Most effective research speed setup?

[Dementor4]

Has anyone done the math on this?

To build more science labs you need more planets and more pops, but those pops and planets make the technology cost more. At some point even a planet you fill entirely with science labs won't be worth the drag on your tech speed.

But what IS that point? Has anyone done the math?

What is the most efficient research setup possible, assuming you need to devote nothing to your own defense?

Three planets? Five? More?

Obviously the results will vary a bit based on how your species/empire is set up and how lucky you get with your nearby planets and such, but I'm looking for a ballpark here.

 

[Larknok1]

Here you go:

https://docs.google.com/spreadsheets/d/1cVf01HyCotTTuxxYNoXzNcyKXFRrQHU8UNxW4vRBUSY/edit?usp=sharing

This just demonstrates how the functions work under two assumptions:

1) Every additional planet adds, on average, 15 additional pops.
2) Your home planet, with 15 pops, has 10 research of each kind.

---

The results are, as follows:

1) Every planet that adds at least 4 research of each kind will always improve the speed at which tech is gained, no matter how many planets you have.

2) No matter how much additional science each planet generates, the efficiency gain per planet trends towards 0 at large numbers.

3) At gain = 15 (15 science of each kind on a planet with 15 pops), the following is true:

From 1 planet to 2 planets, that additional science planet increases your science speed by 101.9% (total speed = 2.02x home planet)

From 2 planets to 3 planets, that additional science planet increases your science speed by 34.2% (total speed = 2.71x home planet)

From 4 planets to 5 planets, that additional science planet increases your science speed by 8.2%. (total speed = 3.88x home planet)

From 9 planets to 10 planets, that additional science planet increases your science speed by 2.6%. (total speed = 4.73x home planet)

 

[Dementor4]

Thanks for that, but I'm not sure I understand it.

If a planet adds 4 research but reduces research speed by at least 10% then as soon as you have a research base of 40, that planet is a net loss... or what am I missing?

 

[GC13]

Thanks for that, but I'm not sure I understand it.

If a planet adds 4 research but reduces research speed by at least 10% then as soon as you have a research base of 40, that planet is a net loss... or what am I missing?

A planet would add more than 10% research, because Pops also cause penalties.

Anyway, the question is how big your penalty was already. If your empire consists of just your homeworld, your base +5 science per category, and +4 science per category, you're sitting on 106 research cost and therefore a base research time of 11.777. Adding another identical planet would increase your research cost to 122 and take you from +9 speed to +13 speed, dropping you to a base research time of 9.38 (a 25% increase). If you already had fifty such planets, you'd have a base research cost of 1,380, a speed of 205, and a research time of 6.73, meaning you'd only drop to 6.72 (a negligible increase in research speed) by adding a fifty-first planet.

Of course this all ignores research stations, but you get the idea: bigger empires research more quickly, just not as quickly as they would without the penalty.

 

[Ewoks_Must_Die]

It's 10% of the *base* cost of a tech per planet, so it's not cumulative.

For example, if a tech costs 100 points and you have 2 planets it'll be 110.

If you have 3 planets it'll be 120.

Plus a bit for your pop count too.

 

[xMer]

except this calculation make assumption that science is done only on planets which is not true for early-mid game.
at beginning of game (which is most important) new planets can grant a lot of off-world science, however it can be also done with frontier outposts.
So it's quite interesting question whether expand or not or when for behave of science.

 

[ApocalipsA]

Go make your spacies intelligent, fanatic materialistic, build a planet full of Labors and create a science ship and a scientist and they shout help the planet reasearch more till 30% anddd you can use 250 influence or less to release 10% more Technology on planet and build a institute for Research and for 1influence per month you can Research 10% faster that is

15% intelligent 15% fanatic materialistig 30% Research ship 10% release 10% institute +10% infinite machine
= +90% tech
you can build science stations and from curators a nice scientist

and some planets are +20% biology or ingeneering xD

 

[Larknok1]

Thanks for that, but I'm not sure I understand it.

If a planet adds 4 research but reduces research speed by at least 10% then as soon as you have a research base of 40, that planet is a net loss... or what am I missing?

Tech takes time to unlock so the crucial ratio isn't (gain ÷ cost increase.) It's (new total science ÷ new total cost. )

To use your example:

If I have 10 research and am about to add a planet that gives me 4 research, and my old tech cost was 40 and the new tech cost is 44, this means my old tech speed was (10/40) = .25, and my new tech speed is (14/44) = 0.32. Therefore I'm now teching (0.32 / 0.25) = 1.27 = 27% faster.

