Okay, I know this may be a bit ridiculous, and some may be thinking, “Really? Who cares?” or “TLDR.” lol. But for those of you who find this interesting or have any ideas, explanations, further calculations, corrections, etc., please join in on the discussion! This is just something I've been tinkering with lately and wanted to share.
TLDR: Here’s a spreadsheet for observation and discussion. If you play on different map sizes, what are your experiences between them? Does this data possibly reflect that? What do you think of the proposed map sizes? Would you prefer playing on them?
Here’s a quick spreadsheet I’ve constructed of some of the data found within CIV5Worlds.xml along with some rough calculations. I’ll explain some things below.
I’d also like to add that I believe there’s an optimal map density when playing games. Civs that are too cramped together hurt the peaceful ones and lessen options/strategies (you’re kind of forced to war, or to rapidly expand before space is gone). Civs with too much room and that are too far apart hurt the aggressive ones (especially the civs whose advantages are to war early) since there’s a longer distance to travel towards targets and it’s easier to just expand out worry-free; again, lessening options. It also decreases the urgency to grab land and expand, which makes the civs whose strategies are to rapidly expand have less gain, especially after they forgo other beneficial things to do so.
For the sake of balance, there should be a target number of cities assumed per map size that allows for a rough amount of space for each civ. Some will expand past that, others will not and will build “taller” empires. But, at the start of the game, each civ generally has options to do as they wish.
Darn, that's ugly. Well, here's the full size: https://lh6.googleusercontent.com/-y...orld_sizes.png
Most columns are pretty obvious, but I’ll explain the others that are a little less so, along with the calculations behind them.
1) Land Hexes: Basically this subtracts all the water tiles from the total. I used an average value of simply 70% water. So, Land Hexes is 30% of the total. I’m just keeping it simple. You can probably go really deep with these calculations and figure out what percentage of cities settle on the coast and utilize those hexes… as well as subtracting mountain, flat snow, and featureless flat desert percentages from the land total. You can maybe even measure fertility and, for example, count featureless flat tundra as only 1/2 a hex.
But, it’s probably not worthwhile, which is why I’ll keep it simple. I figure including things like mountains, snow, and deserts in the calculations will roughly make up for the coastal/ocean waters that a city could be utilizing when settling on the coast. So again, land is 30% of the total. For reference, normal sea level on Small Continents is 75%, Continents is 72%, and Pangaea is 68%. Guess why they’re different? It’s probably because of what I just described regarding coastal cities. A Pangaea will probably have less coastal cities and more inland cities because of its big chunks of land, so it needs more land available for cities to utilize within their workable radii.
2) Target Number of Cities: I don’t believe this has any effect. I just used it as an average to how much each civ should generally expand in my formulas. I’ve read online someone saying this has an effect on starting city placement and the average space between them, but I don’t believe so. I think the process is more sophisticated than that and has more to do with region divisions and land fertility (as in, more densely populated grassland areas than areas near tundra or desert for better balance). In Civ4, I believe it was used for things like national wonders and how many cities you needed with a particular building constructed before you could construct it. So, probably, it’s just one of those leftover relics within the code from Civ4.
3) Hexes per City: The formula = “land hexes” / (“civs” x “target # cities” + “city states”)
This shows an estimate of how many hexes are available per city (including city-state cities since they’re taking up space on the map too). For reference, a city can work a maximum of 37 tiles (yeah, the middle tile isn’t really “worked” but it’s still occupied and even supplying some yields to the city), cultural expansion beyond that is kind of irrelevant. But, all cities rarely reach that, there’s usually overlap between cities, and not all tiles can always be utilized (mountains, deserts, etc.). A city with a radius of 2 tiles is more practical and takes up a total of 19 tiles (if all are worked, it’s at least an 18 pop city). So values here of 20+ are good… some cities will be massive, some others will be small.
