Best use of Great Scientists?

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.

You will want to explore this thread from last Summer: http://forums.civfanatics.com/showthread.php?t=469679

I think you will enjoy the math-y bits.

The current discussion would be in Best Use of Great Scientist - Science VC

http://forums.civfanatics.com/showthread.php?t=489044

At least for most of the game regardless of victory condition. Sometime in Industrial though, UN victory path starts narrowing. It will make the break even point a bit earlier than science, but I don't know how much.
(Cultural break even point even earlier; and as a practical matter usually all bulbed so you don't run out of tiles for Landmarks & Holy Sites)

So when's the best time to stop?

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60-70 turns before victory, in my experience.

For diplo/science i find it acceptable to bulb plastics with one GS, the rest are lined up for a bulb fest in the end.

@Browd: Interesting thread, thanks! Not sure how much of that math is sound though, don't think I agree with some of the assumptions made. And I don't know that anyone noticed the growth paradox. But it did point out something I missed, which is that RAs amplify the effects of academies. That might explain why Sadato got away with planting scientists so late.

@joncnunn: That's a link back to this thread. I think you meant this one:
http://forums.civfanatics.com/showthread.php?t=489044

@Moriarte: Because of the growth paradox, I don't know that you're actually helping yourself by bulbing plastics. In case my explanation above is too dense: You get more beakers overall if you let the population grow as much as possible before using the bulb.

Because of the growth paradox, I don't know that you're actually helping yourself by bulbing plastics.

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Of course i do. For example, i have 4k gold stashed (to buy r.labs in 3 of my towns). I bulb plastics, rush labs, wait 8 turns, bulb few GS, finish rationalism, rush UN with GE and win. Same 8 turns are needed after plastics anyway. 1-2 extra pop won't decide anything here. Is there a faster route in my particular example?

By the way: What growth paradox?

I suppose you're only talking about a science victory? The bulb/plant calculation changes depending upon the victory type, and the thread @http://forums.civfanatics.com/showthread.php?t=469679
is only for science.

For a domination game, shaving 5 or so turns off your acquisition of key techs like machinery, dynamite, and navigation is well worth the cost of losing beakers in T200 (or whenever). Even in an aggressive science game, a dynamic approach to science is usually better -- and much more fun -- than a static approach (i.e., gaining and exploiting a tech advantage in war is worth more than the static beaker numbers suggest). Thus, I would never favor a milestone approach to GS's (i.e., plant them until X turns, and save them until Y turns).

Good point about "best" not always meaning "fastest," Dogmouth. I'm coming to this from the context of an OCC Diplomacy challenge. So yes, that's similar to Science victory, with the goal of earliest finish date. Domination and Culture are different in that they have key techs but no scientific "finish line."

Moriarte, I mentioned the growth paradox in my original post. When you discover science tech early, you get a few extra turns with your science buildings, but you also lose a few turns of growth, which offsets some of the gains. I'm trying to work up an example to demonstrate the problem and to determine how significant it is.

I did some modeling based on my recent games, and I got some good data on bulb timing. For now, I just modeled the difference between bulbing Plastics vs Globalization, but the results are interesting enough that I want to see how it works out for earlier tech.

Findings: In my last game, I started researching Plastics on turn 185 with 35 citizens and 397 bpt. If I let research progress normally in my model, then it finishes on turn 196 with 38 citizens and 522 bpt, including the research lab. If I use a bulb, then it finishes on turn 188 with 36 citizens and 510 bpt. You get the lab earlier, but science output doesn't catch up until the population hits 38 several turns later. The shortfall is small, only about 3%, but it's enough to lose a turn by the end of the game. In my model, you discover Plastics and Atomic Theory 8 turns early, but Ecology and Telecommunications are only 7 turns early. If you wait for Globalization to use the bulb, you finish one turn faster overall.

I've been calling this the "growth paradox," but there's a simpler way to explain it. In round numbers, my example civ produces 400 bpt just before Plastics, 500 bpt with a lab, and 600 bpt at the end of the game. If you bulb Plastics, you save 3,200 beakers and add another 800 from the early lab. That saves you 4,000 ÷ 600 = about 7 end-game turns. If you waited to bulb Globalization instead, with your final tech rate, you will save about 8 turns.

