The 'true' power of your civ

[La Fayette]

This is some kind of inquiry into the causes of the wealth of nations in civ. I started a previous thread named 'building power and growing power', but the discussion wasn't really heated: one reply .
No problem. I go on. Perhaps someone finds it interesting later on.

The whole game of civ is basically a question of power. If you build a powerful civ quickly, you win. If you don't, you lose.
Therefore being able to measure power with some degree of precision is almost like having a target to shoot at, instead of shooting in the dark.
My proposal is to define 3 types of power, that I name 'building power', 'growing power' and 'research power' (BTW if someone finds better names, please let me know).
1) Research power:
Very simple: beakers produced + beakers received as 'one time bonus' when delivering a commodity caravan.
Beakers produced can be transformed into gold (by means of the 'taxes' settings). Beakers received on delivery cannot. Willing or unwilling, you get them and here they are.
2) Growing power:
Much more complicated (but basically a mixture of food surplus, food caravans and WLT*D).
3) Building power:
At first sight it's quite simple: shields + gold. If you build units or improvements 'normally', it's shields. If you rushbuild them, it's gold. My proposal in the previous thread was to consider that 1 shield = 2 gold (which is exactly the case when rushbuilding an improvement, starting with at least 1 shield in the bottom of the box). But 2 important points must be mentioned, that I didn't have in mind when writing the previous thread:
#1: In order not to mix building power and research power, it is wise to measure with the settings at 'zero science'.
#2: It is also wise to measure (or take into account) the amount of gold received from 'one time bonus' (I am currently playing a game where I have a shipchain and a steady trade route (repeated commodity) that brings about 3 times as much gold as the rest of my civ).
Therefore my proposed new formula for Building Power (BP) is:

BP = NS + 0.5 CF + 0.5 OTB, where

NS = Net Shields (Shields produced - Support)
CF = Cash Flow (Gold earned - Gold spent for maintaining improvements)
OTB = One Time Bonus (the simplest way to measure it being to keep a log of deliveries and calculate an average on several turns...)

[Smash]

I'm not much of a mathematician or statistician.I just play.Whatever happens happens...But....I kinda like your BP stat but I'm not sure if you could work delivery bonus in.At least an average of.There are so many variables.

Demand or not

Which square is used to enter..maybe an ai units blocks your previous route in...that will change the bonus

Trade in origin city-often you get to a point where each freight relaces 1 route.This makes your trade arrows bounce up and down from turn to turn

The ai may change governments on you

Tech level..some tech decrease the bonus.

Maybe some others.

how bout a 4th like "Trade Power".Could be based on trade arrows and something like "squares that can be travelled on 1 turn"..hmm....nah I don't like that one.Maybe trade route arrows.Something along those lines.It might combine in some way with Research Power.Or even with BP considering this stat measures your capacity to build freights.

[La Fayette]

Originally posted by Smash
...I kinda like your BP stat but I'm not sure if you could work delivery bonus in.At least an average of.There are so many variables.

I agree that delivery bonus, which is very steady in the game I referred to (repeated commodity and shipchain), is not steady at all in general.
That is why my proposal is to keep a log and calculate an average (for example: (Sum all delivery bonuses during the last 10 turns)/10).
In fact IMHO there is no true value of power (that is why I used quotation marks :'true'), but it is very important, when playing, to have a clear idea of power and where it comes from.

1) The powergraph given by the game is nice to look at, but tells you nothing about where you really stand and how you got there.
2) Then comes a second indicator, the one I call 'Worked Squares' (WS).
WS = (Sum of all city sizes) + Number of cities
IMO this one is important, easy to calculate and meaningful.
If one civ A has 10 cities size 5 (WS = 60), you can bet it is stronger than a civ B with 8 cities size 4 (WS = 40).
But if civ A has no trade at all and civ B has 3 trade routes in each city plus one shipchain, then WS is misleading.
3) My formula has the main advantage to explain somewhat where your power comes from: either shields (maximize them and minimize support) or gold (maximize trade and minimize maitenance costs).
4) I am sure this formula can be improved. Come on guys! Tell us what you think.

