Territory Score Formula!

chiefpaco · February 28, 2002, 16:17

Just thought I'd cut & paste my post from another site into here, in case some just read the Apolyton boards.

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

Arrian · February 28, 2002, 16:23

Well, I'm glad you're doing it, 'cause I don't have the patience.

This confirms what I already thought: fighting early and often is the best way to achieve a high score, and the bigger the map/land mass coverage, the better, since there is no multiplier for map size.

-Arrian

Marquis de Sodaq · February 28, 2002, 18:08

For domination victory, you must average a certain % of the world. Is this calculated with total land in the game, or only land that is within cultural borders? That is, with 1000 tiles of land, will you need to average # / (1000 x #ofturns ) or would the denominator start at 9 per civ and increase as borders expand?

Aeson · February 28, 2002, 18:54

Domination isn't a fixed percentage of landmass or culturally claimed land. Sometimes razing an enemy city (with no increase in your own claimed land) will trigger domination. That would suggest the ratio of Player claimed land to AI claimed land does affect the domination limit, but certainly isn't the only factor involved. Total number of land tiles (and seemingly some water tiles) makes a difference. A lot of testing on the subject has been done over at CivFanatics GOTM forum to no avail. It would be nice if Firaxis would just give us the formula. Whatever it is, it isn't the % given in the manual.

Just a couple tests I ran a while back.
Standard sized map, 1.16f

Total Land, Domination Limit
1862, 1457 (~78%)
1519, 1214 (~80%)
100, 90+ (Domination wasn't triggered)

It would seem that the less total land, the higher the percentage needed to trigger domination. This might also have something to do with the AI's landmass ratio though. In the tests the AI had the same amount of land for the larger 2 maps (49 tiles), and in the 100 tile landmass map, they owned the other 10 tiles. Also I didn't count any coastal, sea, or ocean tiles in any of the tests. The time I held the land didn't matter either, as I could approach the domination limit, and 50 turns later it would be triggered at the same point.

Aeson · February 28, 2002, 18:59

The victory bonus formula should be included in this thread too.

Bonus = (2050 - Date) * Difficulty

Cheiftain = 1
Warlord = 2
Regent = 3
Monarch = 4
Emperor = 5
Deity = 6

Aeson · February 28, 2002, 19:10

To figure out what your score would be if you milked it (at current population and territory levels) until 2050.

TotalPastScore = CurrentOverallScore * TurnsPlayed

CurrentTurnScore = (TurnsPlayed * Increase) + CurrentOverallScore

2050_OverallScore = (TotalPastScore + (CurrentTurnScore * TurnsRemaining)) / 540

SirPleb posted an Excell spreadsheet over at CivFanatics that will handle the calculations. I'm just assuming he uses the same formula, as I don't have Excel to check out how he did it.

ps. Yes I am obsessed with figuring out the scoring system. Figuring out Domination is key to maximizing scoring. I'm still stuck eyeballing it and making educated guesses though, the exact formula is beyond me.

Technoron · February 28, 2002, 20:00

ran the folowing:

built a city and let it grow to 1000 culture level. monarch (*4)

9 turns at 9 tiles
26 turns at 21 tiles
1 turn at 37 tiles

final territory score = 73.7
[[9*9)+(21*26)+(1*37)] / 36] *4 = 73.777

dunno about the rounding. if territory was calculated based on city radius the final score would have been
[[(9*9)+(21*27)] / 36] *4 = 72

==>territory score is based on cultural borders vs land within city radius

also...
built a single city on monarch and immediately added the worker to the population

score for peeps on 3950BC was 8 for content/specs and 0 for happy

made one into an entertainer

score for peeps on 3900BC was 6 for content/specs and 4 for happy.

score on 2850 was 5.3 and 5.3

==> things work the same way for population except that happy people count double.

Dunno how future techs work into it.

Technoron · February 28, 2002, 20:29

Quote:

Domination isn't a fixed percentage of landmass or culturally claimed land. Sometimes razing an enemy city (with no increase in your own claimed land) will trigger domination.

the civilopedia states domination occurs when you have 66% of land within your borders, which doesn't jive at all with your post.

on the other hand....

The PRINTED manual states that domination is triggered by having "the vast majority of the world's land and population" in your borders. Land AND population. So if you raze an enemy city.... well you've suddenly boosted your percentage of the world population and....

Y'know, I think I'm really glad that I'm not obsessed with figuring out the domination equation because I see somebody spending a whole lotta compiling a database of tile and population counts and calculating percentages...

Whoha · March 1, 2002, 00:26

domination requires you to have an average of 66% coverage for the entire game, not 66 at one turn, so depending on how you expanded in the early game you may have to wait awhile before domination catches up with you

Aeson · March 1, 2002, 01:04

Domination is triggered by a certain number of tiles being held on a given turn. It isn't the average of all turns. I've played several games where I was 1 or 2 tiles away from domination for hundreds of turns. I had built out to the domination limit, then reloaded to figure out the exact tile count needed. After that point, anytime that I would build another city or expand my borders, domination would be triggered. If it was the average, then just holding the territory I had would quickly trigger domination.

I know the Civilopedia says 66%. It certainly is not 66% of land tiles, it usually works out to ~80% of the land tiles.

chiefpaco · March 1, 2002, 03:00

Agree with the Land Tiles. Just doing some more investigation, but getting late before I can wrap it up. I have a nice testable 6*6 map & it certainly looks like a land tile count of some kind. I'm still looking on whether the domination count includes water and land, but will check another day. One thing I did notice was that I had a border expand out to the sea & that didn't trigger it, but if I built new city to grab 2 land tiles, it did trigger it. hmm...

Aeson · March 1, 2002, 06:44

I had the same thing happen to me in testing, coast and sea tiles didn't seem to count towards the Domination limit. But SirPleb had a set up where they did count, and I've had games where Domination was triggered when borders expanded over water (not claiming any more land). It's all just very confusing

Thrawn05 · March 1, 2002, 13:05

Does anyone think there is a negative effect on your score if you have overlapping city tiles? And I'm not only talking about your own cities overlapping, but if the AI plants a city that overlaps you or vise-versa.

chiefpaco · April 9, 2002, 15:58

I guess I just wanted to close up the discussion on this thread here at Apolyton, because I started it and I found the answer. I didn't want people to do some old searches & find more questions than answers.

Here's a couple snippits of my the solution process, discussed on other boards:

Domination% = Player's Controlled Tiles (Land + Coast) / Total Map's Tiles (Land + Coast)

Domination Victory occurs when Domination% > 66.66%

By Controlled, I mean the territory in your sphere of influence.

My theory comes as the result testing on various maps but the icing was probably studying the CivFanatics GOTM03 results for each player who submitted a Domination Victory.

Using my new Utility, MapStat, I extracted each player's territory land & coast & calculated that as a percentage of total land & coast. In each case, the Domination triggered as a result of the formula above becoming true.

If anyone has a save that proves otherwise, please post! If anyone agrees with me, post anyway!

- There are a few reports of domination victories happening later than they were supposed to. I believe that it may have to do with 1.07 patched games. They might have made a fix in 1.16 or maybe 1.17. All my testing was with 1.17.

Relevant link:
Mapstat Utility: http://apolyton.net/forums/showthrea...threadid=44644