Harvard, Yale, Princeton and Stanford Cross-Admits for the Class of 2012

I have to make certain assumptions to do the following analysis. First, I have to assume that most of best students in their categories were admitted by at least two of those schools, secondly, that every school tried to get those students while it could without sacrificing its interests like yield or the quality of the students. Here is a sample result for 60 cross-admitted by the Harvard, Yale, Princeton, Stanford and MIT. The data might be a little bit biased toward MIT while they were collected. Therefore, MIT will not be concluded in the analysis.

Action\School-- Harvard Yale Princeton Stanford MIT
admit ----------- 37....... 34 ..... 43 .......30 .......25
% of total ------- 61.7..... 56.7...71.7 ..... 50..... 41.7
matriculate ----- 13........ 15 .... 15 ...... 10...... 7
% of admit ------ 35.1..... 44.1 ... 34.9 .... 33.3 ... 28.0


How many cross-admitted are there by HYPSM? We can use Stanford’s released data to find out. 1,727 out of 2400 admitted students accepted Stanford’s offer of admission to the Class of 2012, placing the yield rate for this admission cycle at a University record high of 72 percent. 431 of them are the first in their families (FIF) to attend four-year university and about 20%, or 345, are legacies. Minus those 776 from 1727 we have 951 left. Since they only won 33.3% of cross-admits, there must be some other groups like athletes or special talents involved. If we assume that Stanford offered x number of students who were in the cross-admit group, then Stanford offered

FIF+legacies: 431+345=776, assume 100% matriculation rate
Cross-admits: x, 33.3% matriculation rate
Athletes/specials: 2400-776-x, assume 100% matriculation rate

for total 2400 admissions. That is, 776+33.3%x+2400-776-x=2400*72%, or x=1008. Since Stanford only tried 50% of the total, we can speculate that there were about 2000 out there. Amazingly as it is, those top 2000 students best in their categories were what every school was looking for. Now look again to see what each school did based on the initial yield (H-74%, Y-69%, P-58%,S-72%), without counting the admitted from the waitlist:

Action\School----Harvard Yale Princeton Stanford
matriculate ----- 1480....1305...1150......1727
cross-admit------ 433.....500....500........333
percent ---------- 29.3....38.3...43.4......19.3

An example of calculation of the number of the cross-admits is Harvard: (% of total)*(% of admit)*(total # of cross-admits)=61.7%*35.1%*2000=433.

Regarding the Collegiate Matchups Table as put by The New York Times in the 2006:

---------Harvard Yale Princeton Stanford
Harvard----- * ----- 65 ---- 75 ----- 73 <----Harvard gets 65% of cross-admits, etc.
Yale --------35 ----- * ----- 62 ----- 60
Princeton --- 25 ---- 38 ---- * ------ 48
Stanford ---- 27 ---- 40 ---- 52 ------ *

the new marchup table looks like

-----------Harvard Yale Princeton Stanford
Harvard----- * ----- 44 ---- 65 ----- 62
Yale --------56 ----- * ----- 62 ----- 40
Princeton --- 35 ---- 38 ---- * ------ 50
Stanford ---- 38 ---- 60 ---- 50 ------ *

Since the table drew from a small sample (about 60 out of 1400-2000 cross-admits), we can only draw the conclusion that Harvard lost cross-admits to all other schools; Yale gained on Harvard, lost to Stanford, about the same as before with Princeton; Princeton gained on Harvard, about the same with Yale and Stanford; Stanford gained on Harvard and Yale, about the same as Princeton.