Inflation in CivIII - Revealed!

[David Weldon]

Ok, so the title is optimistic, but I am going to describe a framework for calculating inflation, and I hope that someone more motivated than I am will then come up with some numbers.

The basis for inflation comes from the cost of each tech. We have to assume that Firaxis did some balancing on the tech costs so that they are reasonably consistent given the time period in which you are researching them.

Definitely by the Medieval Age all research can be done in 4 turns. This will give us a time basis to devalue future techs with. Excess gold will be ignored, due to our complete belief in Firaxis' perfect polishing job.

In the Ancient Age it's a little more difficult because no tech can be learned in 4 turns at the beginning, but there can be a lot more trading and hut bonuses, so I would say that as a wild guess, 4 turns per tech is not too bad of a standard even here.

On different difficulty levels, the AI bonus or penalty may affect their rate of inflation, but that will only affect the player if he trades extensively or is not in the tech lead.

Different sized worlds should be compensated for by the world tech # and the relative production capability of each society (as limited by corruption and other factors). In short, we should work with the standard world, and only later incorporate correction factors for different sized worlds if we find it necessary to do so.

Trading is extremely difficult to handle, so I would propose that we ignore it. The reasoning is that the AI often researches optional techs, causing unnecessary time delays. They then trade techs which allows them to make up those delays. If we focus on the required techs only, and ignore trading, then I think we can come up with a reasonable rate of inflation.

In tracing the timeline, I would recommend that one always go after the cheapest required techs first. That way progress is consistent with a growing economic base so that in theory the same %science will keep techs coming in 4 turns.

After computing the inflation for each 4 turn period of time (i.e. for each new tech), then we can take an average over the whole game, or if the results are disparate enough, then we can take an average over each Age and get some useful (though not perfect) concrete numbers.

[Ray K]

Re: Inflation in CivIII - Revealed!

Originally posted by David Weldon
Ok, so the title is optimistic, but I am going to describe a framework for calculating inflation, and I hope that someone more motivated than I am will then come up with some numbers.

The basis for inflation comes from the cost of each tech. We have to assume that Firaxis did some balancing on the tech costs so that they are reasonably consistent given the time period in which you are researching them.

Definitely by the Medieval Age all research can be done in 4 turns. This will give us a time basis to devalue future techs with. Excess gold will be ignored, due to our complete belief in Firaxis' perfect polishing job.

In the Ancient Age it's a little more difficult because no tech can be learned in 4 turns at the beginning, but there can be a lot more trading and hut bonuses, so I would say that as a wild guess, 4 turns per tech is not too bad of a standard even here.

On different difficulty levels, the AI bonus or penalty may affect their rate of inflation, but that will only affect the player if he trades extensively or is not in the tech lead.

Different sized worlds should be compensated for by the world tech # and the relative production capability of each society (as limited by corruption and other factors). In short, we should work with the standard world, and only later incorporate correction factors for different sized worlds if we find it necessary to do so.

Trading is extremely difficult to handle, so I would propose that we ignore it. The reasoning is that the AI often researches optional techs, causing unnecessary time delays. They then trade techs which allows them to make up those delays. If we focus on the required techs only, and ignore trading, then I think we can come up with a reasonable rate of inflation.

In tracing the timeline, I would recommend that one always go after the cheapest required techs first. That way progress is consistent with a growing economic base so that in theory the same %science will keep techs coming in 4 turns.

After computing the inflation for each 4 turn period of time (i.e. for each new tech), then we can take an average over the whole game, or if the results are disparate enough, then we can take an average over each Age and get some useful (though not perfect) concrete numbers.

Could you rephrase this in the form of a question?

[Gaius Marius]

No offense, but I don't think this is significant. The cost of tech in gold/beakers can be determined if you know the tech cost (in the editor) and the world size.

This number only applies to tech, though. Since the cost of other gold-bought items (support, etc.) doesn't change, there is never really any "inflation" to speak of. Better tech is just more expensive, and it seems inflationary, because your economy is growing and time is progressing. It never costs more to, say, research The Republic if your economy is bigger/more developed. Of COURSE better tech costs more. That's beacuse it's better. It's not inflation when you get a new job and buy a Cadillac, it's just a better car.

In fact, if anything, the lower shield-gold conversion rate after Economics is deflationary. (though the conversion only changes in one direction; rushing is the same cost. Weird economic inefficiency. Does this mean you can make money doing gold/shields arbitrage between your cities? I'll have to check this out)

But any basket of goods has the same value throughout the game. In other words, academic definition of the term aside, figuring this out won't tell you anything about the economic system of the game in the long run.

