territory score formula

I haven't seen any posts for an explanation of the territory scoring system so I did some investigation myself. The reason? I'd like to know how the domination calculation works. So here's step 1, knowing the territory scoring marker may help out. The investigation is still ongoing, but here are my results thus far & some conclusions. Try to stick with me here, I know I never read those long mathematical posts. Maybe start at the bottom & work your way up if you need to.

Scenario under test:
Standard Map, Pangea World, 70% water, Regent, Rome, Roaming.

Some Definitions:
Land Area - A - The square miles given in the F11 statistics screen divided by 100 for my purposes.

Territory Score - S - The territory score given for my civ on the F8 Scoring Screen

I recorded A and S for each turn in my trial game and here are the results. Note: I called the 1st turn of the game (4000BC) turn 0 for reasons stated later. I only built my one city, which I settled on the first turn. I only built some warriors (so no one would threaten me).

Turn - A - S
0 - 0 – 0 (4000BC)
1 - 9 – 27 (3950BC)
2 - 9 - 27
3 - 9 - 27
4 - 9 - 27
5 - 9 - 27
6 - 9 - 27
7 - 9 - 27
8 - 9 - 27
9 - 9 - 27
10 - 21 - 30.6 (3500BC)
11 - 21 - 33.5
12 - 21 - 36
13 - 21 - 38.1
14 - 21 - 39.9

The reason my land area expanded from 9 to 21 was the expansion of my borders due to the culture produced by my palace. An interesting note was that S jumped the same turn as A. It didn't take a turn of A to increase the score, S.

The calculation derivation:
As we can see, it looks like for the first 10 turns (including turn 0), S is simply A*3. I'll remember that. But where does the 30.6 come from? It wasn't too hard to figure out.

Let X represent the average Land Area. That would make X the sum of A each turn divided by the number of turns. At turn 10, there were 9 turns of A=9 and at turn 10, 1 turn of 21. That would mean X=(9*9+21)/10=10.2. Now, recalling that 3 factor yielded 10.2*3=30.6! It worked! And it worked for each successive score!

So the territory score was S=X*3 for this scenario. Where did the 3 come from? After further investigation (I don't want to post all the results here – this is getting long enough), it was the difficulty level. Each difficulty level comes with a multiplier. 1 for Chieftain, 2 for Warlord, 3 for Regent, 4 for Monarch, 5 for Emperor, and 6 for Deity.

The next test was to determine the effect of settling on the second turn, not the first. This made all calculations divide over one more turn. Here were the results with the same scenario as above:
0 - 0 - 0
1 - 0 - 0
2 - 9 - 13.5
3 - 9 - 18.0
4 - 9 - 20.3

As shown, S is now averaged with the 0 score in turn 1. I noted that turn 0 (4000BC) does not seem to factor into the calculations. That's why I call it turn 0 to make the rest of the calculations easier.

Other factors I tested but did not seem to affect the results were the Map Size and Water Coverage.

There was one more observation, which I could term as a very minor bug. If you start a new game but have already quit a game in the same session, your turn 0 Territory Score is equal to the territory score in your last game. Turn 1, however, will show the correct score for your new game. So no big deal.

One other thing, exploring or knowing the rest of the world had no effect on the territory score. I just have seen some predict that it might, but it didn't in my cases.

So here are my conclusions (at least from this mini-test):
- Territory Score is equal to your Land Area average divided by the number of turns played and multiplied by your difficulty level.
- Score for each turn is calculated after your land area gains (that’s why turn 0 looks irrelevant, but isn’t)
- World size & water coverage had no effect on the territory score.

Tests yet to come:
- Larger scale testing, second city, longer period to see if my equation holds.

Recommendations drawn from the investigation:
- Building a City the first turn can lead to a higher score because you have no zero to factor into your territory.
- Playing a higher difficulty mathematically contributes to your score by acting as a territory score multiplier. I did not investigate the contribution to the Citizen score, but it could well be related in a similar fashion.

Aim:
- I'm still on the warpath to find the solution to the domination calculation. Is it tied to the Land Area or Territory. Perhaps I’ll look closer at some posted domination saves.

Pathetic:
- Me . What a long investigation. Why don't I do something more useful?

