Until a few years ago, there were two Stanford Law graduates (and classmates, to boot) on the Supreme Court: Chief Justice William Rehnquist and Justice Sandra Day O’Connor. Although the last person President Obama nominated (unsuccessfully) to the Supreme Court was a Harvard Law (and Harvard College) graduate, the other person widely known to have been under consideration for that nomination, Judge Sri Srinivasan, is a Stanford BA, JD, and MBA. There are plenty of Stanford Law graduates on Federal Courts of Appeals, the level just below the Supreme Court.
Notwithstanding Rehnquist and O’Connor (and a host of other prominent alumni from the 40s and 50s, like Warren Christopher, Shirley Hufstedler, Frank Church, and, yes, John Erlichman), Stanford didn’t really come into its own as a top law school on a par with Yale and Harvard until the 1970s, long after the older current justices graduated, and even now I think Harvard has more people than either Yale or Stanford – both proportionally and in absolute terms, so a lot more – who are aggressive about seeking public prominence. Like, say, Barrack Obama, a former President both of the United States and the Harvard Law Review.
While it’s not odd that Yale has a number of alumni on the Supreme Court, who they are is very random: the two most conservative Justices on the Court (maybe now two of the three most conservative), and the most liberal Justice, all of them Catholic and none of them really the sort of high-level scholar that represents the Yale Law School stereotype. One of them, Clarence Thomas, rarely has anything good to say about Yale. You wouldn’t find a lot of people like any of them at Yale Law.
There are only nine Justices on the Supreme Court at any time, and all sorts of luck is involved in getting nominated and getting confirmed. Having alumni on the Court is more like a happy accident than a real measure of law school strength. The last non-Harvard/Yale Justice was Justice John Paul Stevens, who went to Northwestern Law School. Stevens was a brilliant jurist, but while he was on the Court no one said, “Oh, Northwestern has a Justice on the Supreme Court; that must mean it’s a top 3 or 4 or 5 law school.” And Chief Justice Warren Burger had gotten his law degree at night from the predecessor of William Mitchell College of Law in St. Paul MN. For sure no one thought that made William Mitchell a top law school. (What it did mean is that the person is a lot more important than the law school.)
If you want a sense of a law school’s current prestige (or, put another way, its ability to attract the most impressive students), you can look at where Supreme Court clerks come from. At this point, most of the recent Justices were clerks themselves when they came out of law school. In this decade, the top six are Yale 91, Harvard 90, Stanford 29, Virginia 21, and Chicago and Columbia tied at 17 apiece. Stanford and Yale are the smallest of that group by far (which really underlines how strong Yale Law School is). The ratio between Stanford’s clerks and Harvard’s is close to the ratio between their overall student bodies, and the other three schools are about twice the size of Stanford or Yale. If you go back to 1990 – which would catch most of the people who might be considered for high-level judicial appointments in the future – the top 6 schools are all the same, and the order is Harvard 281, Yale 240, Chicago 100, Stanford 86, Columbia 66, Virginia 57.