[David Weldon]

Oh, but you are so wrong. Let me count the ways...

You contend that a settler is as valuable in 2000AD as in 2000BC?
or a warrior?
Or forgetting about actual units, how about 1000 gold to be spent as you please?
This is the entire argument for Expansionist as a viable civ strength!

Of course there is inflation in the game. The reason is that anything you build now can be considered an investment that pays compound dividends in the future. Perhaps "inflation" should be substituted for "risk free rate of return" so that the net present value of certain investments can be calculated.

I'm not arguing that the techs themselves are what's responsible, only that they give us a measuring stick so that we can generate some actual numbers. For example:

Pottery costs 48 beakers at the beginning of a standard game. If we assume 4 turns (this is for averaging reasons, I know it's tough to actually do it in 4 turns), that means Firaxis believes we can produce 12 beakers per turn at the beginning of the game.

Feudalism costs 624 beakers at the beginning of the Medieval Age. This means that Firaxis believes we can produce 156 beakers per turn at that point.

With 16 required techs between those two points at 4 turns per tech, that's 64 turns. Assuming linear growth, that's 4.1% growth per turn.

If the beaker producion is assumed to be proportional to overall economic growth, then we can now determine the discounted value of investments which pay off later...

Should I build a temple which will allow me to grow my city by one citizen, thus gaining extra production and commerce for the rest of the game, or should I build a few swordsmen to kill my neighbor NOW? This kind of question, as well as more accurate evaluation of the benefits of civ strengths can be answered if we estimate the "inflation" of a typical game.

[Capt Dizle]

You are talking about turn advantage.

What is the most advantagous micromanagement task/thing I can do now in terms of ultimately putting distance between my CIV and the other's at some point in the game.

You are building factories in all of your main cities and now have discovered the tech for building coal plants and hospitals. All of your main cities are at size 12. You have built railroads to connect your cities but have not placed them on all squares so you now have to also choose between concentrating on using railroads to increase food or production.

You have to factor in polution.

What do you do next to create the most turn advantage? Where, if anywhere should your rush buys be done. Shouldn't you build at least one worker in each city before you start the hospitals so that you can rejoin them to instantly boost pop to 13 the second the hospital is finished (letting the worker build railroads in the meantime).

Turn advantage is what the game is about.

Techs are more expensive in the early game than the later game because your growth rate in commerce will exceed the cost factors that have set.

You most certainly can't get the first tech in 4 years nor has Firaxis created a perfect inflation model.

[David Weldon]

I seem to not be making myself very clear. The intended purpose of this thread is to derive a number for the equivalent value of shields and/or commerce given that growth occurs over time. We all know this effect is important, but we don't have a number for it.

The reason I would like to derive this number (the discount rate) is to aid a couple of other threads that have been doing numerical analysis of the value of population rushing and of various civ strengths.

Any number derived in this or any other thread is naturally full of generalizations and inaccuracies. But without a number to begin with, there can be no quantified discussion about various trade-offs.

If you don't believe 4 turns is a reasonable average over the course of the full game, please suggest an alternative. If you don't think using tech costs as a basis for inflation estimation is reasonable, please suggest an alternative.

I suggested those two things because they are fairly easy, fairly normal (according to my own experience), and they don't vary from game to game.

The best thing to do would of course be to record the actual production of your empire at the end of each turn. Then, average the results over all different play styles for all different civ types for perhaps 10 games per variable. This is obviously not viable, thus we have the assumptions and approximations that I have so far suggested, as well as a single calculation using those assumptions. More work needs to be done, and I will do some of it over the holliday if no one else does.

I don't intend to make use of the discount rate to discuss strategy in this thread. I would like to keep focused on what the proper discount rate should be.

[jack_frost]

I don't like most of these kinds of threads.

Simply said, this kind of mathmatical breakdown over simplifies the number of variables actually involved to such a degree that it is not relevant. For another thread which does this (really well) look at the Quantitative Analysis of Civ Strength. He has a point, but IMO his numbers aren't representitive of actual impact - and really aren't useful. The numbers you find might be sort of interesting, but won't be useful.


But if you want to find 'average commerce' per turn. Heres how you could do it. Very rough.

Say you settle a city every 15 turns (optimal builds can do better). Once you settle a city, the speed doubles (again, optimal builds do better). Say during despot pre-construction each population point will produce 2 food per turn. 1.3 shields (the majority will only produce 1 shield). 1.3 commerce. Growth happens at 20 food, then 20, then 30? what ever, find the numbers for city growth. Average time for granaries to increase growth.