I have seen bits & pieces of this calculation scattered around the boards here but I just wanted to try it myself & consolidate it in one place.

Anyone with feedback, analysis, or wants to join the battle, please post.

Rock on! That actually made sense, unlike most of the long mathematical tests I have seen on this forum.

In addition to your notes I think that:

1) Coastal and sea tiles within your sphere of influence count toward territory score. 1 * difficulty per tile, same as land. Ocean is never within your territory.

2) For each turn's score add 2 * difficulty for each happy citizen.

3) For each turn's score add 1 * difficulty for each content or specialist citizen.

4) Coastal at least sometimes factors into domination but sea does not. (Making it somewhat difficult to extend this approach to determine the Domination threshold.)

Edit: I believe it is safe to assume that the calculation holds for the entire game as described. I have used it to project my final score from the difference between the score in two consecutive turns. (Using that difference and assuming the calculation is as you describe, you can work out what the underlying "per-turn" score is for any given turn.) The final score projections made this way from a stable (completely grown, completely happy) situation are a highly accurate match to actual final score a hundred turns later. Which seems to me to confirm the theory, that this calculation remains the same throughout the game.

Dude, you kick arse!

We're fortunate that there are people as patient as you out there to find these formula.

Originally posted by SirPleb
In addition to your notes I think that:

1) Coastal and sea tiles within your sphere of influence count toward territory score. 1 * difficulty per tile, same as land. Ocean is never within your territory.

2) For each turn's score add 2 * difficulty for each happy citizen.

3) For each turn's score add 1 * difficulty for each content or specialist citizen.

4) Coastal at least sometimes factors into domination but sea does not. (Making it somewhat difficult to extend this approach to determine the Domination threshold.)

Edit: I believe it is safe to assume that the calculation holds for the entire game as described. I have used it to project my final score from the difference between the score in two consecutive turns. (Using that difference and assuming the calculation is as you describe, you can work out what the underlying "per-turn" score is for any given turn.) The final score projections made this way from a stable (completely grown, completely happy) situation are a highly accurate match to actual final score a hundred turns later. Which seems to me to confirm the theory, that this calculation remains the same throughout the game.

Click to expand...

Thanks for the votes ppl.

Good work SirPleb. I thought you might be with me here. I have checked the equation in a few games & it has held for small empires. There was one game I had where I believe it held past the 100 Culture/Turn mark from my palace but I didn't record it. Your work certainly helps confirm for the later game and it's good to hear some confirmation too.

By the way, SirPleb, you were right on in this thread, "Attempted Domination" (which I have just re-found & wish I reviewed it before my study): http://forums.civfanatics.com/showthread.php?s=&threadid=14578

and I can credit you with the territory theory calc. That was probably the definitive thread in the domination calculation, IMHO. That is, until we get more figured out.

Ok, about your post:
1) Agreed. Water counts in the "Land Area".
4) What leads you to believe this?

4) What leads you to believe this?

Click to expand...

I think what he is saying is that the water (sea), although it is counted as land in your territory score, it is not used for domination purposes. If it is, then I don't think that's right. Water should be considered your 'territory', but it should not count when you are told you need 66% of the total LAND area.

Originally posted by chiefpaco
4) What leads you to believe this?

Click to expand...

What made me conclude this was a test I did for the Domination threshold after finishing my GOTM#3 game.

By trial and error addition of cities I found that I had been very close to domination in my game. But the tests were very confusing - I tried to refine the number by settling on chosen spots on peninsulas, to get the desired number of land tiles. Then the number of cities involved seemed to change the results! I started suspecting that water tiles were affecting the result in some way.

Using just land tiles (no building near coasts) I learned that claiming 18 tiles more than my save game was ok, but taking 21 more triggered domination.

Next, to test the water tile theory, after claiming 18 more tiles to be just under the limit, I gave a little island I owned, which had a large sphere of influence on coastal and sea tiles, to a rival Civ. That removed roughly 45 tiles from my sphere of influence. I then settled additional land tiles to determine the new limit. I could now claim exactly 24 more tiles than before until domination was triggered. 25 more was too many. So that meant that the island had counted as 22, 23, or 24 tiles in the total land count! (Not precise because the earlier part of the test had left an unknown number of 0, 1, or 2 tiles still being claimable.)