Things get more complicated when you bulb earlier techs like Astronomy. The bulb will save about 900 beakers immediately, plus another 300 from the early observatory. It also gets you a school and a lab a little earlier. If my calculations are correct, you will get Scientific Theory 4-5 turns early for about 250 extra beakers, and then Plastics 3-4 turns early for about 350 beakers. Ultimately, using a bulb for Astronomy gets you about 1,800 extra beakers, which only cuts about 3 turns from the end of the game. It's worth a bit more if it lets you open Rationalism one policy sooner, but the numbers for that are too fiddly to estimate. It's also worth a bit more if you do it during a Research Agreement, but those are also too variable to estimate.

Growth techs like Biology and Penicillin work a little differently. Adding a growth building early will increase your population slightly for the rest of the game. Instead of 8 extra turns with your science building, you get 40-100 turns with a couple of extra citizens. Unfortunately, that's still only a few hundred extra beakers, not enough to make up for using a bulb early.

This brings me to the same place that S.K. Ren started out in that thread from last summer. An academy is better than an early bulb, but is it better than a late bulb? You'd need to calculate how much the academy produces itself, plus the value of earlier science buildings, plus the value it contributes to RAs. Might be too many variables to juggle.

Not mentioning how many GS you have? How many you saved for the final bulb.. (or did you fail there?) did you mistime your rationalism/oxford or not? And the resume: "If you waited to bulb Globalization instead, with your final tech rate, you will save about 8 turns." Sorry, this just isn't remotely mathematical.

The shortfall is small, only about 3%, but it's enough to lose a turn by the end of the game.

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You don't lose science if you bulb r.labs early, you gain it. As i mentioned above, it's probably bad timing on your part. For example:

1.

t.190 plastics bulbed
t.198 6 GS + Oxford + Rationalism finisher bulbed.
t.199 UN is finished with 2x GE (to 1 turn)
t.209 - victory.

2.

t.200 Plastics researched
t.208 7 GS + Oxford + Rationalism finisher bulbed
t.209 UN is finished with 2x GE (to 1 turn)
t.219 - victory.

When it comes to bulbing Research techs, I think it's also relevant to factor in whether you plan to hard build or rush buy the building. If it's the latter, do you immediately have the gold to buy the buildings?

When it comes to Education, Astronomy, and even often Public Schools, I may be a bit cash strapped at these times (I'm also usually signing RA's around then as well). As a result, there are cases where I get the tech, but then need to wait awhile to generate enough gold to buy the building. In such cases, getting the tech earlier (through GS bulbing) does not really help much.

By the time I'm getting to Plastics, my economy is usually set and strong, with plenty of excess cash. So in those cases, I can usually immediately buy a bunch of Research Labs.

Moriarte said:

Not mentioning how many GS you have? How many you saved for the final bulb.. (or did you fail there?) did you mistime your rationalism/oxford or not? And the resume: "If you waited to bulb Globalization instead, with your final tech rate, you will save about 8 turns." Sorry, this just isn't remotely mathematical.

You don't lose science if you bulb r.labs early, you gain it. As i mentioned above, it's probably bad timing on your part.

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I am talking about a mathematical model, not gameplay, so there is no "bad timing" here, just an analysis of two different choices and their consequences. The model doesn't account for everything in the game (e.g., I left out a couple of techs to simplify things), but it reasonably represents the key factors affecting research. The two sequences go like this:

Turn 185: 35 citizens, 397 bpt. Start Plastics.
Turn 196: 38 citizens, 522 bpt. Finish Plastics, build Lab, start Atomic Theory.
Turn 206: 40 citizens, 534 bpt. Finish Atomic Theory, start Ecology.
Turn 217: 42 citizens, 546 bpt. Finish Ecology, start Telecommunications.
Turn 231: 45 citizens, 564 bpt. Finish Telecommunications, start Globalization.
Turn 239: 46 citizens, 570 bpt. Bulb for 4,542 beakers, finish Globalization.

Turn 185: 35 citizens, 397 bpt. Start Plastics.
Turn 188: 36 citizens, 510 bpt. Bulb for 3,186, finish Plastics, build Lab, start Atomic Theory.
Turn 198: 38 citizens, 522 bpt. Finish Atomic Theory, start Ecology.
Turn 210: 41 citizens, 540 bpt. Finish Ecology, start Telecommunications.
Turn 224: 43 citizens, 552 bpt. Finish Telecommunications, start Globalization.
Turn 240: 46 citizens, 570 bpt. Finish Globalization.

Both of these scenarios use exactly one Great Scientist for a bulb. The only difference is the timing of the bulb. If you use it to finish Globalization, you finish one turn earlier than if you use it to finish Plastics.

