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Scoring Formula Calculations
posted by Aeson – January 24, 2003</span>

The scoring system built into Civ III is good for rating 2 things, population and territory. The bonus for early victories is next to useless though, as an &#39;early&#39; conquest will almost always come well before an &#39;early&#39; spacerace victory played with comparable skill. The bonus formula treats all victory conditions equally, and doesn&#39;t compensate nearly enough to compete with milking except on very small maps. For this reason, the in-game bonus for all victories is disregarded entirely, and a new method of rating early victories is put in it&#39;s place.

Based on the map factors described in the summary, each victory condition is given a &#39;best&#39; date. This is the date which is expected to be close to the earliest possible date which the victory condition would be attainable. By taking the date of victory from the player&#39;s game, and comparing it to the &#39;best&#39; date, the resulting ratio is then multiplied by a curve developed to approximate the amount of in-game score being passed up by the player for finishing early. This curve is based off the &#39;max&#39; score for the map. For the purposes of all calculations, the actual turn number for each date is used.

Here is the actual formula for determining the date bonus:

DateBonus = ((540 - PlayerTurn) / (540 - BestTurn)) * Curve
Curve = (MaxScore - (((PlayerTurn / 593)^2 + (PlayerTurn / 3200))* MaxScore))

PlayerTurn: The turn which the player achieves victory.
BestTurn: The predicted &#39;best&#39; turn for that victory type.
MaxScore: The predicted score for a fully milked game.
Curve: This roughly mimics the scoring progression in a milked game.

A graphical representation of the curve: <a href=\'http://gotm.civfanatics.net/games/curve.jpg\' target=\'_blank\'>http://gotm.civfanatics.net/games/curve.jpg</a>

MaxScore is determined by taking the domination limit, figuring out how many citizens that many tiles can support, and then using those numbers to calculate the upper limit for TurnScore. Then a modifier based on map characteristics is applied to the TurnScore to determine what the MaxScore would be. The formula is:

MaxTurnScore = (HappyCitizens * 2) + ContentCitizens + Specialists + Territory
MaxScore = MaxTurnScore * MapModifier

HappyCitizens: An estimate based off of territory. Each tile can be worked by one citizen, so the maximum happy citizens would be one per tile, or the domination limit. Each city &#39;eats up&#39; one of these citizens, so the number of cities will slightly decrease this count.
ContentCitizens: For the purposes of this prediction, all citizens are considered as happy, which would be the case in a well run &#39;milked&#39; empire.
Specialists: The number of specialists is currently predicted based off the average food per tile. The support cost of the tile worker is subtracted from the average, and then the result is multiplied by the domination limit and divided by 2, as each specialist requires 2 food.

The DateScore is then added to the BaseScore to give a total. This total is then compared to the MaxScore prediction to get a percentage, which is then multiplied by 10000 to give the FinalScore.

<span style=\'color:red\'>FinalScore = ((DateScore + BaseScore) / MaxScore) * 10000
BaseScore = (2050 - PlayerScore) * Difficulty

There are several modifiers used to predict the final MaxScore and the condition &#39;best&#39; dates. An excel file with all the modifiers can be found here: http://gotm.civfanatics.net/games/modifier.zip