Benefits of Multiple Builders

Construction Times and Multiple Builders

In AOE and ROR, n builders took T/n time to construct a building where T was the time required for a single builder. When you needed to make several buildings at once, it was often best to have all your builders on one building at a time. The advantage of this was that you could start using buildings before they are all complete while still finishing the last building in the same amount of time as if you had split your builders up.

In AOK, it turns out that the time it takes n builders to construct a building is 3*T/(n + 2). This is a significant difference and I think it explains why people have tended to experience more villager build delays due to unfinished housing in AOK (myself included). If you want to normalize the time by the single builder time T, just find P(n) = 3/(n+2) for different values of n. Here are a few samples: P(1) = 1, P(2) = 0.75, p(3) = 0.60, p(4) = 0.50, p(5) = 0.43, p(6)= 0.38, p(7) = 0.33, p(8) = 0.30, p(9) = 0.27, p(10) = 0.25. Here is a textual explanation of these results:

• A group of 2 builders finishes in 75% of the time that a single builder takes
• A group of 3 builders finishes in 60% of the time that a single builder takes
• A group of 4 builders finishes in 50% of the time that a single builder takes
• A group of 5 builders finishes in 43% of the time that a single builder takes
• A group of 6 builders finishes in 38% of the time that a single builder takes
• A group of 7 builders finishes in 33% of the time that a single builder takes
• A group of 8 builders finishes in 30% of the time that a single builder takes
• A group of 9 builders finishes in 27% of the time that a single builder takes
• A group of 10 builders finishes in 25% of the time that a single builder takes

As an illustration, if I need a building in half the time, I must use four builders instead of the two required in AOE. Also, the benefit of adding builders gets less and less as the total number of builders increases. Whereas using 4 builders cuts the time down to 1/2, using 40 builders only cuts the time down to 1/14th.

There is an equivalent way to think about the build inefficiency that was pointed out by Lord_Captn_Kidd. With a little algebraic manipulation of the build time equation 3*T/(n+2), you can turn it into T/[1 + (n-1)/3]. This form has the easy to remember interpretation that every builder after the first is only 1/3rd as effective as a lone builder.

Here are a few example implications of this construction inefficiency. The general rule here is that it is often better to split your builders up rather than grouping them together.

1. It is even more important during the start of an AOK game to always begin a new house when there is a vacancy of 2. To recover at the last second will cause an even bigger disruption in your economy than it used to in AOE. If you realize that you are down to 1 vacancy, then you need to use 4 builders on a house rather than 2 to make it in time.
2. If you need three towers using three builders, you can get all three up in 50 seconds by separating the builders whereas it would take 3*50*.6 = 90 seconds if you used your builders in a single group.
3. If you need to wall quickly using several builders, put all the builders on different segments. Two builders split apart will finish a 20-tile wall 16 seconds faster than if they were grouped together.
4. I probably would not use more than about 7 builders on any one building unless there was an extreme emergency that justified the inefficiency. Using more than 7, has a minimal return on build-time. A notable exception would be when constructing a wonder which has a single-villager build time of about 58.5 minutes with the treadmill crane. In that case, even a small proportional decrease in build time could make a big difference. I still probably wouldn’t use more than about 30 builders, which would finish the wonder in about 5.5 minutes. Adding 10 more builders only cuts it by a little over a minute while costing you over 1200 in lost resources that those 10 builders could have gathered. Unless I was just swimming in resources, I’d probably rather have that 1200 resources invested in additional defense.

Hope this helps.

gutter_rat