Settler speed bonuses (like USA's French Immigrants card) massively boost gather rates at mills/estates

tl;dr - the 0.5 villager speed boost from the USA's French Immigration gives settlers gathering at mills and estates an 18% multiplicative boost to gather rate.

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For those who don't know, the base gather rates for mills and estates displayed on the UI (0.67 food/s and 0.5 gold/s, respectively) are outright fibs.

This is because settlers tasked to those buildings spend just as much time walking around them and bumping into each other as they do actually gathering, so the real gather rates are (by my measurement) about 0.405 food/s for mills, and 0.311 gold/s for estates. This is why these buildings are so much worse than natural resources, and should be transitioned to as late as possible.

Anyways, with so much time spent walking around, do increases to villager speed (i.e. French Immigration card for USA, which bumps speed up from 4 to 4.5) significantly reduce the wasted time for these gatherers? As it turns out, yes!

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I ran tests as USA with 10 un-upgraded settlers, un-upgraded mills and estates, and measured the total resources gathered over multiple 5 minute intervals. I then did the exact same thing, only having shipped French Immigration. Here are my results:

- Mill gather rate (no Immigration) = 0.405

- Mill gather rate (with Immigration) = 0.476

- Estate gather rate (no Immigration) = 0.311

- Estate gather rate (with Immigration) = 0.368

This translates to an ~18% multiplicative increase to both mill and estate gather rate, which might just be the biggest treaty economic upgrade card in the game!

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Some things to note:

- Farms and Rice Paddies have lower nominal gather rates, but do not have the idle time that mills and estates do, so they end up being roughly equal to their European counterparts in base productivity. I haven't crunched the numbers on these, but because of this I doubt that villager speed (such as that Inca card) would benefit them to the same level.

- This explains a lot to me about the quality of the French treaty economy. Coureurs should also have these relatively better gather rates on mills and estates (more than their 1.25x multiplier), since they innately have 4.5 speed.

- I tried this with hunts too, since there is a lot of idle time in shooting each deer and walking over to them. Alas, I only measured a (roughly) 2% boost to effective hunt gather rate.

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Feel free to experiment on this for yourselves (if you want to take the time), and let me know if you get different results!