Question: What does the research rate curve look like in your games?

[gwillybj]

@Yitzi: I always play my games at Librarian because I just don't like the upper levels. I get too frustrated too quickly and go play something else entirely. In the past week, though, I've been watching how things work out with your patch, and think observations at Librarian are warranted.

[Nexii]

Actually I think the L production curve starts a bit lower, and is a bit steeper

Using L=0.02*TECH^2.7+TECH

TECH  ~LABS
1   1
5   7
10   20
20   85
30   225
40   463
50   823
60   1,325
70   1,988
80   2,830
90   3,870
100   5,124

This is probably a decent estimate for a normal sized map.  Assumes fairly average infrastructure for the tech at hand, and perhaps a few pacts.  I'll have to play some games to test all this out - it may help to have others post their typical labs at various points in the game.

[Yitzi]

Yea, either way with FTs it's something to consider - try to make most improvements divisible by 2x/3x/4x (or all, if multiple former power levels).  The main goal is to just get the ridiculous number of formers down, modders can do what they like for the forest vs farm/solar debate

I think that formula may slightly off what the game gives in practice - seems to overestimate.

I don't think so, as that formula came from actually reading what the game code says.

By what others are saying and my own experiences, I would say L production ends up being somewhere around (X^2.5)/16 per turn, where X is the # of techs you have.

Hmm...so just making it close to quadratic will probably be enough; I don't think a small acceleration of teching speed would be such a bad thing.  (If it still proves to be too much, it can be adjusted further.)

@Yitzi: I always play my games at Librarian because I just don't like the upper levels. I get too frustrated too quickly and go play something else entirely. In the past week, though, I've been watching how things work out with your patch, and think observations at Librarian are warranted.

Definitely; one of my goals is to make it so that Librarian is a good difficulty level for most players.

Actually I think the L production curve starts a bit lower, and is a bit steeper

Using L=0.02*TECH^2.7+TECH

TECH  ~LABS
1   1
5   7
10   20
20   85
30   225
40   463
50   823
60   1,325
70   1,988
80   2,830
90   3,870
100   5,124

This is probably a decent estimate for a normal sized map.  Assumes fairly average infrastructure for the tech at hand, and perhaps a few pacts.  I'll have to play some games to test all this out - it may help to have others post their typical labs at various points in the game.

That would be nice...if we've got 2.7 as the exponent, it may be necessary to have costs grow somewhat faster than quadratic.

[Nexii]

Yea.  I suppose what is sort of unknown is what factors contribute to such a fast-rising tech rate and how much.
- Population increases (not that significant on its own, but workers on improved squares is)
- Advanced terraforming (amplifies #1, and requires tech)
- New facilities, satellites and SPs (requires M/time, and new techs)
- Techs themselves (by unlocking unit specials & chassis, builder SEs, resource caps, global trade pact, specialists)
- Commerce (finding other players and pacting them)

I guess what I'm trying to say is that making tech quadratic  (^2) might be a good start, even though the current growth rate is even faster.  Tech does fuel itself and so by raising the cost, it may slow the L gain curve.  Then again things oddly seem to balance out around my numbers in most games...if you stagnate on tech it can mean more infrastructure built up, thus increasing L by the time you reach higher tech.  Getting ahead of your infrastructure tends to slow down tech, in the same way.

[Yitzi]

And of course nerfing satellites and crawlers will lower it too...I think the best approach is probably to start with quadratic and see how that works.

[Nexii]

Yea, satellites might not even need a major nerf.  At least if you put Sky Hydro further up the tree.  What I'm more interested in seeing is how a faster early game tech rate will influence the game.  As evidenced in my pacifism game, I am only 1/4 through the tech tree after 100 turns in an ideal situation of no war and pacting everyone.  This means the early techs are currently very slow (which you would expect since the curve is linear-ish).  The early techs will have to come a lot faster if the later ones take longer, is what I'm getting at.  This may end up requiring lower M costs on early facilities, although that could cause even faster teching.  Something to think about - it's not as though the curve is perfectly balanced vs M costs of facilities and SPs as it is.  Ascent probably being the worst since it's at the end.  2000 minerals (reduced by IND to 1000 - is 4000 energy).  By the time you get Ascent you would have that in M+E production *per turn*.  Perhaps graphing out typical M/E production over the course of a game would be of some use.  Though that's harder for me to estimate off the top of my head.  Both get modded by facilities, so changing the cost of those facilities will impact growth itself (a recurring theme).

