tl;dr: Legacy status does not provide a meaningful advantage in admissions to elite colleges like Williams. People like Sam Altman and Arjun Narayan ’10 are wrong, either because of genuine ignorance or because of a (unconscious?) refusal to confront the major beneficiaries of admissions preferences: athletes and (non-Asian) racial minorities. (If Sam has complained about extra considerations that Stanford gives football players and African-Americans, I must have missed it.)
Morty [then Williams President Morton Schapiro] noted that a decade or so ago [or perhaps when he arrived?], the average legacy was a 3.3 on the 1-9 scale of academic ranks while the average non-legacy was 2.3. Morty did not seem to be a huge fan of this gap, or of giving legacies such a preference. He then noted that the latest statistics show that legacy and non-legacy are now equivalent (both at 2.3). Morty confirmed, consistent with all the analysis I have done, that being a legacy is not a meaningful advantage in getting into Williams.
Director of Communications Mary Dettloff kindly provided this update for 2017:
I had a conversation with Dick Nesbitt about this, and he says it has long been our policy not to release academic standing information for specific subgroups of students. That said, he also shared that for at least the last 20 years, the legacy students have had equal, if not marginally stronger, SAT scores and Academic Rating when compared to the rest of their classmates.
More importantly, should we be surprised that students whose parents went to elite colleges are much more likely to win admissions to elite colleges themselves? No! Nature and nurture are passed down through the generations now, just as they always have been.
Consider professional baseball. From the New York Times:
A random US man has a 1-in-15,000 chance of playing in the MLB. The son of an MLB player has a 1-in-75 chance. In other words, your odds of playing in the MLB are 200 times higher of your father played. Given that fact, should we be surprised if your odds of coming to Williams are 200 times higher if your parent is an Eph?
The mechanisms in both cases are the same. Genetics play a major role. The specific genes — probably thousands of them — that help you to hit a curve ball are passed from father to son. The genes that aid in doing well in school and on standardized tests are passed on just as easily. Nurture matters. Baseball players probably provide their sons with a better than average environment in which to learn baseball. Ephs who become parents do the same. You should no more be surprised at the high numbers of legacies at elite colleges than at the high numbers of baseball children in the Majors.
However, it is interesting to consider how legacy admissions have evolved in the last 30 years. In the 1980’s, it was tough for Williams to find 75 high quality legacies in drawing from Williams classes of the 1950s. First, the college was much smaller than, with fewer than half the current student population. Second, Williams was much less academically rigorous. (That is, there were plenty of not-very-smart students.)
In the 80’s, there were 500 academically accomplished students per class. Judging/guessing from what we see at reunions, the total number of children of a typical class is at least 500 and probably closer to 1,000. But only 75 or so find spots at Williams! Do the other 425 go to Stanford? Nope. And the same harsh mathematics apply to the children of other elite schools. Since smart people have smart children, the pool of legacies that the College has to choose from is very impressive. Williams does not need to lower standards at all to find 75 good ones.
 To be fair to Altman/Narayan, there are some subtle counter-arguments. First, if it is the case that legacies, as a group, differ from non-legacies on other dimensions besides academic rating, then it might not be fair to compare the two groups directly. Instead, we should compare legacies with non-legacies who “look” like legacies. For example, if legacies are more likely to be white and non-poor, then comparing them with non-legacies is makes no sense. Instead, we should compare them with similarly white/non-poor non-legacies.
Second, it could be the case that legacies come in two flavors: over-qualified and under-qualified. The over-qualified ones are exceptional candidates who turn down Harvard/Yale/Princeton/Stanford for Williams. The under-qualified ones receive substantial preferences in admissions. Combining the two groups creates an overall legacy group which is similar to non-legacies but which “masks” the substantial advantages given to under-qualified legacies.
 Of course, legacy students are much more likely to attend their parents’ alma mater than legacy baseball players are to play for the same team as their fathers. Exercise for the reader: Explore the industrial organization of elite colleges and major league baseball to explain this difference. Perhaps a better view is to consider all the legacy students as a whole, in the same way that the New York Times considers all the legacy baseball players. But this post is already long enough . . .
 sigh, an EphBlog regular, points out this study (pdf) on “The impact of legacy status on undergraduate admissions at elite colleges and universities.” The author argues that legacy status matters a great (or at least did matter in the fall of 2007). I have my doubts. Let’s dive into the details in the comments!