Imperial Perogative better at science than Scientific Ascendancy

[Mastikator]

Scientific Ascendancy gives +10% research

Imperial Prerogative gives +30 admin cap.

For each 1 point above your admin cap you go the base value of science is increased by .3% So at +30 admin cap you save 9% tech cost

Okay so how is 9% lower research cost worth more than 10% research speed?

Let's do the math, this assumes you are well above your admin cap (as you should be)

If you produce 100 points of science, have a +40% bonus to research speed, you're researching a tech that has base cost 5000 and you are 100 points above admin cap.
The cost will be 5000 + 100/100*.3*5000 = 6500
At 100 x 1.4 = 140 points of science you will complete the research in 47 months

Let's compare the effect of taking imperial vs scientific ascendancy

With imperial:
The cost is instead 5000 + 70/100*.3*5000 = 6050
6050/140=43.2 months

With scientific:
The cost is still 6500 and the production goes up to 150,
6500/150=43.3 months

Imperial is 10% better at science

Conclusion: Unless you're taking scientific ascendancy first (don't do that), always choose imperial prerogative over scientific ascendancy.

 

[Siri]

100 over the cap is nothing. Run it with 900, which is more realistic for a wide empire. Being 100 over is quite tall. It just barely ekes it out at 100 over, granted it has benefits for unity too but the farther over 100 you go the more it will go in TAs favour.

 

[Mastikator]

100 over the cap is nothing. Run it with 900, which is more realistic for a wide empire. Being 100 over is quite tall. It just barely ekes it out at 100 over, granted it has benefits for unity too but the farther over 100 you go the more it will go in TAs favour.

...It's just an example for simplicity?

 

[Siri]

...It's just an example for simplicity?

It's an example to skew a result

 

[Surimi]

I made this argument a while back, and I still think it holds true but it isn't quite right to say that it's always better.

Basically, the more over admin cap you are, the more effect research speed boosts will have relative to research cost reductions.

However, imperial perogative does boost a wide variety of things, while technological ascendency only boosts research speed. So I agree that in general imperial perogative is probably stronger in most cases.

 

[Ariphaos]

I've been working on a post going into detail on the math surrounding admin cap.

Imperial Perogative is extremely powerful to start with, but in the late game, it's basically a civic granting ~3% bonuses that you can't replace.

 

[Mastikator]

It's an example to skew a result

Okay let's go with 1000 points over admin cap, +120% bonus to research an 1000 points of science every month to research a 15000 technology


5000 base cost.
15000 + 15000*1000/100*.3 = 60000

With imperial

15000 + 15000*(1000-30)/100*.3 = 58650
1000 x 1000*1.2 = 2200
58650/2200 = 26.6 months to complete

With scientific ascend

15000 + 15000*1000/100*.3 = 60000
1000 x 1000*1.3 = 2300
60000/2300 = 26.0 months to complete

Late game scientific ascendancy is slightly better, early game imperial prerogative is slightly better. Without touching unity imperial is still better IMO, early game power is more important than late game power because of the snowball effect.

 

[Ariphaos]

Getting 120% bonus to research can be difficult. In my current game (where I'm at 1500 over cap) I'm hovering around 90%.

58650/1900 (30.87) vs 60000/2000 (30)

Or in my case

81150/1900 (42.7) vs 82500/2000 (41.25)

Of course, a part of this is that tech ascendancy also sucks.

 

[Siri]

I made this argument a while back, and I still think it holds true but it isn't quite right to say that it's always better.

Basically, the more over admin cap you are, the more effect research speed boosts will have relative to research cost reductions.

However, imperial perogative does boost a wide variety of things, while technological ascendency only boosts research speed. So I agree that in general imperial perogative is probably stronger in most cases.

