When I was in law school, we had an attorney come speak who'd accomplished what was touted as a wildly rare feat: he'd argued TWO cases before the U.S. Supreme Court. To emphasize how rare this is, we were told the Court receives around 10,000 petitions for a writ of certiorari per year and only a fraction of those are granted and heard (less than 100). I was duly impressed, but it turns out I was not doing my due diligence. I didn't ask the right questions when given statistics designed to wow.
Turns out for some attorneys, their petitions are reliably granted by the Court. So, it is quite possible the attorney I heard didn't have a mere 75/10,000 chance of being heard. Instead, his odds were likely much better. Reuters news service did a little research and produced The Echo Chamber, which concluded that in the last nine years, "66 of the 17,000 lawyers who petitioned the Supreme Court succeeded at getting their clients’ appeals heard at a remarkable rate. Their appeals were at least six times more likely to be accepted by the court than were all others filed by private lawyers during that period." Additionally, "[o]f the 66 top lawyers, 63 are white. Only eight are women."
For more on the report, check out the Amicus podcast from Slate.com.