[DaveV]

La Fayette,

As a fellow lover of numbers, I have to approve of your attempts to better quantify the game. I think your BP slightly understates the value of shields relative to gold; shields are worth somewhere between 2 and 4 gold pieces depending on what you're producing. Since I rarely build improvements , I prefer a ratio of 2.5:1. That number is still an oversimplification, of course: you can buy a partial row of a unit at a discount; there are gaps in unit cost (e.g., 70, 90, 110, etc.) so advanced units (e.g. armor, battleship) can't be bought with complete efficiency.

With respect to research power: the ability to trade techs with the AIs greatly complicates the equation. At the expense of great tedium, it is possible to build Marco Polo's Embassy, track each AI's research, and essentially put all the AIs to work as your research partners. MPE also allows the use of Samson's "key civ" discovery. Someone with fewer beakers but a lower research penalty and the capacity to acquire multiple techs from the AIs is in a strong position relative to someone who is playing a purely isolationist game. Number of techs possessed should also be a factor: if my competitor already has three more techs than I, it will take me a while to catch up even if I'm researching faster.

[Marquis de Sodaq]

I like the worked squares idea for approximating production strength of a civ. In play, I rarely think of such things, but knowing it can impact strategy! I'll try to use it when considering what to do. Maybe some ideas will come to mind...

I don't think you'd need to average trade arrows over time, as a formula would simply reflect what applies on the turn for which it is calculated. It would be close for a few turns in either direction, and would greatly simplify calculation.

Indeed, the 1 shield = 2 gold bit should be modified. When rushbuilding a unit,
1 shield costs 2 gold
5 shields cost 11 gold
10 shields cost 25 gold
20 shields cost 60? gold (iirc)
etc.
Knowing there is a huge drop in cost between buying all shields and all but one, there might be a sliding scale multiplier.

[Blaupanzer]

What's wrong with the power graph? (I know you have to "retire" to see it, but other than that?)

Marquis' idea seems intelligent for determining short-term war footing, although I'd be more comfortable with a formula for that "sliding scale." The concept intrigues, but the devil may be in the details.

Power in the "real" world representation in civ for the short-term would include actual existing military, potential cities embodied in existing settlers, and alliances. This in addition to military advances relative to the other civ, worked squares, $, and shields. Money in the coffers actually counts as well, especially if neither power is a democracy.

In the longer term, BP + worked squares + total trade (beakers, luxuries, and taxes) + a factor for tech and caravan trade patterns would work best. However, that last factor would be unavailable for any civ other than your own. Note, I like BP sans the OTB as OTB is part of the factor I suggested (for which I haven't devised a formula either). Many of my more successful SP games have been won by actively trading techs, caravans, and maps with the AIs. GW and UN are a big help in that regard.

Control of the UN is especially helpful. If one wants to emphasize the war game aspect of civ, having it prevents surprise truces; if the AC race, then having stops offesives in their tracks. Do these, the happy wonders, and the sea movement wonders need to be considered? Note Adam Smith is already factored into BP which subtracts maintenance costs. How about Leo's, the War Academy, and Hoover's, all of which dramatically affect production requirements and priorities? Just thinking.

[La Fayette]

dave
about gold and shields, I agree that 2g/1s is rounded down, even when using incremental rushbuilding of units. It works perfectly as long as you have warriors and phalanxes, but it deteriorates a lot afterwards (though 70 is not a hole in the scale after you get howies , but who would be willing to spend more than 70s building one unit when howies are available? ).
I suppose I shall stick to 2 for the early game and switch to 2.5 after discovery of feudalism or gunpowder.

about research, your analysis is perfect IMO. Beakers give the basic power, then Marco and clever use of samson's findings (and vet spies!) help improving it.

Marquis
about gold and shields, I hope my reply to Dave satisfies you.
about averaging delivery bonuses, I don't understand what you mean. Here is what I mean: deliveries are very seldom steady and regular, especially in the early game. You deliver a nice demanded commodity providing 300g, then nothing during 4 turns, then a small one providing 40g, etc... This is irregular, but might be very important or even vital for people like me, who are very keen on long distance foreign trade. Therefore my proposal is to write down any delivery with its date and value (Dave does that already AFAIK). Then you calculate the average that pleases you, and this can be very simple: 300g +40g = 340g. If those were my only deliveries during the past 10 years, I can use 340/10 = 34g/turn as an indicator of what I named OTB (perhaps shorter and better to name it DB for Delivery Bonus)

Blaupanzer
about the powergraph, it tells me nothing about the real power of my civ. I think it emphasizes heavily the 'population' factor that is quite meaningless (already WS is much better than that).
about the rest of your post, there are many ideas in it (thank you BP). I must make them go round for a while in the back of my head before replying.

