alpaca said:
with a lot of noise of course.
It's not noise. They're correlated, systematic uncertainties. You're fitting an exponential curve to a step function; sure, it might fit fairly well on average, but the deviations from that curve aren't random; they'd happen in the same place in every game you played, because they're tied to specific techs and such.
Research output is mostly a step function; you unlock Libraries, Universities, Public Schools, and Research Labs at certain techs, and see a huge increase in research output when you build them. Or you reach the Renaissance and unlock the Rationalism tree, and see a huge increase as you start unlocking those policies and then slow down again once you have them all. Or you go on a conquering spree and see a huge increase as you add new cities to your empire (although the fact that cities lose half their population, by default, mitigates this one). It's not a smooth curve, because each of the above are tied to reaching specific techs or eras, and so you can see them coming. (The only exception to this is how Golden Ages boost money output, which can be used to buy lots of research agreements. But RAs are another topic, below.)
The building thing is especially pronounced. Libraries multiply your research by x1.5. Universities multiply again by x1.5. Public Schools multiply by another x1.667. Research Labs multiply by another x1.667. (And those are all the multiplicative numbers, not the usual +50%+50%=+100% thing.) Add in an Observatory or National College, and you're looking at 7.5 research per population point in the endgame instead of the 1 that a city without any buildings would have. Since nearly all research is population-based, your research rate jumps by a large amount, N turns after reaching the techs that unlocks those buildings, where N is how long it takes to build the new buildings in your larger cities.
So if you reprice the techs to have a much steeper or exponential cost curve, then it cripples anyone who doesn't take those +research techs at the first possible opportunity, and/or gives too big of an advantage to the people who do.
This is why, in my mod, I basically halved the research output of the research buildings instead of raising the costs of the techs. Too much hinges on whether your cities have these structures, and I wanted them to be more comparable to the military buildings, where you'd build them in your larger cities when you had the time but didn't feel obligated to build them as soon as they unlocked. So in my games it peaks at 3.333 resarch per population in the modern era, although my future eras take it a bit higher.
cryptc said:
the research agreements... does anyone know how to turn them off?
In the Eras file, you can just set their prices to something prohibitively large. Each era has a ResearchAgreementCost entry that sets the price for a civ in that era (modified by pacing, of course.) In my own mod I've basically doubled the costs, and it makes a HUGE difference in how often the AI enters into them. It's not just that they're more expensive, it's how much more expensive they are than the other things the AI can spend on. The AI, each turn makes a value decision based on the cash on hand. Does it:
A) Save the money
B) Spend the money on a research agreement
C) Spend the money bribing a city-state
or D) Spend the money rushing a unit or building?
The problem is that in the later eras, RAs cost less than rushing a unit or building, and less than a good bribe. So there'll be plenty of turns where, depending on the AI's cash-on-hand, D isn't an option at all and C is questionable, where it's basically A-vs-B; while it might decide to save on one turn, it'll re-decide the next turn, and if it's going to be 10 more turns before you have enough cash to rush a unit, there are plenty of chances to pull the trigger. So the AI spends the cash on an RA before he has the chance to save up enough to use it for a unit or building.
But when you double the cost of an RA, the situation reverses; the AI will rarely make a research agreement, because he'll almost never have enough cash to do so, having used it several turns earlier to rush something in one of his cities. (Or even if he does have enough money, the chances that anyone else will have enough money any time soon are slim, so he'll spend his before someone else gets up there.) It makes the AI even more dangerous on the mundane level, with more units, better cities, and more city-state alliances, but less of a problem in the tech race.
It's definitely made a huge difference in the play of my own mod on higher difficulties (where the AI gets much more cash than you do).