It's definitely 200% wrong to say it is always better, because it very demonstrably is not. The question is how often it is better, you say it is probably stronger in most cases, I would say it is rather narrow and only holds true for a very specific play style. It is better if you're playing tall in a way that you are going over the admin cap enough to not waste basically any of the increased cap, but less above than a fairly low ceiling. Basically it's good if you're playing very tall, which is already a play style with a debatable efficiency in my mind.

Okay let's go with 1000 points over admin cap, +120% bonus to research an 1000 points of science every month to research a 15000 technology

5000 base cost.
15000 + 15000*1000/100*.3 = 60000

With imperial

15000 + 15000*(1000-30)/100*.3 = 58650
1000 x 1000*1.2 = 2200
58650/2200 = 26.6 months to complete

With scientific ascend

15000 + 15000*1000/100*.3 = 60000
1000 x 1000*1.3 = 2300
60000/2300 = 26.0 months to complete

Late game scientific ascendancy is slightly better, early game imperial prerogative is slightly better. Without touching unity imperial is still better IMO, early game power is more important than late game power because of the snowball effect.

If you're late game enough to have a total boost of +120% you're going to have significantly more than 1000 science per month, especially in a wide empire 1000 above the cap. Probably in the order of at least 3000, but even more is likely unless research is very neglected. 120% essentially means you have everything, including scientific revolution and a science nexus constructed.

That's a lot of bonuses to stack to actually get to 117%, including three random traits in addition to the gene mod one, so definitely not common. And at that time, I had over 14000 research per month. But really, this late in the game is not very useful because it's long past the point where this choice is meaningful. Instead, I will just draw data from one of my personal games where I am in the happy year of ~2300. My total sprawl is 1061 with a base cap of 90, so I am 971 above for a 291,3% penalty. The average research per month across the three fields is 2942, and the average research bonus% is 60 with TA already taken. My current society tech is Admiralty Support Staff 2, with a base cost of 60000.

With the current setup the tech costs 234780 (60000*3.913) total, with a total progress of 4704 per month (2942*1.6) and it will take 49.9 months to finish.
With an Imperial setup the tech costs 229380 (60000*3.823) total, with a total progress of 4413 per month (2942*1.5) and it will take 52.0 months to finish.
For a baseline setup the tech cost is 234780 (60000*3.913) total, with a total progress of 4413 per month (2942*1.5) and it will take 53.2 months to finish.

Imperial reduces the time needed by 1.2 months. TA reduces the time needed by 3.3 months. For the purposes of research in this case, TA is 2.75 times as strong as Imperial. No, it's not slightly better. In a wide empire Imperial is a garbage fire compared to TA (and how good TA is to begin with can certainly be questioned). Imperial will sometimes be the better choice but saying to always choose imperial is awful advice. If you're playing very tall and you want a research and unity boost, go ahead and take it. If you're playing wide, don't touch Imperial. I am not sure it's wise to compare the two either way just because TA is a tier 0 perk and Imperial is a tier 1 and are open at different times and generally compete against different perks.

 

[Fjolsvid]

Don't be in that much hurry to draw these conclusions. Yes, math-wise, you are mostly right and Imperial prerogative also reduces Unity, leader and campaign costs too which helps with other stuff.
However, i do expect updates to the Admin Capacity numbers. Maybe the base number will be increased, maybe costs will be adjusted.
Besides, there is one more angle 30 admin cap is 2 late-game techs. Permanent 10% to all research, however, can't be acquired as easily.

 

[Longprao]

So is it wise to take both? Or would it be a waste of one perk?

 

[Fjolsvid]

So is it wise to take both? Or would it be a waste of one perk?

I generally wouldn't pick Imperial ascension. If you are going wide, +30 to AC won't save you much. The only case where having Imperial Prerogative is guaranteed to be useful is a megacorp due to their increased penalties.

 

[TehJumpingJawa]

I still think the strongest argument is; IP is better in the early game, and being better in the early game is what matters most.

 

[Siri]

So is it wise to take both? Or would it be a waste of one perk?