 

[Larknok1]

Here's the actual math:

X = current, before upgrade, tech number.
Y = tech base cost
Z = current, before upgrade, tech cost.
n = tech that you will gain with an upgrade of a new planet with 15 pops

Therefore, in order for your upgrade to be worth it, you require:

[ (X + n) / (Z + 0.25*Y) ] > ( X / Z )

That's basically just the expression saying:

( New Science / New Cost ) > ( Old Science / Old Cost )

Now, you can solve this inequality pretty simply:

[ (X + n) / X ] > [ (Z + 0.25*Y) / Z ]

[ 1 + n/X ] > [ 1 + 0.25*Y/Z ]

n/X > 0.25 * Y/Z

This is your final solution.

Put in human terms: in order for your tech upgrade to be worth it, the ratio of (the new science you'll gain divided by your current science) must be greater than (0.25 times the base cost of your tech divided by the current cost of your tech.)

So, for example, if your current tech is 40, your current cost is 3600, and the base cost is 2000, then:

n/40 > 0.25 * (2000/3600)

n > 5.5555

That means that if your stats are, as demonstrated above, you'll need at least 5.5555 science in each category on your expansion to speed up your tech.

 

[GC13]

For anyone concerned by the conclusion of the above post, that 5.5555 research points per category would have to be generated by the above planet, please note that the numbers assumed work out to it being a fifth planet added to an empire of four planets, each already producing 8.75 points per category; as long as you can manage 64% of that empire's average with a new planet, you'll break even on or increase your research speed.

 

[Larknok1]

For anyone concerned by the conclusion of the above post, that 5.5555 research points per category would have to be generated by the above planet, please note that the numbers assumed work out to it being a fifth planet added to an empire of four planets, each already producing 8.75 points per category; as long as you can manage 64% of that empire's average with a new planet, you'll break even on or increase your research speed.

That's exactly right. Always use the inequality, not 5.5555. 5.5555 was specific to the numbers I used as an example.

 

[Natonorad]

Yea, I'm reading this thread and not understanding the research aspect at all. I was operating under the assumption, the more research facilities there are = more research points per turn, the faster the research was done. So more planets, more systems = faster research. There may be inefficiencies but I thought this was true. I'm guessing not.

 

[Emraldis]

Yea, I'm reading this thread and not understanding the research aspect at all. I was operating under the assumption, the more research facilities there are = more research points per turn, the faster the research was done. So more planets, more systems = faster research. There may be inefficiencies but I thought this was true. I'm guessing not.

you also need to account for the fact that both colonies, and pops increase the cost of researching new technologies.

 

[Diezy]

If you spend time doing a large expansion wave, you can expect your tech to fall behind, until your colony is populated and the research facilities are estabilished.

But in the long run, considering you get more science from the surrounding space as well, no matter how wide you go, it won't negatively impact the rate at which you get tech, provided, you don't neglect building the tech labs. With governor boosts and observatories, it more than makes up that initial slowdown of extra colony/pops with weak labs!

 

[Natonorad]

If you spend time doing a large expansion wave, you can expect your tech to fall behind, until your colony is populated and the research facilities are estabilished.

But in the long run, considering you get more science from the surrounding space as well, no matter how wide you go, it won't negatively impact the rate at which you get tech, provided, you don't neglect building the tech labs. With governor boosts and observatories, it more than makes up that initial slowdown of extra colony/pops with weak labs!

That's the kind of information I wanted to see.

Thanks.

 

[Untrustedlife]

To people saying large empires still research faster, then why is it that me at 9 planets by the year 2400 (playing tall due to being hemmed in by federations) despite that fact that there are several empires much larger then my own, their fleet power and their tech are both inferior. (with 2 larger empires who have larger fleet power but still far inferior technology).

I only colonize 20+ size worlds.

Why is this?

 

[mudcrabmerchant]

Why is this?

The AI is stupid.

 

[Derp]

To people saying large empires still research faster, then why is it that me at 9 planets by the year 2400 (playing tall due to being hemmed in by federations) despite that fact that there are several empires much larger then my own, their fleet power and their tech are both inferior. (with 2 larger empires who have larger fleet power but still far inferior technology).

I only colonize 20+ size worlds.

Why is this?

You can't compare yourself to AI players, only other human players.