[Yitzi]

Yea, satellites might not even need a major nerf.  At least if you put Sky Hydro further up the tree.

Even so, it means that if you have a minor production advantage over your opponents, you can max out satellites with impunity once you get the tech (as it costs you 120 for a satellite, and it costs them 120 for a 50% chance to take it down, losing their own on failure.)  By making orbital defense pods cheaper and mineral/nutrient satellites more expensive, I think that'll be made harder.

What I'm more interested in seeing is how a faster early game tech rate will influence the game.  As evidenced in my pacifism game, I am only 1/4 through the tech tree after 100 turns in an ideal situation of no war and pacting everyone.  This means the early techs are currently very slow (which you would expect since the curve is linear-ish).  The early techs will have to come a lot faster if the later ones take longer, is what I'm getting at.

The current plan I'm considering would cut very-early-game tech costs by 1/3 to 2/3, depending on difficulty level.

This may end up requiring lower M costs on early facilities, although that could cause even faster teching.  Something to think about - it's not as though the curve is perfectly balanced vs M costs of facilities and SPs as it is.  Ascent probably being the worst since it's at the end.

I feel that projects should be more expensive even in comparison to facilities anyway; even without changing the tech formula, I think late-game projects other than the Ascent could be 2k, with the Ascent being 6k.  With the change, those numbers would go up even higher.

[gwillybj]

What, actually, is the actual unedited research cost formula? I have the Prima guide, and it has what they say is the formula, and it's pretty complicated. In particular, they talk about WORLDSIZE. I'd love to know exactly how it's calculated. I'd like to know for sure, as I'm a bit OCD about research, and so I might be able to contribute to this discussion.

[Yitzi]

What, actually, is the actual unedited research cost formula? I have the Prima guide, and it has what they say is the formula, and it's pretty complicated. In particular, they talk about WORLDSIZE. I'd love to know exactly how it's calculated. I'd like to know for sure, as I'm a bit OCD about research, and so I might be able to contribute to this discussion.

Previously posted:

Ok, I looked at the code and got the actual formula (there are a handful of missing pieces, though.)  So here's the formula; notable changes from the given formula are in bold:

TECHS: Techs you've discovered already (including trading/pods/artifacts, but not the ones you started with).  However, there's one variable that is added, and another that's subtracted; I'm not sure what they are, as I haven't found where they happen, but I think they're just discovered techs that are counted differently by the program (I think the one that's added is techs previously discovered this turn).  Minimum of 1, maximum of 4999.
MOSTTECHS: Highest number of techs discovered by anyone.  The same variable as before is added, but the one that was subtracted isn't here.
DIFF: This is 1 on citizen difficulty, 2 on specialist, 3 on talent or librarian, 4 on thinker, 5 on transcend.

The formula is then:
1. Find (DIFF*4)+8.  AIs instead use 29-(DIFF*3).  Apply to this a minimum of 12-TECHS, and a maximum of 12+TECHS.
2. Take TECHS, and subtract TURNS/8 (or TURNS/12 with tech stagnation), to a minimum of 0 and a maximum equal to the result of step 1 (or 1.5 times the result of step 1 with tech stagnation). 
3. Add the result of step 2 to the result of step 1.
4. Take MOSTTECHS-TECHS and divide by 5, rounding up.  Subtract this from the result of step 3, but no more than 30% the result of step 3 (rounding normally) plus 1.  AIs instead divide by a number dependent on difficulty, ranging from 3 on Transcend to 8 on Citizen, and the maximum percentage ranges from 0% plus 1 on citizen to 50% plus 1 on transcend.
5. Take TECHS, and add 1 for factions with a natural penalty to research, or subtract 1 for factions with a natural bonus to research.  Apply a minimum of 1.  Multiply this by the result of step 4.
6. Modify by WORLDSIZE and faction and alpha(x).txt tech cost modifiers, and add 50% with tech stagnation.