Unless there are specific circumstances at play I wouldn't take either, which is probably the real problem. As a first pick there's things you probably want more than Tech Ascendancy, Interstellar Dominion is a popular pick for instance. This is especially true if you intend to go to war later on and won't just use it for initial land grabbing. For a second pick, I'd rather take my first Ascension Path pick. If I get to pick between getting Imperial and unlocking my Clone Vats, I'm getting those Clone Vats.

 

[Blurb]

For the purposes of comparing technological ascendancy against imperial prerogative, base tech cost and empire science production is mostly irrelevant.
The time it takes to research a technology is (Base cost*Cost modifier)/(Science output*Research Speed). The rate at which technology is researched is the inverse of this.
Using abbreviations, time to tech is then T2T = (BC*CM) / (SO*RS). This can also be written T2T = (BC/SO)*(CM/RS), which is a lot easier to work with.

Comparing an arbitrary change to tech cost modifier (a) versus an arbitrary change to research speed (b):
T2Ta = (BC/SO) / ((CM-x)/RS)
T2Tb = (BC/SO) / (CM/(RS+y))
What is the relative time to tech then? That would be
T2Ta/T2Tb = (CM/(RS+y)) / ((CM-x)/RS)

Note that technology base cost and empire science output disappears completely: we have no reason to care about either of these variables.
A more intuitive explanation is that changing research speed and tech cost does not affect a technology's base cost or the empire's science output, and we can therefore consider those factors as constants.
A mathematical proof is an excellent support for a claim, but the inclusion of irrelevant extra factors is pointless at best and harmful at worst.

Conclusion: Unless you're taking scientific ascendancy first (don't do that), always choose imperial prerogative over scientific ascendancy.

Your arguments do not support this conclusion. Why should a player not grab scientific ascendancy as the first perk?
Your singular example does not prove that imperial prerogative is always a better choice than scientific ascendancy (in terms of improved research rate) - the proof only extends to the circumstances of the example.

 

[TheDungen]

It's an example to skew a result

It doesn't really matter since the effects of being over the cap are linear.

 

[metalosse]

It doesn't really matter since the effects of being over the cap are linear.

Which means that increasing admin cap is stronger when you are not too much over it.

 

[Siri]

A mathematical proof is an excellent support for a claim, but the inclusion of irrelevant extra factors is pointless at best and harmful at worst.

That's not really true. They make it significantly easier to follow the maths because they are more tangible examples from within the game. You think it is pointless because you are clearly much better at things like this than the average person. Personally, I'm good enough at it to figure out I didn't need them, but I'm not good enough to figure out the formula in the way you have, or to explain the process of excluding them in an easily understandable way.

It doesn't really matter since the effects of being over the cap are linear.

It does matter because the relative difference of going from 30 above the cap to 0 above the cap is bigger than that of going from 1030 to 1000. The former is roughly an 8.3% reduction to your relative costs. The latter is 3%.

 

[Madzai]

Unless there are specific circumstances at play I wouldn't take either, which is probably the real problem. As a first pick there's things you probably want more than Tech Ascendancy, Interstellar Dominion is a popular pick for instance. This is especially true if you intend to go to war later on and won't just use it for initial land grabbing. For a second pick, I'd rather take my first Ascension Path pick. If I get to pick between getting Imperial and unlocking my Clone Vats, I'm getting those Clone Vats.

How people manage to get their Ascension Path by second Perk? I'm always lagging behind in terms of techs. It was even true for my Hive Mind game, where id didn't have either techs for terraforming and Gene-modding. And we're are talking about "green" science that is earliest to get.

 

[Objulen]

I've picked up both. Tech superiority provides benefits across the board, and IP benefits tech, unity, and upkeep costs during an early game phase where resources are scarce. The benefits even out late-game, but it's highly useful for my ME.

There's also a mutliplicative effect between reducing tech research costs and boosting research output, so there's a bit of extra synergy.