Stanford or Harvard/Yale/Princeton/MIT, or Others?

When this article was first published on CC, a lot of details were left out. The reason was that I wanted to see any critique or additions to my original post. Obviously the math part of the article may be very complicated to most people and most comments were not critical. Some of the details cannot be obtained as the information for this PIE problem is not complete. After so long it may be the time for me to give more details and let people  reproduce the results.
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Harvard, Yale, Princeton, Stanford and MIT, or HYPSM, are the main five schools that steal  prefrosh among each other. As many evidences from the school newspaper or admission official’s comments show that they don’t really concern to lose profrosh to schools other than the other HYPSM. This analysis was based on the data of Class of 2014 when Harvard and Princeton did not have SCEA. Therefore, the results could be different for the Class of 2016 as all HYPS have SCEA now.
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For Class of 2014, Stanford accepted 2340 students totally, 40 students were accepted from the waitlist[1]. Its total freshman enrollment was 1672[2]. The yield was 71.5%, which means that 668 students were accepted but did not matriculate.
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For those 2340 students accepted [3]:

398 students were also accepted by Harvard;

359 accepted by Yale;

 430 accepted by Princeton;

304 accepted by MIT;

630 accepted by UC Berkeley
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For those 668 non-matriculates [4]:

32% went to Harvard, or 214 Stanford/Harvard cross-admits went to Harvard;

16% or 107 Stanford/Yale cross-admits went to Yale;

14% or 94 Stanford/Princeton cross-admits went to Princeton;

13%, or 87 Stanford/MIT cross-admits went to MIT.
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For cross-admit yields [4]:

Stanford: Harvard=38%:62%;

Stanford: Yale=50%:50%;

Stanford: Princeton=63%:37%;

Stanford: MIT=60%:40%.

Finally, for the detailed distribution of the HYPSM cross-admits:

For those 398 Stanford/Harvard cross-admits, 214 enrolled at Harvard. This means that there were total of 214/62% = 345, or 87% of Harvard/Stanford cross-admits,  went to either Harvard or Stanford.  And hence there should be 345*38% = 131 enrolled at Stanford. The rest of cross-admits, total of 56, enrolled at somewhere else. Direct head-to-head competition: Harvard/Stanford=214:131, or 38% went to Stanford and 62% went to Harvard.
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Similarly for those 359 Stanford/Yale cross-admits, 107 enrolled at Stanford,   107 enrolled at Yale, 145 enrolled at somewhere else. Direct head-to-head competition: Stanford/Yale=107:107, or 50% went to Stanford and 50% went or Yale.
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For those 430 Stanford/Princeton cross-admits, 160 enrolled at Stanford,   94 enrolled at Princeton, 176 enrolled at somewhere else. Direct head-to-head competition: Stanford/Princeton=160:94, or 63% went to Stanford and 37% went or Princeton.
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For those 304 Stanford/MIT cross-admits, 131 enrolled at Stanford,   87 enrolled at MIT, 86 enrolled at somewhere else. Direct head-to-head competition: Stanford/MIT=131:87, or 60% went to Stanford and 40% went or MIT.
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In summary, for those 2340 admits, Stanford admitted 214/0.62+107/0.5+94/0.37+87/.4 = 1016 HYPSM cross-admits, or 1016/2340 = 43.4% of total admits were HYPSM cross-admits. Of those cross-admits, Stanford enrolled 131+107+160+131 = 529  and lost 487 students to HYPM, its HYPSM cross-admits yield was 529/1016 = 52%. Moreover, 529/1672 = 31.6% of Stanford students of Class of 2014, or about a third of the entire class, were HYPSM cross-admits.
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There were 668-487 = 181 admits went to schools other than HYPSM.  None of schools other than HYPM did Stanford lose more than 2% of non-matriculates or  13 students per school[4] – those schools including ALL other Ivies, Chicago, Caltech, Duke, Rice and UCB, etc, for all the reasons that could be.