[La Fayette]

blaupanzer
Here we are:
WS (Worked Squares) is an indicator of size (much better than the powergraph IMHO). If the terrain is roughly the same, you can expect that the capacity to produce of civ A will be about twice the capacity of civ B, if the size of civ A is about twice the size of civ B.

What I am looking for is an indicator of flows, not an indicator of stocks (let us say National Product rather than National Wealth).
There are 3 basic flows in civ: namely food, shields and trade arrows.
Surplus food is the basis of growth in the early game. Combined with shields (and some gold when rushbuilding) it gives you settlers, then new cities, then new territories, etc...IMO valuing your power in the early game is useless, since growth (how many cities?) and basic knowledge (Monarchy, Trade,...) are so much more important (somewhat like 'take off' when studying economics of development). Dave has given 'almost' definitive results in the field of growth (size2 ASAP, then favor shields) and I have given 'almost' definitive results in the field of basic knowledge ('3 arrows' strategy, the shortest path to Monarchy).

Shields (let us say NS = Net Shields, once and for all) are the basis of your strength, and they have special importance due to the fact that there are no multipliers for shields before the endgame (Factories, after Industrialization, tech #40 or so).

Trade arrows are no use as such. They are always converted, into gold or beakers or luxuries, before use. Luxuries are very useful or even necessary under certain circumstances (useful to get WLT*D, necessary to avoid disorder sometimes). IMO it is wise to consider them as 'thrown away' (excess of luxuries = a very easy way to slow down your development).

This leaves us with gold and beakers. My proposal is to define 'Building Power' with a background of 'no research', which means always choosing gold and never choosing beakers, anytime you have a possibility to choose (perfectly aware of the fact that you might be willing to do exactly the contrary when trying to maximize your research power).

All the other factors you mention: peace and war, diplomacy, alliances, knowledge of the map, military strength, treasury, wonders, ...can be considered as plus or minus, and they make this game fun (I wouldn't like to spend my time drawing predictive charts with a computer in my back; I have had enough of that in the real life ).

If I go on comparing, I would say that 2 countries with the same GNP can be very different, and one of them able to swallow the other one in a few days, due to factors other than the GNP.
What my thread was about was correctly measuring the GNP.

[Blaupanzer]

Given the terms just noted, I think your formula works reasonably well for determining both the "GDP" of your own nation and its corresponding GNP by allowing for trade factors (which are VERY simplistic in Civ). However, to know how one is doing in a given game, the question arises as to how your nation is doing relative to the AIs. For that, we must be able to measure their GDP.

The question is: what can we determine about the output of the AI in order to determine his GDP/GNP? We know the accumulated gold at any time if we have an embassy. We can determine the rates for allocating the arrows at any given time by investigating any one city. However, we have no way to identify shields or food unless we investigate every city on the same turn. (This can be done for well-railroaded civs with spies, but it isn't simple. It won't be practical for any long-term monitoring.) Even the formula (incr in gold in one turn/rate in taxes *100 = arrows) won't work without knowing expenses and if the AI rush-built anything that turn.

So, if we know our own GDP, and we factor in trade in some way, how do we use this to determine "power," which is only useful to know in a relative sense? Incidentally, I think your formulae, minus the OTB, are the best way to measure GDP in civ I've ever seen. I just don't see how that translates to "power" without comparitive data on the competitors.

[La Fayette]

Blaupanzer
To say the truth, I have never had the AI in mind when looking at a method for measuring power in civ (I suppose the powergraph is OK for that purpose).
The main reason why I started thinking about that is in fact very close to the idea of 'inquiry into the causes of the wealth of nations'.
IMO this game is first of all a game of balanced development (that's why I love it, and I hope civ3 will go even further in that direction), and before being able to measure precisely where you are, you need to understand how you got there.
I have some sort of a feeling of better understanding of how this game works, and I wished to share that with those willing to read me (and of course I found it fun to think about that during the comparison game organized by the Gits).

[Blaupanzer]

In that sense , well done!