably triggered by him trying to force into their encounter an unwelcome act involving the nether regions. Here's some cases of women certainly filing false rape charges.
In this one, the St. Johns basketball team got accused by a women they met at 2:30am who went back to their hotel room and had sex with several of them. At 4:30am she reported them to the police. The police went to their room; lucky for them, one of them secretly recorded the encounter on his cell phone; what if he hadn't? What if the players had been white, and the girl black? (She was a prostitute, and they had a dispute over money!!!)
Here also a man is rescued by a hidden cell phone camera recording. Makes you wonder how many un-taped encounters get falsely transformed into successful fake rape charges.