References

[1] http://mathacle.blogspot.com/2010/08/yield-to-admit-ratio-yar-for-class-of.html

[2] http://ucomm.stanford.edu/cds/2010.html

[3] http://www.stanforddaily.com/2010/10/08/financial-aid-deficit-may-persist-four-to-five-years-hennessy-tells-stanford-faculty/

[4] http://facultysenate.stanford.edu/2010_2011/minutes/10_07_10_SenD6388.pdf

Stanford's HYPSM Cross-Admits for 2002 - 2010

http://facultysenate.stanford.edu/2010_2011/minutes/10_07_10_SenD6388.pdf

HYPSM Cross-Admit Raw Data

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Raw sample data from CC

Class of 2014

1. Stanford - also admitted to Princeton
2. Yale- also admitted to Princeton
3. Yale- also admitted to Harvard
4. Yale - also admitted to Princeton
5. Stanford - also admitted to MIT, Princeton
6. Yale - also admitted to Harvard
7. Harvard- also admitted to Yale, Princeton, Stanford, MIT
8. Princeton - also admitted to Yale
9. Princeton - also admitted to MIT
10. Princeton - also admitted to Stanford
11. Harvard - also admitted to Princeton , Stanford
12. Princeton - also admitted to Stanford
13. Princeton- also admitted to Harvard, Stanford, Yale, MIT
14. Princeton- also admitted to MIT, Stanford
15. Princeton - also admitted to Harvard, Stanford
16. Harvard - also admitted to Yale, Princeton, and Stanford
17. Princeton - also admitted to MIT
18. Stanford - also admitted to Harvard and Yale
19. Yale - also admitted to Stanford
20. Yale - also admitted to Harvard, Stanford
21. Princeton - also admitted to Stanford
22. Yale - also admitted to Princeton
23. Yale - also admitted to Princeton
24. Yale - also admitted to Princeton
25. Princeton - also admitted to Harvard
26. MIT - also admitted to Harvard
27. Yale - also admitted to Stanford
28. Stanford - also admitted to Harvard, Princeton, Yale, MIT
29. Harvard - also admitted to Yale, Princeton
30. Yale - also admitted to Princeton
31. Yale - also admitted to Harvard
32. Harvard - also admitted to Princeton and Yale
33. Yale - also admitted to Harvard, Princeton, Stanford
34. Harvard - also admitted to MIT.
35. Yale- also admitted to Harvard and Princeton.
36. MIT - also admitted to Harvard.
37. Yale - also admitted to Harvard and Stanford
38. Yale - also admitted to MIT and Stanford
39. MIT - also admitted to Yale, Princeton, Stanford
40. Stanford - also admitted to Harvard
41. Stanford - also admitted to Princeton
42. Yale - also admitted to Harvard and Princeton
43. MIT - also admitted to Princeton
44. Harvard - also admitted to Yale and Princeton.
45. Harvard - also admitted to MIT
46. Princeton - also admitted to MIT
47. Harvard -- also admitted to Princeton
48. Stanford -- also admitted to Harvard
49. Stanford -- also admitted to Harvard
50. Princeton-- also admitted to Stanford
51. MIT - also admitted to Yale
52. Yale -- also admitted to Harvard & Princeton
53. Stanford-- also admitted to Yale
54. Harvard -- also admitted to Yale
55. Yale -- also admitted to Princeton
56. Princeton - also admitted to MIT
57. MIT - also admitted to Harvard and Princeton
58. Harvard - also admitted to Princeton
59. Harvard - also admitted to Yale, Princeton and Stanford
60. MIT - also admitted to Harvard and Stanford
61. Princeton - also admitted to Stanofrd and MIT
62. Stanford - also admitted to Princeton
63. Yale - also admitted to Harvard
64. Harvard - also admitted to Yale and Stanford
65. Harvard - also admitted to Princeton
66. Harvard - also admitted to Yale
67. Stanford - also admitted to Yale, Princeton and MIT
68. Harvard -also admitted to Yale
69. Harvard - also admitted to Yale and Princeton
70. Yale - also admitted to Harvard, Princeton and Stanford
71. Harvard - also admitted to Yale, Princeton, Stanford, MIT
72. Yale- also admitted to Harvard
73. Yale - also admitted to Harvard
74. Princeton - also admitted to Harvard and Yale
75. MIT - also admitted to Stanford
76. MIT - also admitted to Harvard and Stanford
77. Stanford - also admitted to Princeton
78. Princeton - also admitted to Harvard, Yale and MIT
79. Harvard -- also admitted to Yale, Princeton and Stanford
80. Harvard - also admitted to MIT and Princeton