Yes, finishing Plastics early does gain science in the short term. In this example, the city produces an extra 871 beakers in those 8 turns. However, you lose science in the long term. The early bulb only adds 3,186 beakers, whereas an endgame bulb adds 4,542 beakers, a difference of 1,356. That's a net loss of 485 beakers, enough to delay Globalization by a turn.

I already described this in my earlier post, in round numbers: You get about 3,200 from the early bulb and 800 from the lab, but that's only worth 7 endgame turns, compared to about 4,500 from the late bulb, which is 8 turns.

I'm happy to provide more information about my model, especially if something looks wrong, but please go easy on the personal attacks, OK?

I'd guess that later GS's will always result in the greatest bonuses, so for a purely mathcraft/power-gamer viewpoint then bulbing them near the end will shave off the most turns. However there is something to be said about getting access to earlier techs quicker, aside from only beakers per turn. For example, say you get artillery guns that much quicker, which allows you to sack enemy cities with significantly more ease, resulting in more population, snowballing into more science, etc. It is too difficult to quantify something like that, because it varies from game to game.

The same thing goes for accessing social policies/GPT/CPT/whatever quicker. Just based on my own gameplay experience, it seems getting up to and through Industrial era ASAP is top priority. At that point, fertilizer/chemistry/economics unlocks, Rationalism and Industrial policies unlock, artillery guns unlock, railroads unlock. Basically all the major improvements are done, and from there on it is just minor improvements--most of which come so late that it has little effect on the course of the game, such as medical labs.

Is getting access to all the Industrial era improvements/policies/military a few turns earlier worth the cost of bulbing/Oxford? I'd say that is the major question in this thread: Either burn all the science stuff around Industrial, or wait until modern/atomic, or at the very end.

Edit: And posing the question that way, without any hard numbers to back it up it seems like the logical answer is it depends on how much you are going take advantage of the early techs, similar to what Halycan mentioned. Just getting the techs earlier probably isn't enough. But, if you saved enough gold to rush-buy key buildings, or need the quick military techs (frigates/artillery/battleships/bombers) to sweep the map quicker, etc, then the loss of beakers would be worth it (they would be made-up through indirect ways, such as sacked enemy cities, getting key wonders without competition, whatever)

My apologies for nothing much concrete in this response; more of brainstorming than anything. If I have time this weekend I will try and play a couple of games to see if I can contribute something a bit more solid.

Agreed! Shaving a couple of turns off your final UN/spaceship techs is nice, when all else is equal, but sometimes things aren't equal.

One thing I find most intriguing is the possibility that you can translate early-game bonuses into late-game turns. For example, suppose that you produce 120 bpt in the late Medieval Era and 600 bpt in the endgame. You use Oxford University for free Astronomy (858 beakers). That will open the Renaissance 7 turns early, but won't end the game 7 turns early, for reasons explored above. Instead, I suspect that it takes (858 beakers ÷ 600 bpt) = about 1½ turns off the end, not counting the effect of earlier science buildings. I need to experiment with the model to verify this.

BWS said:

I am talking about a mathematical model, not gameplay, so there is no "bad timing" here, just an analysis of two different choices and their consequences. The model doesn't account for everything in the game (e.g., I left out a couple of techs to simplify things), but it reasonably represents the key factors affecting research. The two sequences go like this:

Turn 185: 35 citizens, 397 bpt. Start Plastics.
Turn 196: 38 citizens, 522 bpt. Finish Plastics, build Lab, start Atomic Theory.
Turn 206: 40 citizens, 534 bpt. Finish Atomic Theory, start Ecology.
Turn 217: 42 citizens, 546 bpt. Finish Ecology, start Telecommunications.
Turn 231: 45 citizens, 564 bpt. Finish Telecommunications, start Globalization.
Turn 239: 46 citizens, 570 bpt. Bulb for 4,542 beakers, finish Globalization.

Turn 185: 35 citizens, 397 bpt. Start Plastics.
Turn 188: 36 citizens, 510 bpt. Bulb for 3,186, finish Plastics, build Lab, start Atomic Theory.
Turn 198: 38 citizens, 522 bpt. Finish Atomic Theory, start Ecology.
Turn 210: 41 citizens, 540 bpt. Finish Ecology, start Telecommunications.
Turn 224: 43 citizens, 552 bpt. Finish Telecommunications, start Globalization.
Turn 240: 46 citizens, 570 bpt. Finish Globalization.

Both of these scenarios use exactly one Great Scientist for a bulb. The only difference is the timing of the bulb. If you use it to finish Globalization, you finish one turn earlier than if you use it to finish Plastics.

