Score calculation
The scoring works by averaging your per-turn scores throughout the game. For each turn a (hidden) per-turn score is calculated as:
(Territory + HappyCitizens*2 + ContentCitizens + Specialists) * Difficulty
The total of all your per-turn scores is divided by the number of turns played so far to get your actual game score. I.e. your actual score is the average of your per-turn scores.
“Territory” is the number of tiles which are within your sphere of influence.
“Difficulty” is 1 for Chieftain, 2 for Warlord, 3 for Regent, 4 for Monarch, 5 for Emperor, 6 for Deity.
Early win Score Bonus
If you win before 2050AD, you get a bonus which is added to your regular score. The bonus is calculated as:
(2050 - FinishYear) * Difficulty
If you finish before 10AD, use the year as a negative number in the calculation.
Example: Winning in 310BC in a Regent level game would get a bonus of (2050-(-310))*3 = 7080.
Other Factors in Score
Almost nothing else affects your score. Wonders, cultural value, military size, science learned, etc. – none of these affect the score. There is one tiny exception for learning “future tech” but it counts for so little in score that it is not worth devoting any energy to it.
Maximizing Score
There are basically two ways to maximize your score:
1) Win as early as possible to increase your bonus.
2) Play till 2050AD building up as much territory/population/happiness as possible.
On tiny maps and some small maps it is often possible to get a higher score with the first approach than the second. On some small maps, and almost all medium or larger maps, the score which can be had with the second approach will be highest.
It is of course possible to combine the two goals. When going for an early win bonus it helps to have a higher base score to add to the bonus. But generally I think it will work best to go flat-out for one of the two goals. If going for an early win, try to increase territory, population, and happiness along the way, but don’t slow down for them.
Milking Tips
The remainder of this note is about getting more out of a “milked” game. Some people think that milking is tedious and don’t like it. I find that it can be interesting. It includes some planning in the early and mid game stages to maximize the long-term result. It has an end game “builder” phase after I finish war-mongering. There are a number of trade-offs in it, in building sequences, in trading early gains of one type for later gains of another, etc. I think it is a bit of an art form, not just a simple formula. I won’t address those types of trade-off issues here, the following are just general tips.
To maximize score you want to maximize territory, population, and happiness. And you want to maximize them as early as possible. The earlier you add each increase to your per-turn score, the more impact that increase will have on the averaged result which becomes your actual score.
To maximize the scoring factors of course requires lots of land. So to get the highest score possible one must begin with a conquest approach to the game. You need to have the majority of the world’s land under your control, and as soon as possible, and you will need to boot someone else out to get it. 
After conquering everyone else (and leaving just some weak and controlled Civ or Civs to keep the game going) you can then of course work toward any of the game’s victory conditions, timing your victory to happen in 2050AD.
You want your territory to be the largest possible without triggering a domination win. There is no easy way to tell where this limit is from the game’s information windows. For HOF submissions it is legitimate to keep expanding till you hit domination accidentally, then reload to the prior turn and stay under the limit now that you know where it is. For GOTM submissions this kind of reloading is not allowed, so you have to guess where the limit would be and stay well under it.
There are 3 kinds of water tiles: coastal, sea, and ocean. Ocean does not matter here, it is not included in your territory nor in the domination limit. Sea is important though – it counts toward increasing your territory but does not count towards the domination limit. So getting more sea inside your territory is a good way to increase score.
When milking I build the following in every city: Aqueduct, Marketplace, Hospital, and Mass Transit. (Except cities with limited growth potential of course.) Many of them also need temples for a while, to expand the sphere of influence. While milking I run a Democracy and buy all these improvements.
I irrigate all previously mined tiles. Production is no longer important, increasing population is.
If you automate workers, it is important to use shift-A from the very start when you first automate them. Not the simple “A” command. Workers on “A” automation will run around re-mining some of the tiles you irrigate at the end. It is a major pain trying to find them all and stop them. Better to use shift-A from the start to avoid this.
I often disband factories during the milking phase. I’d rather have less pollution and don’t need the production.
I minimize the military, keeping just enough to safely enclose the last captive rival Civ, plus some to “patrol” the wild lands to stop barbarian camps from popping up. No point paying more wages than that.
It is possible to speed production more (in addition to buying improvements) by transferring shields, e.g. building Modern Armor in core cities and disbanding them in developing regions. This is a nice boost for building but I find it tedious and generally don’t do this, I just wait to generate cash and buy improvements.
After purchasing all improvements (or near the end of that phase) it is time to maximize happiness with the luxury slider.
If you want to really micro-manage, adjusting each town’s specialists frequently can give quite a score boost. The silly city governor frequently changes your settings, making entertainers (which you want for maximum happiness) to scientists or tax collectors. Although resetting these guys frequently can have a significant impact on score I find it too tedious and usually just maximize the luxury slider and let the specialists be allocated badly.
It is important to avoid an accidental cultural win. You need to keep an eye on your total culture and ensure it will not pass 100,000. I usually find it necessary to sell off most temples fairly early. I almost never build Cathedrals or Colosseums – they just increase the cultural victory problem. Later in the game after researching everything I usually find that I also have to sell off most libraries and universities.
Two wonders which are especially nice for score are JS Bach’s and Cure For Cancer because they boost happiness, without requiring any culture-producing city improvements. Smith’s Trading is also especially nice on large maps because it makes the Marketplaces maintenance-free. Longevity is another nice one, dramatically increasing the rate of population growth during the expansion phase of milking.
Finally, something I like to do in milked games which has nothing to do with score, but seems right to me for this kind of game: Improve the landscape. After the last war I use my military to destroy all the so-called “improvements” in territory which I won’t be settling. I then use workers to plant forests, create a simple rail system, and create lots of paths (roads) through the woods. It doesn’t take much longer to do this and the end result seems more satisfying to me.
Links
- See this thread for a detailed discussion of the Domination victory condition and some useful analysis.
- See this thread for a calculator which can estimate your current hidden “per-turn” score.