Are you getting those results on Pangea maps, vadalaz? I've never played them but those numbers seem more feasible on Great Plains type maps (from what I've seen mountain+river cities are in abundance on those maps), no?
Yeah, the numbers I give are very optimistic. I'm not sure what a realistic scenario on an average Pangaea would be, since I haven't played a Pangaea SV (or any first-roll map for that matter) in a really long time.
How big a difference between planting an academy (A) and bulbing (B) do you think is necessary to make bulbing the clearly correct choice?
I think it's hard to say and depends on your late-game beakers and total number of GSs you can get. Let me try to compare them a bit more carefully:
Bulb for Plastics (B)
Let's assume you're averaging x bpt for 8 turns pre-Plastics. Your bulb at this point is worth (8 / 1.1)*x = 7.27x, as Rationalism opener bonus doesn't count towards bulbs. Let's also assume that you can buy all labs at once and they increase your bpt by about 35%. Labs give +50%, but since the bonus is additive, it's actually a 19-31% increase depending on the city, and then there's the raw science you get from the specialist slot and the lab itself, so I think 35% is fair. You get labs 7 turns earlier than a no-bulb-no-academy game, so in total this GS gets you
7.27x + 7*0.35x = 9.72x beakers
and
7 turns of working an extra scientist slot = 42 GPP with garden, LToP, ideology and Humanism
Academy (A)
Let's say the academy gives you m beakers pre-Plastics. You also get some beakers from reaching schools 2 turns faster, I think 150 a turn is a good estimation for an average empire, so 300 total. As for GPP, you reach Printing Press one turn quicker (1 GPP), schools 2 turns quicker (9 GPP), ideology 2 turns quicker (2 GPP). You reach Plastics (m+300)/x turns faster than no-bulb-no-academy, and each endgame bulb is increased by 48*8=384 beakers in the best case scenario. So, assuming 13 bulbs and n beakers from the academy post-Plastics, academy gets you in total:
m + 300 + (m+300)/x * 0.35x + 13*384 + n = 1.35m + n + 5397 beakers (in the 200-turn spreadsheet m = 1250 and n=1500, so total would be 8548.5, slightly better than the spreadsheet prediction)
and
12 GPP described above plus (m+300)/x specialist-turns from getting labs quicker... would be 2 turns in most cases, so that's another 12 GPP, for a total of 24 GPP from the academy.
No bulb, no academy (NBA)
I think [endgame bpt] = [1.8 * pre-plastics bpt] is a reasonable estimation (750 -> 1350, 1000 -> 1800... sounds about right). So if you save the GS for an endgame bulb, you'd probably get around 13x beakers from it.
B will always get you the most GPPs, it gets the last natural GS one turn faster than
A and 2 turns faster than
NBA. Also consider that the earlier you get labs, the earlier you can start bulbing for Rocketry and build Apollo, so for the very best finish times I think this is the correct play.
To summarize:
By turn #t,
B's would get its final scientist and in total
B's GSs would have made roughly 9.72x (Plastics bulb) + 3*10x (Rocketry bulbs) + 10*13x (endgame bulbs) = 169.72x beakers
By turn #t+1,
A would get its final scientist and in total
A's GSs would've made (1.35m + n + 5397) + 160x beakers
By turn #t+2,
NBA would get its final scientist and in total
NBA's GSs would've made 30x + 11*13x = 173x beakers
Bulbing is strictly better than the academy if your x (pre-Plastics bpt) is high enough and the game doesn't last too long for the academy science (m and n) to catch up. In the t200 spreadsheet example, you'd need x > 879.4 bpt for that. Bulbing could still be better with a lower x if you didn't actually need the academy beakers and just wanted your last GS asap though.
With enough cities, a double-bulb into Plastics would get the 14 scientists by turn #t-2 and an extra GS by turn #t+2, which I believe makes it strictly better than NBA. But only if you have an extra city capable of getting that GS out.