Yes, finishing Plastics early does gain science in the short term. In this example, the city produces an extra 871 beakers in those 8 turns. However, you lose science in the long term. The early bulb only adds 3,186 beakers, whereas an endgame bulb adds 4,542 beakers, a difference of 1,356. That's a net loss of 485 beakers, enough to delay Globalization by a turn.

I already described this in my earlier post, in round numbers: You get about 3,200 from the early bulb and 800 from the lab, but that's only worth 7 endgame turns, compared to about 4,500 from the late bulb, which is 8 turns.

I'm happy to provide more information about my model, especially if something looks wrong, but please go easy on the personal attacks, OK?

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You could also take into account:
1. Bulbing plastics and immiediatelly buying Lab instead of building it
2. Placing the scientist in Labs slot and if it will help generate additional GS
3. Amount of cities You have and in which You could buy Lab and place scientist in
4. Whether You have the extra +2 science per specialist policy adopted already

I'm not gonna do the math here as it would be too complex (at least for me ), but let's say You have 10 cities and enough gold to buy Labs there in one turn. In such situation I guarantee, that bulbing Plastics will cause the game to end much sooner than bulbing Globalization

My simulation already assumes that you buy new science buildings immediately and fill specialist slots, with the Secularism bonus (+2 science per specialist). I'm certain that adding more cities would not change the outcome, because that would simply multiply the current numbers by a constant factor, and multiplying a negative is still negative.

I am talking about a mathematical model, not gameplay

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Well, how about talking about both? We are discussing the Game afterall..

Both of these scenarios use exactly one Great Scientist for a bulb. The only difference is the timing of the bulb. If you use it to finish Globalization, you finish one turn earlier than if you use it to finish Plastics.

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That is why i am pointing out the timing. We don't need 'long - term' if the goal is diplo. In an 'optimal' diplomatic scenario you won't be needing GS to bulb any of the 3 last techs. You would want to use Oxford + Rationalism finisher. Hence, you would need a much smaller amount of beakers to uncover preceding techs.

A diplomacy challenge inspired this thread, but it's important to understand the general principles to apply them to other situations, not just diplomacy endgame. I'm really trying to take away something constructive from your posts here, but honestly it just sounds dismissive to me.

Bradd's example is what to do with 1 GS at the plastics point. Moriarte's example is what to do with 7 GS's at the plastics point. In Bradd's example there's 50 turns between plastics and globalization. In Moriarte's example, you're done teching 8 turns after plastics. Having an extra GS (7 instead of 6) at that point makes zero difference. So Moriate's example is basically just saying if you have that many GS's, you're wasting one if you don't use it earlier.

You guys are just talking about 2 completely different situations.

Thanks, Woodszilla. That makes more sense. While "Plastics, 8 turns, and out" is reasonable practical advice for the Diplomacy endgame, it doesn't offer any insight in how to make decisions when you can't simply bulb your way to victory, so it bothered me to keep returning to it.

For example, building the spaceship requires at least 15 techs after Plastics, a lot more if you bee-line it like most people do. You can't wrap that up neatly with freebies, so you need to know how to get the most out of your scientists. Do you get the most bang out of final-tier techs, science techs, growth techs? That's the question I've been looking to answer.

To solve optimization problems, you need to eliminate confounding factors and look at extremes, where the impacts of your decisions are most obvious. You look at what happens when you bulb on turn 1 and the final tier. You look what happens when you bulb just before and after key milestones like Astronomy and Plastics. Those are the places where you'll find clear results, where you'll find surprising results.

So far, I've found two interesting results from experimenting with growth and science models. First, I confirmed my suspicion above that you can translate between turns and beakers in any era by using your science rate as a scale. If you bulb for 800 beakers in the Medieval Era, it'll save you 4 turns in the late Renaissance when you make 200 bpt. You can use that relationship to determine exactly how much free Astronomy will benefit you for the rest of the game, for example. (About half of a final-tier bulb.)

The other surprising thing I found is that early academies are a lot more effective than I expected. I put together a larger model that simulates one tech from each of the 16 tiers. In that simplified tech path, an early academy saved significantly more endgame turns than a final-tier bulb does, and even late academies helped a lot more than I expected. I don't know whether a full tech tree would subdue this effect or exaggerate it – if the latter, then it actually makes sense to plant academies until very late in the game. Unfortunately, a complete analysis also requires a model for research agreements, and I'm not keen on working out all the complexities.