Class of 2013

1) Princeton - ALSO ADMITTED TO: Stanford
2) Harvard - ALSO ADMITTED TO: Yale
3) Yale - ALSO ADMITTED TO: Stanford
4) Harvard - ALSO ADMITTED TO: Yale
5) Princeton - ALSO ADMITTED TO: MIT
6) Harvard - ALSO ADMITTED TO: Yale
7) Stanford - ALSO ADMITTED TO: Yale, MIT
8) Princeton - ALSO ADMITTED TO: HYSM
9) MIT - ALSO ADMITTED TO: Harvard
10) MIT - ALSO ADMITTED TO: Princeton
11) Yale - ALSO ADMITTED TO:Harvard, Princeton
12) MIT - ALSO ADMITTED TO: Princeton
13) Yale - ALSO ADMITTED TO: Harvard
14) Yale - ALSO ADMITTED TO: Princeton
15) Yale - ALSO ADMITTED TO: Stanford
16) Stanford - ALSO ADMITTED TO: Princeton
17) Princeton - ALSO ADMITTED TO: Yale
18) MIT - ALSO ADMITTED TO: Yale, Princeton
19) Yale - ALSO ADMITTED TO: Harvard, Princeton
20) Harvard - ALSO ADMITTED TO: Yale, Princeton, Stanford
21) Stanford - ALSO ADMITTED TO: Yale
22) Princeton - ALSO ADMITTED TO: Harvard
23) Harvard - ALSO ADMITTED TO: Yale
24) Princeton - ALSO ADMITTED TO: MIT, Stanford
25) Yale - ALSO ADMITTED TO: Princeton,Stanford, MIT
26) Harvard - ALSO ADMITTED TO: MIT
27) Harvard-ALSO ADMITTED TO : MIT
28) Harvard - ALSO ADMITTED TO: Yale, MIT
29) Princeton-ALSO ADMITTED TO: MIT
30) Harvard - ALSO ADMITTED TO: Princeton
31) Princeton - ALSO ADMITTED TO: Yale, Stanford, MIT
32) Stanford - ALSO ADMITTED TO: Princeton
33) MIT – ALSO ADMITTED TO: Princeton
34) Yale - ALSO ADMITTED TO: Harvard
35) Yale - ALSO ADMITTED TO: Princeton
36) Yale - ALSO ADMITTED TO: Harvard
37) Yale - ALSO ADMITTED TO: Princeton
38) Harvard - ALSO ADMITTED TO: Stanford
39) MIT - ALSO ADMITTED TO: Harvard
40) Princeton - ALSO ADMITTED TO: Yale
41) Princeton - ALSO ADMITTED TO: Harvard, Stanford
42) MIT - ALSO ADMITTED TO: Princeton
43) Princeton - ALSO ADMITTED TO: Yale
44) Yale - ALSO ADMITTED TO: Princeton
45) Harvard - ALSO ADMITTED TO: Stanford
46) Yale - ALSO ADMITTED TO: Harvard
47) MIT - ALSO ADMITTED TO: Harvard, Yale, Stanford and Princeton
48) Harvard- ALSO ADMITTED TO: MIT
49) Harvard - ALSO ADMITTED TO: Yale, Princeton
50) Princeton - ALSO ADMITTED TO: Harvard, MIT, Stanford, Yale
51) Princeton - ALSO ADMITTED TO: Stanford
52) Stanford - ALSO ADMITTED TO: Harvard, Princeton
53) Yale- ALSO ADMITTED TO: Harvard, Stanford, MIT
54) MIT- ALSO ADMITTED TO: Harvard
55) MIT- ALSO ADMITTED TO: Princeton
56) Princeton- ALSO ADMITTED TO: Stanford, MIT
57) Stanford - ALSO ADMITTED TO: Princeton
58) Princeton - ALSO ADMITTED TO: Yale
59) Yale - ALSO ADMITTED TO: Princeton

