The question of which institutions produce the most Nobel prizewinners is one not just of numbers but of ratios (see Nature 538, 152; 2016). Merely counting doesn't cut it.
We analysed the distribution of US Nobel laureates and members of the US National Academy of Sciences according to their undergraduate institutions (R. Root-Bernstein and K. Pawelec J. Genius Eminence 1, 28–42; 2016). We found that most had trained in California, Illinois, Wisconsin, Massachusetts, New York, Connecticut and New Jersey. Yet after correcting either for the number of scientists per state or by state population, the probability of becoming a Nobel prizewinner or National Academy member was almost the same, irrespective of institution.
The case is entirely different for graduate education, where institution seems to be a dominant factor in future success.