How long does it take a new drop-off point pay off? A discussion in preparation for math

Hey everyone,

Drop-off points are a key part of AoE2's econ and can greatly increase your effective gather rate of villagers.

However, I haven't seen any attempts at generating a math formula/expression to capture when it makes senae.

As I see it, drop-off points are a trade off between taking extra villager time to set-up gathering (both in spent resources and build time) to make gathering the new resource cost less time.

The good thing is that the resource used to make camps is super abundant, so spending 100 wood to just speed up resource gather rates temporarily is worth it, and you will rarely run the risk of be building one lumber camp for one lone 100 wood carrying tree... like the only time where using existing drop-off instead of a new one will ALWAYS be worth it, regardless of the distance.

My thought is that you should definitely build a new lumber camp when getting 200 wood (for 100 wood net) from it saves time compared to getting 100 wood using your exist drop-off point some times away.

You maybe even should build one even earlier, particularly if you can do so at a different wood line and get less congestion for putting new villagers there, but ... I don't want to think about the math for fighting congestion. There's a reason SotL mostly does that experimentally.

It also might make sense to compare gathering 100 of each other type of resource (food/gold/stone) without considering the villager time cost of the wood, for the event where you are flush with wood.... which is likely to happen after booming a bit. Not quite sure if it makes sense for food, because while gold and stone patches are the only easily scalable sources of gold and stone after booming, free food has to compete with just using farms in the late game, and generally lasts less long. (I should probably look up typical resource amounts per patch).