Time for some more legacy math! Although my own daughters are still several years away from their college applications, it is never too early to start thinking about what their chances might be at Williams. Recall our earlier discussion of the fact that there were 94 legacies admitted into the class of 2009 with an average SAT score of 1446.

Thanks to Jim Kolesar, we now know that 68 of these legacies ended up enrolling in the class. Comments:

1) I wonder about the 26 students who didn’t come to Williams. Are these mostly very strong students who choose places like Harvard/Yale/Princeton/Stanford instead? If so, this would suggest that the average SAT score of the students who came to Williams was lower than the 1446 average of the 94 applicants admitted. It is also possible that they are weaker students who realized that Williams might not be the best place for them, but I doubt that.

2) What is the extreme lower-bound for the enrolled legacies? Assume that all 26 of the students who turned down Williams had perfect 1600s. This implies that the 68 enrolled legacies would average around 1390 since (94 * 1446 – 26 * 1600) / 68 = 1387.

3) Can we reject the null hypothesis that enrolled legacies have similar SAT scores to the overall Williams population? No. Note that the SAT average for the class of 2009 is 1425. Solving the appropriate formula for X:

(94 * 1446 – 26 * X) / 68 = 1425

we can see that X = 1500. In other words, if the average SAT score of the accepted legacies who went elsewhere is 1500, then the average for the enrolled legacies would be the same as the average for the entire class. Is 1500 a plausible estimate for those 26 non-enrollees? Sure.

4) Does this imply that legacy status does not positively impact one’s admissions chances? No. Again, the key issue is that 1425 is the average for the entire class. The average for students from wealthy families with college-educated parents is going to be much higher than 1425 because, for good or for ill, the College gives preferences to applicants, independent of race, from poorer, less educated families. Now, the magnitude of those preferences is not large, but it is not zero.

5) Key unknowns are the characteristics of applicants and admitted students who come from families “like” those of the legacy applicants. Although race, wealth and athletic talent are complicating factors, I doubt that the average SAT scores of similar enrolled students in the class of 2009 is much higher than 1475.

All in all, I will stick with my back-of-the-envelope guess that being a legacy, all else equal, is worth about 50 points in combined average SAT score. This is a minor advantage, much lower than the 100 points that tip-level athleticism counts for and 150 points that accrue to URMs.

In other words, if you’re an Eph and your daughter scores 1300 or below (and she is not an athlete, heiress or deeper shade of purple), you better start looking at Colby.