4) Hexes per Civ: The formula = (“land hexes” - “city states” x 20) / “Civs”
This is just another calculation in case one doesn’t like the target city numbers. This one just tells you how many hexes total each civ could have on average. I used a nice, even number of 20 hexes to multiply each city-state by, which would equate to just a bit over a city with a radius of 2.
5) Map Size Increase: This is one is a bit obvious, but just to clarify, this is how much of an increase it is going from the smaller map above to the larger map in the current row. It’s how much of a percentage you would add to the smaller size to equal the next larger size. “larger total hexes below” / “smaller total hexes above”
6) Number of Cities Increase: Similar to the Map Size Increase. (“larger civs” x “larger target” + “larger cs”) / (“smaller civs” x “smaller target” + “smaller cs”)
As for the row sections:
A) The first set of world sizes are the game’s default settings. I also included some of the other data within the default CIV5Worlds file for reference, which I colored differently.
Also, for those wondering what Grain Change is, I believe this has to do with the optimal clumping together of features and terrains and tweaks them for the map sizes.
B) The second set is a conversion of the Civ4 map sizes to Civ5. In Civ 4, 1 unit equaled a 2x2 grid.
The world sizes were:
I had to dig those up from Google. If anybody has Civ4 installed and can verify those numbers, I’d really appreciate it!
They’re nearly identical to Civ5’s values with some adjustments. It looks like the devs made some tweaks to the map sizes when they copied them over from Civ4 (which hurt the ratios a little, but it’s not a big deal). Basically, they added 4 columns and rows to Tiny and they added 2 columns and rows to Small. My guess is that they did this to make those maps a little more “roomier”, since if you look at the data, Small actually becomes the tightest map followed by Tiny under the Civ4 proportions. But the thing I don’t get is why they chopped off 4 zig-zaggy columns (since we have hexes with corners facing up ) from Standard? It made the map tighter and killed the ratio. This size has the most black on either side of the minimap. It kinda bugs me because I’m a Standard player and I want those extra columns and I want a more proportional map! lol
C) The third and last set is a proposed set of map sizes with perfect ratios of 1.6 to see how they work. Basically, the length needs to end with either a 5 or 0 to get a nice whole number when you multiply it by 1.6. Also, all the numbers seem to stick to an even number, so that’s why I stuck with 0 to avoid any possible problems (because I’m not sure if the code needs to divide the map evenly in half or quarters or whatever).
I made the new standard the larger 96x60 map and renamed the 80x50 to “Medium”. Duel disappeared; I figured if someone wants to setup a 1v1 they can just do it on the “Tiny” map since it’s somewhat close to the original duel map. I suppose another option would be to add a 7th map with a size of 32x20 for duels.
Total civ count also increased in some sizes, such as Large and Huge, and generally stayed the same in other sizes, like Small and Medium (which is very close to the default Standard size). I personally like the larger mid-sized map as the new standard, plus a total civ count of 10 just “feels” more like a standard setting than 8, lol. City-states proportionally increase as well and remain in the same ratio to civs, 2:1.
I also used more of a progressive increase in target city totals. With that, you can see that as the map size increases (which is also a bit more gradual and not as jumpy) the total number of cities also increase somewhat proportionally. Also, the “hexes per city” calculations are pretty close to one another and balanced.
To be fair, I tried changing the target city totals in the default Civ5 section as well, but it still didn’t really fix the numbers that well.
So, if we compare the proposed sizes to the default ones:
Tiny = between default Duel/Tiny
Small = close to the default Small
Medium = close to the default Standard
Standard = a bit smaller than default Large
Large = a bit larger than default Large
Huge = default Huge; unchanged
Other observations to be made while looking at the default Civ5 settings:
1) From Duel to Standard sizes, there are really no distinct values between unhappiness per city, research costs, and policy cost increases per city, except Standard has a research cost adjustment of 110%. There's no progressive changes even though the map sizes and number of civs increase.
I have no experience on these smaller sizes. But, theoretically, the smaller the map size becomes from Standard, one might say that: unhappiness from city number could be easier to manage, research could take a bit longer (less trading partners, less population, etc.), and policy costs increases could be a bit more negligible.
