The Income Curve

Due to the fact that, in increased zoom games, the income of smaller cities is SOO much smaller than the income of larger cities, Ive considered adding a "curve" to the way income is calculated. I know a lot of you cartographers dont even consider how you calculate your income, but I do, and I want to make it as accurate and yet playable as possible.

So Ive devised a formula. The formula is t=(1/SQRT(x)/y))z^0.5, where t=the number the city will have as it's income, x is the GDP or whatever you're using to calculate income of the city with the HIGHEST GDP in the game, y is the number of income points associated with THAT city, and z is the GDP of the city you're calculating the income for. Get it? Sounds complicated but it's not really. If you were to graph all your cities, it would form a shape somewhat like this:
http://www.wolframalpha.com/input/?i=x%5E.5

I come to you now to ask if you think this would be a good idea. Think not of any "extra work" involved in the calculations as I already have a pretty strenuous calculation process that would not be made any more difficult with this formula. Think only of benefits or drawbacks to gameplay and realism.

>math

Skrivet av Jim Jimmies, 19.12.2012 at 20:19

>math

Yes, because math is all around you. Deal with it.

Skrivet av Runway1R, 19.12.2012 at 20:23

Skrivet av Jim Jimmies, 19.12.2012 at 20:19

>math

Yes, because math is all around you. Deal with it.

I cant. Thats why Im majoring in music.

Ignoring Roody, does anybody think this is a good idea?

Interesting, it's certainly lower the difference between africa and europe by exemple. Personnaly I think it lower the realism, but realism is'nt the only goal of this game.

For gameplay it have the huge advantage as I said to increase the potential of the poor, continent, area, etcetera of a map
With this a decent player in a poor continent could probably have a chance to win.

However I personnaly think this curve could delete an important point for gameplay, by exemple in the actual europe map moscow paris and london are worth a lot and its a strategic move to get them. If you use your curve probably that these cities would be worth a lot less while the balkans would increase a lot. Sometimes a really rich city surrouded by poorer city can add a lot of strategy in the game.

Also take note that if there is really poor cities inside of a rich country there is no problem, the country bonus is here to fix everything.

I would say that this curve could be great to balance each continent but could be catastrophic for small strategic map with lots of economic variety like europe.

While I see what you're saying, the way the curve is set up is so that no city receives a decrease in income. If x and y were the average of all city's GDP instead of the maximum, I can see why it would be a problem, but this was actually designed for those increased zoom maps like USA and EU, rather than traditional EU, where some parts of a country have a considerable disadvantage against the richer areas.

Oh ok, sorry for the miscomprehension i didnt really take the time to test your curve. So your curve finally will enrich everything except the richest city. Well, the same problem apply, imperialist will be out of use if the poorest area start to be manageable with higher income strat. Also it's needed that some part of a country(continent, map etc) have a considerable disadvantage or else there is less strategy needed.

Anyway test it if you like it, but personnaly I don't think it would be good for the majority of the maps.

When the difference is to big between the richest and poorest places of a map with real gdp data personally i would go with a basic income to every city. That minimum income could be the number required to run the cheapest strategy like PD and Imp without going in debt.

Why would you write SQRT(x) when you write z^0,5 and why 1/SQRT(x)/y, it is the same as 1/SQRT(x)y
London 565b t=
Paris 564b t=
Athens 95b t=
Berlin 96b t=
Amsterdam 47b t=

I will complete when you elaborate what income points are but as it stands t will be a really small number, unless y is a tiny decimal. By only assuming y is one (which isn't by what I get from saying "points"), I'll only do Athens and London here:
Athens t=(1/SQRT(565)*1)SQRT(96)=0,04207*9,7979=0,4122
London t=(1/SQRT(565)*1)SQRT(565)=1
If y is the income you put arbitrarily in the highest income city, it will be an integer and a large one and it will push the inside of the bracket further closer to zero (no pedants shouting about it being as close to zero as 300 billion is thx).
If t is the coefficient multiplied with the actual GDP then it might make some sense (for example, for Athens' 96 to be multiplied by 0,41 but it's too harsh).
In conclusion I don't get what you need that for
Source: http://en.wikipedia.org/wiki/List_of_cities_by_GDP

Income points are the 1-999 number for income assigned to each city. And I really dont understand your calculations, as the formula has worked fine for me for all my calculations for my New America map. Using New York as my base, I was able to calculate a curve for each city with the values as described.

Post your calculations

Skrivet av Aristosseur, 22.12.2012 at 08:15

Post your calculations

my spreadsheet? A chart? What exactly do you want? Because my calculations are pretty complex.

You have posted the formula already so the calculations aren't complex, I want to see your input and results of the richest and a couple of poor cities.

Skrivet av Aristosseur, 23.12.2012 at 06:21

You have posted the formula already so the calculations aren't complex, I want to see your input and results of the richest and a couple of poor cities.

based on New York's 92,251,245* turning into 250

Atlanta's 20,523,345 turns into 118
Albany, NY's 3,429,824 turns into 48
Alpena's 93,142 turns into 8
Houston's 22,867,787 turns into 124

*These are based on the Census Bureau's "sales" figures in thousands by county. I used these because my map uses different borders than by states, and I could not find reliable GDP data by county and business sales by county is the closest I could get. I added up the counties in the "country" to come up with each number. I believe they are roughly comparable.

Would this work with population to reinforcements? or would it totally screw things up?