On looking around the island involved, I could find only one explanation which fits. The island's land (quite small), plus the surrounding coastal tiles within the previous sphere of influence, comes to 22 tiles. (Just the land is way less, also including sea tiles is way more.)

In some other tests done by Aeson, he discovered that the percentage of land required for Domination varies according to the map settings. One of his discoveries was that the required percentage seems to go up as smaller landmasses are involved. To my mind this fits fits with the theory that coastal tiles are being counted. As there are more and smaller chunks of land, the percentage of coastal tiles goes up, and the percentage (when viewed as a percentage of land) would appear to increase.

Bamspeedy: That's sort of right, but not quite what I'm saying. What I'm saying is even MORE weird. There are 3 kinds of water tiles in the game: coastal, sea, and ocean. I think that the territory count includes 2 of them (coastal and sea) and the domination count includes one of them (coastal.) Weird stuff. My bet is there's a simple programming error something like:
#define COUNT_DOMINATION(x) (x <= 9)
where it ought to be (x < 9)

But, even allowing for that, there seems to be something else wrong with the domination threshold too. One bug like the above would still not fully account for the strange things we've seen.

Do you think domination triggers on a certain land holding (i.e. follows something like the Land Area stat), or average (something like the territory)?

I wondered, when you were going through your experiment, were you considering your Land Area or Territory?

Also, Aeson mentioned that the territory your opponents hold could factor in too. Do you believe that is the case as well?

Ok, I see now the GOTM domination debates. Is that where the discussion has gone down? I haven't checked there before...

It seems to me that domination is based on current land holding, not on any averaged-over-time effect. None of the tests so far seem to have shown a sign of being affected by date or expansion over time. When I was experimenting with it I was just counting actual tiles (grid on of course! ), I didn't use any of the Demographic or score info.

I do think now that something somehow related to opponents affects domination. But I don't think it is anything simple like "over X% of the total land within anyone's territorial borders". I think that if reducing an opponent's territory normally triggered domination, by now lots of people would have noticed and reported that. So I am guessing that the interaction which is somehow related to opponents could be a separate bug. I hope that if anyone has more info about it they will jump in and tell us!

The thread where most of the discussion of domination as it related to GOTM (i.e. what triggers it - there are other threads discussing whether it should be enabled) is this one:
http://forums.civfanatics.com/showthread.php?s=&threadid=13305&perpage=20&pagenumber=2
The relevant bits are somewhat spread out throught the thread I''m afraid

Agree with the land aquisition. I have seen the victory trigger by aquiring 2 land squares on a turn, but would not trigger by only aquiring sea squares for many years. That would lead me to believe (only 1 test, mind you) that the sea squares do not factor and that it is likely not an average. The aquisition did come at the expense of 2 land sqaures my opponent had, but I can't tell if that mattered yet.

My current testing is with a little 6*6 map with ocean everywhere else. Have a turn saved where all I have to do is hit 'build city' to win via domination. However, if I don't, no victory for many years before I gave up.

Also have a save right before my only complete game domination where I can capture 1 city to win. I haven't explored it enough by expanding my borders elsewhere because the game keeps crashing on me.

BTW, my high score table is getting really messed up...

why sometimes when all victori type are on do you succeed in conquest victorie, even if the ennemy as 1 city left for 3 turn...
normally happen in early age

is it because at a certain age you can'T win by domination?

Originally posted by Badluck
why sometimes when all victori type are on do you succeed in conquest victorie, even if the ennemy as 1 city left for 3 turn...
normally happen in early age

is it because at a certain age you can'T win by domination?

Click to expand...

You can win domination victories in any age. In my 6*6 experiment, domination victory is triggered in the ancient age. I'd love to be able to answer your first question, but we still don't know how it is calculated.

I wonder by all the different accounts of domination victory - if there is more than one way to trigger it.

BTW, my high score table is getting really messed up...

Click to expand...

When I was testing the early conquest bonus, my scoreboard was entirely filled up with 36060 like scores. HighScores.cv3 can be edited in notepad or any other text editor though. No need for even firing up the Hex Editor to fix things up. It's quite easy to delete any unwanted scores from your HOF, or make some up if you really want.