Though, with regard to city number unhappiness being easier to manage, one could also point out things such as: there are less total natural wonders in the world to find and less total luxuries to obtain and trade for.
2) If you like to manage a lot of cities, Huge is the map size for you since it has, by far, the greatest average of hexes per city. You have a lot of room to expand. Also, to further encourage that, you have much less unhappiness and policy cost increases per city you settle.
3) The map size, Small, is kind of the opposite of Huge and has the least amount of hexes per city on average; the map is a bit more cramped. Standard size would be the next most cramped map size under default settings.
4) Barbarian camps… this one is a little tricky to figure out. At first glance though, compared to the smaller sizes, it seems like Huge would have the most barbarian trouble with more camps spawning around the map. Next would be Large. Perhaps the least barbarian trouble is had by Small.
Also, as we all know, no matter the map size, we always start with a single settler within the Ancient era. So larger map sizes, begin with a lot more fog and vacant tiles until everyone starts expanding. But also, as was said above, it looks like Large/Huge have even more room to expand on top of that anyway.
I “tried” to come up with a formula to observe some values regarding average number of camps:
(“total land hexes” – 37 * (“Civs” + “CS”)) / “fog tiles per camp”
The number, 37, comes from the amount of visible tiles a 2 radius (19 tiles) city would have. Note, this formula doesn’t include any possible units out scouting or near borders. A single unit out in the world could, without obstructions, provide visibility for 7 tiles. If on a hill, 19 tiles. Also, if America is in the game, forget about it. They probably really cut the barbarian camp numbers within the current game; especially if they’re rapidly expanding and exploring (which is also flavorful of them and expected).
Here are the numbers:
So, from this, despite how questionably accurate it may be, it potentially shows that Duel usually has the least trouble with barb camps. As expected, Large and Huge just blast off. I also don’t really have any experiences with Large/Huge, is this usually the case? Are barbarian camps really numerous during the beginning of the game?
Anyway, I may be overlooking some other things, but don’t you think the “Fog Tiles Per Camp” should scale a little better as the map size increases? Huge is a 54% increase in size from Large, yet FTPC only increases by 17% (also, there are inconsistencies above this calculation which further exacerbate this beyond what's seen). I’m not really a math whiz, and I’m sure there are much better formulas out there that someone here can construct.
As we can see from all of this, balancing all these map sizes around the rules of the game is not a paltry task and it’s probably very, very difficult to get everything to a state where it’s all perfectly balanced. But, I think thru some modding, we can take the great work the devs already did in designing it and perhaps create more balanced worlds for game experiences that are more closely related between each size. And not only related, but improved a bit as well.
What do you guys think of the proposed sizes? Do you think they would work well and would you prefer them over the default ones? Or does anybody have any other suggestions or better ideas?
I won't be creating a mod of this yet, since I'll wait and see what Gods & Kings does with these (if they even modify these at all). If anything, I may just make a quick and easy personal mod to the Standard map size to bring the width back up to 84, since that's the only one I like to play on.
But, if anybody else is going to try modding the sizes now, also keep in mind that some values within AssignStartingPlots.lua will have to be tweaked to reflect the proposed map sizes. This isn’t only a modification to CIV5Worlds.xml if you want things balanced and functioning properly. Also, new values will probably need to be created for the aqua columns within the table.
Last edited by jpbar81; 07-04-2012 at 01:17 PM.
Reason: Corrected Image: switched length/width titles and fixed proposed small cs value from 10 to 12
I'm a big fan of consistent scaling. Also, I'm a big fan of using (powers of) the golden ratio, ~1.618, for this sort of regular stepping; 1.6 is as close as you can get with the secondary criteria of "pretty integers." So thumbs up all around.
Following up: this set of concerns is actually the reason I mostly play on Standard. It would be interesting to see a more in-depth analysis here. Relative cash flow should also be analyzed, since it has a major impact on research (via trade agreements) and culture (via CS influence).
Originally Posted by jpbar81