I am still on GnK, and I understand RAs were devalued in BNW. But even at 2 turns of science, the RA calculation still beats rush buying (although its much closer). You do not need 6 friendships, that could be 2 rounds of 3 RAs. The big difference I see is turns. Those 4500 beakers could take 60 turns, whereas your 3000 beakers took only 15 turns! But I think the limiting factor is gold, and if that is the case, then 4500 beakers in 60 turns is better than 3000 beakers in 15 turns.
Well, that is why I am asking! Those people who buy all their universities and public schools are doing so many other things better than I that I don't see any hard conflict. But those expert players can usually so objectively explain their habits, I am confused as to why my rough math doesn't seem to warrant this particular practice.
In G&K, the base output of an RA (before Porcelain Tower and Scientific Revolution) is based upon the two partners' combined beakers generated over the 30 turns of the RA. Your base output of a G&K RA (see details below) will always be greater than your base RA output in BNW, except where you are the RA partner who is producing the lower amount of beakers -- in that case G&K RAs and BNW RAs will have the same base output.
G&K research agreement math:
RA beakers = n% * (min(a/3, (a+b)/6)
where
a = sum of your beakers over RA length
b = sum of your RA partner's beakers over RA length
n% = RA modifier % (base 50% + 25% from Scientific Revolution + 25% from Porcelain Tower)
Using the same numbers from my earlier example, if a = 6000 beakers (average of 200 beakers/turn) and b = 3000 beakers (average of 100 beakers/turn), the base RA output (without Porcelain Tower or Scientific Revolution) for you will be 750 beakers and for your RA partner will be 500 beakers, which represents 5 turns of average beaker production for your RA partner and just under 4 turns of average beaker production for you. In G&K, your beakers/turn are the upper limit on your yield from a research agreement, while in BNW the limit is the lower of the two RA partners' beaker output (and, as noted above, if you are the partner contributing the lower amount, the G&K and BNW yields will be the same).