Average out research times per tech per difficulty level, number of ai, size of map, type of map. How ever you want to abstract this into generality is up to you. Find average number of turns you'll be hitting the 6 pop - pre-aquaduct limit.

The actual beaker costs are all known. Average out improvement and military upkeep per city, and subtract that from income. . . after you've added and subtracted averaged out luxury / resource trades. Apply the income against the science costs taking the growth speed (and 6/12 barriers)...

And bam! You have average cost per turn of research, you can plot growth! And then find growth against cost!

and this will do nothing to better inform your decisions.

[Gaius Marius]

Gold/resources/anything of measurable value is always better now than later, since you can earn benefits between "now" and "later." Interest rates set by the market are supposed to reflect just how much benefit (utility) exists between now and later.

Of course, you know this, but my point is that:

A) This has nothing to do with inflation.

B) There is no market - all of the prices at any given point are constant - but the amount of utility is determined by nothing short of the game situation and your future plans. Even if you know everything about your current situation, it is impossible to predict future utility (because you can't predict the future)

Of course, you know this, too.

Quantification can tell you some interesting things - like the estimated future utility of a settler unit, which is a function of the tiles at city site where the city is, the time it takes to found it and grow, the value of the different goods produced by the city, a risk variable (if the city gets taken, or whatever)...etc. You could come up with a really complicated formula that might tell you something really cool.

This is true for a lot of other things, and for the numerically inclined, would be a good way to make a set of numbers that give rough conversion factors for opportunity costs. There are certainly levels beyond "1 gold = 1 beaker = 8 shields" that would be very, very useful.

But I don't think it's realistic to set a general "cosmological constant" discount rate for the game.

Anyway, I dig the thread, and I think Civ strategy in general could benefit from more rigorous analysis (especially judging from how anecdotal most of it is - see the "my Plasma Trooper Mark XXVII was defeated by a Ground Sloth!!!!!" threads), but I don't want you to get your hopes up about finding a Grand Unifiyng number or anything close to it.

Good luck.

[David Weldon]

Every hear of Fermi Statistics? Enrico Fermi (first name might be misspelled, my apologies) used them to derive the explosive power of the first atomic bomb by dropping bits of paper and seeing how far they were blown sideways by the shockwave when it passed their observation station. He was accurate to less than 10% on a calcuation that took the rest of the scientific community 4 months to finish.

The idea is to make as many assumptions as possible. Some will be over-judged, while others will be under-judged. Statistically, the probabilty of error will be bell-curved, with its initial width based on the error of each assumption. The key is that the width of the curve narrows as more assumptions are made.

In essence, if you make one guess, then your error is limited by the error of that guess. But if you make 100 guesses, then the error of the result is (assuming equal importance for each guess) 1/10th of the error of the average guess.

This is just a sidenote for those that don't think generalities can be accurate. If, on the other hand, you simply don't want to think about any numbers while playing civ, then of course feel free to ignore this and all the other threads that attempt to quantify the value of various things in the game.

[David Weldon]

Gaius:
I have posted elsewhere that I generally agree that "inflation" is an incorrect term, but that I think it gets most people to think about what we are trying to explain correctly. Here's just a quick example of how I think it can be viewed as "inflation"...

Rather than the "basket of goods" approach, think of the "basket of results". Ask yourself how much it costs to take a 20% of the opponent's civilization from him?

In the beginning that might be 1 city guarded by 1 spearman and a warrior. Thus, 3 archers (60 shields total I think?) might be able to accomplish that result.

In the end, it might be 7 cities guarded by mech. inf. and might take 30 modern armor, two carriers, and 20 bombers (mucho shields, I'm sure).

Clearly the cost of doing business has increased. The "good" in the basket is the relative annihilation of your opponent, not whichever units were used for that result.

This illustrates the idea that 1 shield late in the game is worth far less than 1 shield early in the game. Thus "inflation".

[jack_frost]

I hate to say this, but I'd think the variables involved in calculating the power of an explosion has less immediate variables then strat decisions made in civ. Its easier to guestimate outcomes in civ. But the power of an explosion has a certain number of factors, and the nature of the construction limits the variables.

Civ is actually much closer to chess in variables, and potential outcome. Discounting chess research pre-1980 (arguably thousands of years...or at least 60 more serious modern ones) great strides are still being made.

Efforts to break chess theory down into foruma can be illustrated by chess AI design, which has made huge strides (but continues to be imperfect) in the last 20 years, although thousands of differant approaches / implementations have been made.