[Nexii]

Yitzi have you confirmed the formula to the in-game results?  For example I had tech 20 at 828 cost, if year 2101 and in the tech lead.  Transcend game.

1) 5*4+8 = 28, add 12+20 = 32, sum is 60
2) 0 turns so = 0
3) 60 + 0 = 60
4) mosttechs - techs = 0, so nothing subtracted, so = 60 - 0 = 60
5) techs = 20+1 = 21 * 60 = 1260
6) worldsize = 1, cost modifier 1, no tech stag 1, so 1260*1*1*1 = 1260

If anything that formula would seem to imply quadratic, since techs is later multiplied by techs.  But when I graphed out the points in a game where I gave myself the techs 1 at a time, it was linear.  I do agree that techs of opponents and/or mission year are factors, this was just taking them out to simplify.

[Yitzi]

Yitzi have you confirmed the formula to the in-game results?  For example I had tech 20 at 828 cost, if year 2101 and in the tech lead.  Transcend game.

1) 5*4+8 = 28, add 12+20 = 32, sum is 60
2) 0 turns so = 0
3) 60 + 0 = 60
4) mosttechs - techs = 0, so nothing subtracted, so = 60 - 0 = 60
5) techs = 20+1 = 21 * 60 = 1260
6) worldsize = 1, cost modifier 1, no tech stag 1, so 1260*1*1*1 = 1260

If anything that formula would seem to imply quadratic, since techs is later multiplied by techs.  But when I graphed out the points in a game where I gave myself the techs 1 at a time, it was linear.  I do agree that techs of opponents and/or mission year are factors, this was just taking them out to simplify.

If you look at the formula more carefully, you'll see why it's linear:
-Early on, the first factor is 12+TECHS+(TECHS-TURNS/8), so there are both a linear and quadratic term.  Very early, the linear term is stronger, but later the quadratic term starts to show, which is why if you look at the graph you posted it is actually a quadratic early on.
-Somewhat later (at 16 techs for Transcend), it becomes (DIFF*4)+8+(TECHS-TURNS/8), so while there are still linear and quadratic terms, the linear term is now stronger and the quadratic term (which had been starting to seriously dominate) weaker.
-Later on (at 28 techs+1 tech/8 turns on transcend without tech stagnation), it becomes [(DIFF*4)+8]*2, i.e. the curve becomes fully linear.

So while it is quadratic in the early game and early midgame, it's linear later on, resulting in the overall linear tendency.

Your calculation is off in step 1, as step 1 gives either by difficulty or TECHS+12, whichever is more, not their sum.  So what you should have is:
1) 5*4+8=28.
2) 19; it's only techs researched, so the one you started with doesn't count.
3) Add 19 to 28 for 47
4) In the lead, so 0
5) You don't add 1 unless playing as Believers or Drones (or any custom faction with -RESEARCH), so 47*19=893, which is what you have down for 21; it looks like somehow you saved on another tech.  Looking at your chart, it seems that your first researched tech got ignored (I'm not sure what the rules are for when that happens), other than that it seems to fit the formula perfectly.

[Nexii]

Ah gotcha, okay that makes more sense.  I took "apply" as meaning "add".  Most likely I was counting the cost of the next tech when having X number of techs.  I didn't try a base case of a faction with no starting tech.  I didn't really consider it too important, since everyone gets a tech to start by default. 

Good to confirm anyways.

[Impaler]

Thx for the tip on this thread    Nexii, it is indeed exactly what I was looking at.