Class of 2012

1. Yale – also admitted to Harvard
2. MIT – also admitted to Harvard, Princeton, Stanford
3. Yale – also admitted to Princeton
4. Princeton – also admitted to Harvard
5. Princeton – also admitted to Harvard, Yale, Stanford
6. Yale – also admitted Princeton, Stanford
7. Yale – also admitted to Stanford
8. Stanford – also admitted to Harvard
9. Stanford – also admitted to Yale
10. Yale – also admitted to Princeton, Stanford
11. Harvard – also admitted to Princeton, Stanford, MIT
12. Stanford – also admitted to Harvard, Yale, Princeton, MIT
13. Harvard – also admitted to Yale, Princeton, Stanford
14. Harvard – also admitted to Princeton, Stanford, MIT
15. MIT – also admitted to Princeton
16. Harvard – also admitted to MIT
17. Yale – also admitted to Harvard, Princeton
18. Yale – also admitted to Princeton
19. Princeton – also admitted to Harvard, Stanford
20. Princeton – also admitted to Harvard
21. Yale – also admitted to Harvard
22. Princeton – also admitted to Harvard, Yale
23. Yale – also admitted to Harvard, Stanford
24. Princeton – also admitted to Stanford
25. Stanford – also admitted to Yale, Princeton
26. Stanford – also admitted to Harvard, Yale, Princeton, MIT
27. Princeton – also admitted to Stanford
28. Princeton – also admitted to Yale, MIT
29. Princeton – admitted to MIT
30. Harvard – also admitted to Yale, Stanford, MIT
31. Yale – also admitted to MIT
32. Harvard – also admitted to Princeton, Stanford
33. Yale – also admitted to Harvard
34. Princeton – also admitted to Stanford
35. MIT – also admitted to Harvard
36. Princeton – admitted to Yale
37. Harvard – also admitted to Yale, Princeton
38. Stanford – also admitted to Harvard, Princeton, MIT
39. Yale – also admitted to Harvard, MIT
40. MIT – also admitted Yale
41. Princeton – also admitted to Harvard
42. Stanford – also admitted to Yale
43. Harvard – also admitted to Princeton
44. MIT – also admitted to Harvard, Stanford
45. Stanford – also admitted to MIT
46. Harvard – also admitted to Princeton, Stanford
47. Yale – also admitted to Princeton
48. Harvard – also admitted to Yale, Princeton
49. Stanford – also admitted to Princeton
50. MIT – also admitted to Harvard
51. Harvard – also admitted to Yale, Princeton, Stanford, MIT
52. Princeton – also admitted to MIT
53. Harvard – also admitted Yale, Princeton, MIT
54. Princeton – also admitted to MIT
55. Harvard – also admitted Yale, Princeton, Stanford
56. Princeton – also admitted to Yale, Stanford, MIT
57. Stanford – also admitted to Harvard, Yale, Princeton, MIT
58. Yale – also admitted to Harvard, Princeton
59. Yale – also admitted to Harvard, Princeton
60. MIT – also admitted to Princeton

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