Since there seems to be some general interest in date and score calculations, I've just written a quick program to help with some of those.

I've posted it at http://forums.civfanatics.com/showthread.php?s=&threadid=17550

It is based on one I previously did in Excel, but not everyone has Excel of course. This one is a bit nicer and should work if you have Internet Explorer 5 or later or Netscape 6 or later.

i have your excel thing, does thing one do the same thing??
since i doNT' have IE and netscape..

i am using * Mozilla * (from the creator of netscape but free)

i will try to help you guys with calculation

Mozilla should work fine, for most purposes it is the same as Netscape 6, sometimes less stable because it is in ongoing development.

The new calculator does much the same thing as the Excel spreadsheet but prettier. I tuned the calculation a hair, the projected score estimate is now a tad better.

Here's my test map. Let's see if I have enough wizardry to try a screen shot (1st try here). Have no idea yet how people here get such nice & small quality shots, but here goes.

A couple of points from this. First, I'll explain the world. Using the editor, I made a 6*6 island on a Standard map size with just grasslands. No other land is on the world other than this island. Everything else is just ocean.

Pictured here (assuming the picture worked...) is the first turn after achieving domination victory. The difference in my territory was that Tlatelolco just expanded its borders. This expansion claimed 1 coastal square (the one by Tletelolco next to the Indian border) and 6 ocean squares. I thought it was interesting that ocean squares were claimed. I've never seen that before, but I didn't make any sea for this map.

2nd point is that this expansion gained my 43rd Land and Coastal tile. This was my second successful run at producing a domination victory in this map (using Chieftan). Both times, the victory was triggered on the acquisition of my 43rd such point. There are a total of 64 Land & coastal tiles in my map and 43/64=67.2 Percent, just over the 2/3 mark. The turn before this, I held 42 tiles (just under the 2/3 mark) but an equal number of land tiles (because only a coastal tile and some ocean tiles were gained).

Now, I know we have seen some varied results in full games, but I did want to at least put this out as the investigation goes on and I'm still looking at some other numbers for this case.

Maybe I'll get a shot up of the turn before, if this one works...

BTW, thanks for the high scores table tip!

That's a very nice test indeed chiefpaco! It sure seems to strongly demonstrate that the threshold is 2/3 of total(land+coastal).

I guess it might still be that it varies on different kinds of maps or whatever, but why would it? The simplest explanation usually works best. Seems to me now that you've done this experiment, that rule is a very good working hypothesis.

The ocean tiles being within your sphere of influence sure is odd but I can't see a way to make their numbers come into play in what you were testing. I think it is just a strange thing on the side. One possibility: all ocean tiles involved are within the 21-tile "workable" region of your cities. Perhaps the program's logic puts the 21-tile area "in" regardless of whether it is ocean. I notice that India's sphere of influence could extend over the ocean to the SE but does not. Delhi's "workable" area only extends to the coastal tiles. Anyway, regardless of the explanation, I don't think it affects your Domination experiment.

thanks to random game, i think i have found something new!!!!!!!!!!!!!!!!!


here game parameter:

pangea tiny map
chieftain
1 AI = France
i used the multi renamed game to control AI growth...

i stoped is expansion at 1 citi.... and blocked is possible square at 12 or so...
by building citi near...

i had a total of 20 citi and more for a while i i was wondering why i wasn'T winning when i suddenly reallise there was 3 small island 2 of 2 tiles
1 of 12 tiles approx.

so i go build on the first nothing happen
i build on the second and what do i see!!!!!!!

DOMINATION VICTORY

so i had control of more then 75% of all the island..

if you tell me how to post game i will post saved filed, i did save this game at a lot of spot

I'm still looking at some of the other numbers & realize domination still isn't necessarily linked to the Land+Coast, but that just the 1st number to really suggest something.

Good job BadLuck. I agree & think Domination is (at least most easily) triggered by a sudden expansion & not a territory average. And keep up the investigation!

BTW, one cool sidenote. I agree with you SirPleb, that Ocean may go into your domain if you need the tiles for your city count. Just for kicks, I checked what the ocean produced when you put a worker on it. I was disappointed - it was just a red shield, similar to a polluted square.