I just realized something. While it feels intuitive that getting 1 more

is the value of half a specialist, it really isn't that simple. In my save there are 2 farmed fps they can support an extra specialist compared to 2 cottaged fps. So 4

+4

+0

. However, cottages are 3

+3

+2

(a grassland cottage!). They are even in food, so they should be compared, not just give an extra pop to the specialist route (although it does reaches higher size a bit faster).
So a specialist needs to beat not two, but three cottages. Well, it does clearly beat 3 unmatured cottages (2

+2

+2

) when farms+rep spec is (1

+1

+6

) (even ignoring library bonus). But cottages will catch up quickly, and then there is bureaucracy which strongly favors cottages. However, the main benefit of running specialists has always been

, but it's value is not easily put into a mathematical formula. If we value a GS at ~1500

, the first 100 points are worth 15

and a specialist generates 3

-points so +45

per turn

, but then it goes down rather quickly. And obviously cottage-routes aren't ignoring

... So maybe it would be fair to say these

-points will lead to the birth of 5th

, making the cost 500

-points. Still, that's 3*1500/500= +9

extra for the scientist. I know, these are all just assumptions that might be inaccurate, or at least depending on a number of factors.
No definite conclusion, except that running specialists that don't lead to the birth of

is in general bad, even under rep (but I guess everybody knew that already). Cottages are good, because they don't lose food!