Furphy's How To: Calculate Build Time

Note: The How To guide made by the user has been revised with better grammar and punctuation. It has also been revised as a Wiki page instead of a forum thread.
The original link can be viewed here: http://forums.ageofempiresonline.com/forums/thread/325682.aspx
Furphy's How To: Calculate Build Time
The basic unit; the villager.
Villager.BaseBuildingSpeed = 1.0
This is how much a village can commit by default without any gear, technologies, nor milestones.
Unlike the gathering rate formula, a building itself has properties that must be take to calculate build time.
Building.BaseBuildTime = build time for a building
However, this is not the whole formula, you can activate technologies, milestones, equip gears, or recruit advisors which have stats that may boost or reduce this formula.
Those multipliers are:
* M(Villager) = All boosts for the Villager.BaseBuildingSpeed
* M(Building) = All boosts for the Building.BaseBuildTime
When calculating milestones, advisors, gears, and technologies stats, you have to be sure that the building or villager multiplier is affected.
First, take a look on the multipler of the Village.BaseBuildingSpeed "M(Villager)". All upgrades are always multiplied not added.
* For example, if we equipped a Hammer of Kaveh that has +30.60% construction speed, the formula would be:
** M(Villager) = 1.306 (1.0 x 30.60%)
** Villager.BaseBuildingSpeed = 1.0
** Villager.ModifiedBuildingSpeed = Villager.BaseBuildingSpeed * M(Villager) = 1.306
** Villager.ModifiedBuildingSpeed = 1.306.
Next, we look at the building itself and which effect modifies the Building.BaseBuildTime These are things like a Chufu Blueprint (+14.7%) or Walls of Earthern Strength (+4.4%) If we equip those two on an example like a storehouse.
* Storehouse.BaseBuildTime = 30
* M(Storehouse) = 1.147 (Chufu Blueprint) * 1.044 (Walls of Earthern Strength) - 1
* M(Storehouse) = 1.1975 - 1 = 0.1975
**Storehouse.ModifiedBuildTime = Storehouse.BaseBuildTime * (1 - M(Storehouse)
**Storehouse.ModifiedBuildTime = 30 * 0.8025 = 24.075
Why -1 you may wonder? It's because it wouldn't make sense to add build time if you equip gear that reduce the building time – It would only makes sense if gear increased the building time. Now we have our formula.
Now we have to let the villager do his work and have the job done. Rather obvious we can now calculate the time for ONE villager building a storehouse.
* ModifiedBuildtime = Building.ModifiedBuildTime / Villager.BuildingSpeed
* ModifiedBuildtime = Storehouse.ModifiedBuildTime / Villager.ModifiedBuildingSpeed
* ModifiedBuildtime = 24.075 / 1.306
* ModifiedBuildtime = 18.434 seconds (rounded up)
Hooray! It'll take a single villager with the Hammer about 18 seconds to work on a storehouse with the blueprint and walls attached.
Still, what if I want to add more villagers? If you think the building speed is doubled for an additional villager. It's wrong. Each additional villager adds 33% to the building speed. So instead of doubling the time reduced. How do we put that in our build time formula? If N is the number of villagers at the job.
* NewBuildtime = Building.ModifiedBuildtime / Villager.ModifiedBuildingSpeed * (1 + 0.3*(N-1)
* NewBuildtime = 24.075 / 1.306 * (1+0.3*2-1)
* NewBuildtime = 24.075 / 1.306 * (1.3*1)
* NewBuildtime = 24.075 / 1.306 * 1.3
* NewBuildtime = 24.075 / 1.6978
* NewBuildtime = 14.1801 seconds (rounded up)
So, adding an additional villager to the buildup will allow for about a 4 second reduction.
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