BWS
Big Bradd Wolfe
Similar to the current thread about Best use of Oxford University, I'm curious about Great Scientist timing. I'm interested both in experiences and in mathematical arguments. Here's what I've been able to figure out so far.
Academies
I've heard a number of different guidelines for when to stop planting academies. Sadato's Deity OCC Science guide says to keep planting right up until Plastics, but that's certainly too late. At that point, you could easily get 3,000+ beakers from a bulb. It would take about 100 turns to recoup that with an academy, and there simply isn't that much time left in the game by then.
At the other extreme, academies are pure win for the rare times when you can get a Scientist before Education. That early in the game, a bulb is only worth less than 300 beakers. An academy will recoup that in under 25 turns, then go on to provide 12-33 bpt for the rest of the game.
So when's the best time to stop? At some point in the game, it becomes mathematically impossible for an academy to produce as many beakers as a bulb. The exact point varies with empire size and victory condition, but I estimate that it falls somewhere in the Renaissance Era for Diplomatic Victory, maybe a little later for Technological Victory. This matches the advice I've seen to stop planting academies after public schools.
Bulbs
Once you stop planting scientists, when should you use bulbs? Is it best to use them as soon as possible, or should you use them all in a big bang at the end of the game?
Let's assume that you only use bulbs for technology that you need to win the game, and that you avoid mistakes like bulbing right after a growth spurt, like a new science building. In that case, each bulb should cut the game short by about 6-8 turns, depending on your growth rate. Should you save up your scientists and cut those turns off the very end of the game, or should you cut them out of the middle to unlock your intermediate goals sooner?
For example, if you're working toward a Diplomatic Victory, is it best to use all of your scientists together on Ecology, Telecommunications, and Globalization? Or is it better to use them on earlier techs like Scientific Theory, Biology, Plastics, and Penicillin? Does it matter which tech you're using the bulb for? Or is everything on the critical path the same?
There are a couple of disadvantages to using bulbs early, both related to population growth. As growth slows over time, your science rate will become more constant, and bulbs will come closer to the ideal of 8 turns saved. Earlier in the game, growth is faster, and so you might only shorten a discovery by 6-7 turns.
The other disadvantage is more insidious: Suppose you accept the previous disadvantage and use a bulb to discover Scientific Theory in turn 140 instead of 146. Will that cut 6 turns off the end of your game? Maybe not, because the city will be smaller in turn 140 and won't produce quite as much science. It's not a huge difference, maybe 5% at this point in the game, and it'll diminish over time, but you'll probably lose at least one of the turns that you saved. The details differ for growth techs (Biology, Penicillin), but the same basic paradox applies. This isn't a problem for the final techs, because you don't care about your growth or science after that.
That said, there are sometimes overriding concerns. If you need to move up the timeline to avoid missing a social policy deadline, it may be worthwhile to sacrifice a couple turns to avert a bigger problem. Likewise if you need a military upgrade. Also, scientists cost maintenance and count against upkeep. And I've seen many players lament that they miscalculated the number of scientists they needed and let some go to waste.
Academies
I've heard a number of different guidelines for when to stop planting academies. Sadato's Deity OCC Science guide says to keep planting right up until Plastics, but that's certainly too late. At that point, you could easily get 3,000+ beakers from a bulb. It would take about 100 turns to recoup that with an academy, and there simply isn't that much time left in the game by then.
At the other extreme, academies are pure win for the rare times when you can get a Scientist before Education. That early in the game, a bulb is only worth less than 300 beakers. An academy will recoup that in under 25 turns, then go on to provide 12-33 bpt for the rest of the game.
So when's the best time to stop? At some point in the game, it becomes mathematically impossible for an academy to produce as many beakers as a bulb. The exact point varies with empire size and victory condition, but I estimate that it falls somewhere in the Renaissance Era for Diplomatic Victory, maybe a little later for Technological Victory. This matches the advice I've seen to stop planting academies after public schools.
Bulbs
Once you stop planting scientists, when should you use bulbs? Is it best to use them as soon as possible, or should you use them all in a big bang at the end of the game?
Let's assume that you only use bulbs for technology that you need to win the game, and that you avoid mistakes like bulbing right after a growth spurt, like a new science building. In that case, each bulb should cut the game short by about 6-8 turns, depending on your growth rate. Should you save up your scientists and cut those turns off the very end of the game, or should you cut them out of the middle to unlock your intermediate goals sooner?
For example, if you're working toward a Diplomatic Victory, is it best to use all of your scientists together on Ecology, Telecommunications, and Globalization? Or is it better to use them on earlier techs like Scientific Theory, Biology, Plastics, and Penicillin? Does it matter which tech you're using the bulb for? Or is everything on the critical path the same?
There are a couple of disadvantages to using bulbs early, both related to population growth. As growth slows over time, your science rate will become more constant, and bulbs will come closer to the ideal of 8 turns saved. Earlier in the game, growth is faster, and so you might only shorten a discovery by 6-7 turns.
The other disadvantage is more insidious: Suppose you accept the previous disadvantage and use a bulb to discover Scientific Theory in turn 140 instead of 146. Will that cut 6 turns off the end of your game? Maybe not, because the city will be smaller in turn 140 and won't produce quite as much science. It's not a huge difference, maybe 5% at this point in the game, and it'll diminish over time, but you'll probably lose at least one of the turns that you saved. The details differ for growth techs (Biology, Penicillin), but the same basic paradox applies. This isn't a problem for the final techs, because you don't care about your growth or science after that.
That said, there are sometimes overriding concerns. If you need to move up the timeline to avoid missing a social policy deadline, it may be worthwhile to sacrifice a couple turns to avert a bigger problem. Likewise if you need a military upgrade. Also, scientists cost maintenance and count against upkeep. And I've seen many players lament that they miscalculated the number of scientists they needed and let some go to waste.