A few years ago I posted a list of number of Nobel prizes aggregated by undergraduate institution of the winner. A social science researcher who reads this blog got interested in the topic and has compiled much more complete information, which he is preparing to publish.
He reports that the school with the most Nobel + Fields + Turing prizes, normalized to size of (undergraduate) alumni population, is Caltech, which leads both Harvard and MIT (the next highest ranked schools) by a factor of 3 or 4. Caltech beats Michigan by a factor of ~50, and Ohio State (typical of good public flagships) by a factor of ~500!
To obtain a higher statistics measurement of exceptional achievement, he aggregated living members of the National Academy of Science, National Academy of Engineering, and Institute of Medicine, and normalized to size of alumni population over the last 100 years or so. Caltech again comes out first, beating both Harvard and MIT by a factor of about 1.5. Caltech beats Yale and Princeton by a factor of ~4, and Stanford by a factor of ~5. Swarthmore and Amherst are the leading liberal arts colleges. (See list below.) Caltech beats very good public universities by factors ~100 and more typical public universities by factors ~1000.
Berkeley is the best public university in both the Nobel+ and National Academies rankings. Berkeley is roughly tied with Stanford in Nobels+ per alum, but behind in academicians per capita.
As you might expect, correlation of rank order in these lists with average SAT score is pretty high. Likelihood ratios of ~500 or 1000 for high end achievement suggest that 1. psychometric scores used in college admissions have significant validity and 2. high end achievement is correlated to unusually high ability: two schools with very different mean SAT have very different population fractions above some threshold, such as +3 SD. For example at Caltech perhaps half the students are above +3 SD in ability, whereas at an average university only 1 in ~500 are at that level, leading to ratios as large as 100 or 1000!
Colleges ranked by per capita production of National Academy (Science, Engineering, Medicine) members:See also Annals of Psychometry: IQs of eminent scientists, and Vernon Smith at Caltech.
California Institute of Technology
Massachusetts Institute of Technology
Correction! The original post quoted results using an estimate of alumni population derived from recent US News data. However, some schools have changed over time in enrollment, so more precise estimates are required. The lists below use graduation numbers reported to IPEDS from 1966-2013 and probably yield more accurate rankings than what was reported above. The main difference on the Nobel+ list is that the University of Chicago jumps to #3 and MIT falls several notches. On the NAS/NAE/IOM list MIT is #2 and Harvard #3.
Undergraduate Institution | Nobel+ | Bachelor's degrees awarded (1966-2013) | Prize per capita ratio
California Institute of Technology 11 9348 0.001176722
Harvard University 34 81553 0.000416907
University of Chicago 15 37171 0.000403540
Swarthmore College 5 15825 0.000315956
Columbia University 20 68982 0.000289931
Massachusetts Institute of Technology 14 52891 0.000264695
Yale University 13 60107 0.000216281
Amherst College 4 18716 0.000213721
[ For comparison: Penn State and Ohio State ~ 0.0000028 and 0.0000026 ; many schools have zero Nobel+ winners. ]
Undergraduate Institution | NAS+NAE+IOM | Bachelor's degrees awarded (1966-2013) | ratio
California Institute of Technology 78 9348 0.0083440308
Massachusetts Institute of Technology 255 52891 0.0048212361
Harvard University 326 81553 0.0039974005
Swarthmore College 49 15825 0.0030963665
Princeton University 109 50633 0.0021527462
Amherst College 35 18716 0.0018700577
Yale University 112 60107 0.0018633437
University of Chicago 56 37171 0.0015065508
Stanford University 117 79683 0.0014683182
[ For comparison, Arizona State and Florida State ~ 0.000013 ; University of Georgia ~ 0.000008 ]