In other words, "proof by analogy is fraud" (not my quote). The measurements of the two are not comperable, although in actuality, Enrico Fermi's approach is actually more 'holistic' and closer in agreement with my side of this

I don't mean to piss on the parade though. I do know how much fun it is to try to break these things down and attempt to extract hidden treasures from the results. And I wish you luck.

(My over active arguement reflex kicked in, I apologize).

[David Weldon]

Jack:

I have to admit I don't really think I get what you're driving at. The point in my example is that each bit of paper moved a different distance. The average distance, when using each bit of paper as a "guess" gave an extremely accurate estimate, even without a lot of difficult math. There is a book on Fermi Statistics which uses the idea to calculate how many piano tuners there are in New York City (as one of many examples) to show that the "guesses" don't all have to be of similar type, as long as they are able to be overestimated and underestimated and have some impact on the outcome of the calculation.

I brought it all up because of your post in which you assume everything under the sun, one after another, and then use all of these assumptions to come to a conclusion that you feel will do "nothing to better inform your decisions". I feel the result has a real chance of being more accurate than you give it credit for.

In any case I think this is getting _way_ off topic, and I'm sorry to say I helped it get there . My next post will have my results.

[David Weldon]

Here it is, go ahead and start laughing at me...

Assumptions:

1) Tech cost is somewhat related to economic production and overall power.
2) Ancient Age techs take 6 turns each to research
3) Medieval Age techs take 5 turns each to research
4) Industrial and Modern Age techs take 4 turns each to research
5) Cost is based on standard sized world
6) % Growth assumes the growth is constant per turn
7) % Growth uses the # of beakers and # of turns from 7 techs before the current tech as a baseline. [i.e. growth = (cost of current tech/cost of 7 techs ago tech) to the (# of turns) root]

I used a 7 tech window to allow for some long-term drift in growth rates if they were there, and also because when the # of turns gets very large, a tiny change in growth rate can cause a huge cumulative effect.

The #1 assumption is the most liberal one in my opinion, but I feel that it is a good metric for how a "normal" game would progress. We have to trust that Firaxis balanced the tech cost to some degree.

I included all required techs in their lowest-cost order, and I also included some very important optional techs like Republic and Democracy (and therefore Printing Press).

In the Modern Age, I didn't include any techs that weren't required to get the Spaceship.

Results:
The "normal" game takes about 300 turns to research all of the needed techs. This may be a little bit fast because there are 540 total turns in a full game. At this rate you have all the techs by about 1700AD. Remember, though, that I have assumed perfect tech production all the way, with only three optional techs. Since some people have launched by about 1800 (about 400 turns), I don't think it's _too_ far off.

I suspect tech growth in the early game is not as fast as production growth, so although 300 turns looks fast, as a metric for overall growth (not just science growth), the result could be reasonably accurate.

The cost of techs is exponential in nature, meaning that Firaxis assumed something like constant growth would be experienced during the game.

The overall average rate of growth is about 3.5% per turn, and it is very close to constant over the entire game.

I have tried to attach a .jpg with the graphs, if it doesn't work I'll try it again in some follow-up posts.

[Blaupanzer]

There is a significant problem in using tech costs to do marginal rate-of-return analysis. The tech costs are "fixed." That is their variances are based on map size (and, perhaps, some other factor). Therefore an analysis using them as a basis for inflation (or anything else) will always have the same result, regardless of victory goal, wars, etc. Marginal value, however, will be based on the intersection of your strategy (defined by victory sought) and the AI programming to seek its own victories (defined by their starting propensities, e.g., military and religious). Thus, creating borders, gaining reasonable diplomatic access, trading techs, and quelling both the populace and the military options of your opponents, measure in to the economic equation that defines: what should I build next and is this a good offer in trade. The increasing scale of Tech costs will not assist in that equation at all.

[absimiliard]

Perhaps a good method might compare empire-wide production deduce from there. At the start of the game 1 Shield is much more valuable than 1 Shield in the end-game. A ratio could be set up and then divided by time to obtain a "discount rate".

As a brief aside, we bloody well need a decent term for this. It's kind of a depreciation, but in the inverse. Inflation doesn't really work either. Basically we're generally worrying about how much a civ-trait that gives 1000 Shields in the end-game is worth compared to one that gives 10 Shields at the start. I think a conversion rate for Shields, Food, & Commerce is needed as well, then we could sum the full output of an empire into one figure.

It's a classic problem of compounding interest rates. Unfortunately I'm not a financial type so I have no clue what it's actually called given that Economics was many, many, years ago for me.

But I'm pretty sure that comparing output at a starting and ending point then dividing that distance by time is the key though.