I've done some heavy Alphax.txt modding to try to get the kind of tech curve I want, I play on large maps so I tend to be growing both vertically and horizontally well into the late game, so I experience a strongly exponential curve in my Tech output.  The discovery rate, aka turns per tech would fall through the course of the game by at least a factor of 10.

I can slow down things with a reduced Tech rate (35%) and Tech Stagnation, but while this can keep late techs to reasonable times, it has a crippling effect on the early game because the same x10 difference exists between early/late so a 5 turn timer for the late game means 50 turns early game.

So I add a lot of tech bonuses at the start of the game, I put +4 research spread among the starting SE choices, +2 research and +3 Energy on all bases,  and start all factions with a Former and 100 more Energy.  But I still end up with a 'saddle' curve with the early game good, the mid a bit slower then I like and the late still a bit faster then I'd like.  What I want it ~10 turns per tech through the whole game.


Now with regard to the actually formula it looks like intervening in Step #4 would be the way to go, before TECHS is multiplied by the result of step 4 you can take TECHS and raise by a power, or possibly just multiply it by itself to introduce a quadratic progression.  The Step 4 result looks to be introducing a bonus for lagging factions and this looks to be a good thing, we may want to look at expanding the room for this effect.

Your observation that the cost curve moves from quadratic to linear is quite interesting, I wonder if the designers intended this to follow a similar change in the players growth curve.  When the player is expanding vertically and horizontally they will be seeing quadratic growth, but once empty territory is exhausted the player will only be expanding vertically and growth will slow down to linear.  Unfortunately the formula as written ignores World-size when placing this quadratic/linear 'knee' in the progression, it should come later the larger the world size, and I think most people play on maps bigger then the intended size for the formula.

What are your plans for modification at this point?, and if your interested in more testers for this I would like to volunteer.

[Yitzi]

Now with regard to the actually formula it looks like intervening in Step #4 would be the way to go, before TECHS is multiplied by the result of step 4 you can take TECHS and raise by a power, or possibly just multiply it by itself to introduce a quadratic progression.  The Step 4 result looks to be introducing a bonus for lagging factions and this looks to be a good thing, we may want to look at expanding the room for this effect.

The problem is that before step #4 it's constant (depending only on difficulty) past the early sections of the game, so no matter what power you raise it to it won't help.  I think the most important place to intervene is step 2, in particular allowing it to grow past the result of step 1.  That cap is what's really causing the issue.  (I'd also reduce the effect of step 1 somewhat, simply in order to speed things up in the early game.)

Your observation that the cost curve moves from quadratic to linear is quite interesting, I wonder if the designers intended this to follow a similar change in the players growth curve.  When the player is expanding vertically and horizontally they will be seeing quadratic growth, but once empty territory is exhausted the player will only be expanding vertically and growth will slow down to linear.  Unfortunately the formula as written ignores World-size when placing this quadratic/linear 'knee' in the progression, it should come later the larger the world size, and I think most people play on maps bigger then the intended size for the formula.

It's an interesting theory, but even once empty territory is exhausted the player will still not only expand vertically but also get access to new ways to boost tech.  In any case, it seems to be too slow even on Normal maps.

What are your plans for modification at this point?, and if your interested in more testers for this I would like to volunteer.

My current plans for modification have a fair number of things before the tech speed change; once I do add it, though, testers will be welcome.

[Nexii]

Until Yitzi puts this in I would say perhaps playing around with +20 RESEARCH/base might do well.  Tech rate of 20% without tech stag.  This approximates the curve but has a few issues, but I'd try it anyways.  Main issue is it gives a lot more baseline per base, and may overpower Police State ICS.  That base L is modified by facilities though, so a bunch of unimproved small bases shouldn't be too overpowering.  Since the drone fixes, it's a slow strategy to convert out of although quite strong when still in it.

One more edit: running some calcs, you might see around 5 turns / tech early, 10 turns / tech mid, and 5 turns / tech late game.  I will test this out in the interim, as I too would like to see more games go into higher tech before being decided (without the game ending abruptly after completing half the tech tree).